NIST Technical Note 1621 

Optical Radiation Measurements 

Based on Detector Standards 

George P. Eppeldauer, Editor 
NIST Technical Note 1621 

Optical Radiation Measurements 

Based on Detector Standards 

George P. Eppeldauer, Editor 

Optical Technology Division 

Physics Laboratory 

National Institute of Standards and Technology 

Gaithersburg, MD 20899-8441 

March 2009 

U.S. Department of Commerce 

Otto J. Wolff, Acting Secretary 

National Institute of Standards and Technology 

Patrick Gallagher, Deputy Director
Certain commercial entities, equipment, or materials may be identified in this 

document in order to describe an experimental procedure or concept adequately. Such 

identification is not intended to imply recommendation or endorsement by the 

National Institute of Standards and Technology, nor is it intended to imply that the 

entities, materials, or equipment are necessarily the best available for the purpose. 

National Institute of Standards and Technology Technical Note 1621

Natl. Inst. Stand. Technol. Tech. Note 1621, 371 pages (March 2009)

CODEN: NTNOEF 

Front Cover: 

Spectral responsivity calibrations of three transfer-standard extended-InGaAs radiometers 

against the primary-standard cryogenic radiometer at the SIRCUS facility in the 1 μm to 

2.5 μm wavelength range. 

 ii 
Preface 

Improved detector technology in the past two decades opened a new era in the field of optical 

radiation measurements. Lower calibration and measurement uncertainties can be achieved with 

modern detector/radiometer standards than traditionally used source standards (blackbodies and 

lamps). The achievable lower uncertainties provided the motivation to decrease the gap between 

the 0.02 % (k=2) relative expanded uncertainty of cryogenic radiometer measurements and the 

two to three orders of magnitude higher uncertainties of field-level optical radiation 

measurements. 

The NIST Technical Note (TN) 1438 published in 2001 summarized the research and 

development work carried out in the Optical Sensor Group of the Optical Technology Division 

(OTD) since 1989 to develop high optical and electronic performance radiometers with selected 

optical detectors for the 200 nm to 20 μm wavelength range. In this present Technical Note, 

which is the continuation of the TN 1438, 36 research papers, published by the OTD from 1996 

to present, have been selected to show how the high-performance optical radiometers were 

converted into standards and used to realize new spectral-responsivity-based scales. In order to 

utilize the increased performance of the radiometers, new calibration-facilities have been 

developed to realize, maintain, and disseminate the detector/radiometer standards-based scales. 

As a result of the work described in these two TNs most of the calibrations at the OTD are 

performed with the new-generation detector/radiometer standards. 

The spectral power responsivity calibrations that started at the OTD about 30 years ago have 

been extended from the silicon wavelength range for the 210 nm to 20 μm range. New reference 

responsivity scales have been developed on the newly developed Spectral Irradiance and 

Radiance Responsivity Calibrations with Uniform Sources Facility (SIRCUS), where instead of 

traditional monochromators, tunable laser-driven integrating sphere sources are used to decrease 

detector and radiometer measurement uncertainties. The spectral power responsivity calibrations 

have also been extended to spectral irradiance and radiance responsivity calibrations. 

The irradiance mode reference scale was needed for the SIRCUS facility to improve the NIST 

realized SI unit, the candela, and to realize the first spectral-responsivity-based tristimulus color 

scale. New filter-radiometers including photometers, and tristimulus colorimeters have been 

developed for the scale extensions with electronic and radiometric characteristics that will not 

limit the scale realization uncertainties. Silicon-trap and sphere-input InGaAs detectors have 

been developed as highest level transfer standards that can perform 0.05 % (k=2) responsivity 

uncertainties between 400 nm and 1650 nm. These SIRCUS reference standards are directly 

traceable to the primary-standard optical power measuring electrical-substitution cryogenic 

radiometers. 

The radiance responsivity scale was needed to calibrate new-generation optical-radiation 

thermometers to realize the detector-responsivity-based radiance temperature scale and the SI 

unit, the kelvin. The most accurate temperature determination of blackbody sources is based on 

the spectral irradiance and radiance responsivity determinations of the filter (band-pass) 

radiometers that measure the radiation from blackbody sources. For temperature scale 

disseminations, improved transfer- and working-standard radiometers have been developed with 

selected Si, InGaAs, and extended-InGaAs detectors to perform direct thermodynamic 

temperature measurements in a wide temperature range. As an alternative to the source-based 

International Temperature Scale (ITS-90), low-uncertainty detector-based radiation temperature 

measurements can be directly performed with the new Si and InGaAs radiation thermometers 

between 2700 K and 430 K. 

 iii 
For routine spectral power responsivity calibrations in an extended wavelength range, low noiseequivalent-power (NEP) pyroelectric radiometers have been developed that can be operated at 

the low-power-output of traditional monochromators. These radiometers, traceable to the above 

reference detectors, extended the routine spectral power responsivity calibrations to a wavelength 

range from 250 nm to 19 μm. 

The low measurement uncertainties of the radiometric reference scale realizations required 

detector output signal measurements with uncertainties smaller than the uncertainty of the 

radiometric scale realization itself. In order to perform 0.01 % (k=2) electrical output signal 

measurement uncertainties for the detectors, traceability of the photocurrent measurements has 

been established to NIST electrical standards. The calibrated photocurrent meters and the 

different input optics to measure the different radiometric, photometric, and color quantities are 

integral parts of the new generation radiometers. 

Using the calibrated radiometers, the reference responsivity scales have been transferred to other 

NIST calibration facilities to decrease calibration and measurement uncertainties. Now, the 

spectral irradiance and radiance scales (disseminated by lamps) are derived from blackbody 

sources that are calibrated against the filter radiometer standards. Also, the radiometer standards 

are used to validate other existing source-based scales such as the irradiance from a synchrotron 

radiation source. The reference radiometers with the new calibration facilities have also been 

used for the absolute radiometric calibration of digital imaging systems. As a result of the 

photometric scale improvement and the spectral-responsivity-based tristimulus color scale 

development, both regular and special light sources (discharge lamps, color displays/monitors, 

solid-state light sources, etc.) can be measured with low uncertainty resulting in significant 

energy saving and quality improvement. 

With the calibrated radiometers, the NIST detector-standards-based radiometric scales are also 

disseminated to industry, military, and academia. The new calibrations with the lower 

measurement uncertainties support the economic growth and competitiveness of the U.S. electrooptical, lighting, paint, textile, and other industries. They also support the National Aeronautics 

and Space Administration’s (NASA) remote sensing activities. With the improved uncertainties 

of radiometric calibrations and measurements, it became possible to monitor the smaller than 

0.1 % long-term changes of the Earth. The detector-standards-based radiance scale is used to 

validate the calibration sources for the Earth Observing System of the U.S. Global Change 

Research Program. The OTD developed detector-standards-based infrared calibration systems 

have also significantly increased the competitiveness of the U.S. military-defense and security. 

George P Eppeldauer, Ph.D. 

Electronics Engineer, Development and Calibration of Optical Radiometers 

Optical Sensor Group, Optical Technology Division 

National Institute of Standards and Technology 

100 Bureau Drive, Gaithersburg, MD 20899-8441 

 iv 
Table of Contents 

Preface ................................................................................................................................................iii 

1. “Facility for spectral irradiance and radiance responsivity calibrations using uniform 

sources,” Applied Optics, Vol. 45, No. 32, p. 8218-8237, 2006, S. W. Brown, G. P. 

Eppeldauer, and K. R. Lykke. Reproduced with permission of the Optical Society of 

America ........................................................................................................................................1 

2. “Radiometer standard for absolute responsivity calibrations from 950 nm to 1650 nm with 

0.05 % (k=2) uncertainty,” NEWRAD-2008 presentation, to be published in Metrologia, 

G. P. Eppeldauer, H. W. Yoon, Y. Zong, T. C. Larason, A. Smith, and M. Racz .......................21 

3. “Optical characterization of diffuser-input standard irradiance meters,” Optika’98, 5th 

Congress on Modern Optics, SPIE Proc. Vol. 3573, 220-224, 1998. G. Eppeldauer, M. 

Racz, and T. Larason ...................................................................................................................34 

4. “Near infrared radiometer standards,” SPIE Proceedings, Vol. 2815, 42-54, 1996. G. 

Eppeldauer ...................................................................................................................................39 

5. “Calibration of a pyroelectric detector at 10.6 μm with the National Institute of Standards 

and Technology high-accuracy cryogenic radiometer,” Applied Optics, Vol. 36, No.16, 

3614-3621, 1997. T. R. Gentile, J. M. Houston, G. Eppeldauer, A. L. Migdall, and C. L. 

Cromer. Reproduced with permission of the Optical Society of America ...................................53 

6. “Realization of an infrared spectral response scale on a cryogenic bolometer,” Metrologia, 

Vol. 35, 307-315, 1998. A. Migdall and G. Eppeldauer ..............................................................61 

7. “Spectral power and irradiance responsivity calibration of InSb working-standard 

radiometers,” Applied Optics, Vol. 39, No. 31, 5739-5744, 2000. G. Eppeldauer and M. 

Racz. Reproduced with permission of the Optical Society of America .......................................68 

8. “Spectral responsivity determination of a transfer-standard pyroelectric radiometer,” SPIE 

Proceedings, Vol. 4818, 118-126, 2002. G. P. Eppeldauer, M. Racz, and L. M. Hanssen .........78 

9. “Spectral irradiance responsivity measurements between 1 μm and 5 μm,” SPIE 

Proceedings, Vol. 5543, 248-257, 2004. G. P. Eppeldauer, J. P. Rice, J. Zhang, and K. R. 

Lykke ...........................................................................................................................................87 

10. “Development and calibration of pyroelectric radiometer standards at NIST,” SPIE Proc. 

Vol. 6201, pp. 620119-1 to 620119-12, 2006, G. P. Eppeldauer, J. Zeng, and L. M. 

Hanssen ........................................................................................................................................97 

 v 
11. “Extension of the NIST infrared spectral responsivity scale to routine monochromatorbased calibrations using improved-NEP pyroelectric detectors,” NEWRAD-2008 

presentation, to be published in the Metrologia, G. P. Eppeldauer, J. Zeng, H. W. Yoon, B. 

Wilthan, T. C. Larason, and L. M. Hanssen ................................................................................110 

12. “Responsivity calibration methods for 365-nm irradiance meters,” also in IEEE 

Transactions on Instrumentation and Measurement, Vol. 50, No. 2, p. 474-477, April, 

2001, T. C. Larason, S. W. Brown, , G. P. Eppeldauer, and K. R. Lykke ...................................118 

13. “Realization of a spectral radiance responsivity scale with a laser-based source and Si 

radiance meters,” Metrologia, Vol. 37, p. 531-534, 2000, G. P. Eppeldauer, S. W. Brown, 

T. C. Larason, M. Racz, and K. R. Lykke ...................................................................................123 

14. “Uncertainties of Spectral Responsivity Measurements,” Proc. of the 2nd CIE Expert 

Symposium on Measurement Uncertainty, p. 133-138, CIE Central Bureau, 27 Kegelgasse, 

A-1030, Vienna, Austria, 2006, G. P. Eppeldauer, G. Sauter, and J. L. Gardner ........................134 

15. “Realization of the National Institute of Standards and Technology detector-based spectral 

irradiance scale,” Applied Optics, Vol. 41, No. 28, 5879-5890, 2002. H. W. Yoon, C. E. 

Gibson, and P. Y. Barnes. Reproduced with permission of the Optical Society of America ......140 

16. “The NIST detector-based luminous intensity scale,” J. Res. Natl. Inst. Stand. Technol. 

Vol. 101, 109-132, 1996. C. L. Cromer, G. Eppeldauer, J. E. Hardis, T. C. Larason, Y. 

Ohno, and A. C. Parr ....................................................................................................................152 

17. “Spectral response based calibration method of tristimulus colorimeters,” J. Res. Natl. Inst. 

Stand. Technol. Vol. 103, 615-619, 1998. G. Eppeldauer ...........................................................172 

18. “Design and characterization of a photometer-colorimeter standard,” Applied Optics, Vol. 

43, No. 13, 2621-2631, 2004. G. P. Eppeldauer and M. Racz. Reproduced with permission 

of the Optical Society of America ...............................................................................................181 

19. “New photometer standards for low uncertainty illuminance scale realization,” The 26th 

Session of the CIE, July 4-11, 2007, Beijing, China, Proceedings Volume 1, pp. D2-99 to 

D2-102, G. P. Eppeldauer, C. C. Miller, and Y. Ohno ................................................................192 

20. “Improved accuracy photometric and tristimulus-color scales based on spectral irradiance 

responsivity,” 25th Session of the CIE, Conference Proceedings, Vol. 1, D2-30 to D2-33, 

2003. G. P. Eppeldauer, S. W. Brown, C. C. Miller, and K. R. Lykke .......................................197 

21. “Realization and application of a detector-based tristimulus color scale at the National 

Institute of Standards and Technology, USA,” AIC Colour 05 – 10th Congress of the 

International Colour Association, Proc. Part I (Editors, J. L. Nieves and J. H-Andres), 

p.693-696, 2005, G. P. Eppeldauer, S. W. Brown, K. R. Lykke, and Y. Ohno ...........................201 

 vi 
22. “Detector-based calibration procedures for tristimulus colorimeter standards,” CIE Expert 

Symposium on Advances in Photometry and Colorimetry, Turin, Italy, 2008, G. P. 

Eppeldauer, C. C. Miller, and Y. Ohno .......................................................................................205 

23. “Directional error correction of radiometric and photometric standard detectors”, 

Metrologia, Vol. 37, p. 489-492, 2000, M. Racz and G. Eppeldauer ..........................................211 

24. “The realization and the dissemination of the detector-based kelvin,” in Proc. of the 9th 

International Symposium on Temperature and Thermal Measurements in Industry and 

Science TEMPMEKO 2004, Dubrovnik Croatia, 22-25 June 2004, D. Zvizdic, L. G. 

Bermanec, T. Stasic, T. Veliki eds., 59-70, 2004, H. W. Yoon, C.E. Gibson, D. W. Allen, 

R. D. Saunders, M. Litorja, S. W. Brown, G. P. Eppeldauer, K. R. Lykke .................................216 

25. “Thermodynamic-temperature determinations of the Ag and Au freezing temperatures 

using a detector-based radiation thermometer,” Applied Optics, Vol. 46, No. 15, p. 2870-

2880, 2007, H. W. Yoon, D. W. Allen, C.E. Gibson, M. Litorja, R. D. Saunders, S. W. 

Brown, G. P. Eppeldauer, K. R. Lykke. Reproduced with permission of the Optical 

Society of America ......................................................................................................................228 

26. “Uncertainty analysis and maintenance of the NIST detector-based temperature scale, 

Acta Metrologica Sinica,” Vol. 29, No 4A, October, 2008, H. W. Yoon, C .E. Gibson, G. 

P. Eppeldauer, A. W. Smith, S. W. Brown, and K. R. Lykke .....................................................239 

27. “SSE- and Noise-Optimized InGaAs Radiation Thermometer,” Int. J. Thermophysics, Vol. 

28, No. 6, p. 2076-2086, Springer, Online: December 2007,” H. W. Yoon, C. E. Gibson, 

V. Khromchenko, and G. P. Eppeldauer ......................................................................................247 

28. “Linearity of InGaAs photodiodes,” Poster presentation, 8th NEWRAD Conference, NIST, 

Gaithersburg, MD, May 20-24, 2002. Metrologia Vol. 40, S154-S158, 2003, H. W. Yoon, 

J. J. Butler, T. C. Larason, G. P. Eppeldauer. Reproduced with permission of the BIPM. .........263 

29. “Short-wave infrared radiometers design and characterization,” SPIE Defense & Security 

Symposium, Infrared Technology and Applications XXXIII, 9-13 April, 2007, Orlando, 

FL, Proceedings Volume 6542, Part 1, pp. 65420O-1 to 65420O-10, G. P. Eppeldauer and 

H. W. Yoon ..................................................................................................................................268 

30. “Measurement of thermal radiation using regular glass optics and short-wave infrared 

detectors,” Optics Express, Vol. 16, No. 2, pp. 937-949, January 21, 2008, H. W. Yoon 

and G. P. Eppeldauer ...................................................................................................................278 

31. “AC-mode Short-Wavelength IR Radiation Thermometers for Measurement of Ambient 

Temperatures,” Int. J. Thermophysics, Vol. 29, p. 1041-1051, Springer, 2008, G. P. 

Eppeldauer and H. W. Yoon ........................................................................................................292 

 vii 
 viii 

32. “System-level calibration of a transfer radiometer used to validate EOS radiance scales,” 

Int. J. Remote Sensing, Vol. 24, No. 2, 339-356, 2003. B. C. Johnson, S. W. Brown, G. P. 

Eppeldauer, and K. R. Lykke. Reprinted by permission of the publisher, Taylor & Francis 

Ltd. ...............................................................................................................................................303 

33. “Spectral Irradiance and Radiance Responsivity Calibrations using Uniform Sources 

(SIRCUS) facility at NIST,” SPIE Symposium, Denver, CO, August 2-6, 2004, Proc. Vol. 

5542, p. 363-374, S. W. Brown, G. P. Eppeldauer, J. P. Rice, J. Zhang, and K. R. Lykke ........321 

34. “Absolute radiometric calibration of digital imaging systems,” SPIE Proceedings, Vol. 

4306, 13-21, 2001. S. W. Brown, T. C. Larason, C. Habazuit, G. P. Eppeldauer, Y. Ohno, 

and K. R. Lykke ...........................................................................................................................333 

35. “Uniform calibration of night vision goggles and test sets,” SPIE Europe Security and 

Defence Symposium, Electro-Optical and Infrared Systems: Technology and Applications 

IV, Vol. 6737, p. 67370M-1 to 67370M-16, 2007, G. P. Eppeldauer .........................................342 

36. “Traceability of NIST photocurrent measurements to electrical standards,” NEWRAD2008 presentation, to be published in the J. Res. Natl. Inst. Stand. Technol., G. P. 

Eppeldauer ...................................................................................................................................358 
Facility for spectral irradiance and radiance responsivity

calibrations using uniform sources

Steven W. Brown, George P. Eppeldauer, and Keith R. Lykke

Detectors have historically been calibrated for spectral power responsivity at the National Institute of

Standards and Technology by using a lamp–monochromator system to tune the wavelength of the excitation

source. Silicon detectors can be calibrated in the visible spectral region with combined standard uncertainties at the 0.1% level. However, uncertainties increase dramatically when measuring an instrument’s

spectral irradiance or radiance responsivity. We describe what we believe to be a new laser-based facility for

spectral irradiance and radiance responsivity calibrations using uniform sources (SIRCUS) that was developed to calibrate instruments directly in irradiance or radiance mode with uncertainties approaching or

exceeding those available for spectral power responsivity calibrations. In SIRCUS, the emission from

high-power, tunable lasers is introduced into an integrating sphere using optical fibers, producing uniform,

quasi-Lambertian, high-radiant-flux sources. Reference standard irradiance detectors, calibrated directly

against national primary standards for spectral power responsivity and aperture area measurement, are

used to determine the irradiance at a reference plane. Knowing the measurement geometry, the source

radiance can be readily determined as well. The radiometric properties of the SIRCUS source coupled with

state-of-the-art transfer standard radiometers whose responsivities are directly traceable to primary national radiometric scales result in typical combined standard uncertainties in irradiance and radiance

responsivity calibrations of less than 0.1%. The details of the facility and its effect on primary national

radiometric scales are discussed.

OCIS codes: 120.0120, 120.5630, 120.3930.

1. Introduction

Detectors are calibrated for spectral power responsivity over the spectral range from 350 to 1000 nm

at the National Institute of Standards and Technology (NIST) on the spectral comparator facility1 (SCF)

by using a lamp–monochromator system to tune the

wavelength of the excitation source and silicon working standard detectors with responsivities directly

traceable to the NIST high-accuracy cryogenic radiometer (HACR), the primary U.S. national radiometric standard for optical power measurement.2,3

Silicon detectors can be calibrated for optical power

responsivity in the visible spectral region on the SCF

with combined expanded uncertainties k  2at the

0.2% level. However, quantities of interest are often

the amount of light falling on a surface (irradiance) or

the amount of light emitted from a source (radiance).

In many cases, spectral information is required as

well. Consequently, the calibration of filter-based irradiance and radiance meters is frequently needed.

Because of the low flux in the lamp–monochromator

system, instruments cannot be directly calibrated for

irradiance or radiance responsivity on the SCF, and

more complicated approaches must be taken that often

increase the expanded uncertainty k  2in the measurements to the 0.5% level or greater.4 In addition,

the low flux associated with lamp–monochromator

excitation sources 1 Wlimits the effective dynamic range of the system. The out-of-band response

of filter radiometers can be measured only to approximately 0.001% of the peak response while a

dynamic range greater than 106 can be required for

high-accuracy applications. In more advanced applications, spatially nonuniform (e.g., infrared or

ultraviolet) irradiance meters cannot be calibrated

accurately by using the traditional power measurement mode on the SCF and detector-array-based

imaging systems require tests in uniform, monochromatic fields.

With the development of tunable dye lasers in

1970,5,6 high-power, monochromatic, tunable sources

became available for scientific use. Replacing the

lamp–monochromator source with a tunable laser

The authors are with the National Institute of Standards and

Technology, Gaithersburg, Maryland 20899. S. Brown’s e-mail address is steven.brown@nist.gov.

Received 14 February 2006; accepted 27 April 2006; posted 7

July 2006 (Doc. ID 68064).

8218 APPLIED OPTICS  Vol. 45, No. 32  10 November 2006
source has a number of advantages for radiometric

applications, in particular the high-power, very narrow spectral bandwidth, and the extremely low wavelength uncertainty of the laser-based source. Schaefer

and Eckerle7 developed the first laser-based radiometric facility at NIST in 1984. In 1986, independent

irradiance scales maintained by NIST based on blackbody or synchrotron radiation were compared with

scales established on the laser calibration facility

based on silicon photodiode physics traceable to cryogenic radiometry.8 In 1990, absolute spectral radiometric measurements of the melting and freezing

points of a gold blackbody were made at NIST using

the laser-based facility.9 The radiometric temperature

was in agreement with the gold-point value established in the International Temperature Scale of 1990

(ITS-90). In the same time frame, a laser-based radiometric calibration facility was established at the

National Physical Laboratory (NPL) in the United

Kingdom, and the radiometric freezing and melting

temperatures of gold, silver, and aluminum blackbodies were determined with a radiometric uncertainty of

0.04%.10 The results were compared with thermodynamic temperatures established by using constantvolume gas thermometry. Subsequently, several

primary national radiometric standards laboratories

have developed or are developing laser-based calibration facilities, including the NPL in the UK,11

the Helsinki University of Technology (HUT) in

Finland,12 and the Physikalisch-Technische Bundesanstalt (PTB) in Germany,13 as well as at NIST. In

this work, a new laser-based facility developed at

NIST for spectral irradiance and radiance responsivity calibrations using uniform sources (SIRCUS) is

described.

This facility expands on previous work through the

integration of cw, continuously tunable lasers that

cover wide ranges of the spectrum as well as with the

development of high-performance transfer standard

detectors. The expanded continuous spectral coverage has been made possible by recent and continued

advances in laser technology. By exploiting the

developments in laser and detector technologies in

SIRCUS and calibrating filter radiometers that are

used in radiance temperature (pyrometers) and photometry (photometers), the uncertainty of the two

Systeme Internationale (SI) units maintained by the

NIST Optical Technology Division, the kelvin and the

candela, can be reduced.

In Section 2 we describe the principal components

of the facility and give a representative uncertainty

budget for an instrument calibration. In Section 3 we

compare the SCF with SIRCUS. In Section 4 we discuss the effect on NIST scales and facilities. In Section 5, we give examples of calibrations that illustrate

the flexibility of the new facility.

2. Description of Spectral Irradiance and Radiance

Responsivity Calibrations Using Uniform Sources

In the SIRCUS facility, emission from high-power,

tunable lasers is introduced into an integrating sphere

producing uniform, quasi-Lambertian, highly radiant

flux sources. Reference standard irradiance detectors,

calibrated directly against national primary standards

for spectral power responsivity, are used to determine

the irradiance at a reference plane. Knowing the

measurement geometry, the source radiance can be

readily determined as well. Instruments are calibrated directly in irradiance or radiance mode with

uncertainties approaching or exceeding those available for spectral power responsivity calibrations.

There are three components to the SIRCUS facility:

an ultraviolet, visible, and near-infrared (UV–Vis–

NIR) SIRCUS; an infrared (IR) SIRCUS; and a highaccuracy electrical substitution cryogenic radiometer

system called the primary optical watt radiometer

(POWR).14 POWR is a primary standard facility for the

measurement of optical power. The UV–Vis–NIR facility currently operates over the spectral region from

210 to 960 nm; extensions to the short-wave IR, out to

2.5 m, are planned. The IR SIRCUS facility has a

spectral coverage from 700 to 5.3 m using tunable

optical parametric oscillator (OPO) systems and coverage to 11 m using discrete laser sources. Lasers

from both SIRCUS facilities can be introduced into

the POWR radiometer for detector responsivity measurements. Typically, reference instruments used on

SIRCUS are calibrated against POWR. Occasionally,

a second, working-standard absolute cryogenic

radiometer (ACR) is used.15 This system is smaller

and easier to operate than POWR. It is located on a

portable table and can be readily moved between facilities. Intercomparisons using transfer standard detectors establish the equivalence between the two

cryogenic radiometers.

The spectral coverage available with the tunable

lasers ultimately defines the spectral range of the

SIRCUS facility while the quality of the reference

standard detectors and their radiometric uncertainties ultimately determine the uncertainty achievable

on SIRCUS. In this work we focus on the UV–Vis–

NIR facility and limit the discussion to the spectral

range from 210 to 960 nm where silicon reference

detectors are available. A general description of the

SIRCUS facility is given in Subsection 2.A. Sources

and reference detectors are discussed in Subsections

2.B and 2.C. Subsection 2.D outlines the calibration

method. The uncertainties achievable for radiance

and irradiance responsivity calibrations are discussed in Subsection 2.E.

It should be noted that our identification of commercial equipment is for information purposes only.

It does not imply recommendation or endorsement by

the National Institute of Standards and Technology,

nor does it imply that the equipment identified is

necessarily the best available for the purpose.

A. Setup

The SIRCUS facility is shown schematically in Fig. 1.

The output of a high-power, tunable laser is first

directed through an intensity stabilizer that controls

the relative optical power in the beam to within 0.1%

of the set point. A portion of the laser beam is sent

into a traveling Michelson interferometer that mea10 November 2006  Vol. 45, No. 32  APPLIED OPTICS 8219
sures the wavelength of the radiation to within

0.001 nm. A beam splitter sends another portion of

the laser beam into a Fabry–Perot interferometer to

measure the bandwidth and mode stability of the

laser. The laser radiation is typically introduced into

an integrating sphere, often using an optical fiber.

Different size spheres are used depending on the application. Occasionally, a collimator coupled to the

sphere is used as a calibration source. Speckle in the

image from the source, originating from interference

due to the coherent nature of the laser radiation, is

effectively removed either by rastering the beam inside the sphere with a galvanometer-driven mirror9

or by placing a short length of optical fiber in an

ultrasonic bath.11,16 Note that the speckle is still

present but is altered on a much shorter time constant than the observing radiometers, effectively averaging out the distribution. A monitor photodiode is

located on the sphere to correct for any radiant flux

changes in the sphere output between measurements

with the reference instrument and the device under

test. The sources and detectors are located inside

a light-tight box (1.4 m wide, 1.2 m tall, 3.2 m long)

that has been covered on the inside with Ultrapol, a

material with excellent light-absorbing properties:

The measured reflectance is of the order of 0.1%–

0.3% from 300 nm to 2.5 m. Two baffles are typically installed between the source and the detectors

to minimize the effects of stray radiation on the measurement.

The calibrations are performed by direct substitution against primary standard reference irradiance

meters (see Subsection 2.C). For both irradiance and

radiance responsivity calibrations, the distance between the source aperture and the defining aperture

on the reference standard detector is required. An

electronic ruler with a resolution of 5 m measures

the distance between the source and the detectors.

B. Sources

In this subsection we go into detail on the laser systems as well as the different calibration sources,

namely, the integrating spheres and collimators used

on SIRCUS.

1. Lasers

A number of different lasers are used to cover the

spectral range from about 210 to 960 nm (see Fig. 2).

Continuous tunability is provided by dye lasers

and Ti:sapphire lasers that are pumped by either

an argon-ion laser (25 W, all lines visible; 7 W, all

lines UV) or a frequency-doubled Nd:vanadate laser

10 W, 532 nm. A number of discrete wavelengths

are provided by the pump lasers themselves.

Dye laser use has declined in recent years because of

the development of the solid-state Ti:sapphire laser,

but the dye laser is still the easiest method for producing high-power, tunable, cw light in the visible.17,18

Dye lasers at SIRCUS cover the spectral region from

415 to 700 nm; the dyes used include Stilbene 3

415–475 nm, Coumarin 480 470–520 nm, Coumarin 521 505–565 nm,

19 Rhodamine 6G R6G; 550–

620 nm, and DCM 610–700 nm. A separate laser is

used for each dye so that the full tuning range can be

rapidly covered, and no dye change or optical reconfiguration is required. The longer-wavelength dye lasers, with DCM and R6G dyes, are ring lasers. They

are located on a table separate from the other three

dye lasers and are pumped by the 532 nm output

from a frequency-doubled Nd:vanadate laser. The

Coumarin 521, Coumarin 480, and Stilbene 3 lasers

are pumped with the output of an argon-ion laser.

Separate optical fibers, located on each laser table,

couple the radiation from the lasers into the integrating spheres.

Ti:sapphire lasers cover the spectral range from 680

to 1050 nm.20 A frequency doubling of Ti:sapphire

lasers enables us to tune from 350 to 500 nm. Two

different types of frequency doubling are available:

The first approach uses an external power buildup

cavity that requires a frequency-stabilized, singlemode pump laser.21 The second is a home-built

intracavity-doubled Ti:sapphire laser that requires

no frequency stabilization. This system uses a simple

Fig. 2. (Color online) Lasers, output power, and spectral coverage

of UV–Vis–IR SIRCUS.

Fig. 1. (Color online) Schematic diagram of the SIRCUS facility.

8220 APPLIED OPTICS  Vol. 45, No. 32  10 November 2006
z-cavity Ti:sapphire laser. When doubling is required,

the output coupler is removed and two mirrors are

used in its place: a fold mirror (with a 5 cm focal

length) and a flat mirror. The doubling crystal, typically lithium barium oxide (LBO), is located near the

focus of the curved mirror.22 One of the attractive

features of the intracavity-doubling design is that the

system lases without the doubling crystal in place—

ensuring the proper cavity alignment prior to installation of the doubling crystal. It is also less sensitive

to acoustic noise and small frequency fluctuations in

the laser than the external-cavity system.

Over 300 mW of optical power is available from

the dye lasers and the Ti:sapphire laser (with optical

powers of 1 W or greater over much of the spectral

range). The power available from the cw, frequencydoubled radiation is typically in the range from 100 to

200 mW. A variety of standing-wave and ring lasers

are currently used on SIRCUS. With the exception of

the external buildup cavity approach to frequencydoubled light, simple, inexpensive standing-wave dye

lasers and Ti:sapphire lasers equipped with an intracavity, uncoated etalon to ensure narrowband operation are sufficient for all foreseeable radiometric

applications.

Quasi-cw, mode-locked laser systems have been

shown in the past to be equivalent to cw systems for

radiometric calibrations of silicon radiometers, with

no additional uncertainties in the calibration arising

from the quasi-cw nature of the radiation.23,24 A commercial mode-locked system was recently installed in

the facility. The system includes an OPO system for

generation of visible and infrared light, and a frequency doubler, tripler, and quadrupler system for

generation of visible and UV radiation. These nonlinear optical systems take advantage of the pulsed nature of the radiation: It is significantly easier to

generate sum and difference frequency radiation using a mode-locked laser rather than a true cw laser

because of the high peak power of the mode-locked

source. This system generates almost continuously

tunable radiation from 210 to 3 m. One useful feature of the quasi-cw system is that the bandwidth of

the radiation is considerably broader than radiation

from the cw systems. This may help to alleviate the

measurement problems associated with interference

fringes (discussed in Section 6).

Computer-controlled actuators rotate the angle of

the birefringent tuner in the dye and Ti:sapphire

lasers. The minimum step size is determined by the

free spectral range of the etalon in the lasers. For a

1 mm thick etalon, the thickness of the etalons used

on SIRCUS, the minimum wavelength step using the

birefringent tuner is 0.16 nm at 600 nm. For finer

spectral resolution, the etalon angle is changed as

well. Controlling both the birefringent tuner and the

etalon angle, wavelength steps of 0.01 nm or less can

be readily achieved.

2. Integrating Spheres

Different integrating spheres are used, depending on

the radiometric calibration. Small-diameter integrating spheres—with diameters ranging from 2.54 to

5.08 cm—equipped with precision apertures with diameters ranging from 3 to 8 mm are typically used for

irradiance responsivity calibrations. Note that the

areas of the exit apertures are normally measured at

the NIST facility for aperture area measurement.25

Larger-diameter spheres—30 cm in diameter—with

5 to 10 cm diameter exit ports are used for radiance

measurements. The spheres are made of a sintered

polytetrafluoroethylene-based (PTFE-based) coating

that has high diffuse reflectance from approximately

250 nm to 2.5 m.26 Typical irradiance levels at 1 m

using a 2.54 cm diameter integrating sphere with a

5 mm diameter aperture range from approximately 1 to 10 Wcm2

. Radiance levels between 1 and

5 mWcm2

sr are standard for a 30 cm diameter

sphere with a 7.5 cm diameter output port. A monitor

detector is mounted on the sphere wall to monitor

and correct for fluctuations in the source radiant flux

during a calibration. The irradiance is uniform to

within 0.1% over several centimeters at a 1 m separation from the integrating sphere. Similarly, the radiance from the integrating sphere is uniform to

within 0.1% over the central 90% of the exit aperture.

3. Collimator Sources

In earlier work at the NPL, collimated sources made

from spheres with lenses were used in the calibration

of a number of filter radiometers and transmission of

lenses.11 In SIRCUS, off-axis parabolic mirrors are

used to prepare the quasi-collimated source. Mirrors

have the advantage over lenses of achromaticity from

the UV to the IR. In addition to the collimators in

SIRCUS, both on- and off-axis collimator sources

have been developed in collaboration with NASA27

and the U.S. Geological Survey28 (USGS) for the

characterization and calibration of large-aperturearea telescopes. Nonuniformities of 1% or less are

achieved over a 5 cm diameter area with an irradiance up to 2 orders of magnitude greater than with

the integrating sphere alone.

C. Detectors

The uncertainty in the spectral irradiance responsivity

of reference standard detectors is the largest component in the SIRCUS calibration uncertainty budget.

Ultimately, the quality and characteristics of the reference standard detectors determine the uncertainty

achievable on SIRCUS. Silicon tunnel-trap detectors,

configured to operate in both radiant power and irradiance measurement modes, are the highest-level reference standards used in the SIRCUS facility. They

cover the spectral range from 300 to 960 nm. Reflectance traps with specially designed Si detectors that

are stable under UV exposure are used for calibrations in the 210 to 350 nm spectral region.

1. Reference Standard Silicon Tunnel-Trap Detector

Trap detectors consist of multiple silicon photodiodes

oriented such that the incident radiation reflected

from one detector impinges on a second detector.29

Hamamatsu model S1337 (Ref. 30) photodiodes are

10 November 2006  Vol. 45, No. 32  APPLIED OPTICS 8221
typically used in trap detectors to utilize the physical

model of internal quantum efficiency (IQE) for spectral responsivity extrapolation and interpolation.3 The

IQE is the ratio of the number of collected electrons to

the number of photons absorbed by the detector after

the front surface reflection loss; the S1337 photodiodes

are chosen because of their extremely high IQE (close

to 1). A detector’s external quantum efficiency (EQE) is

equal to the IQE times the term 1  reflectance. In

trap detectors, the reflection loss is minimized by having incident reflected radiation impinge on the next

photodiode in succession, leading to the absorption of

almost all the incident radiation. Measuring the sum

of the photocurrents from the photodiodes that make

up the trap detector, the EQE can be very close to

unity. This type of detector is frequently called a

quantum-flat detector.

The schematic of the transmission tunnel-trap

detectors used on SIRCUS, with the input aperture

included, is shown in Fig. 3.31 By choosing different

size photodiodes, the aperture area and the field of

view (FOV) could be maximized. Two 10 mm 

10 mm and four 18 mm  18 mm silicon photodiodes,

equivalent to the Hamamatsu S1337 model photodiodes, were packaged in a triangular-shaped,

light-trapping arrangement. The photodiodes were

selected for large and equal shunt resistance, an

important consideration for the signal current-tovoltage conversion.31 The beam propagates in the

tunnel-trap detector from the first photodiode (behind the aperture) to the last (sixth) photodiode. Photodiodes 3 and 6 are not shown for better illustration.

The small amount of radiation that exits the back of

the trap detector can be utilized for alignment or can

be measured for detector transmittance measurements in spectral responsivity determination. A conical light trap attached to the trap detector output

absorbs the transmitted radiation and minimizes the

effect of ambient stray light for low-level optical radiation measurements. The photodiodes in the trap

detectors are not temperature controlled. The trap

detectors have been characterized for both electrical and optical performance. In Subsection 2.D, the

trap detector’s response linearity, spatial uniformity,

and angular responsivity are discussed along with

the spectral power responsivity calibration against a

high-accuracy cryogenic radiometer.

2. Monitor Detectors

Silicon detectors mounted on the integrating sphere

sources monitor the source radiance and correct for

any small changes that occur during a calibration

caused by fluctuations in the laser power input into

the integrating spheres. To avoid interference fringes

in the monitor signal (caused by residual coherence in

the output radiation of a sphere source), the window

of the silicon monitor detector is removed, or a diffuser is placed between the silicon detector and the

integrating sphere. Both the reference standard trap

detectors and the monitor detectors operate in dc

measurement mode.32

D. Method of Calibration

A calibration relates the measured quantity from a

radiometer, usually current or voltage, to the radiometric quantity being measured, e.g., radiance or

irradiance, through the instrument’s responsivity. Determination of an instrument’s responsivity and an

evaluation of the associated uncertainties are required

in a calibration. The substitution method is used for

calibrations in SIRCUS. NIST reference standard irradiance meters determine the irradiance at a reference plane. From the irradiance at the reference plane,

which is usually the plane of the detector aperture, the

radiance of a source can be determined by knowing the

distance between the detector and source apertures, as

well as the area of the source aperture. The instrument

being calibrated, or device under test (DUT), is then

placed in front of the source and its signal is recorded.

The laser is blocked and the dark signal is recorded

prior to each measurement. The responsivity (at the

excitation wavelength) is the instrument’s net output

signal (with the dark signal subtracted from the light

signal) divided by the radiometric quantity to be measured.

The characterization of an instrument and an understanding and evaluation of all meaningful sources

of uncertainty are crucial for a proper calibration. A

calibration without an associated uncertainty table is

of limited use. The evaluation and expression of uncertainty is generally difficult and time consuming; it

is not unusual to have incomplete or inaccurate information in an uncertainty table. Determining how

best to express a particular uncertainty component

can be confusing. There are a variety of useful references that provide definitions and recommendations

for describing and establishing the uncertainties encountered when calibrating a radiometer.33

A measurement equation is a mathematical expression describing the relationship between the

measured source-related radiometric quantity and

the instrument responsivity. The simplified measurement equation for an irradiance responsivity

calibration is

Fig. 3. Beam propagation through the six-element transmission

tunnel-trap detector. Detectors 3 and 6 have been removed from

the diagram.

8222 APPLIED OPTICS  Vol. 45, No. 32  10 November 2006
RDUT  iDUT

itrap

Rtrap  iDUT

itrap

strap A, (1)

where RDUT is the irradiance responsivity of the device under test, Rtrap is the irradiance responsivity of

the trap, strap is the power spectral responsivity of the

trap, A is the area of the aperture on the trap, and i

is the photocurrent. The photocurrent is converted to

voltage in a transimpedence amplifier and then measured with a multimeter.

Equation (1) assumes that the reference planes of

the DUT and trap are in the same plane, i.e., that the

defining apertures are located the same distance

from the point source. In many cases, they are located

in different planes. In Subsection 2.D.4, it is shown

that, for the aperture sizes and operating distances

used on SIRCUS, the sources can be treated as point

sources. For a point-source geometry,

I E1d1

2  E2d22

, (2)

where Iis the radiant intensity of the source; E1 is

the irradiance at reference plane 1, located a distance

d1 from the source; and E2 is the irradiance at reference plane 2, located a distance d2 from the source. In

many cases, the reference plane of the DUT is not

known and must be determined radiometrically.

There are two types of uncertainty components, designated Type A and Type B. Type A uncertainties

are evaluated using statistical methods, and Type B

uncertainties are evaluated using models or other external information. The term standard uncertainty

refers to an estimated standard deviation. Assuming

each uncertainty component is independent from the

others (the components are uncorrelated), the combined standard uncertainty is the root sum square of

the individual uncertainty components. Often, the different variables are not completely independent from

one another, and correlations between these variables

need to be taken into account.34,35

The expanded uncertainty is the product of the combined standard uncertainty and a coverage factor k,

where the value of k is chosen based on the desired

level of confidence. Typically the expanded uncertainty

is reported with k  2, corresponding to a confidence

level of 95%. A confidence level of 95% means that

there is a 1 in 20 chance that a measurement will fall

outside the interval. A coverage factor k  3 corresponds to a confidence level of 99%, meaning there is

a 1% chance that a measurement will fall outside the

stated interval. In reporting the uncertainty for a

measurement, the components of standard uncertainty are listed and their designation stated (A or B).

The uncertainty table should also identify and distinguish random components from systematic components that are common to all wavelengths. This

information is important when combining the spectral measurements, for example in measuring the

band-integrated response of filtered detectors.

The dominant uncertainties of the spectral irradiance responsivity scale originate from systematic errors in the absolute scale transfer from the cryogenic

radiometer. Temperature variations within the facility, while small, may also contribute to the overall

uncertainty in certain spectral regions. The radiometric stability of the source (and monitor detector) and

the irradiance uniformity at a reference plane contribute to the overall uncertainty in the measurement.

Additional uncertainties from the radiometric characteristics of the DUT need to be quantified to establish

the uncertainty in the calibration (and subsequent

measurements of a source). Typically, the instrument’s

response linearity, temperature dependence, polarization dependence, and out-of-FOV blocking are

measured. The current-to-voltage converter and the

multimeter used to measure the signal need to be characterized and their contribution to the overall uncertainty established. Finally, both short-term stability

(repeatability) and long-term stability (to monitor

degradation in time) should be considered.

In the following subsections, we discuss the uncertainty components in a typical irradiance responsivity calibration. The components are combined into an

uncertainty budget in Table 1. These are representative numbers only. The uncertainty in an irradiance

responsivity calibration may differ slightly, depending on the details of the calibration and the DUT.

1. Detector-Based Spectral Irradiance Responsivity

Scale

The reference standard tunnel-trap detectors hold the

spectral irradiance responsivity scale on SIRCUS. As

no light is reflected back from the trap detector to the

aperture, the aperture area and the trap detector spectral radiant power responsivity can be determined sepTable 1. SIRCUS Uncertainty for an Irradiance Responsivity Calibration

Uncertainty Component

Relative Standard

Uncertainty

[%]

Type A Type B

Reference detector responsivity

Radiant power responsivity

(400 to 920 nm)

0.025

Aperture area 0.004

Response uniformity 0.005

Cosine dependence 0.01

Polarization 0.00

Linearity 0.00

Temperature 0.003

Source characteristics

Radiant flux 0.005

Wavelength (0.01 nm) 0.005

Irradiance uniformity 0.005

Determination of the

reference plane

0.01

I–V Gain 0.01

Voltmeter reading 0.005

Irradiance 0.032

Transfer to device under test

(estimated)

0.030

Combined standard

uncertainty (k  1) (%)

0.044

10 November 2006  Vol. 45, No. 32  APPLIED OPTICS 8223
arately. The spectral irradiance responsivity of the

trap detector is calculated as the product of the aperture area and the spectral radiant power responsivity

of the trap detector. The spectral radiant power responsivity of the tunnel trap was measured by direct

substitution against the working standard ACR (Section 2). The spectral power responsivity (in AW) is

proportional to the EQE and the wavelength. The proportionality factor is ehc, where e is the elementary

electron charge, c is the speed of light in vacuum, and

h is the Planck constant. The measured EQE of one of

the working standard trap detectors (T-01) versus the

wavelength (82 laser wavelengths) is shown in Fig. 4.

The EQE is equal to 0.996 to within 0.1% between 600

and 920 nm. The relative combined standard uncertainties in the detector responsivity are 0.05% between 400 and 960 nm and 0.1% between 350 and

400 nm. A fit to the data points, illustrated in Fig. 4,

shows that the reproducibility error of the responsivity determinations is very small, especially between

500 and 900 nm. That is, the uncertainty in the fit to

the EQE is smaller than the uncertainty determination at each wavelength. Additionally, there are correlations among these absolute points.35 Neither

have been considered or included in the uncertainty

budget listed in Table 1.

The trap detector was then equipped with a precision circular aperture whose area was measured on an

interferometrically controlled x–y translation stage

with a video microscope by using edge detection.25 The

relative standard uncertainty of the area determination for the 5 mm diameter aperture of the trap detector was 0.004%.25

The spectral radiant power responsivity of the

reference standard trap detectors was measured in

underfilled (total beam power measurement) mode. In

the irradiance mode, the incident flux overfills the aperture. The radiant flux falls on different regions of the

trap detector for the two measurement modes. While

typically small for silicon trap detectors, the spatial

nonuniformity in responsivity of the trap detector can

produce the ultimate limiting uncertainty component

for the reference irradiance responsivity scale when

the primary standard, in our case the ACR, measures

radiant power. Dust is the primary cause of nonuniformity in the responsivity because the reference trap

detectors are nonwindowed devices. To propagate the

low uncertainties in power responsivity to irradiance

responsivity, the detector’s spatial response uniformity, as well as the area of the defining aperture, must

be measured. The response of a reference trap detector

was recently found to be uniform to within 0.01% over

the entire area of the entrance window (with the

aperture removed).

When measuring a point source, the expected responsivity in irradiance mode is a cosine dependence on the angle of rotation of the detector from

the plane normal to the incident flux. Deviations

from the expected response can give rise to errors

when measuring extended sources. Figure 5 shows

the normalized angular responsivity of the tunneltrap detector when it is equipped with a circular

aperture of 5 mm in diameter. The responsivity deviation from the cosine function is less than 0.02%

within a 6° FOV. For an 8° FOV, the deviation is

approximately 0.05%. This feature makes it possible

to use these trap detectors as transfer standards for

monochromator-based facilities where the beam convergence angle is smaller than the unvignetted FOV

of the tunnel-trap detector.

2. Radiometric Characteristics of the Trap Detector

The radiation from an integrating sphere is typically

unpolarized.36 If polarized light is required for a calibration, a collimator can be used with a polarizer in

the beam.

Linearity is easily checked by changing the laser

power with the intensity stabilizer at the input to the

fiber. The ratio of the signal of the DUT or reference

trap to the monitor signal as a function of power should

Fig. 4. Silicon tunnel-trap detector EQE versus wavelength.

Fig. 5. Angular responsivity of the tunnel-trap detector.

8224 APPLIED OPTICS  Vol. 45, No. 32  10 November 2006
be a straight horizontal line. Figure 6 is a representative plot of a silicon detector’s response linearity over

four decades. Some silicon detectors have been measured to be linear over 14 decades.37,38

The temperature in the SIRCUS facility was

maintained at a nominal temperature of 22 °C. Typical variations were of the order of 0.5 °C or less,

though in extreme cases, variations of the order of

2 °C were observed. The temperature, pressure,

and humidity inside the light-tight enclosure can be

monitored and corrections can be made if necessary.

The temperature coefficient of Hamamatsu S1337

photodiodes (the type of silicon photodiode used in the

trap detectors) has been measured.1 It was found

that there was negligible dependence below 950 nm

0.01%Kbut that the dependence rose quickly to

0.2%K by 1000 nm.39 A similar dependence should

be seen in trap detectors using these diodes.

3. Source Characteristics

The radiant power and wavelength stability are two

of the primary uncertainty components. A laser intensity stabilizer keeps the laser power level constant

to within 0.1%. The lasers used as excitation sources

are equipped with etalons to reduce the wavelength

uncertainty from mode hopping. The wavelength uncertainty is of the order of 103 nm with a typical

bandwidth of the order of 103 nm. The wavelength

uncertainty is dominated by the dependence of the

index of refraction of air on temperature, humidity,

and pressure. The wavemeter corrects for the temperature and pressure dependence and can be programmed to correct for the humidity.

The sequence for measurements of a DUT is to first

measure the trap and monitor signal, then move the

stage so that the DUT versus the monitor signal is

measured, then move back to the trap measurement.

If any change is observed in the trap-to-monitor ratio

greater than 0.01%, additional measurements are

made and the data are averaged. Typically, from 9 to

16 samples are averaged for each data point. Occasionally additional samples are taken, for example,

when measuring the out-of-band response of a filter

radiometer under test.

The irradiance at a reference plane should be spatially uniform to limit the magnitude of corrections for

different size entrance pupils. In Fig. 7(a) we show the

irradiance distribution at a reference plane approximately 1 m from the exit port of a 25.4 mm integrating

sphere equipped with a 5 mm diameter aperture. In

Fig. 7(b) we show a horizontal slice across the center

of the distribution. As shown in Fig. 7, the irradiance

is uniform to within 0.1% over the central 2 cm

in both the horizontal and vertical directions. The

entrance apertures of most irradiance meters calibrated on SIRCUS have diameters significantly

smaller than 4 cm, and no correction for irradiance

nonuniformity at the reference plane is applied.

4. Distance

The distance between the source and trap detector

apertures (reference planes) is measured optically and

mechanically. For a point-source geometry, the irradiance should follow an inverse square law, i.e., the irFig. 6. Detector response linearity. The signal-to-monitor ratio as

a function of the signal (related to incident optical power).

Fig. 7. Irradiance uniformity at a reference plane 1 m from the

irradiance source. (a) Two-dimensional map of the irradiance distribution; (b) horizontal slice through the vertically centered irradiance.

10 November 2006  Vol. 45, No. 32  APPLIED OPTICS 8225
radiance should be a function of 1d2

, where d is the

distance between the two reference planes. The relative distance between the source and the detector is

measured with an electronic ruler that has a quoted

resolution of 5 m.40 The three-axis detector translation stage is moved in the horizontal direction, and

the detector and monitor signals are acquired as a

function of relative distance. The ratio of the trap

signal to the monitor signal is then plotted as a function of distance and fit with a nonlinear least-squares

algorithm.41 Figure 8 illustrates an optical distance

measurement, with the dots measuring trap-tomonitor ratios and the solid curve being the fit to the

data. The data were fit to the expression

y  m1m0  m2

2, (3)

where the radiant intensity is given by m1, the zero

offset of the fixed source is m2, and m0 is the position

of the stage measured by the electronic ruler. The

uncertainty in the fit to m2 is 28.7 m. Since we know

the zero offset from this fit, we also know the absolute

separation at any value of the electronic ruler with an

uncertainty of 28.7 m. To validate the radiometric

measurements, we also measured the aperture

separation by using a calibrated ruler. The two separate techniques used to measure the distance between the source and the detector reference planes

agreed usually within 50 m. Given a 50 m uncertainty in the trap reference plane, the uncertainty in

the irradiance at a given reference plane for distances

of 1 m or greater is less than 0.01%.

For radiometers with a known reference plane, we

use a micrometer to make sure that the DUTs and the

reference trap aperture lie in the same plane. By using

a micrometer, the reference planes can be aligned to

within approximately 10 m. Consequently, this approach significantly reduces the uncertainty in the

irradiance at the DUT reference plane. If the DUT

reference plane is not known, it is optically determined by using Eq. (3). For a non-point-source geometry, the full equation including the spatial extent of

the source and detector is required42; the uncertainties remain the same.

5. Current-to-Voltage Conversion (I–V Amplification)

The uncertainty of the current-to-voltage (I–V) conversion43 was 0.01% for gain selections between

104 VA and 107 VA. At these gains, the uncertainty

of the feedback resistors in the I–V converter was

0.01% k  1for the decade nominal resistance values. The uncertainty increased to 0.014% at the

108 VA gain where two 50 M resistors (each with

0.01% resistance uncertainty) were connected serially. Because the resistance uncertainty of 109 

resistors is 0.5% or higher, a gain of 109 VA was

radiometrically calibrated against a gain of 108 VA

by measuring the same stabilized optical power. The

gain uncertainty for this highest gain selection was

0.02%. The low uncertainties in gain can be achieved

only if the dark reading is substracted from the signal

plus the dark reading of the trap detector radiometer

(which includes the I–V converter) using a shutter

positioned upstream in the laser beam. The temperature coefficients of the resistances were 0.001%°C

for gain selections between 104 VA and 107 VA.

The maximum temperature change in the lighttight box is 2 °C. Given an equal probability distribution for the temperature, the uncertainty in the

resistance arising from the temperature coefficient is

0.001% 23  7  104

%.33

6. Transfer to Test Instrument

To achieve the lowest possible uncertainties on

SIRCUS, the instrument should be designed with the

calibration in mind. The uncertainty in the transfer to

a test instrument is listed in Table 1 as 0.03%. This is

for a well-designed, well-characterized, stable radiometer. Nonideal instrument characteristics such as

stability, temperature dependence, long-term drift,

and out-of-field response, all contribute to increased

overall uncertainty in a calibration. Interference

fringes from multiple reflections of incident radiation

at optical surfaces have been observed in the calibration of instruments with windows and other optical

elements if they are not wedged or antireflection

coated. For example, the absolute spectral responsivity of a pyrometer (discussed in Subsection 4.A) calibrated on SIRCUS is shown in Fig. 9, in both a

logarithmic [Fig. 9(a)] and a linear [Fig. 9(b)] scale.

Interference fringes (the sinusoidal oscillations in the

responsivity) are emphasized in the expanded view

[Fig. 9(c)]. The presence of interference fringes increases the difficulty in the calibration if they must be

measured during the calibration or increases the uncertainty in the calibration.

As an aside, we have found that interference fringes

are ubiquitous, caused mainly by the window on the

photodiode or parallel-surface windows in the device,

or filters.12 A complete mapping of the fringes is possible on SIRCUS because of the narrow spectral bandwidth and wavelength stability of the lasers and

because the laser wavelength can be tuned automatically. In certain calibration approaches—for example,

Fig. 8. Radiometric determination of the distance between two

aperture planes. Dots are measured trap-to-monitor ratios; solid

curve is a fit to the data.

8226 APPLIED OPTICS  Vol. 45, No. 32  10 November 2006
using lamp–monochromator systems—the fringes are

not observed. Interference fringes occur when the coherence length of the source is as long as or longer than

the size of the interfering structure. For example, interference fringes will most likely be present from multilayer coatings even for an incoherent source such as

a lamp. If they are not observed, it is likely because the

fine structure in the spectral responsivity caused by

interference fringes is being averaged over the finite

source bandwidth. However, the averaging may not

be complete, and artifacts caused by the incomplete

cancellation of the fringes can lead to erroneous

results. Also, errors can arise in the determination

of an instrument’s effective aperture area using the

scanning method if fringes are present.12 In this

case, the instrument should be calibrated directly

in the irradiance mode to obtain the lowest achievable uncertainties.

7. Radiance Responsivity Calibrations

For radiance responsivity calibrations, the uncertainty budget differs only slightly from the uncertainty budget derived for irradiance responsivity

calibrations. In a radiance responsivity calibration,

the average radiance over the entire integrating

sphere exit port area is measured by the reference

trap detector, while instruments being calibrated

typically image variously sized central regions of

the exit port. Errors in calibration can occur if the

sphere radiance is nonuniform, giving different average radiance depending on the area of the exit

port being imaged. While the sphere’s nonuniformity can be mapped and corrections applied, for the

lowest uncertainty measurements, it is desirable to

keep the sphere’s nonuniformity as small as possible. Many researchers have calculated baffle arrangements for spheres to improve the radiance

uniformity within the exit port for different input

source configurations. We have found empirically

that if the input laser beam impinges on the sphere

wall close to the exit port, no baffles inside the

sphere are needed.

The integrating spheres used for radiance responsivity calibrations on SIRCUS have been designed to

allow the incident laser light to hit the sphere wall

near the exit port. The spatial uniformity of one of

the spheres, a 30 cm diameter Spectralon-coated integrating sphere with a 7.5 cm diameter aperture,

was mapped using a radiometer with a narrow

1°FOV. Fixed at a distance of 0.5 m from the

sphere, the target spot diameter of the radiometer at

the sphere exit port was approximately 12.5 mm. The

radiometer was translated in 6 mm increments and

the radiance recorded at each position. The sphere

radiance was spatially uniform to within 0.1% over

the entire sphere exit port (Fig. 10). Radiance is a

conserved quantity. As long as the DUT is imaging an

area within the exit port, the distance from the DUT

to the sphere exit port is not critical for radiance

responsivity calibrations.

Fig. 9. Absolute spectral irradiance responsivity of a filter radiometer, namely, the AP1 pyrometer, shown on (a) a logarithmic

and (b) a linear scale. (c) Expanded view of the responsivity showing large oscillations arising from multiple reflections of the incident flux between surfaces within the instrument.

10 November 2006  Vol. 45, No. 32  APPLIED OPTICS 8227
E. Calibration Procedure

Before an instrument can be calibrated, it must be

aligned with respect to the integrating sphere, as

must the reference standard detector. To align the

system, a laser is used to define an optical axis. Both

the integrating sphere and the detectors are then

aligned to the optical axis. The optical axis is typically

set to be parallel to the direction of motion of a linear

translation stage that moves perpendicular to the

sphere exit port (the z axis defined in Fig. 11). The z

axis translation stage sits on a pair of rails and is

manually translated. A linear encoder records the

stage position along the rails.

As illustrated in Fig. 11, to define the optical axis,

a laser beam is incident on a pellicle beam splitter

that is mounted on the z-axis rail system. A mirror

is positioned behind the pellicle to retroreflect the

light directly back into the laser. The pellicle is in a

mirror mount and is adjusted to reflect light that is

then aligned to be parallel to the translation stage.

This is done by first mounting an iris near the

pellicle beam splitter on the translation stage and

aligning it so that the laser light is centered on the

iris aperture. Then the iris is moved by using the

translation stage to lie some distance away from

the pellicle. The angle of the pellicle beam splitter is

adjusted so that the light reflected from it goes

through the iris aperture. These two steps are repeated until the beam is centered on the iris at the

two translation stage positions. At this point, the

optical beam is parallel to the translation stage, and

the optical axis is defined.

To align the detectors, the motorized x–y translation

stage is positioned such that the laser is centered on

each detector (one at a time), and the reflection from a

flat reference plane on the detector is parallel with the

incident beam. For each detector, a computer registers

and stores the alignment position. The retroreflected

beam (from the mirror behind the pellicle) is automatically aligned parallel to the rail. The sphere exit port

is then centered on this beam (and the angle adjusted

to coalign the reflected laser beam with the incident

beam).

The alignment between the detectors and the integrating sphere is radiometrically validated by

translating the detectors in the x and y directions

and recording the signals as a function of stage

position. The stage position giving the maximum

signal from each instrument is compared with the

stage position derived from the optical alignment

procedure. The two positions typically agree to

within 1 mm, well within the desired alignment

uncertainty.

1. Calibration Protocol

The entire data collection sequence is automated.

Initially, an electronic shutter that blocks the laser

radiation before it enters the optical fiber is closed,

and a background signal is acquired for both the

reference standard trap detector and the sphere

monitor. Then the shutter opens and the signals

from the trap and the monitor on the sphere are

recorded. The signals are initially amplified using a

current-to-voltage amplifier44 and then fed into a

digital multimeter.45 The signal from the multimeter is averaged for several seconds. The mean

reference-to-monitor ratio and the standard deviation of the ratio are recorded. After this, the stage

moves to the DUT position, and the data acquisition

sequence is repeated. This gives the DUT mean

signal-to-monitor ratio and the standard deviation

of the ratio. The standard deviations of the ratios

are monitored; trap detector measurement standard deviations larger than 0.01% are an indication

of laser power instabilities.

Under routine calibration conditions, the intensitystabilized laser wavelength is read by the wavemeter

and transferred to the computer during each measurement. Along with mean ratios, the mean and standard

deviations of the wavelength are recorded. This allows

ready identification of laser wavelength instabilities

during a scan. Occasionally, for faster data acquisition,

the wavelength is recorded only at the beginning of the

acquisition sequence. Following the data acquisition

Fig. 10. Contour plot of the sphere radiance uniformity within the

exit port; 0.1% steps.

Fig. 11. Schematic of the alignment method for SIRCUS.

8228 APPLIED OPTICS  Vol. 45, No. 32  10 November 2006
sequence, the wavelength is changed and the sequence

is repeated.

3. Comparison with the National Institute of Standards

and Technology Lamp–Monochromator-Based

Calibration Facility

The high optical power available with laser-based calibration systems enables us to calibrate instruments

directly for either radiance or irradiance responsivity.

The low wavelength uncertainty of the laser is instrumental in reducing the calibration uncertainty for

filtered instruments. The source radiance uniformity

also permits rapid characterization and calibration of

digital imaging systems. Some of the advantages of the

laser-based calibration approach over a conventional

lamp–monochromator-based approach are illustrated by the calibration of a photoelectric pyrometer

(PEP), an instrument used to radiometrically determine the temperature of a blackbody.46 The instrument is equipped with a narrow bandpass filter

1 nmfor spectral selectivity.

For accurate radiance temperature determinations,

the instrument’s spectral out-of-band responsivity

must be measured as well as its in-band responsivity.

Figure 12 shows the relative spectral responsivity of

the PEP determined on SIRCUS compared with the

relative spectral responsivity determined using the

lamp–monochromator system in the SCF. As shown in

Fig. 12(a), the spectral responsivity measured with the

lamp–monochromator system is dominated by the

spectral bandwidth of the source and deconvolution of

the spectrum by using the source slit scatter function

is required. In contrast, the fine detail in the spectral

responsivity is easily measured on SIRCUS because of

the monochromatic nature of the source. Note that

there are several overlying data points at each wavelength along both the rising and falling edges, demonstrating the extreme wavelength stability of the

SIRCUS facility. Because of the low flux in the lamp–

monochromator system, the out-of-band responsivity

is limited to approximately 106 [Fig. 12(b)]. In contrast, the out-of-band responsivity can be measured

to the 109 level in the SIRCUS facility.

In SIRCUS, instruments are calibrated in their operational state: at the system level, with entrance pupils overfilled. This approach avoids unforeseen errors

that can occur using other calibration approaches. For

example, consider the measurements of the relative

spectral responsivity of a single channel filter radiometer known as a standard lamp monitor (SLM).47 The

SLM can be operated in irradiance or radiance mode,

depending on the foreoptics. The irradiance mode configuration has a Teflon diffuser, a window, an interference filter, and a silicon photodiode. The instrument’s

relative spectral responsivities (RSRs) are used to

band integrate the response to an illumination source.

The RSR of a SLM was measured on the SCF. During

these measurements, the flux from the monochromator exit slit was imaged onto the center of the diffuser.

In this case, the irradiance collector was underfilled by

the incident radiant flux. The SLM was also calibrated

in irradiance mode for absolute spectral responsivity

on SIRCUS. In this case, the irradiance collector was

overfilled by the flux from the laser-illuminated integrating sphere. A comparison of the two results by

using peak-normalized data showed that the relative

spectral responses did not agree (Fig. 13). There was

no dependence on the f# of the incoming flux. However, spatial maps of the relative response at multiple

Fig. 12. Relative spectral responsivity of the PEP measured on

SIRCUS and on the SCF: (a) linear scale; (b) log scale.

Fig. 13. Relative spectral responsivity of the SLM measured in

underfilled mode (SCF) and in overfilled mode (SIRCUS).

10 November 2006  Vol. 45, No. 32  APPLIED OPTICS 8229
fixed wavelengths within the in-band region showed

that the irradiance responsivity was not spatially

uniform (due to the diffuser), leading to the observed

differences. These measured differences can cause

errors in the band-averaged measurements of spectral irradiance when the spectrum of the source being

measured differs from that of the calibration source.

4. Application to Primary Radiometric Quantities

and Units

The NIST Optical Technology Division is responsible for maintaining two fundamental SI units, the

unit for temperature, the kelvin, above 1234.96 K,

and the unit for luminous intensity, the candela. In

the following subsections we describe the effect of

SIRCUS calibrations on reference standard pyrometers used to measure the radiance temperature of

blackbody sources and photometers used to measure

the illuminance of standard lamps. Using SIRCUS to

develop a detector-based validation of the spatial distribution of the radiant flux from a standard synchrotron source predicted by the Schwinger equation is

also discussed.

A. Radiance Temperature

For temperatures above the freezing temperature of

silver, the ITS-90 (Ref. 48) is defined in terms of spectral radiance ratios to one of the silver-, gold-, or

aluminum-freezing temperature blackbodies using the

Planck radiance law.49 In the ITS-90, the assigned

temperatures for the aluminum, silver, and gold freezing points result from thermometry using ratio pyrometry from the mean of two different and conflicting

constant-volume gas thermometry measurements at

lower temperatures. There are thermodynamic temperature uncertainties of the freezing points of the

primary metal blackbodies that arise primarily from

the uncertainties in the lower temperature gas thermometry.

Because of the use of spectral radiance ratios, the

temperature uncertainties of ITS-90 assigned blackbody, uTBB, increase as the square of the temperature ratios according to

uTBB uTFP

TFP

2 TBB

2

, (4)

where TFP and uTFPare the temperature and the

uncertainty of the fixed-point blackbody and TBB is

the temperature of the higher temperature blackbody. The increases in the temperature uncertainties

can be reduced by using absolute radiometry with pyrometers traceable to cryogenic radiometers, and the

resulting temperature uncertainties can be smaller

than those measured using the ITS-90 techniques.10,50

To decrease the uncertainties in the radiance temperature scale at NIST and, ultimately, in the thermodynamic temperature assignment of the metal

freezing-point temperatures, a pyrometer—denoted

the Absolute Pyrometer-1 (AP1)—was built to radiometrically measure blackbody temperatures.50,51 Spectral selection is achieved by using a narrowband

interference filter with a center wavelength at 650 nm

and a bandpass of 10 nm. The filter is temperature

stabilized to near room temperature, and the hermetically sealed silicon photodiode has a two-stage thermoelectric cooler for operation at 15 °C. It has a

noise-equivalent power (NEP) of 3 fW at an electrical

bandwidth of 0.3 Hz. The radiometric characteristics,

e.g., stability and linearity, for example, of the AP1

have been established.51

The AP1 was calibrated for absolute spectral radiance responsivity on SIRCUS. As shown in Fig. 9,

it has a peak responsivity between 647 and 652 nm,

a FWHM bandwidth of approximately 10 nm, and

out-of-band blocking better than 107

. Interference

fringes with an amplitude of 0.5% were observed in

the responsivity. The absolute spectral responsivity

was therefore measured with 0.03 nm resolution. The

AP1 subsequently measured the melt and freeze cycles of silver and gold fixed-point blackbodies. The

signal from the AP1 is converted to temperature using the equation:

iu   sL	uLu, Td, (5)

where sLis the absolute spectral responsivity of

the AP1, 	u is the emissivity of the blackbody, and

Lu, Tis the radiance of the blackbody derived from

Planck’s equation.50

The noise-equivalent temperature at the gold (and

silver) freezing temperature is 2 mK, and the noise

will not be the dominant component of the total

temperature uncertainties. The AP1 was calibrated

twice on SIRCUS, once in 2003 and again in 2005.

Using the SIRCUS 2003 calibration, the expanded

uncertainty k  2in the radiometric measurement

of the gold (or silver) freezing-point blackbody was

approximately 0.15%. The radiometric uncertainties

can be related to the uncertainties of the temperature

determinations from the derivative of the Wien approximation, which shows the relationship between

the uncertainty in radiance, L, to the uncertainty in

blackbody temperature, T:


L

L  c2


T

T2 . (6)

In Eq. (6), c2 is the second radiation constant, and 

is the wavelength. Using Eq. (6), an uncertainty of

0.15% in radiance responsivity at 650 nm will lead to

an uncertainty of 121 mK in the measurement of the

melting and freezing temperature of the gold-point

blackbody, which is slightly larger than the ITS-90

uncertainty, as shown in Table 2.52 The AP1 was

recently recalibrated on SIRCUS by using the 2004

trap-detector responsivity scale (Table 1). By using

the new calibration, the expanded uncertainty in the

radiometric measurement of the gold point is reduced

to approximately 0.09%. With the reduced uncer8230 APPLIED OPTICS  Vol. 45, No. 32  10 November 2006
tainty from SIRCUS, the corresponding temperature

uncertainty derived from the uncertainty in the radiometric measurement of the gold-point blackbody

can be reduced to approximately 72 mK, significantly

lower than the ITS-90 uncertainty.

These results are, in effect, the first step toward

implementation of a detector-based thermodynamic

temperature scale. SIRCUS can be used to calibrate

optical pyrometers directly, eliminating the dependence on a blackbody and the ITS-90. As discussed

by Yoon et al.,50,53 moving from a source-based to

a detector-based spectral irradiance (and radiance)

scale can greatly reduce the radiometric uncertainty

in the measurement of higher temperature sources.

B. Photometry

The redefinition of the candela in 1979 coupled photometric and radiometric units54 and made it possible to

realize and maintain photometric units by using detectors as well as sources. Following the redefinition,

many national laboratories, including NIST, derived

and maintained the candela (and derived photometric

units) using calibrated standard detectors traceable to

cryogenic radiometry rather than standard lamps

traceable to primary standard blackbodies and international temperature scales.55,56 Since 1992, the candela has been maintained at NIST by using a group of

eight standard photometers.57 The overall relative expanded uncertainty (k  2) for the NIST illuminance

unit realization is currently 0.39%.57

There are several components in the uncertainty

budget related to the determination of the photometer

relative spectral responsivity using the lamp–

monochromator system in the SCF.1,57 The uncertainties in these components can be significantly reduced

or eliminated by realizing the illuminance scale on

SIRCUS. The spectral responsivity scale will be reduced from a standard uncertainty of 0.11% currently

measured on the SCF to 0.075% because of the reduction of transfer steps from the high-accuracy

cryogenic radiometer. The luminous efficiency function defined by the Commission Internationale de

l’Eclairage (CIE), V, is a strong function of wavelength. The SIRCUS wavelength scale, with uncertainties reduced to less than 0.01 nm from the SCF’s

wavelength uncertainty of 0.1 nm, reduces the relative standard uncertainty for this component from

0.04% to 0.004%. A significant set of uncertainty

components results from the geometry of the SCF

output beam. The SCF uses f9 optics to focus the

light to a 1 mm spot that is used to calibrate the photometers, whereas the photometers are normally used

in a far-field condition. SIRCUS can calibrate photometers in a geometrical configuration identical to the

application geometry, eliminating errors caused by different interreflection patterns inside the photometer

between the calibration and application.

In addition, since SIRCUS calibrates the detector

in irradiance mode instead of power mode, the uncertainty of the aperture size and the uncertainty due to

the nonuniform spatial response of the photometer

are eliminated. Combined the uncertainty contribution from these components can be reduced from

0.12% (Ref. 57) to less than 0.01%. The overall relative expanded uncertainty k  2for the NIST illuminance unit realization is expected to be reduced to

0.24%, a 40% reduction from the uncertainty in the

current scale, when the new illuminance scale is

realized. The new illuminance scale will lead to an

expected overall relative expanded uncertainty of

0.27% k  2for the NIST candela.

The current photometric working standard photometers were not calibrated on SIRCUS because

large interference fringes (of the order of 10%) were

observed in the spectral responsivity of those instruments. A trap-detector-based tristimulus colorimeter

was developed to realize a detector-based color scale

(see Subsection 5.A.). As a first step toward the new

SIRCUS-based photometric scale, the irradiance responsivity of the photometric (Y) channel of the colorimeter was determined. An aperture mounted on

the front surface of the colorimeter defines the reference plane for irradiance and illuminance measurements. Because of the thick color filter combinations58

and the removed photodiode windows, all four channels of this colorimeter showed fringe-free operation on

SIRCUS. Use of feedback resistors in the photocurrent

meters with 0.001%°C temperature coefficient of resistance, 0.01% uncertainty of their decade nominal

values, and realizing loop gains larger than 104 in dc

measurements for all signal-gain selections, the uncertainty of the photocurrent-to-voltage conversion

was 0.01%.31

From the SIRCUS-measured spectral irradiance responsivity of the photometric channel (between 360

and 950 nm), the illuminance responsivity was calculated.59 Thereafter standard lamps were measured

in the photometry calibration facility to compare the

illuminance responsivities of the same channel determined from both the existing (SCF-based) and the

new (SIRCUS-based) scales. The colorimeter was

calibrated on SIRCUS twice, with the calibrations

separated in time by 15 months. The illuminance

responsivity of the photometric channel from the two

SIRCUS calibrations agreed within 0.1%. The average illuminance responsivity from the two SIRCUS

calibrations was 4.911 nAlx, 0.35% higher than the

SCF-based illuminance responsivity.

Our investigations showed that the SCF-based

illuminance responsivity (used in the present photoTable 2. Comparison of the Results of Radiometric Determinations of

the Gold- and Silver-Point Blackbody Temperatures Using the AP1

Pyrometer with the ITS-90 Values

TAP1

(K)

u (TAP1)

(K)

(k  2)

T90

(K)

u (T90)

(K)

(k  2)

TAP1  T90

(K)

Au-point

blackbody

1337.344 0.121 1337.33 0.100 0.014

Ag-point

blackbody

1234.956 0.106 1234.93 0.080 0.026

10 November 2006  Vol. 45, No. 32  APPLIED OPTICS 8231
metric scale) is low by approximately 3% because of a

beam-clipping problem caused by the small apertures

in the working standard photometers. Comparisons

of the spectral responsivity determined on SIRCUS

and the SCF show spectral shifts as large as 0.5 nm

and responsivity differences as large as 1%.

C. Synchrotron Radiation

Schwinger described the nature of radiation that is

emitted from the acceleration of relativistic particles.60 In a synchrotron accelerator, electrons are

confined to a circular path and continuously emit

radiation tangential to their direction. Magnets are

used to control the energy and direction of electrons

in the synchrotron. Like blackbody radiation, synchrotron radiation is absolutely calculable from the

knowledge of a very few parameters. Blackbody radiation follows from Planck’s law: Knowledge of the

temperature and emittance allows for calculation of

all radiation emanating from the blackbody. Synchrotron radiation is defined by the Schwinger equation:

The electron beam current, magnetic field, and the

orbital radius completely define the radiation field.

The NIST Synchrotron Ultraviolet Radiation Facility (SURF III) is a particularly simple synchrotron

storage ring. The electrons are confined to a circular

orbit in a vacuum chamber by a dipole magnet with an

extremely uniform magnetic field (104 nonuniformity in the magnetic field). The angular distribution

and intensity of radiation is dependent on the electron beam energy and the wavelength of the emitted

radiation. To validate the expected spatial distribution, three filter radiometers were constructed with

band-center wavelengths at 254, 400, and 800 nm,

respectively. A simplified schematic of the filter radiometers is shown in Fig. 14(a). These filter radiometers contain a precision aperture, a diffuser, an

interference filter, and a photodiode, and they are not

polarization sensitive. The filter radiometers were

calibrated for irradiance responsivity on SIRCUS; the

absolute spectral responsivity of the 400 nm filter

radiometer is shown in Fig. 14(b). They subsequently

measured the angular distribution and intensity of

the emitted radiation at a known beam current and

magnetic field at SURF III.61 The filter radiometer

results are shown in Fig. 15. By numerically integrating the response of the radiometers and the calculated angular distribution of the intensity of emitted

radiation, the spatial distribution of the radiant flux

from SURF III can be calculated for different wavelengths. The quantitative results for the three filter

radiometer wavelengths are given by the solid curves

in Fig. 15. There are no adjustable parameters in the

calculations. The results at 400 nm have been multiplied by a factor of 3 and the results at 800 by a

factor of 15 to show all the results on the same figure.

The calculated, or predicted signals as a function of

angle agree with the measurements to better than

0.5%.

5. Applications

The unique characteristics of SIRCUS give us the

versatility to address a wide range of optical metrology issues in addition to applications related to the

Fig. 14. (a) Schematic diagram of the filter radiometers that were

calibrated for irradiance responsivity on SIRCUS and used to measure the angular distribution of radiation and intensity at SURF

III. (b) Absolute spectral irradiance responsivity of the 400 nm

filter radiometer.

Fig. 15. (Color online) Angular distribution pattern from SURF

measured with three filter radiometers. The solid curve is the

calculated distribution pattern.

8232 APPLIED OPTICS  Vol. 45, No. 32  10 November 2006
measurement of fundamental sources or to the realization of fundamental SI units. We briefly discuss

other applications in the following subsections.

A. Detector-Based Color Scale

A tristimulus colorimeter standard was developed by

using temperature-stabilized filters in front of a silicon

tunnel-trap detector to realize a detector-based color

scale.58 The tristimulus colorimeter is composed of four

channels consisting of filter combinations with the trap

detector designed to mimic the CIE color-matching

functions62 with small spectral mismatch. The spectral

mismatch of the realized channels is characterized

by the CIE f1 values.63 The filter combinations are

mounted in a temperature-controlled (heated) filter

wheel that can be moved between the trap detector

and the front aperture. The aperture plane is the

reference plane of the illuminance-mode photometer–

colorimeter, and it is in the plane of the front cover. A

precision current-to-voltage converter is attached to

the top of the instrument. Electronic and radiometric

characterizations, including current-to-voltage conversion uncertainty and spatial, angular, and spectral responsivity, have been done.

The tristimulus colorimeter was calibrated on

SIRCUS as a first step in the establishment of a

detector-based color scale.64 When utilizing the uniform irradiance at the detector reference plane from

the small sphere source of the SIRCUS, the nonuniformity of spatial responsivity of the filters and the

detector in the tristimulus colorimeter will not contribute to measurement uncertainty. Also, interreflections

between optical components will be the same for the

calibration and subsequent applications, and their contribution to radiometric measurement error will cancel. The combined expanded uncertainties k  2in

the absolute spectral irradiance responsivities of the

individual channels, neglecting correlations, are estimated to be 0.15% or less. From the spectral irradiance responsivity curves, the broadband calibration

factors of the colorimeter channels can be calculated,

and the tristimulus values of a test light source can

be measured. For a Planckian radiator (a light source

with a well-known spectral distribution), a 0.15% uncertainty in the spectral irradiance responsivity of

any one channel of a tristimulus colorimeter will

result in a chromaticity coordinate uncertainty of

0.0004 for both x and y. These uncertainties correspond to an uncertainty of 4 K in color temperature,

a factor of 2 less than the uncertainties of current

primary color temperature lamp standards.

B. Stray Light Characterization of Spectrographs

Spectrographs are spectroradiometers with multielement array detectors that can acquire an entire

spectral image over some finite spectral region simultaneously. Spectrographs commonly consist of

an entrance port, a dispersing element (such as a

grating) to spatially resolve the spectral components of the incident radiation, and mirrors to image the entrance port (often a slit) onto a reference

plane where the array detector is located. Because

of the dispersing element, the spatial image of the

entrance port falls on different regions of the detector array, depending on its wavelength; broadband

sources form an image across the entire array. The

spectral coverage of a spectrograph is determined

by the size of its detector array, the dispersion properties of its grating, and its optical layout. Compared with conventional, scanned grating systems,

source spectral distributions can be acquired in a

matter of seconds, as opposed to minutes. The ability to rapidly acquire a spectrum has led to the use

of array-based systems in a variety of radiometric,

photometric, and colorimetric applications where

acquisition speed is an issue, for instance, on a

production line, or in cases where the source being

measured is not stable over extended periods of

time.

The measurement uncertainties of spectrographs

are often larger than conventional scanning spectrometers. Spectrographs are single grating instruments

and there are intrinsic limitations in the background

signal originating from radiation scattered from imperfections in the grating and other optical elements.

This unwanted background radiation, called stray

light, while small—of the order of 104 or less of

the incident spectral radiance in a single grating

spectrograph—can give rise to unforeseen errors, often much larger than anticipated, when the spectral distribution of a source being measured differs

significantly from the spectral distribution of the calibration source. In comparison, a conventional scanning spectrometer is often constructed as a doublemonochromator instrument (double grating or prism

grating) that has a stray light level lower than 106

.

In many applications, the spectral distributions of

the test source and the calibration source differ significantly. Spectrometers are typically calibrated against

standard incandescent lamps with correlated color

temperatures (CCTs) ranging from 2800 to 3100 K.

Most of the emission from these sources lies in the red

and NIR regions. Measurement errors, often significant, arising from stray light are inevitable when

instruments calibrated against standard lamps subsequently measure light sources that have dissimilar

spectral distributions, such as LEDs, displays, discharge lamps, and fluorescent lamps. In these situations, stray light is often the dominant source of

spectrograph measurement error.

Algorithms have been developed to correct the

output of a spectrograph for stray light based on

the spectral imaging properties of the instrument.

The tunable lasers available on SIRCUS are used to

characterize a spectrograph’s response for stray

light. Figure 16 is a semilogarithm plot of spectra

acquired from a spectrograph with excitation wavelengths ranging from 350 to 800 nm. Each spectrum

is a single image normalized by the peak value. The

strong central peak in each image (or spectrum) in

Fig. 16 corresponds to the image of the entrance slit

formed on the detector array. The broad shoulder and

finite baseline are signals from radiation that is not

10 November 2006  Vol. 45, No. 32  APPLIED OPTICS 8233
properly imaged onto the detector, i.e., from stray

light within the spectrograph. By measuring the system response at a number of wavelengths, the evolution of the image as the excitation wavelength moves

across the array can be determined. Based on these

measurements, a stray light correction algorithm can

be implemented that reduces the errors and associated uncertainties arising from stray light an order of

magnitude or more.47,65,66 For an accurate characterization of spectrometers for this correction, the input

optics must be illuminated by uniform monochromatic radiation at many wavelengths in irradiance

or radiance mode. The SIRCUS facility is effectively

utilized to achieve the necessary measurements.

C. Solar Irradiance

Sun photometers are filter radiometers used to determine atmospheric optical properties at different wavelengths. Primary standard reference sun photometers

are calibrated at high altitudes by using the Langley–

Bouguer technique. In this calibration approach, a series of measurements at different solar zenith angles

are made over the course of a day, giving a range of

measured signals as a function of zenith angle (or air

mass). The measurements are then extrapolated back

to zero air mass, giving an instrument signal corresponding to the expected signal in the absence of any

intervening atmosphere.67 Reductions in the uncertainties in irradiance responsivity calibrations of

primary standard reference Sun photometers using

laboratory standards would allow for meaningful comparisons with the results from the Langley–Bouguer

method, resulting in independent values for the exoatmospheric solar irradiance at the set of measurement

wavelengths.

Global networks of Sun photometers are used to

provide detailed mapping of atmosphere optical

properties, for example, aerosol concentrations and

distributions. Sun photometers that are part of

the Aerosol Robotic Network68 (AERONET) are calibrated for irradiance responsivity against reference primary standard Sun photometers using the

cross-calibration technique at the NASA Goddard

Space Flight Center (GSFC).67 The cross-calibration

technique consists of near-simultaneous solar observations with the uncalibrated instrument and a

calibrated reference Sun photometer. Reducing the uncertainties in network instruments by using laboratory standards would validate the uncertainties in the

calibration transfer and could improve the characterization of the atmosphere.

Because Sun photometers measure solar irradiance, their responsivity is typically low, and they are

difficult to calibrate using lamp–monochromator systems. To demonstrate the feasibility of calibrating

Sun photometers on SIRCUS, two multichannel Sun

photometers were calibrated and the results compared with standard cross calibrations.69 To compare

the cross-calibration results to the SIRCUS calibrations, the SIRCUS-derived irradiance responsivities

s() were used to predict a top-of-the-atmosphere

(TOA) signal VoSIRCUS:

VoSIRCUS  sEd, (7)

where sis the spectral responsivity of one of the

radiometer channels and Eis an exoatmospheric

solar irradiance spectrum. In this work we used the

exoatmospheric solar irradiance spectrum developed

by Thuillier et al.70 To perform the integration, the

sand the Ewere interpolated to a uniform

wavelength interval of 0.25 nm and integrated. The

750 nm channel results agreed with the cross calibration to within 0.15%, the 490 nm channel to within

0.85%, and the 440 nm channel to within 5.76%.

The dominant source of uncertainty in the SIRCUSbased predicted TOA signal was the uncertainty in the

solar irradiance spectrum. Assuming an 1.5% combined standard uncertainty in the absolute value and

given a step size of 1 nm in the region of interest, we

were able to validate the cross calibration with an

expanded uncertainty k  2of 4%. The agreement

for the 490 and 750 nm channels were within the

combined uncertainties, but the 440 nm results were

not and warrant further investigation.

The measurements demonstrated that SIRCUS irradiance levels were high enough to calibrate Sun

photometers. Current uncertainties in the exoatmospheric solar irradiance depend on the wavelength,

but in atmospheric transmittance windows in the visFig. 16. Spectrograph images as the incident wavelength is

changed and the central image moves across the array.

8234 APPLIED OPTICS  Vol. 45, No. 32  10 November 2006
ible spectral region, they are estimated to be approximately 0.5% to 1%. Calibration of primary standard

Sun photometers on SIRCUS with 0.1% uncertainties or less would enable us to differentiate between

exoatmospheric solar irradiance spectra and could

lead to a reduction in the uncertainties in the exoatmospheric solar irradiance spectrum. This has implications for global climate change studies because the

exoatmospheric solar irradiance is one of the primary

forcing functions driving the global climate.

Additional applications include the development

of wavelength standard reference materials with reduced uncertainty71 and the characterization and calibration of instruments with large entrance pupils,

such as telescopes and remote-sensing sensors.72

6. Summary

We have described a laser-based calibration facility for

irradiance- and radiance-measuring instruments. In

this facility, high-power tunable lasers were introduced into integrating spheres by using optical fibers,

producing uniform, quasi-Lambertian, highly radiant

flux sources. Reference standard irradiance detectors,

calibrated directly against national primary standards

for spectral power responsivity, were used to determine the irradiance at a reference plane. Instruments

were calibrated directly in irradiance or radiance mode

with uncertainties approaching or lower than those

available for spectral power responsivity calibrations

in traditional lamp–monochromator facilities. The

implications for fundamental radiometric measurements, including radiance temperature, photometric,

and synchrotron source measurements, were described. Finally, advanced applications to realize the

first detector-based color scale, to correct stray light in

spectrographs, and to measure solar irradiance by using this facility were briefly outlined.

Work continues on reducing the uncertainties associated with measurements on SIRCUS as well as the

spectral coverage and laser powers available. In Table

1 we calculated the uncertainty in the irradiance responsivity at a single wavelength. In practice, in determining the uncertainty in measuring the irradiance

of a source by using a filter radiometer as an example,

the responsivity was integrated over a wavelength

range. The irradiance responsivity was determined

for a large number of wavelengths, typically 100 or

more, over the in-band range. Calculating the bandintegrated responsivity, the random components in the

uncertainty budget were reduced by the square root of

the number of measurements, and only systematic

components in the uncertainty budget contributed to

the uncertainty in the measurement. We have neglected the reduction in the uncertainty from integrating the responsivity over a finite number of elements.

The spectral coverage of the SIRCUS facility for

spectral responsivity calibrations is determined by

the high-reflectance range of the coating of the integrating sphere sources, the wavelength coverage of

the standard reference and monitor detectors, and

the spectral coverage of the tunable laser systems.

Spectralon and similar PTFE-based coatings have

high reflectance from 250 to 2500 nm. The spectral

coverage of the UV–Vis–NIR SIRCUS facility has

been extended into the UV and the short-wave infrared (SWIR) regions with the integration of a quasicontinuous-wave, mode-locked OPO–sum-frequency

system. This system gave us nearly continuous tunability from 210 to 3.0 m.

Research is being conducted on reference detectors to extend the radiant power responsivity scale

from 350 down to 200 nm and from 1 out to 2.5 m

and beyond. Reference UV reflectance-type trap detectors using nitride-passivated UVG-100 diodes73 as

well as PIN-UV100 diodes73 have been developed to

extend the wavelength coverage from 350 down to

200 nm. Recently, a UV trap detector was calibrated

for radiant power responsivity over the spectral

range from 210 to 400 nm with an expanded uncertainty k  2of 0.05% or less. Finally, a variety of

irradiance-measuring working standard radiometers

have been developed for the NIR range, including

single-element Ge, InGaAs, and extended InGaAs detectors.74,75 With their calibration against an ACR,

the low uncertainty in the SIRCUS irradiance scale

will be extended into the IR spectral range.

The authors thank the U.S. Air Force Metrology for

funding this work under contract 98-435. They also

acknowledge the early and continued support of John

Grangaard, USAF (ret.) and the significant contributions to the work by B. Carol Johnson, Howard Yoon,

Yuqin Zong, Thomas C. Larason, C. Cameron Miller,

and Ping-Shine Shaw from the NIST Optical Technology Division.

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10 November 2006  Vol. 45, No. 32  APPLIED OPTICS 8237
Radiometer standard for absolute responsivity calibrations from 950 nm to 1650 nm 

with 0.05 % (k=2) uncertainty 

G. P. Eppeldauer, H. W. Yoon, Y. Zong, T. C. Larason, A. Smith, and M. Racz 

National Institute of Standards and Technology 

Gaithersburg, Maryland USA 

Abstract 

A near-IR radiometer standard with similar performance to silicon trap-detectors has been 

developed to calibrate detectors and radiometers for absolute spectral power, irradiance, 

and radiance responsivities between 950 nm and 1650 nm. The new radiometer standard 

is utilized at the Spectral Irradiance and Radiance Responsivity Calibrations using 

Uniform Sources (SIRCUS) which is the reference calibration facility of NIST for 

absolute responsivity. The radiometer is a sphere-detector with a unique geometrical 

arrangement and it can convert the radiant-power responsivity scale of the primarystandard cryogenic-radiometer into a reference irradiance responsivity scale. The 0.05 % 

(k=2) scale conversion uncertainty is dominated by the two largest uncertainty 

components of the radiometer: The spatial non-uniformity of responsivity of less than 

0.05 % in power mode and the 0.03 % angular responsivity deviation from the cosine 

function in a five-degree angular range in irradiance mode. These small uncertainty 

components are the results of a tilted input aperture (relative to the sphere-axis) and four 

symmetrically positioned InGaAs detectors around the incident beam-spot in the sphere. 

With the new radiometer standard, it is expected that a thermodynamic temperature 

uncertainty of 10 mK (k=2) can be achieved at 157 o

C the freeze temperature of the In 

fixed point blackbody. 

1. Introduction 

The primary basis of modern radiometry is the measurement of optical power with a 

cryogenic electrical-substitution radiometer. The spectroradiometric quantities such as 

spectral irradiance and spectral radiance can be derived from the primary power 

measurements. However, the derivation of the spectroradiometric quantities from optical 

power requires the use of spatially-uniform and Lambertian detectors. These detectors 

serve as power-to-irradiance converters. In the visible and near-infrared wavelength 

regions, up to 960 nm, silicon trap detectors, introduced in 1983 [1], are the lowest 

uncertainty transfer standards. Using these silicon reference detectors, 0.06 % (k=2) 

uncertainty can be achieved in irradiance measurement mode [2]. In the near-infrared 

(NIR) region, between 950 nm and 1650 nm, where the use of Si detectors is not possible, 

trap detectors using either Ge or InGaAs photodiodes have been constructed [3, 4]. Since 

the Ge or InGaAs photodiodes have much smaller shunt resistances than Si, the 

combinations of large area, NIR diodes in parallel electrical connections have resulted in 

low shunt resistance devices with much worse radiometric and electronic performances 

than Si trap detectors [5]. Also, the spatial non-uniformity of the internal-quantumefficiency limited their power measurement uncertainties to about 0.3 % (k=2). 
Another approach to obtain detectors with high spatial uniformity and Lambertian 

angular responsivity is to utilize an integrating sphere as the input to detectors which are 

directly attached to the sphere. Previous designs using InGaAs photodiodes have utilized 

either a single photodiode placed perpendicularly from the entrance aperture or multiple 

diodes facing the sphere center [6, 7]. 

Among other applications, the need for low-uncertainty radiance responsivity calibrations 

is driven by the possible thermodynamic temperature realizations in the near-infrared 

wavelength region where a 0.05 % (k=2) absolute radiance responsivity uncertainty is 

needed to achieve a 10 mK (k=2) uncertainty in the measurement of the In-point freezing 

blackbody at 157 o

C. In the last 25 years, these low uncertainty requirements could not be 

achieved with regular near-IR detectors; it was possible only with silicon trap detectors 

up to 960 nm. In order to achieve this low uncertainty in the near-IR, a new type of 

power-to-irradiance converting radiometer standard is needed that will not limit the 

uncertainty of the spectral responsivity propagation from the primary standard cryogenic 

radiometer. This new radiometer will be the reference detector of the Spectral Irradiance 

and Radiance Responsivity Calibrations using Uniform Sources (SIRCUS) facility for the 

near-IR range where up until now these low uncertainty spectral responsivity calibrations 

could not be performed. 

We describe the design and characterization of a novel near-IR radiometer transferstandard that makes it possible to perform spectral power and irradiance responsivity 

calibrations with uncertainties lower than 0.05 % (k=2). 

2. Preliminary sphere-detector experiments 

For spatial and angular responsivity tests, a Ge radiometer was attached to the exit port of 

a 5 cm diameter Spectralon#

 coated integrating sphere with 90o angle between the 

entrance and exit ports. The spatial uniformity of this simple (no baffles) and asymmetric 

Ge sphere-detector with an 8 mm diameter input-aperture is shown in Fig. 1. The aperture 

plane was (traditionally) normal to the sphere-axis. The obtained maximum nonuniformity is 0.6 % at 1500 nm using a 1.1 mm diameter scanning beam with 0.5 mm 

increments. The poor uniformity is caused by the asymmetric arrangement of the sphere 

input and output ports. 

The angular responsivity test was performed with the same sphere-detector arrangement, 

but the sphere-aperture diameter was decreased to 3.5 mm to obtain improved sphere 

performance and better Lambertian angular response. First, as in traditional spheredetector designs, the aperture plane was normal (0o

 tilt) to the sphere optical axis. The 

incident beam was produced by an FEL lamp, located 3 m away from the detector. As 

shown in Fig. 2, at 0o

 tilt (see legend), the angular response curve is flattened around the 

0o

 incidence angle because part of the reflected incident beam escaped through the 

entrance aperture of the sphere. The curve normalization was performed at the 0o

incidence angle. As a result of this problem, the angular responsivity is different from the 

cosine function, the ideal angular responsivity of detector irradiance measurements. The 
difference from the cosine is about 0.2 % at + 4o

 and - 4o incidence angles. The structures 

within the response curve are dominated by lamp instabilities. 

-6

-4

-2

0

2

4

6

mm

-6

-4 -2 0 2 4 6

mm

0.990

0.995

1.000

1.005

1.010

Relative Responsivity

Fig. 1. Spatial uniformity of responsivity of a traditional Ge sphere detector at 1500 nm. 

In the following steps, the angular responses of the Ge sphere-detector were measured at 

different aperture tilt-angles (between the normal of the aperture-plane and the sphereaxis). The tilt-angles were increased to check if the angular response relative to the above 

measurement (at 0o

 tilt) can be improved. The incidence angle (x-axis) was changed as 

above, by rotating the sphere-detector around the center of the sphere-aperture. During 

these angular response scans, the sphere-detector was rotated in a plane perpendicular to 

the plane where the entrance and the exit ports are. The normal of the aperture plane was 

increased from 0o

 (relative to the sphere axis) to 18o in increments shown in Fig. 2. 

During the angular response tests, at all tilt angles, the incident beam (at the 0o

 incidence 

angle) was always perpendicular to the plane of the input aperture. The measured 

response curves are shown in a +/- 10o range of the incidence angle. At a large enough 

tilt-angle of the aperture plane (relative to the sphere axis), the angular response curve 

becomes similar to the cosine function. For aperture-plane tilt angles of 12o

 and 18o, the 

first specular reflection from the sphere wall could not escape from the sphere (as it 

happened at 0o

 tilt) therefore the normalized responses do not show a suppressed cosine 

curve anymore. The reason of the slight angular shift relative to the cosine function is a 

close to 1o

 alignment error in the rotation of the sphere-detector. 

The above spatial and angular responsivity results show that traditional sphere-detectors, 

with 90o

 angle between the entrance and exit ports and where the aperture plane is 

perpendicular (not tilted) to the sphere axis, have significant spatial and angular 

responsivity errors, therefore, they are not suitable for absolute power and irradiance 

mode measurements with the required less than 0.1 % (k=2) responsivity uncertainty. It 

also has been shown with the preliminary angular response tests (at different aperture tilt 

angles relative to the sphere axis) that the non-Lambertian angular response can be 

significantly improved if the input aperture plane is tilted at least 12o

 relative to the 

sphere axis. This improvement was verified in the rotation plane perpendicular to the 

plane where the aperture and the detector are located. 
0.985

0.990

0.995

1.000

-10 -5 0 5 10

18o

12o

6o

3o

0o

cosine

Incidence angle [o]

Fig. 2. Angular response of a Ge sphere-detector 

at different tilt angles of the input aperture plane relative to the sphere-axis. 

The influence of the sphere-detector asymmetry (90o

 between the sphere aperture and the 

detector) for the angular response was tested as well. This test was performed with the 

18o

 tilt (of the aperture plane relative to the sphere-axis) in the plane where the aperture 

and the detector are located. To make this test, the previous angular response 

measurements were repeated after a 90o

 rotation of the sphere-detector (around its optical 

axis) and the previous measurement geometry (pivot point and fixed lamp distance) was 

used again. The obtained angular response curve significantly deviated from the cosine 

function. The measured asymmetric curve is shown in Fig. 3 (at 18o tilt of the aperture 

plane relative to the sphere-axis). The asymmetric angular response is caused by the 

asymmetric arrangement of the sphere entrance and exit ports in the plane of the rotation. 

(The rotation changes the incidence angle.) The deviation from the cosine is about 0.4 % 

at a 4o incidence angle. This error in the angular responsivity can be significantly 

decreased if multiple detectors are symmetrically arranged relative to the incident-beamproduced spot on the sphere wall. A symmetrical detector arrangement can improve the 

spatial uniformity of responsivity as well. 

The preliminary angular-response measurement results verified that using 18o

 tilt in the 

plane of the input aperture (relative the sphere-axis), the escaping radiation can be 

trapped and the angular responsivity to the cosine can be restored. Probably, there is a 

very small enhanced reflection peak at 0o

 in the BRDF of the Spectralon wall-coating 

since this material is not an ideal Lambertian reflector. This material-characteristic 

produced the flattened angular response. Also, the trapped specular-component of the 

first reflection could improve the spatial uniformity of responsivity which is important for 
low-uncertainty radiant power measurements. The results in Fig. 3 show that the 

traditional 90o

 aperture-detector arrangement should be changed to a symmetrical 

detector arrangement relative to the incident-beam-produced spot on the back of the 

sphere-wall. A symmetrical detector arrangement can be implemented using multiple 

detectors instead of a single element detector. 

0.985

0.990

0.995

1.000

-10 -5 0 5 10

18o

cosine

Incidence angle [o]

Fig. 3. Angular response of a traditional Ge sphere-detector 

where the 90o

 separated entrance and exit ports are in the plane of the rotation. 

3. Design of the sphere-InGaAs radiometer 

In order to improve the spatial and angular uniformity of the responsivity and to obtain 

lower responsivity uncertainties in a calibration transfer, a near-IR transfer standard 

radiometer has been designed. The new radiometer has an integrating-sphere receiver 

with the optical axis of the entrance aperture tilted away from the sphere-axis. Four 

temperature-controlled InGaAs photodiodes, selected for high shunt resistance, are 

symmetrically positioned in the sphere wall around the incident beam spot such that they 

cannot see each other. 

 

The geometrical arrangement for the input of the sphere-detector is shown in Fig. 4. A 

new position is needed for the aperture to obtain the maximum useful acceptance angle 

without beam clipping and to avoid any flux loss through the entrance aperture owing to 

the back reflection of the specular component of the incident beam from the sphere wall. 

The tilted aperure and the two unclipped beam-limits are illustrated. The incidence angle 

of the left limit-beam (relative to the sphere axis) is 6°, the other side limit-beam is 

determined by the sphere wall. The new entrance axis of the sphere is the aperture axis, 

which splits the angle between two limit-beams. The measurements and calculations for 

the available components showed that the optimum value of the angle between the sphere 

axis and the aperture axis is 17.5°. 
Fig. 4. Sphere-detector with a tilted aperture input. 

The cross-section of the sphere-InGaAs detector housing is shown in Fig. 5. The aperture 

axis is tilted by 18o

. The housing is temperature controlled with a thermo-electric (TE) 

cooler/heater attached to the back of the Al-housing. As shown on the picture of the 

sphere-detector in Fig. 6, a heat sink is attached to the back side of the TE cooler/heater. 

The four 1 mm diameter InGaAs detectors are selected for equal shunt resistance and 

they are parallel connected with each other. They are symmetrically positioned around the 

incident beam produced “hot” spot such that they cannot see each other. The stabilized 

26 o

C temperature of the sphere-housing propagates to the metal cans of the detectors. 

4. Sphere-InGaAs radiometer characterizations 

In Fig. 6, the sphere-InGaAs detector with a 5 mm diameter input aperture was 

characterized at the Spectral Comparator Facility (SCF) by scanning with a 1 mm 

diameter beam. The measured spatial uniformity at 1200 nm is shown in Fig. 7. The 

maximum-to-minimum responsivity change is less than 0.05 %. The spatial uniformity 

tests were repeated at 1000 nm and 1600 nm. The pattern of the spatial non-uniformity of 

responsivity was different at each wavelength. The maximum-to-minimum responsivity 

change was also 0.05 % at 1000 nm and it increased to 0.075 % at 1600 nm. With a larger 

beam spot positioned in the aperture-center, the beam positioning error in the power 

responsivity measurement can be decreased by about a factor of two. 

The noise-equivalent-power (NEP) was determined from output noise and spectral power 

responsivity measurements between 950 nm and 1650 nm. Figure 8 shows the NEP 

results from two spectral scans compared to the NEP of a Ge trap detector [8]. The 
Fig. 5. Cross-section of the sphere-InGaAs detector. 

Fig. 6. Picture of the sphere-InGaAs detector. 
Fig. 7. Spatial uniformity of the sphere-IGA detector 

with a 5 mm diameter input-aperture at 1200 nm. 

obtained data verify that the dominating noise of the sphere-InGaAs detector is white 

noise, specifically, resistor noise. The resistor noise, which originates from the parallel 

connection of the shunt resistance and the feedback resistance, is dominated by the 

resultant shunt resistance of the four parallel connected 1-mm detectors. The resultant 

shunt resistance was 33 MΩ for four non-selected photodiodes (set-1) and 50 MΩ for 

four photodiodes selected for equal shunt resistance of 200 MΩ (set-2). The expanded 

uncertainty of the shunt resistance measurements was 10 % (k=2). The feedback 

resistance of the current-to-voltage converter during the spectral measurements was 

100 MΩ. The average NEP was 5 pW/Hz1/2 for run-1 and 5.5 pW/Hz1/2 for run-2 using 

set-1 with the 33 MΩ shunt resistance. Since the resultant shunt resistance of the Ge trap 

detector is only 1 kΩ, its dominating noise is 1/f noise. The 1/f noise determined NEP of 

the Ge trap detector was 30 pW/Hz1/2. 

Figure 9 shows the repeatability of four spectral responsivity scans at the SCF. The 

responsivity differences shown on the Y-axis are in the 0.05 % level between 950 nm and 

1350 nm and also between 1450 nm and 1650 nm. The larger differences at 1400 nm are 

caused by the atmospheric absorption. 

The sphere-InGaAs detector angular responsivities were measured on a photometer bench. 

The illuminating source was a Wi41G lamp. This lamp had significantly smaller intensity 

fluctuations than the FEL lamp used in the preliminary experiments shown in Fig. 2. 

Otherwise, these measurements were performed similarly to the preliminary tests. Since 

the separation between the lamp and the sphere-detector was about 3 m, the lamp 

operated like a “point source” for the sphere-InGaAs detector. Two baffles were located 

between the lamp and the sphere-detector to minimize stray light on the detector. The 

detector was mounted on a rotation stage and it was rotated around the aperture-center in 

the horizontal plane. To repeat the angular responsivity measurements in the vertical 

plane, the sphere-detector was 90o

 rotated on the rotation stage around its optical axis. 

The measurement results are shown in Fig. 10. The ratios of the measured responses to 
the cosine function are shown versus the rotation (incidence) angle of the sphere-InGaAs 

detector. The curves are normalized. The deviations from the cosine function are 0.03 % 

if the (full-angle) field-of-view of the sphere-InGaAs detector which is limited to 5o. 

The long-term stability of the sphere-InGaAs detector is an important issue. Our 2-years 

long stability tests on several InGaAs makes and models verified that these photodiodes 

Fig. 8. NEP comparison of the sphere-IGA and the Ge-trap detectors. 

Fig. 9. Responsivity differences (repeatability) of four spectral responsivity scans. 

0

5

10

15

20

25

30

35

900 1000 1100 1200 1300 1400 1500 1600 1700

Sph-IGA run-1

Sph-IGA run-2

Ge trap

Wavelength [nm]

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

700 900 1100 1300 1500 1700 1900

Wavelength [nm]

D ifference [% ]
(even if they are not temperature stabilized) exhibit less than 0.2 % instabilities between 

1.0 μm and 1.6 μm. Also, when measurements are not performed, a protecting cap is 

mounted to the entrance port of the sphere to keep the dust and dirt outside. The low-NEP 

(high sensitivity) makes it possible to decrease throughput changes with gray spherecoatings where the reflectance factors are significantly smaller than unity. The sphereInGaAs detector will be calibrated against the cryogenic radiometer yearly, to calibrate 

out long-term changes. 

0.9990

0.9992

0.9994

0.9996

0.9998

1.0000

1.0002

-4 -3 -2 -1 0 1 2 3

90 degree rotated

0 degree rotated

Incidence angle [o]

Fig. 10. Response/cosine versus incident angle to the normal 

of the 8 mm diameter input-aperture of the sphere-detector. 

5. Calibration procedure 

The SIRCUS scale derivation is illustrated in Fig. 11. The new sphere-InGaAs detector 

(shown with the earlier used 90o

 aperture–detector arrangement) is calibrated against the 

cryogenic radiometer for absolute spectral power responsivity. Following the radiant 

power responsivity scale transfer, an irradiance mode tie point is derived from a silicon 

trap detector at about 950 nm. An alternative solution is to use an area-calibrated aperture 

in front of the sphere-detector for power-to-irradiance mode conversion. The irradiance 

mode sphere-InGaAs detector is the reference detector for the SIRCUS in the NIR range 

to 1650 nm. 

Other (test) irradiance detectors can be calibrated against the sphere-InGaAs reference 

detector when they both measure the irradiance from an integrating sphere source of the 

SIRCUS. For absolute radiance responsivity calibrations, a large sphere-source is used at 

SIRCUS and its exit-port radiance is determined against the new sphere-InGaAs detector 

when the distance d is measured between the source aperture and the detector aperture. 

Test radiance meters are calibrated against the detector-based radiance of the large 
sphere-source. In order to achieve the required 0.05 % (k=2) absolute radiance 

responsivity uncertainty, the uncertainty components are kept small and the sphereInGaAs detector will not limit the overall uncertainty of the responsivity scale transfer. 

 

Fig. 11. The SIRCUS responsivity scale derivation using a sphere-InGaAs detector. 

6. Future applications 

In addition to the SIRCUS irradiance and radiance responsivity scale extension to the 

near-IR, the sphere-InGaAs detector can be used for fiber coupled spectral power 

responsivity scale transfer with sub-pW NEP and high coupling efficiency. The sphereInGaAs detector with the 0.05 % (k=2) radiance responsivity uncertainty, also can be 

used to determine the thermodynamic temperature of a 157 o

C Indium point (blackbody 

radiator) with 10 mK (k=2) uncertainty. Also, because of its excellent spatial uniformity 

of responsivity, it can be applied for international spectral power responsivity 

comparisons with decreased uncertainties compared to presently used single-element or 

trap near-IR quantum detectors even if the incident beam sizes are different (as was the 

case in the CCPR K2.a). We are planning to increase the area of the InGaAs detectors to 

increase responsivity. Also, the detectors will be cooled to increase their shunt resistance 

and to obtain lower output noise. According to our estimation, the NEP of an improved 

sphere-InGaAs detector can be as low as 50 fW/Hz1/2. This is equal to the NEP of silicon 

tunnel-trap detectors built with shunt-resistance selected photodiodes. We also plan to 

extend the spectral range to 2.5 μm using cooled extended-InGaAs detectors. 
7. Conclusions 

This is the first time that a near-IR transfer standard detector with similar performance to 

silicon trap detectors has been developed. Recent responsivity scale realizations on the 

SIRCUS facility demonstrated that silicon trap detectors can propagate the low 

uncertainty radiant power scale of the cryogenic radiometer to 960 nm with a minimal 

increase in the uncertainty. Because of the increasing demand for less than 0.1 % (k=2) 

responsivity calibrations at the SIRCUS facility between 950 nm and 1650 nm, a transfer 

standard near-IR radiometer was needed that can propagate the primary responsivity 

scale similarly to the silicon trap detectors. A novel sphere-input radiometer (with tilted 

input aperture to the sphere axis and a symmetrical arrangement of four InGaAs detectors 

to the incident beam spot on the sphere-wall) has been developed with electronic and 

radiometric characteristics similar to silicon trap detectors. The two dominant 

responsivity uncertainty components (originating from the spatial non-uniformity and the 

angular responsivity deviation from the cosine) in a power to irradiance/radiance scale 

transfer could be decreased to less than 0.05 % (k=2). The new device with its improved 

responsivity uncertainty is used as the highest level reference radiometer of the SIRCUS 

facility for near-IR irradiance and radiance mode spectral responsivity calibrations. The 

radiometer standard can be utilized to realize a detector-based radiation temperature scale 

down to 157 o

C with a 10 mK (k=2) uncertainty. There are also other application areas, 

such as fiber coupled spectral power responsivity measurements where the coupling 

efficiency can be high using this sphere-input standard. It also can be used as a traveling 

transfer detector to compare international near-IR responsivity scales in both power and 

irradiance measurement modes with significantly lowered responsivity uncertainties. 

 

# Certain commercial equipment, instruments, or materials are identified in this paper to foster 

understanding. Such identification does not imply recommendation or endorsement by the National 

Institute of Standards and Technology, nor does it imply that the material or equipment are necessarily the 

best available for the purpose.

References 

1. E. F. Zalewski and C. R. Duda, “Silicon photodiode device with 100 % external 

quantum efficiency,” Applied Optics, Vol. 22, No.18, p. 2867-2873, 1983. 

2. S. W. Brown, G. P. Eppeldauer, and K. R. Lykke, “Facility for Spectral Irradiance 

and Radiance Responsivity Calibrations using Uniform Sources,” Applied Optics, Vol. 45, 

No. 32, p. 8218-8237, 2006. 

3. K. D. Stock, R. Heine, and H. Hofer, “Spectral characterization of Ge trap 

detectors and photodiodes used as transfer standards,” Metrologia, Vol. 40, p. S163–S166, 

2003. 

4. M. Lopez, H. Hofer and S. Kuck, “High accuracy measurement of the absolute spectral 

responsivity of Ge and InGaAs trap detectors by direct calibration against an electrically 
calibrated cryogenic radiometer in the near- infrared,” Metrologia, Vol. 43, p. 508–514, 

2006. 

5. A. Lamminpaa, M. Noorma, T. Hyyppa, F. Manoocheri, P. Karha, and E. Ikonen, 

“Characterization of germanium photodiodes and trap detector,” Meas. Sci. Technol., Vol. 

17, p. 908–912, 2006. 

6. Ana Carrasco-Sanz, Felix Rodrıguez-Barrios, Pedro Corredera, Sonia Martın-Lopez, 

Miguel Gonzalez-Herraez and Marıa Luisa Hernanz, “An integrating sphere radiometer 

as a solution for high power calibrations in fiber optics,” Metrologia, Vol. 43, p. S145–

S150, 2006. 

7. L. P. Boivin “Properties of sphere radiometers suitable for high-accuracy cryogenicradiometer-based calibrations in the near-infrared,” Metrologia, Vol. 37, p. 273–8, 2000. 

8. J. H. Lehman and X. Li, “A transfer standard for optical fiber power metrology,” 

Applied Optics, Vol. 38, p. 7164-7166, 1999. 
Optical characterization of diffuser-input standard irradiance 

meters 

George Eppeldauera, Miklós Ráczb, and Thomas Larasona

a

Optical Technology Division of the National Institute of Standards and Technology 

Gaithersburg, MD 20899, USA 

b

Guest Researcher at National Institute of Standards and Technology from the Hungarian 

Academy of Sciences Research Institute for Technical Physics and Materials Science 

P.O. Box 49, Budapest-114, Hungary 1525 

ABSTRACT 

Standards quality irradiance meters have been developed at the National Institute of Standards and Technology 

(NIST) to realize a detector based spectral irradiance scale. The design criteria and the optical and radiometric 

characterization of diffuser-input irradiance meters are discussed. The input geometry optimization is described for 

a broad-band InGaAs irradiance meter when measuring a 2856 K incandescent light source. The directional 

responsivity of the fabricated InGaAs and Si irradiance meters matches the cosine function with a maximum 

deviation of 0.15 % within a 12° field-of-view (FOV). Irradiance from sources of different sizes (incident beams 

with different f/numbers) can be measured over a wavelength range of 350 nm to 1800 nm. 

Keywords: aperture, cosine function, directional responsivity, detector, diffuser, irradiance, photodiode, 

radiometer, spectral responsivity, working standard. 

1. INTRODUCTION 

The detector spectral responsivity scale of NIST is based on an electrical substitution High Accuracy Cryogenic 

Radiometer (HACR)1

. The HACR measures the radiant power of intensity stabilized laser lines with a relative 

standard uncertainty of 0.021 %. After a scale derivation procedure2

, large-area, single-element Si3 and Ge4,5

photodiode working standards are calibrated for spectral power responsivity. The uncertainty of the spectral power 

responsivity is wavelength dependent. The relative standard uncertainty is about 0.1 % in the visible, 1 % in the 

UV, and 2.5 % in the near-infrared range when the responsivity is transferred to test detectors2

. 

In order to extend the detector based spectral power responsivity calibrations to irradiance responsivity, standards 

quality irradiance meters had to be developed. The beam geometry at calibration and the different applications 

varies from parallel (collimated) to 12° full angle (6° incidence angle). In order to achieve high measurement 

accuracy, the directional characteristics of the detectors have to follow the cosine law in this angular range. The 

directional characteristics were controlled up to a 10° incidence angle to assure the proper cosine response of the 

detectors within the desired angular range. The design and optical characterization of these meters are discussed for 

an InGaAs irradiance meter. The described optimization procedure was utilized for a Si irradiance meter as well. 

2. SPECTRAL CHARACTERISTICS 

The spectral characteristics of the irradiance meters are determined by the photodiode and the flashed opal glass 

diffuser used in the meter. In Fig. 1 the spectral responsivities of the Si and InGaAs photodiodes and the irradiance 

meters can be seen. The magnitudes of the irradiance responsivities are similar for the two meters because the 

larger aperture (8.0 mm diameter) of the Si meter produces higher irradiance responsivity than the smaller aperture 

(6.4 mm diameter) of the InGaAs meter. Sources with either monochromatic or known (e.g., Planckian) spectral 

power distributions can be measured with these broadband irradiance meters. 
Fig. 1. Spectral responsivities of the Si and InGaAs photodiodes and the corresponding irradiance meters. 

3. DIRECTIONAL CHARACTERISTICS 

The directional responsivity measurements were performed on the NIST photometry bench. Several tungsten 

incandescent lamps were used as non-calibrated radiation sources. The color temperature of the lamps was set to 

2856 K or lower. The irradiance meters to be measured were mounted on a rotational stage and the input apertures 

were positioned on the rotation axis. The distance between the lamps and the rotation axis was about 3.25 m. The 

quality of the directional responsivity data was characterized with the Commission Internationale de L’Éclairage 

(CIE) directional error f2(ε,φ): 

f2( ) ε,φ = Ereading (ε, φ) −1 (1) Ereading ( ) ε = 0° ⋅ cosε

where Ereading(ε,φ) and Ereading(ε = 0°) are the readings for an irradiance, E, arriving at the angles of incidence ε and 

0o respectively. φ is the azimuth angle. Because the irradiance meters are circularly symmetrical, they were only 

tested at two perpendicular φ values. 

Drawings of the NIST developed diffuser-input irradiance meters can be seen in Fig. 2. The FOV limiters reject 

optical radiation outside the FOV. The input apertures determine the reference plane and the active area of the 

irradiance meters. The diffusers dominate the directional responsivity of the meters. The detectors are temperature 

controlled by thermoelectric coolers and are electrically shielded. The temperature of the InGaAs and Si 

photodiodes are controlled to -30 °C and +25 °C respectively. 

Fig. 2. Input optics cross-section of the InGaAs (a) and Si (b) irradiance meters. 
The geometry of the input optics of the irradiance meters was optimized experimentally. Several flashed opal glass 

diffusers were tested with a Cary 4a spectroradiometer in the 400 nm to 1700 nm wavelength range because their 

visual appearance was not the same. The diffusers were separated into four groups according to their diffuse 

reflectances of about 27 %, 31 %, 35 %, and 40 % at 1400 nm. As can be seen in Fig. 3, the diffuse reflectance of 

the samples decreases with increasing wavelength. 

Four sizes of apertures were also tested. Their diameters were approximately 3.5 mm, 6.4 mm, 8.0 mm, and 

11.5 mm. The optimal aperture-diffuser pair was chosen experimentally. Every possible combination was 

measured for angular response and the CIE f2(ε) error functions were evaluated. Fig. 4 shows the f2(ε) functions for 

the 0° to 10° incidence angle range at a given φ value. The f2(ε) functions can be seen for combinations with the 

6.4 mm aperture and the four different diffusers in Fig. 4a. Whereas Fig. 4b shows the f2(ε) functions for 

combinations built with a 40 % reflectance diffuser and the four different apertures. 

Fig. 3. Diffuse spectral reflectance of the flashed opal glass diffusers. The vertical line shows the wavelength of the 

diffuser selection. 

Fig. 4. Directional error of different aperture-diffuser pairs for a circular InGaAs photodiode with a diameter of 

5.0 mm. Figure 4a shows the measurement results for four different diffusers with the 6.4 mm aperture. Figure 4b 

shows the results for four different apertures with a diffuser reflectance of 40 %. 
As can be seen, the angular responsivity depends upon the diameter of the aperture and the quality of the diffuser. 

Two pairs of aperture-diffuser were found to have adequate directional characteristics, the 6.4 mm aperture with a 

40 % diffuser and the 8 mm aperture with a 35 % diffuser. The 6.4 mm aperture and 40 % diffuser pair had better 

spatial responsivity characteristics and was selected for the InGaAs irradiance meter. The selected diffuser pair had 

an effective area 11.0 % smaller than the geometrically measured area. For the other pair, the effective area was 

18.4 % smaller than the geometrically measured area because of the larger spatial nonuniformity. 

It follows from Figs. 3 and 4a that the optimum cosine response depends on the wavelength. Consequently, the 

input geometry has to be optimized for the wavelength (or the spectral distribution) of the source to be measured. 

4. RESPONSIVITY CALIBRATION AND SPATIAL CHARACTERISTICS 

An x-y scanning procedure was used to determine the integrated irradiance responsivity and the effective aperture 

area of irradiance and illuminance meters6

. This irradiance calibration method uses only detector standards instead 

of conventional standard sources. The procedure where a small beam overscans the input aperture of the meter, also 

provides information on the spatial responsivity uniformity of the detector. The output signal of the detector was 

measured as a function of the position of the beam. The wavelength was selected for the sensitivity range of the 

photodiode, 780 nm for Si and 1500 nm for InGaAs. Fig. 5 shows the spatial responsivity of the InGaAs meter with 

the 6.4 mm aperture and the 40 % diffuser. The diameter of the beam was 1.1 mm. Each distance step of the scan 

was 0.5 mm. The position of the beam relative to the center of the aperture is measured on the horizontal axes, 

while the output signal of the irradiance meter is drawn on the vertical axis. The irradiance meter output signal is 

normalized to the signal measured in the central position. In Fig. 5a the response uniformity of the active area is 

shown and in Fig. 5b the radiation scattered from the area surrounding the aperture can be seen. 

Fig. 5. Spatial responsivity distribution plots of the diffuser-input InGaAs irradiance meter with a 6.4 mm aperture 

and a 40 % diffuser. Figure 5a shows the uniformity of the sensitive area, while Fig. 5b shows the stray radiation. 

The effective area of an irradiance meter can be calculated as the ratio of the integrated irradiance responsivity to 

the radiant power responsivity in the center of the aperture. The effective area is utilized in flux transfers when the 

measured irradiance (in the meter’s aperture plane) is transferred to another device, e.g., the exit port of a radiance 

source7

. In such cases, geometrical aperture area measurements are not needed. When a diffuser is used between 

the aperture and the photodiode to maintain the cosine response of an irradiance meter, a side effect is the decreased 

responsivity toward the edges of the photodiode. Because of this side effect, the effective area can be significantly 

different from the geometrically measured area of the aperture. The measured effective area of the InGaAs 

irradiance meter with the 6.4 mm aperture was 28.6 mm2

 ± 0.5 %, while the geometrical area is 

32.08 mm2

 ± 0.075 %. The effective area of the Si meter was measured at two different wavelengths of 563 nm and 

815 nm. The area change was 0.29 %, well within the uncertainty of the radiometric effective area measurement. 
5. UNCERTAINTIES 

The uncertainty components in addition to the uncertainty of the spectral power responsivity calibrations2 originate 

from several sources. The uncertainty of the integrated irradiance measurement method is estimated to be 0.5 %, 

the directional error of 0.15 % for the optimized meters, and the integrated stray radiation of 0.1 %. The relative 

combined standard uncertainty of an irradiance measurement with the Si meter is 1.6 % at 350 nm. The standard 

uncertainty decreases to 0.94 % at 400 nm and is almost constant at 0.54 % in the visible to 925 nm. From 925 nm 

to 1800 nm where the InGaAs irradiance meter is used, the estimated standard uncertainty is about 1.2 % from 

925 nm to 1345 nm and increases to about 2.6 % between 1350 nm and 1800 nm. 

6. CONCLUSION 

Diffuser-input irradiance meters have been developed with InGaAs and Si photodiodes as working standards. The 

wavelength range of the two irradiance meters covers the 350 nm to 1800 nm wavelength region. The irradiance 

meters were calibrated against the NIST detector spectral power responsivity scale. The flashed opal glass diffusers 

were measured and grouped according to their diffuse reflectance. A range of apertures was tested with the 

different diffusers. Diffuser and aperture pairs were selected for optimum cosine response and minimum spatial 

responsivity non-uniformity. The CIE directional error was f2(ε) = 0.15 % or less for the irradiance meters in the 0°

to 10° incidence angle range. The total irradiance responsivity of the meters was determined from spatial 

responsivity integrals over the aperture area during a scanning procedure. The standard irradiance meters, that hold 

the spectral irradiance responsivity scale of the SCF facility, can measure spectral irradiance with an estimated 

combined standard uncertainty of 0.54 % in the visible range. 

7. ACKNOWLEDGMENTS 

The authors thank Donald Lynch of Reyer Corporation for the irradiance meter fabrication, Yuqin Zong for helping 

in the directional response measurements, Sally Bruce for making the spectral responsivity and spatial uniformity 

measurements, Joel Fowler for the aperture area measurements, and Yvonne Barnes for helping in the diffuse 

reflectance measurements. 

8. REFERENCES 

1. Gentile, T. R., Houston, J. M., Hardis, J. E., Cromer, C. L., and Parr, A. C., “National Institute of Standards and 

Technology high accuracy cryogenic radiometer,” Appl. Opt. 35 (7), 1056-1068 (1996). 

2. Larason, T. C., Bruce, S. S., Parr, A. C., “Spectroradiometric Detector Measurements: Part I-Ultraviolet 

Detectors and Part II-Visible to Near-Infrared Detectors,” National Institute of Standards and Technology 

Special Publication 250-41 (1998). 

3. Eppeldauer, G. and Hardis, J. E., “Fourteen-decade photocurrent measurements with large-area silicon 

photodiodes at room temperature,” Appl. Opt. 30 (22), 3091-3099 (1991). 

4. Eppeldauer, G., “Near Infrared Radiometer Standards,” SPIE 2815 Optical Radiation Measurements III. 42-54 

(1996). 

5. Eppeldauer, G., “Electronic characteristics of Ge and InGaAs radiometers,” SPIE 3061 Infrared Technology 

and Applications XXIII. 833-838 (1997). 

6. Cromer, C. L., Eppeldauer, G., Hardis, J. E., Larason, T. C., Ohno, Y., Parr, A. C., “The NIST Detector-Based 

Luminous Intensity Scale,” J. Res. Natl. Inst. Stand. Technol., 101 (2), 109-132 (1996). 

7. Johnson, B. C., Cromer, C. L., Saunders R. D., Eppeldauer, G., Fowler, J., Sapritsky, V. I. and G. Dézsi, “A 

Method of Realizing Spectral Irradiance Based on an Absolute Cryogenic Radiometer,” Metrologia, 30, 309-

315 (1993). 
Near Infrared Radiometer Standards 

George Eppeldauer 

Optical Technology Division 

National Institute of Standards and Technology 

Gaithersburg, Maryland 20899 

ABSTRACT

 We are developing new detector-based radiometric scales in the near infrared to extend 

existing spectral radiant power calibrations1

 to spectral irradiance and radiance calibrations. High 

accuracy irradiance and radiance meters have been developed to realize these new detector-based 

radiometric scales. Mechanical, optical, and radiometric design considerations of Ge and InGaAs 

radiometers are discussed. Calibration principles and design considerations of the calibration 

setup are also described. Several results of preliminary radiometric characterizations are 

reported. 

1. INTRODUCTION

 At present, standard quality high-accuracy radiometers for spectral irradiance and 

radiance measurements are not available in the near infrared (NIR) wavelength range. Most 

national laboratories offer detector calibrations only for spectral radiant power responsivity. 

Irradiance meters2

 frequently show response changes if the geometry (f/#) of the measured optical 

radiation changes. This usually happens in applications where the beam geometry reaching the 

irradiance meter is different than at calibration. In these situations the reflectance pattern inside 

the radiometer input optics can change. This change will result in irradiance response errors. 

Similarly, radiance meters frequently measure signal from outside of the source target area3

. 

Here, again, the measurement results contain significant errors. In cases like this, the input optics 

of these radiance meters may not be properly designed, resulting in a poor out of field-of-view 

(FOV) blocking4

. 

 Sensitivity of NIR radiometers is an important issue in many radiometric applications. 

Typically, the peak radiant power level at the exit slit of a monochromator is a few μW only. The 

low power end of the signal can be several orders of magnitude smaller. In most monochromator 

applications, photomultiplier detectors are used to measure low level NIR signals. Similarly, low 

temperature black-bodies have extremely small radiance in the visible range and somewhat larger 

in the NIR. Radiance temperature meters measure radiance (scaled in temperature) in a narrow 

wavelength interval. Frequently used photomultiplier tubes5

 could be substituted with high 

sensitivity NIR detector-circuit packages in these radiance temperature meters by switching from 

the visible to the NIR range. 

 The quality of NIR detectors have improved a lot in the past decade. As a result of 

improved fabrication procedures, a 40 % to 50 % internal quantum efficiency increase was 

reported on Judson J16 P26

 Ge photodiodes at the beginning of the decade7. The peak internal 

quantum efficiency was between 0.8 and 0.9. The reported shunt resistance of a 10 mm diameter 

photodiode was only 100 Ω. As introduced by Stock, the aging rate of the earliest Ge photodiode 

version was lower than +/- 0.5 % per year and was wavelength dependent. Within the 7 mm 

diameter central part of the photodiode active area the spatial response non-uniformity was less 

than +/- 0.5 % and increased at shorter wavelengths. Stock and others reported better spatial 

response uniformity for Ge photodiodes as compared to InGaAs8

. They used a small integrating 
sphere in front of the InGaAs photodiode to reduce the spatial response non-uniformity. 

However, the sphere decreased the absolute responsivity by a factor of about 300. 

 In our earlier publication9

, InGaAs, Ge, and InAs photodiodes were characterized. The 

average internal quantum efficiency of the tested mesa epitaxial type InGaAs photodiodes was 

0.975 at 1.3 μm. The position dependent change of the internal quantum efficiency was +/- 0.5 

%. However, because of the position-dependent reflectance change, the external quantum 

efficiency, which was proportional to the absolute response, changed 4 % as a function of 

position across a diameter of a windowless InGaAs photodiode. These InGaAs photodiodes were 

linear over three decades of radiant power as measured at the high power end (0.8 mW 

maximum). They showed much higher shunt resistance at room temperature and higher external 

quantum efficiency than the few Ge and one InAs photodiodes examined in that study. 

 As a continuation of our previous NIR detector study9

, further internal quantum efficieny 

measurements were made on planar diffusion InGaAs photodiodes10. The measured internal 

quantum efficiencies were about 0.9 at 1.15 μm and 1.3 μm, and about 0.88 at 1.52 μm. The 

reason for these smaller values of the planar diffuse devices is that the junction was less shallow 

and the passivation was worse than for the mesa grown photodiodes. Also, the zinc dopant 

penetrates deeper than in the mesa technique, resulting in larger diode capacitance. With antireflection coating, these devices showed specular reflectances of about 2 %. All tested InGaAs 

photodiodes were p-on-n devices. The Ge photodiodes were constructed of p-type base material 

into which was diffused a shallow n-type junction. This construction is similar to those reported 

above7

. 

 The reason for adopting the planar diffuse technology to InGaAs manufacture was to 

produce larger area devices with greater stability. In the mesa device, the edge of the junction 

extends to the edge of the wafer and is therefore not protected. At present, it seems to be more 

important to produce high stability than to achieve 100 % internal quantum efficiency on InGaAs 

photodiodes, which was the goal of the previous studies9, 10.

 In the present work, large area, planar structure InGaAs photodiodes with dielectric 

passivation and large area Ge photodiodes similar to those reported above7

 are used. The 

diameters of the active areas are 5 mm for both the InGaAs and Ge photodiodes. They were all 

selected for high shunt resistance to obtain high sensitivity11. All photodiodes are hermetically 

sealed in standard packages of the same size, and cooled by two stage thermoelectric coolers. 

The temperature of the photodiodes is monitored by thermistors and controlled by temperature 

controllers12. Since lasers are used in these measurements, the photodiode chips are tilted by 1° 

to 2° out of parallel with the package window to avoid interference. Also, the sapphire windows 

have 20’ of wedge. The surfaces of all photodiodes are of optical quality. 

2. SCALE REALIZATION

2.1. Radiant power response scale

 The detector response scale derivation scheme is shown in Fig. 1. The primary standard 

is an electrical substitution high accuracy cryogenic radiometer (HACR)13 which measures laser 

power. At present, eleven laser lines are used between 320 nm and 950 nm. Silicon trap 

detectors14 are calibrated against the HACR at the different laser lines. Interpolation between the 

calibrated points gives the spectral radiant power responsivity of a trap detector in A/W between 

406 nm and 920 nm14. The spectrally calibrated transfer standard trap detector(s) are used on the 

Visible Near Infrared Spectral Comparator Facility1

, where working standard silicon photodiodes 

are calibrated against the trap detectors by using a substitution technique. The spectral power 
response scale is extended from the silicon wavelength range to the NIR range with a pyroelectic 

transfer detector. The relative response of the gold-black coated pyroelectric detector is 

determined from spectral reflectance measurements of its coating. The coating transmission is 

negligible. Temperature controlled working standard Ge detectors are calibrated for spectral 

responsivity against the known response of the pyroelectric detector. Test NIR detectors can be 

calibrated for spectral radiant power responsivity (in A/W) against the working standard Ge 

detectors between 700 nm and 1800 nm. 

 The goal of our scale realization work is to derive the spectral irradiance and radiance 

response scales from the existing radiant power response scale. To achieve this goal standard 

quality radiometers were developed. Optical and radiometric design considerations are discussed 

of two different kinds of irradiance meters and a radiance meter. The characterization results of 

the radiance meter are discussed in this paper. The electronic characteristics of the radiometers 

and the detailed radiometric characterization of the irradiance meters will be discussed in 

consecutive papers. The scheme of the new calibration setup where the new radiometers are 

utilized is described in this paper. The scale realization measurements and the error budget of the 

new scales will be discussed in the final paper. 

2.2. Spectral irradiance and radiance response scales

 In a previous NIST project15, an irradiance meter composed of a silicon photodiode, an 

interference filter, an integrating sphere, and an input aperture was calibrated against a standard 

silicon detector using a laser beam. In this manner a detector-based irradiance scale was derived 

from the radiant power response of the standard silicon detector. 

 HACR

Ultraviolet-Visible-NIR-IR

Radiant Power Scale

Spectral Radiant Power Response Scale

Visible-NIR small area non-uniform 

monochromatic source / comparator

Power / Irradiance 

 meters

 VIS-NIR large area uniform-field 

monochromatic source / comparator

Spectral Irradiance / Radiance Response Scales

 Irradiance/Radiance 

 meters

Silicon Trap 

 Detector

Pyroelectric 

 Detector

Fig. 1. Detector response scale derivation scheme 
This irradiance meter was then used to measure the spectral irradiance of two other beam 

geometries at the laser wavelength. The other two sources were standard spectral irradiance 

lamps (blackbody source-based scale) and the electron storage ring, SURF-II. The detector-based 

scale at the test wavelength, was 0.76 % lower than the source-based scale, and 0.25 % higher 

than the electron storage ring scale. Because of the high spatial response uniformity within the 

aperture area, the total uncertainty for the detector-based irradiance scale was 0.5 %. In contrast, 

the uncertainty of the source-based irradiance scale was 1.68 %. Throughout this paper, all 

uncertainty values are given as a relative expanded uncertainty with a coverage factor of k=2. 

This is equivalent to an uncertainty consisting of two standard deviations about the mean of a 

normalized Gaussian distribution. 

 In our earlier report16, a technique had been described for realizing spectral irradiance 

scale using a large-area, high temperature, uniform black-body source and filter-radiometers that 

are calibrated on a detector-based system. The goal of this project was to reduce the 

measurement uncertainties in the present source-based spectral irradiance scale21. The filter 

radiometers were calibrated on the NIST Spectral Comparator Facility1

, and the aperture areas 

were measured by flux comparison with a uniform source17. Six filter radiometers covering the 

visible and NIR wavelength ranges were used to measure a known irradiance source (FEL lamp). 

The measurements agreed with predictions to within 1%18. Comparisons were also conducted 

with three NIST standard photometers, and similar agreement was observed. Since the 

temperature and radiance calibration of the gold point blackbody source is also detector-based19, 

the agreement will be improved if the input geometry of the filter radiometers is modified. The 

new input geometry requires a diffusing input element within the aperture area to realize the 

cosine function of illuminance measurements with a high accuracy. 

 In radiant power response calibrations, the active area of the detectors was underfilled by 

the monochromatic beam and the detectors measured radiant power. Since the diameter of the f/9 

calibrating beam at the NIST Spectral Comparator Facility is small (i.e., it can be changed from 

1.2 mm to a few mm) and is spatially non-uniform, irradiance measuring radiometers cannot be 

overfilled with this beam. Otherwise, their irradiance responsivity would change as a function of 

detector aperture positioning. Instead, the detector area, within the limiting aperture, is mapped 

(scanned) with the small, non-uniform beam, and the average power responsivity, savg, is 

determined versus wavelength, λ. The spectral irradiance responsivity, sE(λ), of a silicon or NIR 

irradiance meter is derived from its own spatially averaged spectral radiant power responsivity: 

 sE(λ) = F cosα savg(λ) [A m2

/W] (1) 

where m2

 is the unit of the known aperture area F, A is the unit of the detector output current, W 

is the unit of the measured beam power, and α is the angle of the incident beam. The angle of 

incidence is the angle between the normal of the aperture plane and the axis of the incident beam. 

If the incident beam is different from perpendicular (relative to the aperture plane), the irradiance, 

as measured by the irradiance meter, will change according to the cosine of the incidence angle20. 

Note that α is constant in eq. 1. If the incident beam is not parallel, α is no longer a constant, but 

can take a range of values depending on the f/#. In this case the integral of cosα will be measured 

for all incident angles (changing α) of the beam. 

 The calibrated irradiance meter can be used as a standard to calibrate test irradiance 

meters by substitution in a large enough, spatially uniform monochromatic field. The large and 
uniform monochromatic fields are realized by either a collimator or an integrating sphere coupled 

to the output of a monochromatic radiation source. 

STANDARD 

IRRADIANCE 

 METER

DVM1

DVM2

COMPUTER

DRIVE

RADIANCE or 

IRRADIANCE 

TEST DEVICE

INTEGRATING 

SPHERE

OPTICAL FIBER

EQUIPMENT FOR D

FLUX TRANSFER

LIGHT TIGHT BOX

MONOCHROMATIC 

 BEAM

TEMPERATURE 

CONTROLLED 

MONITORING 

DETECTOR

Fig. 2. Block scheme of the detector radiance/irradiance response calibration setup 

 Figure 2 shows the block scheme of our detector radiance/irradiance response calibration 

setup, which is being constructed. Instead of a traditional lamp-monochromator assembly, high 

intensity monochromatic sources, such as lasers or filtered lamps/arcs are to be used to produce 

the monochromatic beam for the integrating sphere. The radiance of the sphere wall is monitored 

by a two-color (Si on top of InGaAs) detector which can hold the spectral radiance scale after 

scale realization. A standard irradiance meter is used to calibrate the monochromatic, large 

output area, Lambertian source of the sphere (or a plaque) for spectral radiance, L(λ). At the 

NIST Spectral Comparator Facility the standard irradiance meter is calibrated first for spectral 

power responsivity, s(λ), which is the wavelength dependent ratio of the detector output current, 

I, to the radiant power, P, as measured by the detector. A precision aperture of known area is 

mounted in front of the detector. If necessary, savg(λ) can be used instead of s(λ). The distance, 

D, between the source aperture and the detector (irradiance meter) aperture is measured. The 

output current of the standard irradiance meter is: 

 I(λ) = s(λ) P(λ) [A], (2) 

where P(λ) is the spectral radiant power from the sphere source as measured by the standard 

irradiance meter. The spectral radiance can be calculated from P(λ), applying the geometric 

extent, GD

21: 

 L(λ) = P(λ) / GD [W m-2 sr-1] (3) 

 The geometric extent, GD, can be given by the standard expression which describes the 

flux transfer between circular, parallel, and coaxial apertures with radii rS (for the source 

aperture) and rD (for the detector aperture), and separation, D, 

GD = (π

2

/2){(D2+rS

2

+rD

2

) - [(D2+rS

2

+rD

2

)

2

 - 4 rS

2

 rD

2

]

1/2} [m2

 sr] (4) 
 As a second step, the radiance meter measures the above determined radiance of the 

sphere source. The spectral radiance response of the radiance meter (test device in this case) is a 

ratio of its output current or voltage to the measured sphere radiance versus wavelength. 

 Test irradiance meters can be substituted for the standard irradiance meter in the uniform 

monochromatic irradiance of the sphere source. This is a simple irradiance response calibration 

method for large area irradiance (test) meters. The same irradiance is measured by both 

irradiance meters. This irradiance is calculated from the irradiance response of the standard 

irradiance meter. The irradiance response of the test device is then determined from its output 

current or voltage reading and the calculated (and measured) irradiance, versus wavelength. 

 The response of the standard irradiance meter has to be the same for the f/9 calibrating 

beam and the beam geometry at radiance and irradiance measurements (radiation from the 

Lambertian source). 

 Properly designed NIR radiometers are the key components in realizing the above 

described radiometric scales for the NIR wavelength range. 

3. MECHANICAL AND OPTICAL DESIGN OF NIR RADIOMETERS

3.1. Radiant power meter

 Figure 3 shows the design of the photodiode-housing for radiant power measurement. 

The TO-8 photodiode package is plugged into the center hole of the threaded holder. The 

threaded holder is limited to a FOV of +/- 30° for the photodiode to block radiation from the 

sides. During radiant power (W) measurement, the active area of the photodiode is underfilled by 

the incident beam. No aperture is needed in front of the photodiode for this measurement. 

However, the spatial response non-uniformity of the photodiode has to be in the order of 0.1 % to 

get repeatable radiant power responsivities (A/W) for different beam sizes and beam positions. 

The threaded holder can be used to mount different accessories, such as filters and/or apertures, in 

front of the photodiode. The heat from the bottom of the photodiode case is conducted by the 

copper plate to the heat sink where it is dissipated. On the side of the heat sink there is a 

connector for the temperature controller. The photodiode is connected to the input of the 

electronic unit through a connector in the adapter ring. The optical unit, which involves the 

adapter ring, can be detached from the electronic unit. The connector gives a direct access to 

both the photodiode leads and the input of the current-to-voltage converting electronics11. As a 

result of this design consideration, the gain linearity calibration of the signal measuring 

electronics can be done directly. 

3.2. Irradiance measurement

 In irradiance measurements, according to equation 1, the flux (radiant power) is measured 

within the aperture area of a detector. The incident flux has to overfill the aperture area. The 

measured irradiance (the flux collected by the aperture) depends on the angle of incidence. At a 

scale realization the area of the precision aperture has to be known. Test or secondary standard 

irradiance meters do not need apertures of known area. They are usually calibrated against 
O 63.5 mm

Threaded Holder

Photodiode Hole

Teflon Ring

Copper Plate

Heat Sink

Adapter Ring

Connector

Electronics Housing

Fig. 3. Ge or InGaAs photodiode housing for radiant power measurements 

standard irradiance meters, by substitution. If the field of irradiation is uniform, the spatial 

response uniformity of the detector does not have to be very good. In this case, the output 

electrical signal of the meter is determined by the average responsivity of the detector within the 

aperture area. The relation between the output electrical signal and the input irradiance is linear if 

the short circuit current of the photodiode is measured. The meters are calibrated for irradiance 

responsivity as a function of wavelength. 

 The most important requirement for an irradiance meter is to design its front geometry to 

satisfy the cosine law of irradiance measurements for the overall angular range of the incident 

flux. Figure 4.a shows a bare detector with a very thin aperture on top of it. This is the simplest 

and most ideal design for eliminating reflections from the aperture edge and between the front 

surface of the detector and the back surface of the aperture for all possible input beam geometries 

(from parallel to a given f/#). However, in most applications the aperture cannot be positioned on 

top of the bare detector. In our present work, both the Ge and the InGaAs photodiodes are 

located in hermetically sealed cases with windows on top. Similarly, in many applications, filters 

are needed between the aperture and the detector to modify the overall spectral responsivity. 

Figure 4.b shows the ideal situation where the incident beam is perpendicular to the aperture and 

the detector, and therefore there are no inter-reflections between the two in spite of a gap between 

them. In detector calibrations the monochromatic beam is usually not parallel. In Fig. 4.c the 

incident beam has a given f/#. In Fig. 4.d the incident beam is not normal to the aperture plane of 

the irradiance meter. In the last two cases there are inter-reflections between the apertures and 

the detectors. If filters are used and/or the detector case has a front window, additional reflections 

will happen22. In these situations the internal reflectance pattern depends on the beam geometry 

and the cosine law of irradiance measurements will work only with a decreased accuracy. 

However, if the irradiance meter performs accurate cosine measurement within its FOV, the 

absolute irradiance response can be determined with high accuracy for the different input beam 

geometries. 
α

β

(a) (b) (c) (d)

β

Fig. 4. Traditional input optics of irradiance meters with different incident beams 

(a) Bare detector with a thin aperture on the top 

(b) The incident beam is perpendicular to the plane of the aperture 

(c) The incident beam has a given f/# 

(d) The incident beam is not perpendicular to the plane of the aperture 

60o

FOV Limiting Aperture

Precision Aperture

Diffuser

Photodiode

Teflon Ring

Copper Plate

Fig. 5. Cross-section showing the input optics of a diffuser-type irradiance meter 

3.3. Diffuser-type irradiance meter

 Figure 5 shows the modified front piece (threaded holder) of the photodiode-housing for 

irradiance measurements. A flashed opal glass diffuser is located between the very thin aperture 

(black nickel coated copper) and the photodiode to eliminate internal reflections and to produce a 

spatially uniform surface within the aperture area. The goal is to maintain the high accuracy of 

the cosine function of irradiance measurements. Without the right input geometry, the shape of 

the cosine function could be altered greatly, resulting in low measurement accuracy. 
0.5

0.6

0.7

0.8

0.9

1.0

-80 -60 -40 -20 0 20 40 60 80

Opal

Spectralon

Observation angle [°]

Fig. 6. BTDF of flashed opal glass and Spectralon diffusers at normal beam incidence 

0

0.2

0.4

0.6

0.8

1

0

30

60

90

120

210

240

270

300

330

Lambertian

Measured

Incident Beam Flashed Opal Glass

Fig. 7. Ideal Lambertian (continuous) and flashed opal glass (dashed) 

angular transmittance distributions 

 The goniometric (Bidirectional) Transmittance Distribution Function (BTDF) of two 

different diffusers were tested at 600 nm, with normal beam incidence on the NIST High 

Accuracy Reference Reflectometer-Spectrophotometer23. The normalized radiance of 

transmission values for two materials as a function of observation angle are shown in Fig. 6. The 

3.2 mm thick Spectralon diffuser showed a large forward scatter between +/- 10°. The radiance 

of the transmittance of the 2.5 mm thick flashed opal glass was constant in a reasonably wide 
angular range. Figure 7 shows that the ideal Lambertian curve (solid circle) and the measured 

opal glass transmittance (dashed circle) curve are close to each other. Consequently, the higher 

quality flashed opal glass diffuser was selected for our irradiance meter developments. 

 As it is shown in Fig. 5, a small (5 mm diameter) photodiode can receive the Lambertian 

radiation from a large (16 mm diameter) opal glass diffuser which is illuminated through a large 

(8 mm diameter) aperture. By this method the photodiode measures the radiation at the center of 

an extended-source diffuser, where the radiance from the diffuser is constant. The beam 

geometry may change roughly from f/1 to parallel. The FOV is determined by the front aperture 

and the precision aperture. There is a baffle between the two apertures to minimize the measured 

stray radiation. 

F/2

PRECISION 

APERTURE 

 O 7.98 mm

O 8.5 

mm

O 50 mm

INPUT BAFFLE TUBE

SPECTRALON SPHERE UNIT

DIFFUSER

PHOTODIODE

COPPER PLATE

HEAT SINK

O 50 mm

Fig. 8. Cross section of a sphere-input irradiance meter 

3.4. Sphere-type irradiance meter

 Figure 8 shows another radiometer input geometry for accurate irradiance measurements. 

In this sphere-input irradiance meter the diffusing element, which gives the uniform input surface 

within the aperture area, is a small integrating sphere. The shape of the incident beam can change 

between f/2 and parallel. The FOV is limited by the precision aperture and the front aperture of 

the input baffle tube. The sphere wall is made of machined Spectralon6 diffusing material, which 
has a reflectance of 99 %. The irradiance on any part of the sphere wall is almost the same and 

proportional to the input flux (radiant power) collected by the aperture. A plane-parallel diffuser, 

located in the exit port of the sphere, is part of the sphere wall. It is irradiated by the multiple 

reflections within the sphere. Its Lambertian transmitted radiation is measured by the Ge or 

InGaAs photodiode. The efficiency of the flux transfer between the diffuser and the photodiode15

is determined from the geometry between them. The flux coupling efficiency, κ, for a 5 mm 

diameter photodiode, an exit port diameter of 10.5 mm, and a separation (between the diffuser 

and the photodiode) of 6.5 mm, is equal to 8.5 %. The efficiency, τ, of the 50 mm diameter 

sphere with its two ports and a diffuser (with a transmittance of 36 %) located in the exit port, is 

equal to 21 %. The overall radiant flux efficiency is κ τ = 0.018, resulting in a signal attenuation 

of 56. High flux must be sacrificed in order to achieve standard quality spatial response 

uniformity. 

CAMERA 

LENS

EYEPIECE

FIELD STOP 

 MIRROR

SECOND 

IMAGING

HEAT 

SINK

ADAPTER & 

CONNECTOR

PHOTO 

DIODE

 CURRENTTO-VOLTAGE 

CONVERTER

 GAIN 

SWITCH

OUTPUT

APERTURE 

 STOP

Fig. 9. Optical/mechanical scheme of a radiance optics as attached to the irradiance meter 

3.5. Radiance meter

 Radiance is a source characteristic which can be measured by radiance meters. Usually, 

extended sources are characterized by radiance measurements. The requirement from a standard 

quality radiance meter is to have a well-defined measurement angle to measure the source target 

area only. 

 Figure 9 shows the simplified optical/mechanical design of our radiance meter where the 

input optics are attached to the radiometer base-unit with a Bayonet mount. The beveled aperture 

mirror serves as a field stop, and it is positioned into the focus of the 35 mm focal length camera 

lens. Beveling is important to minimize stray radiation. This camera lens has a broad-band antireflecting (AR) coating, resulting in high transmittance in the visible and NIR ranges. The 

surroundings of the source target area can be viewed through the eye-piece. The target radiation 

is imaged to the center of the photodiode through the second imaging optics. The second imaging 

optics has an important role to produce a well defined FOV and a very efficient out-of-FOV 

blocking. The original aperture stays in front of the photodiode, and it is underfilled. There is a 

dominant aperture stop in front of the second imaging optics in order to keep the flux response of 

the optics constant for different target distances of the adjustable focus camera lens. 
0.0001

0.0010

0.0100

0.1000

1.0000

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

Rotation angle of meter [degree]

Fig. 10. Radiance measurement profile (point spread function) of a radiance meter 

 Figure 10 shows the point spread function of our previous generation radiance meter, 

similar to the one in Fig. 9, with a 50 mm focal length camera lens and a 0.7 mm diameter field 

stop. The plot shows the measured radiance of a small source-spot versus rotation angle of the 

radiance meter. The roughly 3 mm diameter source spot was about 2 m away from the radiance 

meter. The pivot point of the radiance meter was the center of the field stop. The figure shows 

that the radiance measurement angle of the meter was about 1° and the out-of-FOV blocking was 

larger than four decades. The radiance response of the standard radiometer was measured at 

target distances between 1 m and 2 m. Figure 11 shows that the radiance response did not change 

more than the uncertainty of our measurements, which was 0.1 %. 

0.998

0.999

1

1.001

1.002

1 1.2 1.4 1.6 1.8 2 2.2

Target distance (m)

Fig. 11. Change of radiance responsivity of an adjustable focus radiance meter 

4. CONCLUSIONS

 Mechanical, optical, and radiometric design criteria of radiant power, irradiance, and 

radiance measuring radiometers have been discussed for high accuracy applications. The 

described standards quality NIR radiometers are being used to realize the NIST detector-based 

irradiance and radiance scales between 0.8 μm and 1.8 μm. The principle of radiometer 

calibrations and the design considerations for the calibration set-up have also been discussed. The 

paper describes the first part of the NIR scale realization work. Design criteria for wide dynamic 

range DC and AC detector signal measuring electronics, electrical and radiometric NIR detector 

characterizations with performance comparison of Ge and InGaAs radiometers, and NIR detectorbased scale realizations with error budget determination will be described in consecutive papers. 
5. ACKNOWLEDGEMENTS

 The author thanks Don Lynch of Reyer Corporation for the radiometer fabrication related 

work, George Andor of Hungarian Office of Measures for the BTDF measurements, Gyula Dezsi 

of Hungarian Office of Measures and Robert Saunders for participating in the construction of the 

radiance/irradiance calibration set-up, and Yoshi Ohno for helping in the radiance/luminance 

response measurements. 

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Calibration of a pyroelectric detector

at 10.6 mm with the National Institute of

Standards and Technology high-accuracy

cryogenic radiometer

T. R. Gentile, J. M. Houston, G. Eppeldauer, A. L. Migdall, and C. L. Cromer

The National Institute of Standards and Technology ~NIST! is establishing an infrared detector calibration facility to improve radiometric standards at infrared wavelengths. The absolute response of the

cryogenic bolometer that serves as the transfer standard for this facility is being linked to the NIST highaccuracy cryogenic radiometer ~HACR! at a few laser wavelengths. At the 10.6-mm CO2 laser line, this

link is being established through a pyroelectric detector that has been calibrated against the HACR. We

describe the apparatus, methods, and uncertainties for the calibration of this pyroelectric detector.

1. Introduction

To meet the growing need for calibrated detectors at

infrared wavelengths, the National Institute of Standards and Technology ~NIST! is establishing an infrared detector calibration facility.1 The goal of this

facility is to provide absolute responsivity calibrations of detectors in the 2–20 mm spectral region with

a relative expanded uncertainty of ;4% ~2 sigma!.

To serve as a transfer standard detector, a cryogenic

bolometer has been constructed.2,3,4 The calibration

of this bolometer is being linked to the NIST highaccuracy cryogenic radiometer ~HACR!5 at a few laser

wavelengths. At the 10.6-mm CO2 laser line, the

link to the HACR is being established through a calibrated pyroelectric detector. In this paper we describe the apparatus, methods, and uncertainties for

a calibration of the pyroelectric detector against the

HACR. The transfer of the calibration from the pyroelectric detector to the bolometer will be the subject

of a separate paper.

The HACR is a cryogenic electrical substitution

radiometer that serves as a primary standard for

optical power measurements and has been used to

measure radiant power at visible wavelengths with a

relative standard uncertainty of 0.021%. The

HACR is best suited for measurements at an optical

power level of between 0.1 and 1 mW, but the response of the bolometer becomes nonlinear at power

levels above a few microwatts. Hence an indirect

calibration is performed. First a pyroelectric detector is calibrated against the HACR, and then the

cryogenic bolometer is calibrated against the pyroelectric detector. This approach is also convenient

because the pyroelectric detector is compact, easily

portable, relatively simple to use, and operates at

room temperature. Its dynamic range is suitable for

bridging the range between several microwatts and 1

mW, although a somewhat lower noise floor would be

desirable. The main disadvantage of the pyroelectric detector is the spatial nonuniformity in its response. Although a thermopile detector was tested

as an alternative transfer detector, we chose the pyroelectric detector because of reduced susceptibility

to noise due to thermal drift.

We describe the apparatus and methods of the calibration in Section 2 and the measurement results

and uncertainties in Section 3.

2. Apparatus

A. High-Accuracy Cryogenic Radiometer

As the HACR has been described in detail elsewhere,5

here we provide only a brief overview of the instrument. A diagram is shown in Fig. 1. The HACR is

an electrical substitution radiometer operated just

above the boiling point of liquid helium. An electrical substitution radiometer links a measurement of

optical power to the watt by comparing the temperThe authors are with the National Institute of Standards and

Technology, Gaithersburg, Maryland 20899.

Received 3 September 1996; revised manuscript received 2 January 1997.

3614 APPLIED OPTICS y Vol. 36, No. 16 y 1 June 1997
ature rise induced in an absorbing mass by incident

optical radiation to that obtained by electrical heating. The absorbing mass is a cavity designed for

nearly complete absorption of laser radiation. Operation at cryogenic temperatures allows a large,

highly absorptive cavity to be used without significantly increasing the time constant, and the radiative

coupling of the cavity to its surroundings is reduced.

These features improve the equivalence of optical and

electrical heating. However, cryogenic operation

also requires a vacuum Dewar, necessitating a window between the cavity and the laboratory. To reduce the reflection loss, this window is oriented at the

Brewster angle, and appropriately polarized light is

used. To facilitate alignment of the laser light into

the cavity and to measure the amount of laser light

scattered out of the beam, two sets of four annular

quadrant silicon photodiodes, each 50 mm in diameter with a 9-mm-diameter central aperture to pass

the beam, are located along the optical path within

the HACR. ~Although these detectors were not directly usable with the infrared beam, they were used

with a visible alignment beam that was spatially

overlapped with the infrared beam.! The apertures

in the quadrant photodiodes are the limiting apertures in the HACR.

B. Laser System

The laser system is shown in Fig. 2. As with the

apparatus previously described for visible wavelengths,5 the primary goal is to generate a geometrically well-defined beam with stable power. The

power was stabilized using an acousto-optic laser stabilizer6 with an external feedback detector. A welldefined beam spatial profile was obtained using a

spatial filter with an overfilled pinhole. Because the

output power of the CO2 laser is 4 orders of magnitude higher than the level that can be used with the

HACR, it was also necessary to attenuate the laser.

While this could be accomplished with either attenuating filters or nearly crossed polarizers, both methods have disadvantages. A filter’s attenuation could

be affected by temperature rise induced by high

Fig. 1. Diagram of the NIST high-accuracy cryogenic radiometer.

Fig. 2. Diagram of the laser system. W1, W3, W4, ZnSe-wedged windows ~there is an additional wedged window W2 located just before

L2 that is not shown!; L1, L2, L3, L4, ZnSe lenses; AOM, acousto-optic modulator; P1, P2, polarizers; PH, pinhole; A1, A2, apertures; FD,

HgCdTe feedback detector; S, shutter; C, chopper; M, steering mirror; PD, pyroelectric detector. The reflection from the steering mirror

is out of the plane of the diagram.

1 June 1997 y Vol. 36, No. 16 y APPLIED OPTICS 3615
power levels, while crossed polarizers could degrade

the polarization purity of the beam. Because of

these drawbacks, most of the attenuation was accomplished by reflecting the beam from ZnSe-wedged

windows instead of steering mirrors. For each window, only one of the reflected beams was used, while

the other reflected beam was blocked. An attenuation factor of ;300 was obtained from the four

wedged windows in the system. This approach also

provided monitor beams and a method for overlapping the alignment He–Ne beam with the CO2 beam,

as described below.

The source was a 5-W, air-cooled, grating-tuned,

vertically polarized CO2 laser operated with a frequency stabilizer. The laser was operated on the

P~20! line @wavelength equals 10.5910 mm ~Ref. 7!#,

with a TEM00 transverse mode. After exiting the

laser, the diverging beam was reflected by a wedged

window ~W1!, collimated by a ZnSe lens ~L1!, and

passed through an acousto-optic modulator ~AOM!

that is part of a power stabilizer. ~The beam transmitted through W1 was used to monitor the laser’s

output power or to determine its wavelength using a

CO2 spectrum analyzer.! When rf power is applied

to the AOM, a fraction of the laser light is deflected

into a secondary beam, thereby providing control of

the power in the primary beam. Farther down the

beam path, a HgCdTe feedback detector ~FD! sampled the beam and provided the input to the stabilizer’s feedback circuit. This system maintained the

power of the laser beam to within 0.1% over the

course of an hour. The feedback detector was located as far downstream in the beam path as possible

within the constraint of this detector’s sensitivity.

After the AOM, the beam passed through a polarizer ~stack of six ZnSe plates, P1! and was reflected

from another wedged window ~referred to as W2, but

not shown!. For most of the measurements this polarizer simply improved the vertical polarization of

the beam, but it was also used in conjunction with a

wire grid polarizer located farther downstream ~P2!

for relatively minor attenuation of the beam ~less

than a factor of 3!. The beam was attenuated by

rotating P1, while the polarizer P2 reestablished the

vertical polarization required to minimize the reflectance from the Brewster window. The polarization

of the beam incident upon P2 was nearly vertical

because vertically polarized light is preferentially reflected from the wedged windows. When additional

attenuation was required, a thin 12% transmitting

filter ~25-nm-thick layer of NiCr deposited on 100-

nm-thick substrate! was placed just before P2.

Using a thin filter avoided possible interference effects and deflection of the beam.

A well-defined beam spatial profile was obtained by

using a spatial filter with an overfilled pinhole. The

laser light was focused with a 8-cm focal length ZnSe

lens ~L2! onto a 250-mm-diameter pinhole ~PH!.

This beam overfilled the aperture, creating an Airy

diffraction pattern. ~The amount of overfilling was

also used to attenuate the beam by a factor of between 2.5 and 7.! The diameter of an iris ~A1! was

adjusted to allow only the 13-mm-diameter central

spot of the diffraction pattern to pass through. The

diameter of the aperture corresponded to the location

of the first minimum of the diffraction pattern, thus

defining the beam diameter with minimal scattering

from the aperture. A 12.5-cm focal length ZnSe lens

~L3! produced a long beam waist between the pyroelectric detector ~PD! and the limiting apertures inside the HACR dewar. At the waist, 85% of the

power fell within a 3-mm beam diameter and 99%

within a 5 mm diameter. The beam was then reflected from another wedged window ~W3!, while the

transmitted beam was focused by a ZnSe lens ~L4!

onto the feedback detector. Finally, the beam was

reflected from the last wedged window ~W4!, where it

was spatially overlapped with a visible alignment

beam. The alignment beam was provided by a

He–Ne laser and prepared with a similar optical system ~not shown!. The total attenuation of the CO2

laser beam along the optical path to the HACR was a

factor of 3000 or more, reducing the 3-W output

power of the laser down to 1 mW or less.

The polarizer P2 was adjusted to minimize the reflection from the ZnSe Brewster window on the

HACR, and a mirror ~M! reflected the laser light into

the HACR. ~This reflection is out of the plane of Fig.

2.! Whereas the final steering mirror could affect

the polarization of the beam if the direction of the

polarization were at an arbitrary angle to the plane of

incidence, this effect was negligible in this system

because the light was polarized parallel to the plane

of incidence of the mirror. A computer-controlled

shutter ~S! was used to block the laser during electrical heating of the cavity and to measure the background signal from the pyroelectric detector. A

chopper ~C!, which is required for use with the pyroelectric detector, was located after the shutter and

operated at a chopping frequency of 40.0 Hz. In addition, an 8-mm-diameter aperture ~A2! located just

before the final steering mirror was used to block

residual scattered laser light.

The infrared beam was aligned into the HACR by

being spatially overlapped with the He–Ne laser.

Although the alignment of a visible beam into the

HACR is usually optimized by minimizing the scattered light signal from the quadrant photodiodes, the

sensitivity of this method was limited by the high

level of scatter from the ZnSe Brewster window at

633 nm. Instead, the diameter of the He–Ne beam

was made to be larger than the infrared beam, in fact,

nearly as large as the apertures in the annular quadrant photodiodes. This approach provided a sensitive method to align the He–Ne beam into the HACR.

After this alignment procedure, the He–Ne beam was

blocked. The difference between the displacement of

the He–Ne and CO2 beams due to the ZnSe Brewster

window is only 0.15 mm. The alignment was tested

by establishing that the temperature rise of the cavity due to the infrared beam was a maximum and not

unduly sensitive to small changes in the alignment of

the final steering mirror. As described below, small

changes were also made in the alignment to test for

3616 APPLIED OPTICS y Vol. 36, No. 16 y 1 June 1997
change in the measured responsivities of the pyroelectric detectors.

C. Pyroelectric Detectors

Lithium tantalate detectors, coated with black paint

to absorb infrared light, were calibrated against the

HACR. A pyroelectric material has a permanent

electric dipole moment. A change in the temperature of the material changes the magnitude of this

moment, requiring a flow of charge. If a chopped

source of optical power is absorbed by a pyroelectric

material, the resulting time variation in its temperature will produce a measurable ac current. This

current can be detected by use of a lock-in amplifier,

with the chopping frequency used as the reference.8

Two 1 cm 3 1 cm pyroelectric detectors,9 here referred to as PD1 and PD2, were calibrated against the

HACR. These particular pyroelectric detectors were

chosen because of their large area. Unfortunately,

as discussed below, the black paint coating supplied

with the detector proved to have lower than desired

absorption in the infrared. For the most part, we

will describe and show data only for PD2, which is

being used to calibrate the bolometer. The results

for PD1 are comparable, but because of accidental

damage that occurred during the course of this work,

its spatial uniformity was degraded. We also calibrated a third pyroelectric detector that is part of a

commercial electrical substitution pyroelectric radiometer ~ECPR!. This detector was calibrated with

and without the electrically calibrating circuitry operational.

PD1 and PD2 were each mounted in a small aluminum box with a 13-mm-diameter entrance aperture.

The boxes were mounted on a computer-controlled,

motor-driven carousel, which positioned each detector

in the infrared beam. Atmospheric absorption between the pyroelectric detector and the HACR is

,0.01% ~Ref. 10! and was neglected. To minimize the

uncertainty due to the spatial response nonuniformity

of the detector, we used an algorithm for reproducibly

positioning the detector in the infrared beam: For

each of the two axes transverse to the beam, the detector was positioned midway between the two locations at which the detector response was 50% of its

maximum value.

The spatial nonuniformity observed in the response of PD2 is shown in Fig. 3. We obtained these

data by scanning the detector over a 6 mm 3 6 mm

region in 0.5-mm steps, using the same size beam as

was used for the calibrations. For the region within

0.5 mm ~2 mm! of the center, the maximum variation

in the detector response is 60.8% ~62.6%! and is

primarily along one direction. This rather substantial nonuniformity is likely to vary from detector to

detector and could be improved with a better absorbing coating. We estimate the reflectance of the pyroelectric detector to be at least 25% at 10.6 mm,

based on comparing the responsivity at 10.6 mm to

that measured at 633 nm with a calibrated visible

detector.11 ~The value of 25% assumes that the reflectance is close to zero at 633 nm.! Using a halfwave plate to rotate the polarization of the infrared

beam, we found the polarization dependence of the

detector’s responsivity to be ,0.05%.

The temperature dependence of the responsivity

for lithium tantalate is weak. The responsivity is

proportional to the ratio of the pyroelectric coefficient

to the specific heat. The temperature dependence of

this ratio was measured by Glass and Lines12; from

their data one can estimate the expected temperature

dependence of the responsivity to be 0.1% K21 at

room temperature. Using a temperature-controlled

box, we measured 0.16% K21

, roughly consistent with

the predicted result.

This work was carried out over a period of a few

months, during which time we saw no evidence for

any long-term change in the calibration of the pyroelectric detectors. However, the stability of these

detectors over a period of years remains to be established.

D. Measurement Instrumentation

The output signal from each detector was sent to a

transimpedance amplifier with a gain of 108 VyA, and

then to a lock-in amplifier that was sensitive to only

the fundamental Fourier component of the waveform

at the chopping frequency. The in-phase output of

the lock-in amplifier was read by a digital voltmeter.

The phase was set manually to minimize the out-ofphase signal. The component of relative standard

uncertainty in the responsivity S due to the uncertainty in setting the phase was 0.02%.

The system, consisting of the pyroelectric detector

and preamplifier, was calibrated as a unit. The responsivity was defined to be the amplitude of the ac

voltage output from the preamplifier, assuming a perFig. 3. Contour plot illustrating the spatial uniformity of the

responsivity of pyroelectric detector PD2. These data were obtained by scanning of the 3-mm-diameter beam ~85% of power! in

0.5-mm steps.

1 June 1997 y Vol. 36, No. 16 y APPLIED OPTICS 3617
fectly square optical waveform, for a given dc optical

power that would be incident on the detector if the

chopper were removed. The responsivity is given by

S 5 VCdyGCsPL, (1)

where V is the in-phase output of the lock-in amplifier

in millivolts, G is a correction factor for the absolute

response of the lock-in, PL is the infrared power in

mW as determined by the HACR, Cd is the chopper

duty cycle, and Cs is a small correction factor associated with the deviation of the optical waveform from

a perfect square wave ~described below!. Because

the HACR has a 4-min time constant, PL is the average power in the chopped beam.

We determined the chopper duty cycle by measuring the ratio of the infrared power with the chopper

turned on to that obtained with the chopper off. Because the pyroelectric detector responds only to

chopped radiation, it was necessary to install a second chopper in the beam path. Operating the second chopper at a much higher frequency ~400 Hz!

allowed lock-in detection at the second chopper’s frequency without interference from the primary chopper. The duty cycle was independently determined

with the HACR and also with a He–Ne laser and a

visible detector. We obtained Cd 5 0.4964 with a

standard uncertainty of 0.001.

The measured responsivity of the entire system

was found to change by 0.25% Hz21 at the 40.0-Hz

chopping frequency. This dependence was almost

entirely due to the preamplifier’s 3-dB point at 110

Hz. ~This preamplifier, originally designed for dc

applications, was used simply because it could be

immediately dedicated to these measurements and

may be replaced in the future.! For a standard uncertainty of 60.1 Hz in the chopper frequency, the

relative standard uncertainty in the responsivity is

only 0.025%.

The magnitude of the fundamental component in

the output from the pyroelectric detector depends on

the shape of the optical waveform, which is primarily

determined by the beam size and the chopper blade

geometry. The two-blade chopper has an inner diameter of 5 cm and an outer diameter of 11 cm, which

yields a mean chopper opening width of 6.3 cm.

Thus, for a beam diameter of 5 mm at the chopper,

the output of the preamplifier should exhibit a rise

time of only 8% of the half-period, which is due only

to the chopper. ~The observed rise time was roughly

twice this value, owing to the limited frequency response of the preamplifier.! We have corrected the

measured responsivities to the ideal conditions of a

perfectly square optical waveform, which would only

be obtained with an infinitely narrow beam. To determine this correction, labeled Cs in Eq. ~1!, we measured the effect on the responsivity of changing the

beam diameter at the chopper from 6 mm to under 1

mm and found Cs 5 0.9980 with a standard uncertainty of 0.0005. ~Because this correction is independent of the detector used, these measurements

were performed more easily at a visible wavelength.!

Because this correction is small, the calibration is

quite insensitive to the beam size and spatial profile.

To determine the correction G for the absolute response of the lock-in amplifier, we used a square wave

with a known amplitude. We obtained this square

wave by illuminating a silicon photodiode with a

chopped He–Ne laser beam. The detector’s output

was sent to a fast transimpedance amplifier. We

determined the amplitude of the square wave by

turning off the chopper and measuring the dc voltage

from this amplifier with a high accuracy digital voltmeter. ~The uncertainty in the measurement of dc

voltage is negligible.! This measurement was performed with the lock-in amplifier on the 500-mV

range. A range-to-range correction factor was determined for the 10-mV range, which was used for most

of the pyroelectric detector measurements. The total correction factor for the 10-mV range was G 5

0.9023 with a standard uncertainty of 0.002. Note

that a 1-V amplitude square wave, sent into an ideal

sine-wave lock-in amplifier, produces an output of

0.9003 ~54yp=2! V. The value of G for each of the

other ranges that were used with the pyroelectric

detectors were also measured; these correction factors were typically within 1% of 0.9003 and were

measured with a relative standard uncertainty of

0.1%.

E. Measurement Sequence

The details of the automated sequence for HACR

measurements are described in Ref. 5. Briefly, the

sequence consists of one optical measurement cycle,

in which the temperature rise of the cavity due to the

laser light is determined, followed by electrical heating, in which the quantity of electrical power required

to reproduce this temperature is determined. The

entire sequence takes ;45 min. The response of the

pyroelectric detectors was measured during the electrical heating cycle.

3. Measurement Results and Uncertainties

A. Measurement Results

The results of several responsivity measurements of

PD2 are summarized in Table 1 and shown in Fig. 4.

Each data point is the mean responsivity for a given

session of data acquisition, in which typically 15–20

measurements were obtained. We calibrated the

detector over an infrared power range from 0.011 to

0.35 mW, with no other deliberate change in conditions. ~These data are the first seven entries in Table 1 and are shown by filled circles in Fig. 4.! As

described below, this series of measurements allowed

us to establish an uncertainty due to background

effects. For the remaining data points, small

changes were made in the measurement conditions to

test the sensitivity to certain systematic effects that

are discussed below. ~These data are the last four

values in Table 1 and are shown by open squares in

Fig. 4.!

In Fig. 4, the uncertainty bar shown on each data

point corresponds to the relative standard deviation

3618 APPLIED OPTICS y Vol. 36, No. 16 y 1 June 1997
of the mean in the measurements of S for the given

session. ~For the results at 1.05 mW and below 0.2

mW, which were not obtained on the 10-mV lock-in

range, an additional contribution of 0.1% has been

added in quadrature to yield the total uncertainty

bar.! The increased standard deviation at low values of PL is due to comparable contributions from the

noise floors of the HACR5 and the pyroelectric detector. The slight decrease in responsivity at the lowest power levels could indicate a systematic effect

associated with background subtraction. This decrease was seen for both pyroelectric detectors but

not for the ECPR, which suggests a possible systematic error in the calibration of the pyroelectrics.

However, fitting the data to a form that models such

a background error5 yielded a relative standard uncertainty component of 0.05% at our typical calibration power of 0.35 mW.

We now restrict the discussion to the data obtained

at power levels of 0.2 mW or above. For a typical

session of data acquisition, the relative standard deviation in repeated measurements for either V or PL

was typically 0.15%. The primary source of this

variation was drift in the power of the infrared beam.

For S the relative standard deviation was only 0.1%

or less because slow drift in the infrared power does

not affect the measurement of S.

The data shown by open squares were obtained

with small changes to the calibration conditions.

These changes included removing the detector from

the carousel, repeating the alignment algorithm, and

small variations in the alignment of the laser beam

into the HACR. The goal of these changes was to

establish the reproducibility of the calibration, given

the known spatial nonuniformity of the detector and

the difficulty in aligning the infrared beam into the

HACR. ~For our work here we are primarily interested in our ability to reproducibly calibrate the detector using our alignment algorithm. The related,

but separate, issue of the transfer of this calibration

to the cryogenic bolometer will be discussed in another paper.!

We determined the average responsivity ~Sa 5 6.89

mVymW! by averaging the data obtained at power

levels above 0.2 mW. The relative standard deviation of this data set is 0.31%, which is substantially

larger than the relative standard deviation of the

mean for any given session of data acquisition.

Hence the reproducibility of the calibration was affected by both unintentional and imposed changes in

calibration conditions. The small relative standard

uncertainty of 60.05% that is due to the typical variations of 60.3 K in the ambient laboratory temperature can account for only a small portion of the

observed 0.31% relative standard deviation. We believe the most likely cause is the known spatial nonuniformity of the detector. From Fig. 3 we see that

a change of 60.2 mm in the location of the detector or

the beam can result in a 60.3% change in the measured responsivity. We believe that spatial uniformity could explain most of the observed variation in

the measurements of S. We assign a type A relative

standard uncertainty13 of 0.31% to the reproducibility of the calibration, which includes effects of spatial

nonuniformity and beam alignment.

As a final test of the quality of the alignment into

the HACR, we shifted the location of the focus farther

along the beam path so that it was between the two

limiting apertures in the HACR. If the beam had

been slightly obstructed by these apertures, shifting

the focus would cause the measured responsivity to

decrease. We observed a decrease of 1.0% in the

measured responsivity for detector PD2, whereas the

responsivity of PD1 was nearly unchanged. This

suggests that the effect was not due to alignment into

the HACR but some other effect that was different for

the two detectors. Changing the location of the focus did require realigning the detectors and also inTable 1. Measured Values of the Responsivity S of the Pyroelectric

Detector PD2 for a Range of Infrared Power Levels and Other Variations

in the Conditions of the Calibrationa

PL

~mW!

S

~mV/mW!

sm/S

~%!

~S 2 Sa!/Sa

~%!

0.3397 6.880 0.03 20.17

0.3392 6.893 0.04 0.03

0.3203 6.897 0.03 0.09

0.2599 6.894 0.02 0.04

0.07379 6.880 0.11 20.16

0.03079 6.873 0.21 20.26

0.01375 6.815 0.41 21.11

1.051 6.904 0.10 0.18

0.3395 6.888 0.02 20.04

0.3421 6.924 0.01 0.48

0.3368 6.849 0.04 20.61

a

The mean responsivities of the relative standard deviation of

the mean, smyS, are listed for each session of data acquisition. The

percentage deviation of each responsivity from the average responsivity ~Sa 5 6.89 mVymW! is also listed; the average is based on the

data obtained at power levels above 0.2 mW.

Fig. 4. Percentage deviation of each responsivity S listed in Table

1 from the average responsivity Sa; the average is based on the

data obtained at power levels above 0.2 mW. The data shown by

filled circles were obtained with no deliberate change in conditions

to test for linearity of the detector and background effects. The

data shown by open squares include changes in the conditions of

the measurements that are described in the text.

1 June 1997 y Vol. 36, No. 16 y APPLIED OPTICS 3619
creased the beam size at the detectors a small

amount. These changes, in conjunction with the

spatial nonuniformity of the detectors, could explain

the observed 1.0% shift in the responsivity for PD2.

Hence we have not increased the uncertainty in the

reproducibility in the calibration because of this measurement.

B. Corrections for Window Transmittance and Scattered

Laser Light

The uncertainty components in these calibrations are

listed in Table 2. The method used to evaluate each

uncertainty component ~type A or type B! is also

listed. We now discuss the combined uncertainty

component in the measurement of PL by the HACR.

The infrared power PL is given by

PL 5 ~1yT!@~NPHyA! 1 PS#. (2)

where PH is the electrical heater power that yields

the same temperature rise of the cavity as that produced by the infrared beam, PS is the estimated infrared power scattered out of the field of view of the

cavity, A is the absorptance of the cavity, T is the

transmittance of the entrance window of the HACR,

and N is a factor to take into account any nonequivalence between the infrared and electrical heating.

For this work, the type B uncertainty in the measurement of PL by the HACR is dominated by the uncertainties in T and PS, which are discussed in detail

below. Other HACR uncertainties discussed in Ref.

5 are less than 0.01%, which is negligible for this

work.

The transmittance of the window was measured on

the optical table before and after the series of measurements with the HACR. Although this is a simple measurement in principle, care was required

because of the nonuniformity of the available detectors. The transmittance was determined by measuring the signal on a pyroelectric detector with and

without the window in the beam. Because the window translates the beam, the detector must also be

translated so that the beam is still incident upon the

same location on the detector. Any error in this relocation leads to an error in the measured transmittance. We measured a transmittance of 0.9993 6

0.0004 before the series of HACR measurements and

0.9962 6 0.0008 afterward, where the uncertainties

quoted are the standard deviations of the mean for

each group of measurements ~16 measurements for

the before data and 7 for the after data!. These

transmittance measurements were separated by 4

months, and we believe that the decrease in transmittance was due to accumulation of contaminants

on the window. We used the average value of T 5

0.9978 6 0.0018 to determine PL, where the standard

uncertainty quoted is equal to the sum of half the

difference between the before and after values, plus

the uncertainties quoted for the before and after data,

added in quadrature.

Before measuring the transmittance, the window

reflectance was minimized by adjusting the polarizer

P2 and the angle of incidence of the beam on the

window. We minimized the reflection, rather than

maximizing the transmittance, so that the procedure

was the same as that performed when the window

was installed in the HACR. ~Because of the slow

time constant of the HACR, it is difficult to maximize

the transmittance by observing the temperature of

the cavity.! Furthermore, we measured the reflectance to establish that the same value was obtained

when the window was installed in the HACR. Using

one of the pyroelectric detectors, we measured the

reflectivity of the window to be 0.1% 6 0.03%.

Scattered laser light refers to light that is incident

upon the detector to be calibrated but scattered out of

the field of view of the absorbing cavity in the HACR.

For visible wavelengths there is little scattered laser

light, and it is measured by annular silicon photodiodes located along the optical path within the

HACR. Because scattered infrared laser light cannot be measured by the photodiodes in the HACR, we

estimated the correction for scattered laser light by

simulating the usual trajectory of the beam into the

HACR on the optical table: Just before the final

steering mirror, the beam was deflected with a mirror. A window was placed in the beam where the

HACR window would normally be located. To colTable 2. Components of the Combined Relative Standard Uncertainty of 0.48% in the Calibration of the Pyroelectric Detector Transfer Standard

Against the HACR at an Optical Power Level of 0.35 mWa

Uncertainty Component Type

Value of

Correction

Component of

Uncertainty ~%!

Reproducibility A 0.31

Background A 0.05

G B 0.9023 0.20

Cd B 0.4964 0.20

Cs A 0.9980 0.05

Chopper frequency and lock-in phase B 0.03

Combined standard uncertainty in PL B 0.21

Window transmittance ~T! 0.9978 0.18

Scattered optical power ~PS! 0.61 mW 0.1

a

The uncertainties are identified as type A or type B relative standard uncertainties. The measured values of corrections to the data are

also listed.

3620 APPLIED OPTICS y Vol. 36, No. 16 y 1 June 1997
lect only the scattered light, we used a 15-cm focallength concave mirror with a 9-mm central aperture.

This mirror was located near the position of the quadrant photodiodes in the HACR dewar, which also

have 9-mm-diameter apertures. Detector PD1 was

used to detect the reflected light from this mirror.

We measured PS to be 0.18% of the incident infrared

power. Most of this scattered light was not due to

the window. It is difficult to establish how close this

measurement is to the actual value that PS was during our calibrations. On the basis of the repeatability of the measurement and the sensitivity to changes

in the beam alignment, we estimate an relative standard uncertainty component of 0.1% due to scattered

light, about half the value of the correction itself.

4. Conclusion

We have calibrated a pyroelectric detector against

the HACR at a wavelength of 10.6 mm with a combined relative standard uncertainty of 0.48%. This

detector is being used to calibrate the transfer standard cryogenic bolometer for an infrared comparator

facility. The calibration of the bolometer, which is

being performed with a different laser system, will be

discussed in another paper. The primary issue in

the accuracy of the bolometer calibration is the spatial uniformity of the pyroelectric detector. Minimizing this uncertainty requires reproducing the

alignment procedure and beam characteristics that

were used for the HACR calibration. We believe

that the transfer of this calibration can easily be done

with a conservative relative standard uncertainty of

62%, and with careful attention to detail, a relative

standard uncertainty of 60.6% should be achievable.

We are investigating detectors with improved spatial uniformity, which can be obtained by using goldblack coatings or a light-trapping arrangement.14,15

Colleagues in our laboratory have produced gold-black

coatings with less than 1% reflectance at the CO2 laser

wavelength. An alternative solution is to calibrate

the cryogenic bolometer directly against the HACR.

This approach would require improving the sensitivity

of the HACR, attenuating the beam for the bolometer

by a precisely known amount, further quantifying the

bolometer’s nonlinearity, or some combination of these

changes. Finally, work is in progress at NIST to develop a large-area silicon bolometer that could have

both high sensitivity and a sufficiently large dynamic

range to be used easily with the HACR.

References and Notes

1. A. Migdall, G. Eppeldauer, and C. Cromer, “IR detector spectral responsivity calibration facility at NIST,” in Cryogenic

Optical Systems and Instruments VI, J. B. Heaney and L. G.

Burriesci, eds., Proc. SPIE 2227, 46 –53 ~1994!.

2. G. Eppeldauer, A. L. Migdall, and C. L. Cromer, “Characterization of a high sensitivity composite silicon bolometer,”

Metrologia 30, 317–320 ~1993!.

3. G. Eppeldauer, A. L. Migdall, and C. L. Cromer, “A cryogenic

silicon resistance bolometer for use as an infrared transfer

standard detector,” in Thermal Phenomena at Molecular and

in Cryogenic Infrared Detectors, M. Kaviany, D. A. Kaminskii,

A. Majumdar, P. E. Phelan, M. M. Yovanovich, Z. M. Zhang,

eds. ~American Society of Mechanical Engineers, New York,

1994!, Vol. 277, pp. 63– 67.

4. G. Eppeldauer, A. L. Migdall, T. R. Gentile, and C. L. Cromer,

“Absolute response calibration of a transfer standard cryogenic

bolometer,” in Photodetectors and Power Meters II, K. Murray

and K. J. Kaufmann, eds., Proc. SPIE 2550, 36 – 46 ~1995!.

5. T. R. Gentile, J. M. Houston, J. E. Hardis, C. L. Cromer, and

A. C. Parr, “National Institute of Standards and Technology

high accuracy cryogenic radiometer,” Appl. Opt. 35, 1056 –

1068 ~1996!.

6. Model LS-10.6, Cambridge Research and Instrumentation,

Inc., 21 Erie Street, Cambridge, Mass. 02139. Certain trade

names and company products are mentioned in the text or

identified in an illustration in order to adequately specify the

experimental procedure and equipment used. In no case does

such identification imply recommendation or endorsement by

the National Institute of Standards and Technology, nor does

it imply that the products are necessarily the best available for

the purpose.

7. R. J. Pressley, ed., Handbook of Lasers With Selected Data on

Optical Technology ~CRC, Cleveland, Ohio, 1971!, p. 331.

8. R. W. Boyd, Radiometry and the Detection of Optical Radiation

~Wiley, New York, 1983!, pp. 219 –223.

9. Servo Corporation of America, 111 New South Road, Hicksville, New York 11802-1490.

10. W. L. Wolfe and G. J. Zeissis, eds., Infrared Handbook, 3rd ed.

~Infrared Information Analysis Center, Environmental Research Institute of Michigan, Ann Arbor, Mich., 1989!, pp.

5– 69.

11. T. R. Gentile, J. M. Houston, and C. L. Cromer, “Realization of

a scale of absolute spectral response using the NIST high

accuracy cryogenic radiometer,” Appl. Opt. 35, 4392– 4403

~1996!.

12. A. M. Glass and M. E. Lines, “Low-temperature behavior of

spontaneous polarization in LiNbO3 and LiTaO3,” Phys. Rev. B

13, 180 –191 ~1976!.

13. B. N. Taylor and C. E. Kuyatt, “Guidelines for evaluating and

expressing the uncertainty of NIST measurement results,”

Tech. Note 1297, 2nd ed. ~National Institute of Standards and

Technology, Gaithersburg, Md., 1994!.

14. D. J. Advena, V. T. Bly, and J. T. Cox, “Deposition and characterization of far-infrared absorbing gold black films,” Appl.

Opt. 32, 1136 –1144 ~1993!.

15. R. J. Phelan, Jr., J. Lehman, and D. R. Larson, “Electrically

calibrated pyroelectric detector—refinements for improved optical power measurements,” in Photodetectors and Power

Meters, K. J. Kaufmann, ed., Proc. SPIE 2022, 160 –163 ~1993!.

1 June 1997 y Vol. 36, No. 16 y APPLIED OPTICS 3621
REALIZATION OF AN INFRARED SPECTRAL RADIANT POWER RESPONSE 

SCALE ON A CRYOGENIC BOLOMETER 

Alan Migdall and George Eppeldauer 

National Institute of Standards and Technology 

Optical Technology Division 

Abstract 

An ambient temperature Infrared Spectral Responsivity Comparator Facility has been developed at 

NIST to calibrate infrared detectors and radiometers for spectral and spatial responsivities. Test 

detectors are substituted for working- or transfer-standard radiometers in the output beam of a 

monochromator. InSb working standard radiometers have been developed and characterized to 

hold the spectral responsivity scale between 2 μm and 5.4 μm. The InSb working standard 

radiometers were calibrated against the transfer standard cryogenic bolometer that is tied to the 

primary standard cryogenic radiometer of NIST. The cryogenic bolometer holds the infrared 

power responsivity scale between 2 μm and 20 μm. The combined standard uncertainty (k=1) of 

the spectral power responsivity scale, as realized on the cryogenic bolometer, is +/- 0.25 %. 

Key Words: bolometer; calibration; infrared detectors; radiometry; scale; spectral irradiance 

responsivity; spectral power responsivity. 

1. Introduction 

The National Institute of Standards and Technology (NIST) has developed an IR radiant power 

responsivity scale for the spectral range from 2 μm to 20 μm. This scale is required for a facility 

that provides a detector-based calibration of IR detectors (1, 2). The scale operates at much higher 

sensitivities (input power levels are 10 μW to 20 pW) than existing IR scales (between 500 μW 

and about 0.1 μW) (3), while using a transfer standard detector with a flat spectral responsivity over 

the entire spectral range. The scale has been realized on a cryogenic bolometer, which accounts 

for the improved sensitivity relative to a pyroelectric detector based scale. The responsivity of this 

bolometer has been determined by multiple ties (4) to a primary standard, the NIST High Accuracy 

Cryogenic Radiometer (HACR) (5). In addition, an independent method was used to determine the 

relative response of the bolometer over the entire spectral range. The uncertainty over the entire 

spectral range of 2 μm to 20 μm is typically better than 0.25 %, with the typical uncertainty of an 

individual measurement made with the bolometer being about 0.8 %. 

Working standard InSb radiometers (6) have been developed for the 2 μm to 5.4 μm wavelength 

range to hold the spectral responsivity scale. They are easy to use relative to the sophisticated 

bolometer that requires liquid He sensor-temperature and continuous computer control/monitor for 

responsivity change corrections (7). Infrared test detectors with good spatial response uniformity 

can be calibrated against the InSb working standard radiometers in radiant power measurement 

mode. Spatially nonuniform infrared detectors can be used for accurate radiometric measurements 

when they are calibrated against the working standard InSb radiometers in irradiance measurement 

mode. 
2. Spectral Responsivity of the Transfer Standard Bolometer 

To determine the radiant power responsivity of the bolometer, its relative response was determined 

over its entire spectral range from measurements of bolometer components. This relative response 

shape was then tied down at many wavelengths via Si, Ge, and pyroelectric transfer detectors to 

the HACR. The bolometer consists of a sapphire disk with a heat sensor on one side and a gold 

black absorptive coating on the other side. Incident radiation is detected as a temperature rise. 

Because the bolometer operates by sensing energy deposited within its absorber, its relative 

response is just the product of the absorptance of the bolometer’s coating and the transmittance of 

the window of the cryogenic dewar. For more details on the device construction and 

characterization, see References 7, 8, and 9. 

The spectral absorptance of the bolometer gold black coating was measured using a Fourier 

Transform Infrared (FTIR) spectrometer system with hemispherical collection optics. This 

allowed the total reflectance (diffuse and specular) to be measured. The results are shown in Fig. 

1. 

-0.050

0.000

0.050

0.100

0 5 10 15 20

Reflectance

Wavelength [μm]

mean= 0.00749

σ= 0.20 

σ/√n= 0.00063

Figure 1. Total bolometer reflectance 

Two additional measurements were made using laser sources. At 0.633 μm and 10.6 μm, the 

reflectances were determined to be (1.2±0.3) % and (0.5±0.3) % respectively. [(The uncertainties 

reported in this paper are all standard uncertainties as defined in Ref. 10 (coverage factor k=1).] A 

linear fit to the FTIR data from 2 μm to 17 μm indicated a minimal slope with a value not much 

larger than its uncertainty. Because of this, the FTIR reflectance data were simply averaged 

yielding a wavelength independent reflectance value, R=0.75 %. This is consistent with the values 

and uncertainties of the two laser reflectance measurements. Because the IR termination of the 

reflectance data beyond 17 μm was due to low FTIR sensitivity rather than a variation of gold 

black, it is expected that an extrapolation of this data will be valid to at least 20 μm. 

The transmittance of the bolometer window was measured from 600 nm to beyond 18 μm. The 

Infrared Spectral Comparator Facility (IR SCF) was used to measure the transmittance of single 

KBr window samples from 2 μm to 20 μm (see Fig. 2a.). The mean size of the error bars was 

about 0.1 % for the region from 2 μm to 16 μm. The IR SCF was used to measure the 

transmittance difference of two window samples as shown in Figure 2b. The mean difference 
between the two measurements was 0.016 % with a standard deviation of 0.2 %. These small 

differences allow for window replacements, while using this standard deviation as the uncertainty. 

These small differences also indicate that the spatial uniformity of the windows, which was not 

specifically tested, should be significantly below these levels. 

0.89

0.90

0.91

0.92

4 8 12 16 20

Transmittance

Wavelength (μm)

error bars are stdev of 5 to 9 pts.

0.89

0.90

0.91

0.92

-0.01

0

0.01

4 8 12 16 20

sample 2

sample 1

(T1-T2)/T1

KBr Transmittance

(T1-T2)/T1

Wavelength (μm)

(T1-T2)/T 1 2-19 μm stats

Minimum -0.0078

Maximum 0.0068

Mean 0.000156

Std Dev 0.0021

Figure 2. (a) Spectral transmittance of one and (b) two KBr windows and their relative differences. 

The relative spectral response of the bolometer as shown in Figure 3 is the product of the window 

transmittance and the bolometer gold black absorptance. Except for a pair of 1 % to 2 % dips 

(most likely due to window coating absorption lines) the bolometer response is quite flat. The 

uncertainty for the 2 μm to 20 μm region is 0.36 %, the quadrature sum of the 0.2 % KBr 

transmittance uncertainty and the 0.3 % gold black absorptance uncertainty. In the 0.6 μm to 2 μm 

region, the transmittance uncertainty is so small that the gold black absorptance uncertainty 

dominates the total uncertainty. 

To convert the relative spectral curve just discussed into an absolute scale, it was necessary to 

determine the absolute responsivity at one, or preferably, more wavelengths. This was done by 

comparison to Si, Ge, and pyroelectric standard detectors, which were themselves tied to the 

HACR primary standard. The comparisons were made at specific wavelengths using laser sources 

at 0.633 μm, 1.3 μm, and 10.6 μm and over a continuous range from 600 nm to 900 nm using the 

quartz lamp and the IR SCF itself as the source. Even though the VIS/NIR calibrations are outside 

of the intended range of the IR SCF, those measurements are important because of their accuracy 

and to verify the spectral flatness of the bolometer. 

The overall bolometer spectral response is shown in Fig. 4, where it is overlaid on the responsivity 

determined from the bolometer reflectance and window transmittance. This determination is a 

relative spectral curve, requiring a single scale factor to fit all of the absolute measurements. The 

resulting curve shown is T(1-R)*0.3913 V/μW. As can be seen from the figure, this response is a 

good fit, well within the uncertainties. For the VIS/NIR region the data shows excellent 

smoothness reflecting the quality of the Si and Ge transfer standards. 
0.880

0.890

0.900

0.910

0.920

0

0.002

0.004

0.006

0.008

0.01

0.5 1 1.5 2

Transmittance

Stdev

Transmittance

Standard deviation

Wavelength (μm)

Figure 3. Transmittance of the KBr bolometer-window. 

The IR region shows much higher variation due to the poorer quality of the pyroelectric transfer 

detector, which had much lower signal to noise ratio, poorer spatial response uniformity, and 

involved a more difficult calibration transfer. The overall good fit of the curve shape to the actual 

measurements over the 0.6 μm to 11 μm range indicates excellent selfconsistency. This should be 

emphasized as the overall data set includes three independent transfer detectors and a continuous 

spectral source as well as a laser source. This high level of selfconsistency increases confidence in 

the regions where absolute measurements were not directly made. 

The overall scale factor of the relative response curve was determined by taking the ratio of the 

bolometer responsivity to the predicted relative response (T·(1-R)). The weighted mean of all the 

ratio data was 0.3913±0.00015 (The uncertainty is the standard deviation of the mean). The 

weights used were the ratio uncertainty (the quadrature sum of the uncertainties of the responsivity 

measurements and the responsivity curve). This constant is a scale factor to convert the relative 

response curve to an absolute scale. 

All uncertainty components were included, so the nonstatistical uncertainty correlations are 

ignored here. This analysis assumes a single scale factor over the entire wavelength range. To test 

this, the ratios of the responsivity measurements to the now absolute predicted responsivity were 

plotted versus wavelength and fit to a line. As shown in Fig. 5, the fit stays within ±0.25 % of 

unity indicating that any systematic tilting of the relative curve is less than this value. A second 

analysis was done that included some correlations in the component uncertainties with very little 

change of the final uncertainty (11).
0.33

0.34

0.35

0.36

0.37

0.38

1 10

Bolometer Responsivity (V/μW)

Wavelength(μm)

T*(1-R)*scale factor

Si Ge Pyroelectric

Only error bar caps are

shown here for clarity.

2 20

1.31 μm laser 

measurement

Figure 4. Radiant power responsivity of the bolometer. 

The different analysis schemes support an overall uncertainty of ±0.25 % in the absolute 

responsivity scale as shown by the solid curve in Fig. 4. This uncertainty when combined with the 

uncertainty associated with an individual bolometer radiant power measurement at a specific 

wavelength (about 0.75 %) gives an overall bolometer power responsivity scale uncertainty of 

about 0.8 %. This is the uncertainty that can be expected for a bolometer measurement of radiant 

power made at a single wavelength within the 2 μm to 20 μm range of the IR SCF (assuming 

adequate measurement time is allowed so as not to be limited by bolometer signal noise). This 

uncertainty is comparable to the quoted uncertainty of a similar IR scale also set up for detector 

calibrations (3). 

3. Conclusion 

NIST has developed an IR spectral responsivity scale. The radiant power responsivity scale was 

first implemented on a high sensitivity cryogenic bolometer between 2 μm and 20 μm. The power 

responsivity scale uncertainty is comparable with the best existing IR responsivity scales. Working 

standard and test infrared detectors and radiometers can be calibrated against the cryogenic 

bolometer. 
0.96

0.97

0.98

0.99

1

1.01

1.02

1.03

1.04

1 1

c= 0.39130

Responsivity/T(1-R)*c

Wavelength (μm)

0

y=a+b λ

a=0.9975±0.0014

b=0.00072±0.00026

χ

2

=70.4

Figure 5. Ratio of the bolometer power responsivity to the scaled relative response. 

4. References

1. Migdall, A., Eppeldauer, G., and Cromer, C., “IR Detector Spectral Responsivity Calibration 

Facility at NIST,” Cryogenic Optical Systems and Instruments VI, SPIE 2227, 46-53, 1994. 

2. Parr, A.C., “A National Measurement System For Radiometry, Photometry, and Pyrometry 

Based upon Absolute Detectors, NIST Technical Note 1421, 1996.

3. Nettleton, D.H., Prior, T.R., and Ward, T.H., “Improved Spectral Responsivity Scales at the 

NPL, 400 nm to 20 μm,” Metrologia, Vol. 30, 425-432, 1993. 

4. Migdall, A. and Eppeldauer, G., “Realization of an infrared spectral radiant power response 

scale on a cryogenic bolometer,” Metrologia, Vol. 35, 307-315, 1998. 

5. Gentile, T.R., Houston, J.M. and Cromer, C.L., “Realization of a scale of absolute spectral 

response using the National Institute of Standards and Technology high-accuracy cryogenic 

radiometer,” Appl. Opt. 35, 1996, 4392-4403. 

6. Eppeldauer, G.P., Migdall, A.L., and Hanssen, L.M., “InSb Working Standard Radiometers”, 

Metrologia, Vol. 35, 485-490, 1998. 

7. Eppeldauer, G., Migdall, A.L., Gentile, T.R., and Cromer, C.L., “Absolute response 

calibration of a transfer standard cryogenic bolometer”, SPIE, Proc. Vol. 2550, 36-46, 1995. 

8. Eppeldauer, G., Migdall, A.L., Cromer, C. L., “Characterization of a High Sensitivity 

Composite Silicon Bolometer,” Metrologia, Vol. 30, 317-320, 1993. 
9. Eppeldauer, G., Migdall, A.L., and Cromer, C.L., “A Cryogenic Silicon Resistance 

Bolometer for use as an Infrared Transfer Standard Detector,” Thermal Phenomena at 

Molecular and in Cryogenic Infrared Detectors, edited by M. Kaviany et al., ASME, HTDVol. 277, New York, NY, 63-67, 1994. 

10. Taylor, B.N. and Kuyatt, C.E., Guidelines for Evaluating and Expressing the Uncertainty of 

NIST Measurement Results, Natl. Inst. Stand. Technol. (U.S.), Tech. Note 1297, 1994. 

11. Migdall, A.L., Eppeldauer, G.P., NIST Measurement Services: Spectroradiometric Detector 

Measurements: Part III-Infrared Detectors, NIST Special Publication 250-42, 1998. 
SPECTRAL POWER AND IRRADIANCE RESPONSIVITY CALIBRATION 

OF InSb WORKING STANDARD RADIOMETERS

George Eppeldauer and Miklos Racz*

National Institute of Standards and Technology 

Optical Technology Division 

Gaithersburg, Maryland 20899 *

 Guest researcher from the Hungarian Academy of Sciences 

Research Institute for Technical Physics and Materials Science1

Abstract 

New, improved performance, InSb power/irradiance meters have been developed and 

characterized to hold the National Institute of Standards and Technology (NIST) spectral 

responsivity scale between 2 μm and 5.1 μm. The InSb radiometers were calibrated against the 

transfer standard cryogenic bolometer that is tied to the primary standard cryogenic radiometer of 

NIST. The InSb radiometers serve as easy-to-use working standards for routine spectral power 

and irradiance responsivity calibrations. The spectral irradiance responsivities were derived from 

the spectral power responsivities utilizing the measured area of the apertures in front of the InSb 

detectors. 

1. Introduction 

High sensitivity infrared radiometer standards can eliminate signal level problems caused by the 

weak outputs of commonly used thermal sources. An accurate infrared spectral responsivity scale 

has been realized on pyroelectric detectors at the National Physical Laboratory.1 The responsivity 

calibration of an InSb transfer standard detector has been reported for metrological applications 

between 1 μm and 3 μm.2

 The new infrared spectral responsivity scale developed at NIST has 

been realized on a cryogenic bolometer3 that operates at much higher sensitivities (input power 

levels are 10 μW to 20 pW) than pyroelectric detector based scales (between 500 μW and 1 μW). 

Working standard InSb radiometers4

 have been developed for the 2 μm to 5.4 μm wavelength 

range to hold the spectral responsivity scale. They are easy to use relative to the sophisticated 

cryogenic bolometer5

 that requires liquid He sensor-temperature and continuous computer 

control/monitor for responsivity-change corrections.6

 Design, characterization, and spectral 

power responsivity calibration of the improved performance second-generation InSb radiometers 

is discussed in this paper. Realization of a new spectral irradiance responsivity scale is described 

also for the 2 μm to 5.1 μm wavelength range. Infrared test detectors with good spatial response 

uniformity can be calibrated against the InSb working standard radiometers in radiant power 

measurement mode. Spatially nonuniform infrared detectors can be used for accurate radiometric 

measurements when they are calibrated against the working standard InSb radiometers in 

irradiance measurement mode. 

2. Mechanical structure of the InSb radiometers 

 

1

 Current position is with the Konkoly Observatory, Budapest, Hungary 
Following the first-generation 4 mm diameter InSb detectors4

 second generation InSb radiometers 

have been developed in cooperation with EG&G Judson.7

 Large area and selected high-shuntresistance detectors are mounted in the 77 K dewars. These InSb detectors were designed to 

minimize the problem of flashing4

 even when exposed to short wavelength optical radiation. 

Precision apertures of 6.4 mm diameter are mounted in all dewars in front of the 7 mm diameter 

InSb photovoltaic detectors. Long-snout and short-snout dewars have been developed for 

different applications. In the long-snout version, as shown in Figure 1, a 17° field-of-view (FOV) 

limiter is realized with a cold second aperture positioned 50 mm away from the precision 

aperture. The advantage of this arrangement is that laser beams can be measured if a wedged 

Dewar-window is used to avoid interference and to produce a large enough separation between 

the primary and reflected beams in the plane of the precision aperture. Also, the background 

rejection is higher here than in the short-snout Dewar because of the 31° partial (clipped) FOV. 

The separation between the two apertures is only 7.2 mm in the short-snout Dewar. This unit is 

used only for non-coherent radiation measurements where easy alignment is an issue. The 

background produced signal is higher in the short-snout unit because of the 90° overall FOV (the 

unvignetted FOV remained 17°). Optical filters can be mounted inside the cylindrical holder of 

the cold FOV limiter. These radiometers can be used in both radiant power and irradiance 

measurement modes. 

Fig. 1. Mechanical-optical construction of the second generation (long-snout) InSb radiometer. 

3. DC background and AC noise test of the InSb radiometers 

The current-to-voltage converter gains of the InSb radiometers were designed to achieve a DC 

thermal background-induced output voltage of less than 5 V. 

An infrared collimator was used for AC noise tests. The infrared collimator was built from a 

variable temperature blackbody (BB) radiator, a 25 cm diameter reflecting (collimating) mirror, 

and a detector stage. An aperture wheel, a chopper, and then a shutter (this was the closest to the 

BB) were located in front of the BB cavity. The output voltage from the current-to-voltage 

converter of the InSb radiometer was measured with a lockin amplifier. 

The noise floor of the second-generation InSb radiometers was tested with a 40 Hz chopping 

frequency while the shutter was closed. From 10 measurements, a 6.7 pA standard deviation was 

calculated for the current noise of the broadband InSb-1 radiometer when the electrical bandwidth 
was 0.5 Hz. This corresponds to a noise equivalent photocurrent of 5 pA/Hz1/2. The InSb-1 

radiometer is a short-snout unit without any cold filter. This is our most frequently used working 

standard. 

For very high sensitivity measurements, the background rejection of the long-snout InSb 

radiometer was further increased by installing a cold filter (Model BBP-3200-3590-D from 

Spectrogon US, Inc.)7

 with a bandpass of 3.2 μm to 3.6 μm (FWHM). The current-to-voltage gain 

could be increased from the 3 x 104

 V/A maximum of the short-snout unit to 106 V/A where the 

DC background-caused output voltage was 1.6 V. A noise equivalent power (NEP) of 0.22 

pW/Hz1/2 was obtained at the peak responsivity of the filtered InSb radiometer. The dynamic 

(signal) range was six orders of magnitude at the 106

 V/A gain. 

4. Calibration facility and procedure 

All measurements were performed on the Ambient Infrared Spectral Comparator Facility 

(IRSCF).8

 The optical-mechanical scheme of the facility is shown in Fig. 2. 

The light sources were a 100 W tungsten halogen lamp from 2 μm to 3.65 μm, and a 45 W 

ceramic glower from 3.65 μm to 5.7 μm. The sources were imaged to the entrance aperture of the 

prism-grating double monochromator using spherical and flat mirrors. A chopper was positioned 

in front of the entrance aperture. Either 1 mm or 2 mm diameter apertures could be used. An 

input iris was mounted on the spherical mirror to adjust the solid angle of the beam entering the 

monochromator. The flat mirror was removable using a kinematic mount. The bandpass of the 

monochromator was about 1% of the selected wavelength. Laser beams could be introduced into 

the monochromator when the flat mirror was removed. The laser inputs were used either for 

wavelength calibration or to scan detectors with a small spot for high resolution spatial response 

tests. Order sorting filters were used at the exit aperture of the monochromator to improve the 

out-of-band blocking of the prism (KRS-5) pre-disperser of the monochromator. Off-axis 

paraboloid mirrors imaged the output beam to the detectors. The f/# of the output beam could be 

controlled with another iris. The detectors measured the total radiant power of the incident 

monochromatic beam (focussed into a 2 mm diameter spot on the detector surface) in underfilled 

mode. The kinematic mount of the bolometer was held by a separate stage where it could be 

tilted rotated, and shifted. Three InSb radiometers could be aligned on a second detector stage 

which was mounted on the computer moved Z (vertical) translation stage. Both detector stages 

were mounted on the computer controlled Y (horizontal) translation stage. 

Spatial response scans were made along the horizontal and vertical diameters of all detectors 

before measurements to determine the location of the beam spot in the center of the detector. 

The calibration procedure included a number of spectral scans in different wavelength intervals. 

During a scan, the computer set the wavelength, moved the bolometer into the beam where the 

test points8

 and the output signal were measured, then the first InSb radiometer was moved into 

the same beam where its output signal was measured as well. During the responsivity scale 

derivation, a large enough number of measured points and scans were selected to make the 

statistical evaluation easier. After all InSb radiometers were measured at a selected wavelength, 

the scan was repeated at a 25 nm or 50 nm increment. 
Fig. 2. Optical-mechanical scheme of the Ambient Infrared Spectral Comparator Facility 

5. Measurement results 

Those electronic and radiometric characteristics of the second generation InSb radiometers were 

measured which could influence the performance of the spectral responsivity calibrations. 

5.1. Frequency dependent signal responsivity

The frequency dependence of the InSb radiometer responsivity was measured to allow response corrections 

for different chopping frequencies in different applications. Usually, the DC signal responsivity is 

reported. The measured responsivity curves of the InSb-1 radiometer are shown in Fig. 3 at 

transimpedances of 10 kΩ, 20 kΩ, and 30 kΩ. The 30 kΩ feedback resistor was used in the responsivity 

calibrations at the IRSCF. The lowest 3 dB roll-off frequency was about 400 Hz. The roll-off frequencies 

were determined from curve fits to a single time constant equivalent circuit of a low-pass RC filter.9

 The 

chopping frequency (for a given application) should be selected to be 40 Hz or less to keep the operating 

point on the plateau of the responsivity curves. 

Normalized signal response

10 kΩ

604.5 Hz

20 kΩ 1354 Hz

30 kΩ

401.5 Hz

0.7

10

0.75

0.8

0.85

0.9

0.95

1

1.05

100 1000

Chopping frequency [Hz]

Fig. 3. Frequency-dependent signal responsivity curves of the InSb-1 radiometer at different gains.
5.2. Spatial response 

Horizontal and vertical scans were made through the detector centers with 2 mm diameter beam 

spots. The goal of these measurements was to check the spatial response uniformity of the 

detectors. The scans were made to find the plateau for power responsivity measurement and also 

to calculate an uncertainty component for the uncertainty budget. Beam clipping was avoided by 

working in the center of the measured plateau. 

Figure 4 shows the horizontal and vertical response scans of the InSb-1 radiometer. The response 

difference is shown for both scans relative to the response in the detector center. The scans 

appear to show that the degree of non-uniformity is 0.36% along a vertical diameter calculated as 

the standard deviation from seven points on the plateau. The non-uniformity along the 

perpendicular (horizontal) diameter was much lower. The average run-to-run standard deviation 

for the seven points was 0.05%. 

5.3. Spectral power responsivity 

The measured spectral power responsivity curves of the second generation InSb-1 and the first 

generation InSb-0 radiometers are shown in Fig. 5. The curves were calculated from a number of 

spectral responsivity scans performed in a few weeks period. The responsivity at each 

wavelength was determined from the average of at least four substitution measurements against 

the transfer standard cryogenic bolometer. Both the transfer- and working-standards were 

underfilled by the incident monochromatic radiation. The graph also shows the 100% external 

quantum efficiency10 (EQE) (discussed below). The second generation detector has improved 

spectral responsivity. A roughly 5% dip at 4.2 μm and a smaller dip at 2.7 μm were caused by 

atmospheric absorption because the length of the optical path was different for the InSb detectors 

as compared to the transfer standard bolometer. The dips at 4.2 μm are shown with thinner lines. 

Only the monochromator was purged. The other small dips at 3.2 μm were caused by absorption 

inside of the InSb Dewars. Dip-free responsivity curves could be obtained by either extending 

the purged beam-passes or applying responsivity corrections. The right-side Y-axis combines the 

relative uncertainties (k=1) of the two detector spectral responsivity measurements. Uncertainties 

are not shown for the 4.2 μm absorption band where high accuracy calibrations are not suggested. 

Increased uncertainties can be seen at the other absorption bands. The low uncertainties reflect 

the small changes (drift) during a short substitution measurement at a selected wavelength. The 

uncertainties of the InSb-0 detector are lower because of the better spatial response nonuniformity. 

5.4. Spectral irradiance responsivity 

The spectral irradiance responsivity of the working standard radiometers was determined to 

calibrate test detectors with large spatial response non-uniformity. The response non-uniformity 

of these test detectors can be averaged out if they are calibrated in irradiance measurement mode 

where both the standard and the test irradiance meters are overfilled with a uniform field of 

radiation. 

The spectral irradiance responsivity of the standard meter is equal to the product of the spectral 

power responsivity and the area of the precision aperture in front of the detector. The second 

generation InSb irradiance meters were built and used for two different applications. In the first 

one, the broad-band detector was utilized as a working standard in a short-snout Dewar. In the 
second application, a cold filter with a band-pass from 3.2 μm to 3.6 μm (FWHM) was used in a 

long-snout Dewar to measure the very low irradiance levels in the infrared collimator (mentioned 

in Section 3). This irradiance mode working standard was used to calibrate the infrared 

collimator and it also measured the area of very small apertures (in the aperture wheel of the 

collimator) radiometrically relative to a large (mechanically measured) reference aperture. The 

details of the collimator calibration and its aperture area measurements are beyond the scope of 

this paper. The power levels measured on the collimator were lower than 0.1 mW where the 

detector non-linearity is much less than 1%.2,4 At 106

 V/A gain and 800 °C BB temperature, the 

signal-to-noise ratio of this irradiance meter was 2 x 103 when the smallest collimator aperture 

(0.2 mm diameter) was tested. 

-6

-4

-2

0

-3 -2 -1 0 1 2 3

Response difference [%]

Position [mm]

horizontal

vertical

Fig. 4. Horizontal and vertical response scans of the InSb-1 radiometer. The curves show the response 

differencies relative to the response in the detector center. 

0

0.5

1

1.5

2

2.5

0.8

1.2

1.6

2

2.4

2 2.5 3 3.5 4 4.5 5 5.5

Power responsivity [A/W]

Relative uncertainty [%]

Wavelength [μm]

100%

EQE

InSb-1

InSb-0

Fig. 5. Spectral responsivity curves of the first generation (InSb-0) and second generation (InSb-1) 

radiometers are shown. The responsivities measured at the 4.2 μm absorption band are shown where the 

curves become thinner. The thoretical limit of the responsivity is the 100 % EQE line. The two curves at 

the bottom are the uncertainties (scaled on the right-hand Y axis). 
5.5. External quantum efficiency

The external quantum efficiency is EQE = 1239.48 * s/λ where s is the responsivity and λ is the 

wavelength. Also, EQE = (1-ρ) * IQE where ρ is the reflectance and IQE is the internal quantum 

efficiency equal to the ratio of the number of collected electrons to the number of photons 

absorbed by the detector. The EQE of the second generation InSb detectors was almost twice that 

of the first generation devices. The highest EQE of 75% was calculated between 3.6 μm and 3.7 

μm for the InSb-1 detector. Both radiometer generations had sapphire windows with a 

transmittance of about 90% at 3 μm. The InSb-1 radiometer was equipped with a 1.8 μm cut-on 

(cold) filter. This filter has a transmittance of 90% to 95% for wavelengths longer than 2 μm. 

From the measured (and calculated) EQE and the signal loss caused by the window and the coldfilter, a reflectance of about 10% can be estimated for the InSb-1 detector. The IQE is close to 

unity. The InSb-0 (first generation) radiometer was not filtered. 

6. Uncertainties 

The uncertainties were evaluated and expressed according to the guidelines of the NIST 

Technical Note 129711 and the ANSI/NCSL Z540-2-1997 U.S. Guide to the Expression of 

Uncertainty in Measurement (GUM).12 The modelling of the measurand (the spectral power 

responsivity) and its measurement procedure have been discussed in detail in the NIST Special 

Publication 250-42,8

 where the uncertainty components were evaluated for the spectral 

responsivity determination of the transfer standard cryogenic bolometer. 

In the present example, the power responsivity scale was derived from the cryogenic bolometer to 

the working standard InSb-1 radiometer. The responsivity scale uncertainty of the bolometer 

dominates the uncertainty budget of the InSb working standard. The additional uncertainty 

sources of this scale derivation are summarized in Table 1. The uncertainty components that 

contribute to the overall uncertainty are described below. 

The uncertainty components, caused by the spatial response non-uniformity of the bolometer and 

InSb detector were calculated from spatial response scans as the standard deviation of the 

measured data points. All the utilized data points were located on the plateau of the response 

curves measured along the detector diameters, indicating that the incident beam was not clipped 

by the input optics of the radiometers. Because of the limitations in the vertical moving of the 

bolometer stage, only horizontal scans were made on the bolometer. The standard deviation from 

the horizontal scan represented the spatial response non-uniformity of the bolometer in the 

uncertainty budget. 

The measurement noise was obtained from the standard deviation of the average responsivity. 

The InSb radiometer was substituted for the bolometer at least four times at each wavelength. 

The measurement noise includes the signal changes due to component instabilities (e.g. source 

fluctuations) and wavelength dependent (random) uncertainties of the monochromator. The longterm drift of the source did not produce any additional uncertainty component because the 

detector substitution at each wavelength took care of this problem. Also, the chopper duty-factor 

(open-to-close ratio) related uncertainty components could be neglected because the same 

chopper was used for both the bolometer and the InSb radiometer. 

The frequency instability of the chopper produced an uncertainty component in the frequency 

dependent responsivity corrections. The InSb radiometer responsivity correction was determined 

from the data fits of multiple 3 dB signal roll-off measurements at different photocurrent-to-
voltage gains. The photocurrent-to-voltage gains were measured against a standard current 

source (calibrator). The gain correction uncertainty includes the gain calibration uncertainty and 

the gain instabilities as well. 

Table 1 

 ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

Uncertainties of power responsivity calibration with the working standard InSb-1 radiometer 

outside of the atmospheric and Dewar absorption bands 

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

 Uncertainty (k=1) [%] 

 Uncertainty origin Type A11 Type B 

 Infrared spectral responsivity scale (on the bolometer)8

 0.8 

 Bolometer spatial response non-uniformity 0.24 

 InSb-1 spatial response non-uniformity (horizontal) 0.05 

 InSb-1 spatial response non-uniformity (vertical) 0.36 

 Noise of the bolometer responsivity measurement 0.19 

 Noise of the InSb-1 radiometer responsivity measurement 0.15 

 Responsivity correction of the InSb-1 radiometer to 0 Hz 0.07 

 Bolometer preamplifier gain correction8

 0.18 

 InSb-1 radiometer gain correction 0.07 

 Lockin amplifier gain correction8

 0.12 

 Bolometer responsivity corrections (temperature, bias, 

 3 dB roll-off measurements, and non-linearity) 0.2 

 InSb response non-linearity2,4 0.1 

 Wavelength shift of the monochromator from 2 μm to 3.7 μm 0.3 

 Wavelength shift of the monochromator from 3.7 μm to 5.1 μm 0.1 

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

 Relative combined standard uncertainty from 2 μm to 3.7 μm 1.0 

 Relative combined standard uncertainty from 3.7 μm to 5.1 μm 0.95 

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

Table 2 

 ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ 

Uncertainties of irradiance responsivity calibration with the working standard InSb-1 radiometer 

 ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

 Uncertainty [%] 

 Uncertainty origin Type A Type B 

 Power responsivity of the InSb-1 radiometer 1.00 

 Aperture area measurement of the InSb-1 radiometer 0.075 

 Directional responsivity of the InSb-1 radiometer within f/4 0.18 

 ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

 Relative combined standard uncertainty (k=1) 1.024 

 ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

The uncertainty components originating from the lockin amplifier gain calibrations, the bolometer 

temperature, bias voltage, 3 dB roll-off frequency, and non-linearity corrections were discussed in 

our previous publication.3,8 The uncertainty component caused by the InSb response nonlinearity was taken from previously published results on similar InSb detectors.2,4 
The uncertainty budget was determined for two wavelength ranges because the effect of the 5 nm 

maximum possible wavelength shift of the monochromator caused higher uncertainty between 2 

μm and 3.7 μm as compared to the uncertainty component between 3.7 μm and 5.1 μm. We have 

not specified any responsivity uncertainties between 4.2 μm and 4.3 μm. High accuracy 

measurements should not be done (without purging) within this wavelength band where the 

atmospheric absorption is very high. All the uncertainty components in Table 1 are specified 

outside of the absorption bands. The roughly 1% uncertainty components within the 2.7 μm and 

3.2 μm absorption bands produced peaks in the combined uncertainties in Fig. 5. 

Table 2 is an extension of Table 1 for irradiance responsivity measurements using the same 

working standard (InSb-1) radiometer. The aperture area was calculated from the average of 

several diameter measurements. The diameters were measured with a collimated beam geometry 

on an optical microscope. The aperture is positioned less than 1 mm away from the detector. The 

International Commission on Illumination (CIE) recommended13 directional error f2(ε) was 

calculated from directional (angular) response measurements of the InSb radiometer. The f2(ε) 

was smaller than 0.5% between -7° and 7° which is roughly the angular range of the f/4 incident 

beam. The standard deviation of the directional responses within this angular range was 0.18%. 

This uncertainty component is used for unknown source distribution if the angular range of the 

source is within f/4. 

7. Conclusion 

High electronic and radiometric performance InSb radiometers have been developed, 

characterized, and calibrated to hold the spectral power and irradiance responsivity scales between 

2 μm and 5.1 μm. The relative uncertainty (k=1) of the responsivity scales maintained by the 

working standard radiometers is about 1%. Test infrared radiometers can be calibrated against the 

working standard InSb radiometers in both power and irradiance measurement modes. 

8. References 

1. Nettleton, D.H., Prior, T.R., and Ward, T.H., “Improved Spectral Responsivity Scales at the 

NPL, 400 nm to 20 μm,” Metrologia, Vol. 30, 425-432, 1993. 

2. L-P Boivin, Properties of indium antimonide detectors for use as transfer standards for 

detector calibrations, Appl. Opt. Vol. 37, pp. 1924-1929, 1998. 

3. A. Migdall and G. Eppeldauer, “Realization of an Infrared Spectral Radiant Power Response 

Scale on a Cryogenic Bolometer”, Metrologia, Vol. 35, p. 307-315, 1998. 

4. G.P. Eppeldauer, A.L. Migdall, and L.M. Hanssen, “InSb Working Standard Radiometers,” 

Metrologia, Vol. 35, p. 485-490, 1998. 

5. G. Eppeldauer, A. L. Migdall, and C. L. Cromer, “A cryogenic silicon resistance bolometer 

for use as an infrared transfer standard detector,” in HTD-Vol. 277, pp. 63-67, Thermal 

Phenomena at Molecular and in Cryogenic Infrared Detectors, M. Kaviany, D. A. Kaminski, 

A. Majumdar, P. E. Phelan, M.M. Yovanovich, and Z. M. Zhang, eds. (The American Society 

of Mechanical Engineers, New York), Book No. H00908-1994. 
10

6. G. Eppeldauer, A.L Migdall., T.R. Gentile, and C.L Cromer., “Absolute response calibration 

of a transfer standard cryogenic bolometer,” in Proc. Vol. 2550, Photodetectors and Power 

Meters II, K. Muray and K. J. Kaufmann, eds. SPIE, pp. 36-46, 1995. 

7. Identification of commercial equipment to specify adequately an experimental problem does 

not imply recommendation or endorsement by the National Institute of Standards and 

Technology nor does it imply that the equipment identified is necessarily the best available 

for the purpose. 

8. A.L. Migdall and G.P. Eppeldauer, Spectroradiometric Detector Measurements: Part III - 

Infrared Detectors, NIST Special Publication 250-42, US Government Printing Office, 

Washington, DC, 1998. 

9. G.P. Eppeldauer, Noise-Optimized Silicon Radiometers, J. Res. Natl. Inst. Stand. Technol. 

Vol. 105, pp.209-219, 2000. 

10. T.C. Larason, S.S. Bruce, and A.C. Parr, Spectroradiometric Detector Measurements: Part I -

Ultraviolet Detectors and Part II - Visible and Near-Infrared Detectors, NIST Special 

Publication 250-41, pp. 35, US Government Printing Office, Washington, DC, 1998. 

11. B.N. Taylor and C.E. Kuyatt, Guidelines for Evaluating and Expressing the Uncertainty of 

NIST Measurement Results, National Institute of Standards and Technology, Tech. Note 

1297, US Government Printing Office, Washington, DC, 1994. 

12. ANSI/NCSL Z540-2-1997, American National Standard for Expressing Uncertainty – U.S. 

Guide to the Expression of Uncertainty in Measurement, National Conference of Standards 

Laboratories, Boulder, CO, 1998. 

13. CIE Publ. No. 53 (TC-2.2), Methods of Characterizing the Performance of Radiometers and 

Photometers, Central Bureau of the CIE, A-1033 Vienna, P.O.Box 169, Austria, 1982. 
Spectral responsivity determination of a 

transfer-standard pyroelectric radiometer 

George Eppeldauer, Miklos Racz* and Leonard Hanssen 

Optical Technology Division 

National Institute of Standards and Technology (NIST) 

Gaithersburg, Maryland 20899–8441 

*Guest Researcher at NIST from the Hungarian Academy of Sciences, 

now at Konkoly Observatory, Budapest H-1121, Hungary 

ABSTRACT 

A NIST-developed pyroelectric radiometer was characterized and calibrated to extend the NIST high 

accuracy spectral responsivity scale from the visible range to the ultraviolet (UV) and infrared (IR). The 

transmission of the gold-black coated LiNbO3 pyroelectric material is negligibly small, therefore the 

absorptance, equal to (1-reflectance), is proportional to the responsivity of the detector. The spectral total 

reflectance of the coating was measured with integrating spheres and spectrophotometers to determine the 

relative spectral responsivity from the UV to the IR. The relative spectral responsivity was converted into 

absolute spectral power and irradiance responsivities by measuring the total power in a 442 nm stabilized 

laser beam. The reference device for absolute calibration was a Si trap-detector calibrated against the 

primary standard cryogenic radiometer. The calibrations were repeated with 31 months separation. A 

0.3 % long-term shift in the reflectance was measured between 800 nm and 19 μm. The 28 % reflectance 

at 10.6 μm increased the 0.1 % spatial responsivity non-uniformity in the visible (where the reflectance was 

0.4 %) to 8 %. The spectral power and irradiance responsivity scales of the pyroelectric radiometer have 

been realized between 250 nm and 2.5 μm with a relative standard uncertainty of less than 0.34 % 

(coverage factor k=1). 

Keywords: absolute responsivity, gold-black coating, infrared, irradiance, pyroelectric detector, radiant 

power, radiometer, reflectance, relative response, transfer standard, ultraviolet 

1. INTRODUCTION 

The subject of the present work is to extend the ambient-background detector-based responsivity scale of 

NIST to a wide wavelength range with improved uncertainty. The present NIST responsivity scale 

uncertainty is about 1 %1

 in the 2 μm to 20 μm range [1, 2] and close to 1 % in the 250 nm to 400 nm range 

[3]. The uncertainty from 920 nm to 1.8 μm increases from 0.5 % to 1.8 %, respectively [4]. In the 

reference (silicon) spectral range, between 406 nm and 920 nm, the responsivity scale uncertainty is only 

0.03 % [5]. A new facility is being developed at NIST for Spectral Irradiance and Radiance Responsivity 

Calibrations with Uniform Sources (SIRCUS) [6]. The purpose of this facility is to decrease the 

uncertainty gap between the reference scale and the extended scales. In order to achieve this goal, a group 

of improved performance transfer standard radiometers is being developed. The SIRCUS facility operates 

in the 250 nm to 2500 nm range. This range is determined by the useful reflectance coverage of the 

Spectralon coating of the integrating sphere sources and the spectral coverage of the monitor and working 

standard silicon and extended InGaAs photodiodes. The design and most of the radiometric and electronic 

characterizations of a high performance LiNbO3 pyroelectric radiometer have already been published [7]. 

We describe here the radiometric characterizations and calibrations needed to extend the high accuracy 

responsivity scale to the 250 nm to 2500 nm range. The gold-black reflectance measurements were made 

 

1 All uncertainties discussed in this paper are relative standard uncertainties with a coverage factor of one. 

Property of the United States Government. Not subject to copyright.
between 250 nm and 19 μm. The reflectance measurements were repeated after 31 months to check the 

long-term stability of the transfer standard radiometer and the repeatability of the spectral reflectance 

measurements. Spatial responsivity tests are described at 10.6 μm where the high reflectance of the coating 

increases the spatial non-uniformity of responsivity. For the highest accuracy responsivity scale extension, 

a group of pyroelectric radiometers will be used. Here, the scale extension work is described only for the 

LiNbO3 pyroelectric transfer standard radiometer. 

2. SPECTRAL REFLECTANCE MEASUREMENTS

The transmission of the gold-black coated detector is negligibly small, therefore the absorptance, equal to 

1-reflectance, is proportional to the responsivity of the detector. We measured the spectral near-normal 

(directional-hemispherical) reflectance of the gold-black coated detector to determine the relative spectral 

responsivity. 

The spectral reflectance of the gold-black coated pyroelectric detector had already been measured with a 

modified Perkin-Elmer2

 spectrophotometer between 800 nm and 1.8 μm [7]. Similar measurements were 

made on the same detector with a Cary-5E spectrophotometer between 250 nm and 830 nm. In both cases, 

the spectral reflectance was compared to a white polytetrafluoroethylene (PTFE) reflectance standard. The 

zero reflectance was obtained when a light trap replaced the pyroelectric detector at the sample port of the 

integrating sphere. The integrating sphere collected the diffuse radiation reflected back from the detector 

surface. The monochromatic input beam was directed to the surface of the detector at a 6° angle of 

incidence. The 8 mm diameter detector-aperture was removed during the reflectance measurements to 

avoid beam clipping. The two spectral reflectance curves, measured on the different spectrophotometers, 

are shown in Fig. 1. 

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

200 400 600 800 1000 1200 1400 1600 1800

Reflectance

Wavelength [nm]

Fig. 1. Spectral reflectance of the gold-black coated pyroelectric detector. 

The dashed curve was measured on a Cary-5E spectrophotometer. 

The solid curve was measured on a modified Perkin-Elmer spectrophotometer. 

 

2 Certain commercial equipment, instruments, or materials are identified in this paper to foster understanding. Such 

identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, 

nor does it imply that the materials or equipment are necessariliy the best available for the purpose. 
As the measurement was noisy between 800 nm and 1800 nm, a curve-fit is shown in that range. The 

uncertainty of the reflectance measurements was 0.1 % between 250 nm and 1600 nm and it increased to 

0.23 % at 1800 nm. These measurements were made in September, 1999. 

In order to extend the high accuracy responsivity scale to the infrared (IR) range, the absolute directionalhemispherical reflectance of the LiNbO3 pyroelectric detector was measured between 1 μm and 19 μm. 

The IR reflectance measurements were made on a Fourier Transform (FT) spectrometer in both September 

1999 and April 2002. The April 2002 results are shown in Fig. 2 to illustrate that the reflectance is higher 

than 50 % at 19 μm. A Quartz beam splitter and a tungsten halogen lamp source was used in the FT 

spectrometer for the 1 μm to 3.3 μm wavelength range. A Ge coated KBr beam splitter with a ceramic 

glow-bar source was used for wavelengths longer than 3.3 μm. The uncertainty of the IR reflectance 

measurements ranges from 0.1 % near 0.01 reflectance to 1.5% at 0.5 reflectance. 

0.0

0.1

0.2

0.3

0.4

0.5

4 8 12 16

Reflectance

Wavelength (um)

Fig. 2. IR spectral reflectance of the gold-black coated pyroelectric detector. The beam splitter and the 

source of the FT spectrometer were changed at 3.3 μm. 

3. LONG TERM STABILITY OF SPECTRAL ABSORPTANCE 

The spectral absorptance (1-reflectance) values of the September, 1999 and the April and June 2002 

measurements are summarized in Fig. 3 between 250 nm and 3.5 μm. The measurements were made with 

a large time separation to check the long-term stability of the gold-black coated detector and the 

repeatability of the calibrations. The 1-reflectance curves are shown only up to 3.5 μm to show the 

measured differences on a more magnified scale. The FT spectrometer measurements start at 1 μm. The 

noise in all September 1999 measurements is averaged out. The April 2002 measurements started at 

500 nm to check the changes up to 1.5 μm. The noise at 800 nm increased due to a detector change (from 

photomultiplier tube to PbS detector) in the spectrophotometer. The noise in the FT measurement (April 

2002) at the 1μm region was caused by the poor signal-to-noise ratio. The graph shows a 0.3 % shift in the 

1-reflectance values between the September 1999 and the April 2002 measurements for wavelengths longer 

than 800 nm. The results obtained with the two independent reflectance measurement methods in April 

2002 agreed within 0.1 % in the 1 μm to 1.5 μm range where they overlap. The measured shift at 500 nm 

was negligibly small. In order to check for possible changes in the UV, the reflectance was measured from 

325 nm to 500 nm in June 2002. As the same 0.3 % shift was measured for wavelengths longer than 800 
nm using two different methods, the reason of the shift was the change in the gold-black coated detector. 

The measured change in the 325 nm to 500 nm range was less than 0.1 %.

4. SPATIAL RESPONSIVITY IN THE INFRARED 

In our September 1999 measurements, the reflectance of the gold-black coated LiNbO3 pyroelectric 

detector was less than 1 % between 800 nm and 1800 nm [7]. The spatial response non-uniformity was 

+/- 0.1 % at 633 nm. High reflectance can increase the spatial response non-uniformity resulting in a large 

uncertainty in radiant power measurements where the detector is underfilled by the incident beam. 

In order to determine the useful wavelength range of a responsivity scale extension with the LiNbO3

pyroelectric radiometer, the non-uniformity of the spatial responsivity was measured at a wavelength where 

the reflectance of the gold-black coating was much higher than 1 %. Figure 4 shows the result of a spatial 

responsivity scan at 10.6 μm where the reflectance is about 28 %. The scanning beam diameter was 

0.4 mm. The contour plot shows an 8 % maximum-to-minimum change in the responsivity. The 

reflectance at 633 nm was about 0.4 % in September 1999 [7]. The 28 % reflectance at 10.6 μm is a factor 

of 70 higher. This is the reason that the non-uniformity of the spatial responsivity increased from the 0.1 % 

level to 8%. We can conclude that the increase in the non-uniformity of the spatial responsivity is 

proportional to the increase of the reflectance and the proportionality factor is one. 

0.975

0.980

0.985

0.990

0.995

1.00

400 800 1200 1600 2000 2400 2800 3200

1-Reflectance

Wavelength [nm]

September 1999

April 2002

June 2002

Fig. 3. The absorptance (1-reflectance) versus wavelength of the gold-black coated pyroelectric detector 

measured at two different times using two different measurement setups. 

If we do not improve the absorptance (e.g. by multiple reflections on the detector surface or with coatings 

of lower reflectance in the IR), the upper wavelength limit for high accuracy scale extension will be 

2.5 μm. The reflectance at this wavelength is 1.27 %, about 3 times higher than the 633 nm value. The 

uncertainty component at 2.5 μm, originating from the non-uniformity of the spatial responsivity, will be 

about 0.3%, equal to the 31 months reflectance change measured on the gold-black coated pyroelectric 

detector. 

5. SPECTRAL RESPONSIVITY 

The updated 1-reflectance curve is shown on the left Y axis of Fig. 5. This curve includes the April 2002 

measurement results between 500 nm and 2.5 μm. Since the long-term reflectance change was negligibly 

small between 325 nm and 500 nm, the 250 nm to 500 nm results measured in September 1999, are also 
included in the curve. The small step at 1.5 μm shows the very small difference between the Cary-5E and

the FT reflectance measurements made in April 2002. The power responsivity scale is shown on the right 

Y axis. The absolute tie point is shown with an open triangle at 442 nm. The tie point was obtained from 

radiant power measurement on October 1, 1999 directly after the relative spectral responsivity 

determination. The detector substitution method was used on the SIRCUS facility. Both the py

radiometer and the reference TS07 silicon (reflectance type) trap detector measured the same 23.6 μW total 

power in a collimated (and chopped) HeCd laser beam. The power of the 442 nm beam was controlled to a 

constant value using a laser beam stabilizer. The trap detector was calibrated against the primary standard 

cryogenic radiometer for radiant power responsivity. The 442 nm responsivity of the pyroelectric 

radiometer was 1.010 x 10-7 A/W at 109

 V/A gain and 10.1 Hz chopping frequency. The duty cycle 

chopped radiation was 50 %. 

roelectic 

of the 

0.96

1.03

1.01

0.98

0.98

1.00

0.97

0.96

1.01

1.02 0.97 1.00

1.02

1.04

1.02

1.02

-5 -4 -3 -2 -1 0 1 2 3 4 5

-5

-4

-3

-2

-1

0

1

2

3

4

5

X (mm)

Y (mm)

Fig. 4. Spatial response uniformity contour-plot of the gold-black coated LiNbO3 

he temperature of the pyroelectric detector was monitored by a thermistor. As the temperature coefficient 

 R = f R 

here Rc is the pyroelectric radiometer responsivity at the calibration temperature Tc and f is a correction 

 f = 1 + (0.0015 ΔT) 

here ΔT = Tc - Tm. Tm is the temperature of the detector in a measurement after the responsivity 

given 

pyroelectric radiometer at 10.6 μm. The scanning beam diameter was 0.4 mm. 

T

of the pyroelectric detector responsivity is 0.15 %/°C [7], the responsivity can be corrected for different 

measurements. The corrected responsivity will be: 

m c

w

factor. The f correction factor can be calculated from the temperature coefficient of the detector 

responsivity and the ΔT temperature difference: 

w

calibration. ΔT is determined from thermistor resistance measurements at calibration and then at a 

application. The thermistor was attached to the pyroelectric detector [7] and its resistance was previously 

calibrated versus temperature. 
The pyroelectric radiometer has a 60 Hz roll-off in the responsivity when the highest gain is selected [7]. 

Accordingly, the responsivity at a 10 Hz chopping frequency is not constant. For rotating choppers the 

frequency has to be controlled to a constant value. If the frequency changes, responsivity corrections are

needed to minimize frequency dependent responsivity changes. Better stability was obtained when the 

rotating chopper was substituted by a tuning fork chopper. The tuning fork chopper was tuned to a stable 

10.1 Hz and frequency dependent responsivity corrections were not needed. 

0.972

0.976

0.980

0.984

0.988

0.992

0.996

1.00

0.0984

0.0988

0.0992

0.0996

0.1

0.1004

0.1008

0.1012

500 1000 1500 2000 2500

1-Reflectance

Responsivity [μA/W]

Wavelength [nm]

Y = M0 + M1*x + ... M8*x8 + M9*x9

M0 0.996

M1 5.6222e-06

M2 -4.4275e-09

M3 2.9764e-13

R 0.99934

Fig. 5. The April 2002 spectral power responsivity scale of the LiNbO3 pyroelectric detector. 

he uncertainty of the trap detector responsivity was 0.05 % [6]. The dashed line in Fig. 5 is a third order 

The uncertainty budget of the April 2002 spectral resp vity scale as extended by the LiNbO3

bsolute 

3 % 

or irradiance responsivity measurements, a black-Nickel coated Copper aperture was mounted in front of 

T

polynomial fit to the 1-reflectance curves. The overall responsivity variation of the pyroelectric detector 

was about 1 % between 250 nm and 2.5 μm.

onsi

pyroelectric radiometer is shown in Table 1. The relative combined standard uncertainty of the a

and relative responsivity calibrations is 0.15 %. The non-uniformity of the spatial responsivity was 

wavelength dependent. The largest overall combined uncertainty of 0.34 % was dominated by the 0.

spatial non-uniformity in the responsivity of the pyroelectric detector at 2.5 μm. The overall combined 

uncertainty was 0.18 % in the ultraviolet and 0.25 % between 1 μm and 2 μm. 

F

the pyroelectric detector. The 0.1 mm thick aperture was very close to the detector to minimize unwanted 

signal increase caused by reflections between aperture and detector. The area of the aperture was measured

twice. The average area was 49.962 mm2

 with an uncertainty of 0.036 %. The irradiance responsivity is 

the product of the aperure area and the spectral power responsivity. The irradiance responsivity at the 

442 nm tie point was 5.05 x 10-6 A mm2

/W. The overall combined uncertainties of the irradiance 

responsivity scale realization are similar to the overall combined uncertainties of the radiant power

responsivity scale realization. 
The long-term changes in the extended spectral responsivity scale, maintained by the LiNbO3 pyroelectric 

transfer standard radiometer, are shown in Table 2. The 0.3 % long-term change of the spectral 

responsivity is an uncertainty component that can be separated from the scale realization uncertainties. 

This component can be decreased by more frequent responsivity scale realizations. 

6. FUTURE SCALE EXTENSION TO THE INFRARED 

Our near-future goal is to extend the high accuracy spectral responsivity scale up to 20 μm. The high 

accuracy IR scale is needed for the SIRCUS-IR facility we have started to develop recently. 

One way to keep the dominant uncertainty component, the non-uniformity of the spatial responsivity, small 

is to mount a reflecting dome to the front of the detector. The dome can produce multiple reflections for 

the incident beam resulting in lower reflectance loss and higher signal absorption. The other way to 

improve the spatial uniformity is to make better coatings. Earlier made gold-black coatings, selected for 

low IR reflectance, showed less than 1 % reflectance even at 20 μm [2]. Using one or both of the two 

methods, the uncertainty component caused by the non-uniformity of the spatial responsivity can be 

significantly decreased. 

We have started realizing the high accuracy spectral responsivity scale from 200 nm to 20 μm using three 

pyroelectric transfer standard radiometers. Two LiTaO3 pyroelectric radiometers equipped with reflecting 

domes are being developed in addition to the LiNbO3 pyroelectric radiometer discussed in this paper.

Table 1 

Uncertainty budget of the April 2002 spectral power/irradiance responsivity scales 

Uncertainty factor Type A Type B Combined 

[%] [%] [%] 

Absolute responsivity calibration: 

Trap detector spectral power responsivity 0.05 

Trap detector repeatability 0.04 

Trap current-to-voltage gain 0.04 

Laser beam instability 0.02 

Pyroelectric detector gain 0.04 

 Pyroelectric detector temperature dependent 

response (at 0.1 °C change) 0.015 

Pyroelectric detector frequency dependent response 

 with 0.025 Hz change at 10.1 Hz and 109

 V/A gain 0.07 

Relative responsivity calibration: 

Spectral reflectance measurements 0.1 

Relative combined standard uncertainty 0.15 

Pyroelectric detector non-uniformity of spatial responsivity: 

 250 nm to 1 μm 0.1 0.18 

 1 μm to 2 μm 0.2 0.25 

 2 μm to 2.5 μm 0.3 0.34 

Irradiance responsivity: 

 Aperture area 0.036 

 Multiple reflections between aperture and detector 

 at 2.5 μm (worst case) 0.05 

250 nm to 1 μm 0.19 

 1 μm to 2 μm 0.26 

 2 μm to 2.5 μm 0.34 
Table 2 

Long-term (31 months) responsivity changes 

for wavelengths longer than 800 nm 0.3 % 

from 500 nm to 800 nm 0.1 to 0.3 % 

for wavelengths shorter than 500 nm 0.1 % 

Using three transfer standard devices, individual long term response changes can be minimized by using 

the average responsivity of the group. The dominant uncertainty component of the total uncertainty will 

come from the spectral reflectance measurements. According to our preliminary measurements, the

reflectance with a dome and improved coating can be less than 0.25 % at 19 μm. The small non-uniformity 

of the spatial responsivity, caused by the low reflectance, will result in an uncertainty component of 

less than 0.1 %. At present, the temperature of the LiNbO3 pyroelectric detector is monitored for 

temperature dependent responsivity corrections. The temperature of the LiTaO3 pyroelectric detectors is 

controlled to a constant value. Accordingly, the temperature dependent uncertainty of the responsivity will 

be much smaller than 0.1 %. The signal will be chopped with a tuning-fork chopper to minimize frequency 

dependent responsivity changes. This is an important requirement for high signal-gain selections where the 

signal roll-off of the photocurrent meters is at low (about 60 Hz) frequencies. Our realistic goal is to 

achieve an overall responsivity scale uncertainty of about 0.15 % outside of the 406 nm to 920 nm 

reference range. 

7. CONCLUSIONS 

The NIST high accuracy spectral responsivity scale from the 406 nm to 920 nm reference range was 

extended to a wider range of 250 nm to 2500 nm. The extension was made with a NIST developed high 

performance LiNbO3 pyroelectric transfer standard radiometer. As the transmission of the detector goldblack coating was negligibly small, the absorptance, equal to 1-reflectance, was proportional to the relative 

responsivity of the radiometer. Spectral reflectance measurements were made with an uncertainty of 0.1 %. 

The measurements were made twice, with 31 months separation. During this time, an 0.3 % constant 

reflectance decrease was obtained between 800 nm and 19 μm. The 0.1 % non-uniformity of the spatial 

responsivity at 633 nm, where the reflectance is 0.4 %, increased to 8 % at 10.6 μm where 28 % reflectance 

was measured. The large non-uniformity of the spatial responsivity limited the power responsivity scale 

extension to 2.5 μm. The relative spectral responsivity was converted into spectral power and irradiance 

responsivities by making an absolute tie point at 442 nm, where no long-term reflectance change was 

measured. In contrast to the 0.5 % to 1.8 % uncertainty of the present NIST (extended) responsivity scales, 

the uncertainty of the new wavelength-extended scales was less than 0.34 %. 

As a continuation of the above scale realization work, the high accuracy spectral responsivity scale is being 

extended to 20 μm using two additional NIST developed LiTaO3 pyroelectric radiometers. The two new 

radiometers have improved gold-black coatings and are equipped with reflecting domes to further increase 

absorption and uniformity of spatial responsivity. While the temperature of the LiNbO3 detector was 

monitored, the LiTaO3 detectors are temperature controlled to minimize temperature dependent response 

changes. The group average will be used to decrease the effect of individual response changes. The 

expected uncertainty of the planned responsivity scale extension is about 0.15 % from 200 nm to 20 μm. 

ACKNOWLEDGEMENTS 

The authors thank John Lehman for developing the high performance pyroelectric detectors, Haimei Gong 

for participating in the spatial responsivity characterizations, Edward Early and Simon Kaplan for their 
participation in the spectral reflectance measurements. This work was supported by the U. S. Air Force 

Metrology under contract numbers CCG-461 and CCG-439. 

REFERENCES 

1. Eppeldauer G. and Racz M., Spectral power and irradiance responsivity calibration of InSb workingstandard radiometers, Applied Optics, Vol. 39, No. 31, p. 5739-5744, 2000. 

2. Migdall A. and Eppeldauer G., Realization of an Infrared Spectral Radiant Power Response Scale on a 

Cryogenic Bolometer, Metrologia, Vol. 35, p. 307-315, 1998. 

3. Shaw P-S., Larason T. C., Gupta R, Brown S. W., Vest R. E., and Lykke K. R., The new ultraviolet 

spectral responsivity scale based on cryogenic radiometry at Synchrotron Ultraviolet Radiation Facility III, 

Rev, Sci. Instr., Vol. 72, No. 5, p. 2242-2247, 2001. 

4. Shaw P-S., Larason T. C., Gupta R, Brown S. W., and Lykke K. R., Improved near-infrared spectral 

responsivity scale, J. Res. NIST, Vol. 105, No. 5, p. 689-700, 2000. 

5. Gentile T. R., Houston J. M., and Cromer C. L., Realization of a scale of absolute spectral response using the 

NIST high accuracy cryogenic radiometer, Appl. Opt. Vol. 35, No. 22, p. 4392-4403, 1996. 

6. Brown S. W., Eppeldauer G. P., and Lykke K. R., NIST Facility for Spectral Irradiance and Radiance 

Response Calibrations with a Uniform Source, Metrologia, Vol. 37, p. 579-582, 2000. 

7. Lehman J., Eppeldauer G., Aust J. A., and Racz M., Domain-engineered pyroelectric radiometer, 

Applied Optics, Vol. 38, No. 34, p. 7047-7055, 1999. 
Spectral irradiance responsivity measurements 

between 1 μm and 5 μm 

G. P. Eppeldauer, J. P. Rice, J. Zhang, and K. R. Lykke 

Optical Technology Division 

National Institute of Standards and Technology 

Gaithersburg, Maryland, 20899-8441 

ABSTRACT 

Infrared radiometers for irradiance measurement have been developed at the National Institute of Standards and 

Technology (NIST). These high performance irradiance meters are used to realize and maintain the spectral irradiance 

responsivity scale between 1 μm and 5 μm. They are also working standards that disseminate the infrared irradiance 

responsivity scale to other institutions and facilities. Both design considerations and responsivity scale transfer to the 

irradiance meters are discussed. The radiometers were calibrated for spectral irradiance responsivity on the new NIST 

Infrared Facility for Spectral Irradiance and Radiance Responsivity Calibrations using Uniform Sources (IR-SIRCUS). 

The spectral irradiance responsivity calibrations described are derived from absolute cryogenic radiometers. 

1. INTRODUCTION 

In addition to InGaAs, Ge [1, 2], and InSb [3] working standard radiometers developed earlier, extended-InGaAs (EIGA) 

radiometers have been developed at the National Institute of Standards and Technology (NIST) to fill a gap between 

1.8 μm and 2 μm in the infrared (IR) spectral responsivity scale. The radiometers can measure irradiance from about 

0.8 μm to 5.1 μm. The InGaAs irradiance meter was calibrated earlier [4] against the NIST detector spectral power 

responsivity scale [5] using the raster scan method [6]. The EIGA radiometer has been calibrated against an Electrical 

Substitution Bolometer (ESB) [7] that was calibrated against an electrical substitution type absolute cryogenic 

radiometer (ACR) using silicon trap detectors [8]. The InSb radiometers were calibrated earlier against a cryogenic 

bolometer [9] that was calibrated against the primary standard cryogenic radiometer (HACR) [10-12] of NIST. 

At present, on the Infrared Facility for Spectral Irradiance and Radiance Responsivity Calibrations using Uniform 

Sources (IR-SIRCUS) [13], spectral irradiance responsivity measurements are performed between 1 μm and 5 μm with 

an extended uncertainty (k=2) of 3 % using the above infrared radiometers. The irradiance responsivity scale transfers to 

both the EIGA radiometer and selective InSb radiometers are described below. 

2. DESIGN OF THE EXTENDED-InGaAs RADIOMETER 

The EIGA radiometer can measure irradiance between 1 μm and 2.5 μm. The design of the radiometer head that includes 

the input optics and housing is shown in Fig. 1. The 3 mm diameter photodiode is located in a sealed case. The case has 

a borosilicate window on the front. The window, a flashed opal glass (transmitting) diffuser, and a thin aperture are glued 

together (at the edges) and are plugged into an aluminum holder. There is a thread on the front side of the holder that 

makes it possible to either apply a protecting cap or to screw the whole radiometer head into a flange located on the top 

of the sphere source. The holder and the bottom surface of the photodiode-case are attached to a copper plate that 

delivers the dissipated heat to a heat sink. A thermo-electric (TE) cooler and a thermistor are also located inside of the 

photodiode-case to apply temperature controlled cooling for the photodiode. The leads from the TE cooler and the 

thermistor are connected to a 4-pin connector at the bottom of the aluminum housing. A temperature controller can be 

connected to this connector through a shielded cable. The operating temperature of the photodiode is -20 o

C. The 

photodiode leads are connected to a BNC connector located also on the bottom plate of the housing. The preamplifier 

(discussed below) can be connected to the BNC connector using a short coaxial cable. The housing of the radiometer 

head is electrically shielded. 
71 mm

O 33 mm

cap

holder

Cu plate

photodiode with TE 

cooler and thermistor

diffuser

aperture

heat sink

cylinder

BNC 

connector

4-pin 

connector

Fig. 1. Housing of the extended-InGaAs radiometer head. 

3. ELECTRONIC DESIGN CONSIDERATIONS 

A short-circuit current measuring preamplifier was needed that has a small enough input resistance for the low shunt 

resistance EIGA photodiode. It was also necessary to measure chopped radiation when the irradiance responsivity scale 

was derived from the ESB. The simplified circuit diagram of the photodiode current meter is shown in Fig. 2. 

P

V

OA

C

R

I

P

RS

CJ

Fig. 2. Simplified circuit diagram of the EIGA photodiode preamplifer. 

The photocurrent IP of photodiode P is measured by the current-meter. The current-to-voltage conversion in the current 

meter is realized by an operational amplifier OA that has a feedback impedance Z (parallel connected feedback resistor R

and capacitor C). The OA has a low-frequency (DC) open-loop gain of about A=106

. The OA output voltage V is 

attenuated to its input by A, resulting in a very small voltage drop on photodiode P. The photodiode impedance ZP is the 
parallel connection of its shunt resistance RS and junction capacitance CJ. The input impedance of the current meter will 

be [14]: 

ACj R

CRjA A

R

A

Z Z

ω

ω

+

= + == 1

)1(

1

I (1) 

where ω is the angular frequency. The rewritten form of Eq. (1) shows that the input impedance of the current meter can 

be calculated as the parallel connection of the down-transformed R and the up-transformed C: 

( )

1 1

1

I

1 − −

−

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ ⎟ + ⎠

⎞ ⎜

⎝

⎛ = ACjA

R Z

ω

 (2) 

 

The requirement for short-circuit current measurements is: 

ZI << ZP. (3) 

 

The shunt impedance of the photodiode determines not only the linearity of photocurrent measurements but also the 

voltage gain (amplification) for the input drift and noise of the amplifier [15]. Also, the shunt resistance can dominate the 

uncertainty of the photocurrent-to-voltage conversion [16]: 

1

P 1

1

− + = G

R

I

V (4) 

where G is the loop gain. The photocurrent-to-voltage conversion R, which is the signal gain at zero frequency, will be 

accurate only if G>>1. When chopped radiation is measured, this condition must be achieved for the signal (chopping) 

frequency. 

The loop gain, which is the product of A and β (the feedback attenuation), can be written as [14]: 

i 2

00 1

1

1

1

ωτ

ωτ

ωτ

β j

j

j

AG

+

+

+ = (5) 

where A0 is the 0 Hz (DC) open-loop voltage gain of the OA and β0=RS/(RS+R) is the DC feedback attenuation. The 

inverse feedback attenuation 1/β is equal to the voltage gain for the input noise and drift. If a photodiode with high RS is 

selected, the feedback attenuation β0 will be close to unity, resulting in high G and low voltage gain for noise and drift. 

The feedback resistors R of the OA can change in a wide range, from 1 kΩ to 100 MΩ to measure photocurrent in a 

wide dynamic range. 

 

The shunt resistance of the 3 mm diameter EIGA photodiode is only a few hundred οημ at room temperature. At the 

operating temperature of -20 o

C, we measured 25 kΩ and 40 kΩ shunt resistances for two photodiodes, respectively. The 

junction capacitance was CJ=1.8 nF. CJ will be increased significantly by the parallel connected, up-transformed 

feedback capacitor AC. 

In short-circuit current measurements, when photodiode with low junction capacitance is selected, the measurement time 

constant is determined by the feedback impedance: 

( ) . J RC

A

RACC = +

τ = (6) 
As a design example, in Eq. 5, the differentiating time constant τ can cancel the integrating time constant τ2. This is 

called full frequency compensation. The time constant τ2=RSCJ when R>>RS [14]. In our case, for RS=25 kΩ, τ2=45 μs, 

and for RS=40 kΩ, τ2=72 μs. 

At the maximum gain of R=108 Ω, the input resistance, equal to RI=100 Ω, will result in a non-linearity in the 

photocurrent measurement of 0.4 % for RS=25 kΩ and 0.25 % for RS=40 kΩ. At R=107 Ω, the non-linearity will decrease 

to significantly less than 0.1 %. 

As AC >> CJ for CJ=1.8 nF, a measurement time constant (for full frequency compensation) of τ = RC = 72 μs could be 

obtained at R=108 Ω if C was equal to 0.7 pF. However, it is difficult to achieve such a low parallel capacitance. A 

realistic stray (parallel) capacitance in a well designed circuit layout is about 2 pF. Consequently, only partial frequency 

compensation can be achieved at the highest signal gain of R=108 Ω, which will result in a 3 dB roll-off frequency of 0.8 

kHz. (No external capacitor will be connected parallel to R=108 Ω.) However, at R=107 Ω, the 45 μs (or 72 μs) 

compensating RC time constant can be achieved. C = 4.5 pF will result in a signal 3 dB roll-off frequency of 3.5 kHz. 

After this full compensation, the dominating integrating time constant of G will be τi from the fi=10 Hz roll-off frequency 

of the OA open-loop voltage gain A. This roll-off frequency is very convenient to obtain high G for all R at a chopping 

frequency of about 10 Hz. Usually, R is changed in decade steps to cover a wide dynamic signal range. The parallel C

capacitors can be increased in decade steps (from 5 pF at 107 Ω) with the decade step decrease of R (from 107 Ω) to 

perform frequency compensations for all R. Care should be made at low R selections where the starting condition of 

R>>RS cannot be achieved anymore. At these low gain selections, the full frequency compensations can be achieved only 

when τ2 is correctly calculated from the non-simplified equation [14]. Otherwise, partial frequency compensations will 

be performed that are still adequate to perform high enough G at the signal (chopping) frequency at these signal gain 

selections. 

The OA has to be selected to satisfy the noise, drift, input current, and bandwidth requirements [16]. 

4. IRRADIANCE RESPONSIVITY SCALE TRANSFER TO 2.5 μm 

The reference spectral irradiance responsivity scale from a silicon trap detector that was tied to an ACR was transferred 

to a cryogenically cooled ESB. The ESB operates at liquid helium temperature and uses a chopper [7]. In the open 

position of the chopper, the optical radiation overfills the 5 mm diameter precision aperture of the ESB. This radiation is 

converted into heat on the gold-black-coated silicon bolometer. Through the action of an electronic servo loop, this heat 

is equalized with the electrical heat applied to the same bolometer in the closed position of the chopper. In equilibrium, 

the electrical heat power (output signal) is equal to the radiant power originating from the irradiance (input signal) of the 

overfilled aperture. 

The relative spectral responsivity of the ESB was determined from two spectral measurements. The directionalhemispherical spectral reflectance of the gold black coated bolometer surface was measured with an integrating sphere 

[17]. The absorption of the bolometer, equal to one minus reflectance, is proportional to its responsivity. The spectral 

absorption of the bolometer was multiplied by the spectral transmittance of the ESB dewar window to obtain the overall 

relative spectral responsivity. Three tie points from a silicon trap detector between 738 nm and 820 nm were measured. 

One of these (at 790.4 nm) was used to convert the relative spectral responsivity into absolute spectral irradiance 

responsivity. The other two were used to assess the uncertainty component due to choice of tie point wavelength. Figure 

3 shows the spectral irradiance responsivity of the ESB with the tie point at 790.4 nm. Curve fits were applied to the 

measured relative spectral response data. An 8th order polynomial fit was applied below 1800 nm and a 4th order 

polynomial fit was used above. The broad, smooth variations are caused by the spectral transmittance change of the 

coated KBr window of the ESB dewar. 

For the ESB irradiance measurements, a 15 Hz, 50 % duty-cycle chopper was used to modulate the laser beam 

introduced into an integrating sphere. The sphere exit port was used as a uniform monochromatic irradiance source. 

Both the ESB and the trap detector measured the irradiance from the sphere source. For the trap-detector measurements, 

the chopper was stopped in its open position and the measurements were made in DC mode. The demodulated DC 

output of the ESB and the DC output of the trap-detector were read out by a digital voltmeter. 
0.181

0.182

0.183

0.184

0.185

0.186

0.187

500 1000 1500 2000 2500 3000

Wavelength (nm)

Fig. 3. ESB spectral irradiance responsivity 

The ESB responds to the amplitude of the chopped radiation, which is the DC level that is present when the chopper is 

stopped. Thus, no chopper correction needs to be applied to the ESB output signal. Since the trap-detector was used in 

DC mode, no chopper correction needs to be applied to the trap-detector responsivity either. 

For the tie points, irradiance responsivity measurements of the ESB and trap-detector to the same sphere radiant 

intensity, Io, were made and recorded. The radiant intensity of the sphere is independent of which detector is viewing the 

sphere: 

2

ee

2

tto == dEdEI (7) 

where Ee is the irradiance on the ESB, dt is the separation between source and trap-detector apertures, and de is the 

separation between source and ESB apertures. The irradiance Et at the trap-detector is known from the measured output 

signal Yt, the known responsivity st, the gain Gt, and the aperture area At of the trap detector: 

ttt

t t AsG

Y

E = . (8) 

Combining Eqs. (7) and (8) leads to the measurement equation for the ESB irradiance responsivity: 

2

t

2

e ttt

t

e

e

e e d

d AsG

Y

P

E

P

s == (9) 

where Pe is the ESB output signal (electric power). In practice, se is given in W/Wcm-2, Pe in W (the product of the 

measured V and A of the ESB electrical heater), Ee in W/cm2

, Yt in V, Gt in V/A, st in A/W, At in cm2, de and dt in cm. 

The spectral irradiance responsivity from the ESB was transferred to the EIGA#2 working standard radiometer. The 

irradiance responsivity scale transfer is shown below. 

Both the ESB and the detector-under-test (DUT, EIGA#2 in this case) measured the same radiant intensity from the 

laser-illuminated integrating sphere at the IR-SIRCUS facility. The chopping frequency was again 15 Hz. Similarly to 

Eq. (7): 
2

dd

2

eeo == dEdEI (10) 

where subscript d stands for DUT. 

Earlier, the ESB responsivity was referenced to the amplitude of the chopped radiation. In the present scale transfer, 

both the DUT and the monitor were photodiodes. Since they were chopped during measurements, a chopper correction 

must be applied to reference their values to the amplitude of the chopped radiation. That is for the ESB, 

 (11) = EsP eee

but for the DUT, as read out by a lock-in amplifier, 

d ddd

π

2 = EGsY (12) 

where Yd is the output signal of the DUT (EIGA#2). The pre-factor appears because the lock-in amplifier indicates the 

rms value of the fundamental Fourier sine-wave component [18] of a 50 % duty-cycle square-wave applied to its input. 

Gd is the gain of the DUT current-to-voltage converter. 

Combining Eqs. (10) through (12) leads to the measurement equation for the EIGA#2 irradiance responsivity: 

2

ed

2

d e

e

d

d

2

π

dG

d s PY s = (13) 

Since the same monitor photodiode was used during both the ESB and the DUT output signal measurements, and output 

signal ratios were consistently used at IR-SIRCUS, we use a form of the measurement equation written in terms of 

output signal ratios: 

2

ed

2

d e

m

e

m

d

d 2

π

dG

d s

Y

P

Y

Y

s = (14) 

where Ym represents the monitor output signal. The spectral irradiance responsivity of the EIGA#2 was derived from the 

ESB in the overall wavelength range. 

The spectral irradiance responsivity of the EIGA#2 working standard is shown in Fig. 4. Interpolations were applied 

between the measured data points to obtain a continuous curve. Cubic spline interpolation was applied above 1800 nm 

and smooth-type interpolation was used for the shorter wavelength range (using KaleidaGraph Data Analysis and 

Graphic Presentation [19] software). The effect of the atmospheric absorptions bands on the spectral responsivity of the 

EIGA#2 cannot be seen because the separations dd and de were roughly equal during the responsivity scale transfer. 

At present, there are not enough data points for the overall wavelength range to perform accurate responsivity 

interpolation everywhere. The largest gap is between 1989 nm and 2253 nm where the measurements were switched 

from using the signal output to the idler output of an optical parametric oscillator (OPO) based on a periodically-poled 

lithium niobate (PPLN) crystal. This OPO was pumped by a 1.064 μm quasi-cw (220 MHz, 7 ps) mode-locked 

Nd:YVO4 laser and the wavelength was tuned by changing the grating period and the temperature of the crystal. Also, 

the interpolation is poor around 2.4 μm where the slope of the responsivity change is steep. 
The relative expanded uncertainty (coverage factor k=2) of the ESB spectral irradiance responsivity calibration) is 0.6 %. 

The uncertainty budget that applies only for the irradiance responsivity tie points of the working standard irradiance 

meter EIGA#2 is shown in Table 1. 

0.01

0.02

0.03

0.04

0.05

0.06

0.07

1000 1200 1400 1600 1800 2000 2200 2400 2600

Wavelength [nm]

Fig. 4. Spectral irradiance responsivity of the EIGA#2 working standard. 

The uncertainty of the ESB output signal / monitor output signal dominated the uncertainty budget in Table 1 because of 

the different time constants in the ESB and the monitor-detector. 

Table 1 

Uncertainty budget of the irradiance responsivity tie points 

of the working standard EIGA#2 irradiance meter 

_________________________________________________________________________ 

Uncertainty component Type A Type B 

 [%] [%] 

Absolute responsivity calibration: 

ESB position 0.23 

DUT position 0.3 

ESB irradiance responsivity 0.3 

ESB output signal/Monitor output signal 0.89 

DUT output signal/Monitor output signal 0.37 

DUT lockin amplifier measurement 0.13 

_________________________________________________________________________ 

Relative combined standard uncertainty 1.1 % 

Relative expanded uncertainty with k=2 2.2 % 

5. IRRADIANCE RESPONSIVITY MEASUREMENTS TO 5 μm 

Selective InSb radiometers were calibrated for spectral irradiance responsivity on the IR-SIRCUS as well. The irradiance 

source this time was a 2.5 cm diameter Infragold-LF coated integrating sphere with an exit-port diameter of 6 mm. The 

output beam from the PPLN OPO was tunable between 1466 nm and 4920 nm. The beam was always chopped at 13 Hz 

before the entrance of the sphere source. Two baffles were located between the sphere source and the moving stage 
where the reference and test (selective InSb) radiometers were mounted. The reference detector was the InSb1 irradiance 

meter calibrated earlier against a transfer standard cryogenic bolometer [9] that was calibrated against the HACR. The 

radiometers were placed at ≈1.1 m from the sphere source. The baffles minimized the stray radiation on the detectors. A 

monitor radiometer was mounted in front of the first baffle close to the optical axis but outside of the baffle opening. The 

output voltages from the current-to-voltage converters of the reference, test, and monitor radiometers were measured by 

sine-wave measuring digital lock-in amplifiers. The three lock-in amplifiers were attached to the computer of the IRSIRCUS facility. 

The selective InSb radiometers were calibrated against the InSb1 radiometer using the substitution method described 

above for the EIGA#2 calibration. The difference between this and the above substitution method is that here both the 

reference and test radiometers are measured by the same kind of lock-in amplifier while above only the test radiometer 

(EIGA#2) signal was measured with a lock-in amplifier and the ESB was not. In this substitution, the lock-in gain factors 

are cancelled and the pre-factor (in Eqs. 13 and 14) is not needed in the measurement equation. In all measurements, 

both the test and reference radiometer signals were divided by the signal of the monitor detector. The ratio 

measurements were repeated 20 times at each wavelength to reduce the uncertainty contribution from the noise in the 

detector signals. 

The irradiance responsivity of the test detector is: 

2

rd

2

d

d r dG

dG s YY s r

r

d = (15)

where subscript r stands for reference and subscript d for DUT. 

The irradiance responsivity determination is made at each laser wavelength using this measurement equation. 

The spectral irradiance responsivity curves of the selective InSb radiometers are shown in both linear (left vertical axis) 

and logarithmic (right vertical axis) scales in Figs. 5 to 7. The dominant uncertainty of the spectral responsivity 

determinations originated from the effect of laser intensity noise. The relative expanded uncertainty (k=2) of the InSb 

spectral irradiance responsivities is 3 % at all wavelengths. The uncertainty is determined from the 2.05 % (k=2) 

responsivity uncertainty of the InSb1 reference irradiance meter [9], and additional uncertainty components. The 

additional components are the residuals of the source intensity fluctuations, photocurrent measurement uncertainty, gain 

switching uncertainty, stray radiation of irradiance measurements, length (detector-to-source separation) measurements, 

wavelength measurements, interpolation uncertainties, and background dominated detector noise. 

0

2 104

4 104

6 104

8 104

1 105

1.2 105

1.4 105

100

101

102

103

104

105

4200 4300 4400 4500 4600 4700 4800 4900

lin Y axis

log Y axis

Wavelength [nm]

Fig. 5. Spectral irradiance responsivity of InSb#5 at 2 x 105 V/A gain 
The EIGA#2 was calibrated against the InSb1 reference radiometer at 2.35 μm to compare the above two different 

irradiance responsivity scales (where they overlap). The expanded relative uncertainty of this responsivity determination 

was 3 % (same as for the selective InSb irradiance meters). The responsivity obtained was 2.6 % higher than the 

0.0682 A/(Wcm-2) EIGA#2 responsivity derived from the ESB. This responsivity deviation is in accordance with the 2.2 

% (in Table 1) and 3 % relative expanded uncertainties of the two different EIGA#2 responsivity determinations. 

0

1 105

2 105

3 105

4 105

5 105

6 105

7 105

101

102

103

104

105

106

3000 3200 3400 3600 3800 4000

lin Y axis

log Y axis

Wavelength [nm]

Fig. 6. Spectral irradiance responsivity of InSb#6 at gain 106 V/A 

0 100

5 103

1 104

1.5 104

2 104

10-1

100

101

102

103

104

3400 3600 3800 4000 4200

lin Y axis

log Y axis

Wavelength [nm]

0

Fig. 7. Spectral irradiance responsivity of InSb#7 at gain 2.94 x 104 V/A. 

6. CONCLUSIONS 

The NIST spectral irradiance responsivity scale from the 405 nm to 920 nm wavelength range has been extended to 5 μm 

using improved performance irradiance meters. The transfer standard ESB was calibrated against the ACR through a 

silicon trap detector to convert its relative spectral irradiance responsivity into absolute. The ESB irradiance responsivity 

scale was transferred to the EIGA#2 working standard radiometer. The relative expanded uncertainty (k=2) of the 

irradiance responsivity at the calibration wavelength (tie) points is 2.2 % on the EIGA#2 radiometer. Spectrally selective 

InSb irradiance meters were calibrated with 3 % uncertainty (k=2) against the reference InSb1-new irradiance meter that 
has a traceable responsivity to the HACR. The different responsivity scales were compared at 2.35 μm by calibrating the 

EIGA#2 against both the ESB and the InSb1-new radiometer. The two scales were different by 2.6 % at 2.35 μm where 

they overlap. Work is being continued to extend the spectral irradiance responsivity scale of the IR-SIRCUS facility 

further in the infrared with decreased uncertainty. 

REFERENCES 

1. Eppeldauer, G., Electronic characteristics of Ge and InGaAs radiometers. SPIE proceedings, 1997. 3061-97: p. 833-

838. 

2. Eppeldauer, G., Near Infrared Radiometer Standards. SPIE proceedings, 1996. 2815: p. 42-54. 

3. Eppeldauer, G.P., Migdall, A.L., and Hanssen, L.M., InSb Working Standard Radiometers. Metrologia, 1998. 35: p. 

485-490. 

4. Eppeldauer, G.P., Racz, M., and Larason, T.C., Optical characterization of diffuser-input standard irradiance 

meters. SPIE Proc., 1998. 3573: p. 220-224. 

5. Larason, T.C., Bruce, S.S., and Parr, A.C., Spectroradiometric detector measurements. NIST Special Publication, 

1998. 250-41. 

6. Cromer, C.L., et al., The NIST detector-based luminous intensity scale. J. Res. NIST, 1996. 101(2): p. 109-132. 

7. Rice, J.P., An electrically substituted bolometer as a transfer-standard detector. Metrologia, 2000. 37: p. 433-436. 

8. Eppeldauer, G.P. and Lynch, D.C., Opto-mechanical and electronic design of a tunnel-trap Si- radiometer. J. Res. 

NIST, 2000. 105(6): p. 813-828. 

9. Eppeldauer, G.P. and Racz, M., Spectral Power and irradiance responsivity calibration of InSb working standard 

radiometers. Appl. Opt., 2000. 39(31): p. 5739-5744. 

10. Gentile, T.R., et al., National Institute of Standards and Technology high-accuracy cryogenic radiometer. Applied 

Optics, 1996. 35(7): p. 1056-1068. 

11. Gentile, T.R., et al., Calibration of a pyroelectric detector at 10.6 μm with the NIST High-Accuracy Cryogenic 

Radiometer. Applied Optics, 1997. 36: p. 3614-3621. 

12. Migdall, A.L., and G.P. Eppeldauer, Realization of an IR spectral radiant power response scale on a cryogenic 

radiometer. Metrologia, 1998. 35: p. 307-315. 

13. Lykke, K.R., et al., Development of a monochromatic, uniform source facility for calibration of radiance and 

irradiance detectors from 0.2 to 12 microm. Metrologia, 1998. 35: p. 479-484. 

14. Eppeldauer, G., Chopped Radiation Measurement With Large Area Si Photodiodes. J. Res. NIST, 1998. 103: p. 153-

162. 

15. Eppeldauer, G. and Hardis, J.E., Fourteen-decade photocurrent measurements with large-area silicon photodiodes 

at room temperature. Applied Optics, 1991. 30: p. 3091-3099. 

16. Eppeldauer, G., Noise-optimized silicon radiometers. J. Res. NIST, 2000. 105(2): p. 209-219. 

17. Eppeldauer, G.P., Racz, M., and Hanssen, L.M., Spectral responsivity determination of a transfer-standard 

pyroelectric radiometer. SPIE Proceedings, 2002. 4818: p. 118-126. 

18. Model SR830 DSP Lock-In Amplifier, Manual, Rev. 1.4. Stanford Research Systems, Inc., 1995. 

19. Disclaimer, The mention of certain commercial products in this paper is for information purposes only and does not 

constitute an endorsement of the product by the authors or their institutions. 
Development and calibration of pyroelectric radiometer standards 

at NIST 

G. P. Eppeldauer, J. Zeng, and L. M. Hanssen 

Optical Technology Division 

National Institute of Standards and Technology 

Gaithersburg, Maryland 20899 

ABSTRACT 

The reference spectral power responsivity scale of NIST is being extended from the silicon range to the infrared (IR) 

using pyroelectric radiometers. Two transfer standard pyroelectric radiometers have been developed at NIST. The main 

design consideration was to obtain only a minimal increase in the measurement uncertainty during the responsivity scale 

extension. Domain engineered LiNbO3 and regular LiTaO3 pyroelectric detectors were used in the two radiometers. 

Both detectors are gold-black coated and temperature controlled. Reflecting domes are attached to the radiometer inputs 

to decrease the reflectance loss and to improve the spatial uniformity of responsivity in the infrared. Four commercial 

pyroelectric detectors have been added to the group and used as working standards. The relative spectral responsivity of 

all pyroelectric detectors was determined from spectral reflectance measurements. The radiant power responsivity tie 

points were derived from Si trap and single element detectors traceable to the NIST reference responsivity scale. The 

pyroelectric radiometers have been characterized for frequency and temperature dependent responsivity, noise, spatial 

non-uniformity of responsivity, angular responsivity, and linearity. The expanded (relative) uncertainty of the spectral 

power responsivity calibrations ranged between 0.5 % and 1.2 % (k=2) within the 1 μm to 19 μm range. 

1. INTRODUCTION 

Infrared detector standards are being developed for the 2 to 2.5 μm [1], the 3 to 5 μm [2], [3], and the 8 to 12 μm [4] 

atmospheric windows where the absorption lines will not affect the uncertainty of the responsivity measurements. The 

present work describes the development of pyroelectric transfer standard radiometers and also the use of commercially 

available pyroelectric detectors. 

The pyroelectric transfer standard radiometers were primarily developed to extend the reference radiant power 

responsivity scale from the end of the silicon wavelength range at 1 μm to the 8 to 12 μm range (and beyond) with the 

lowest possible measurement uncertainty. It was shown earlier that gold-black coated domain engineered LiNbO3

pyroelectric detectors can be applied for responsivity measurements with about 0.1 % (k=1) responsivity uncertainty in 

the near infrared range [5]. As increased reflectance in the longer wavelength infrared results in increased nonuniformity of the spatial responsivity [1], reflecting domes are mounted at the inputs to minimize reflection losses [6], 

[7]. The commercial pyroelectric detectors are used as working standard radiometers to propagate the NIST infrared 

responsivity scale to different applications.

2. RADIOMETER DESIGN 

The radiometers were designed and selected with optimum radiometric and electronic characteristics to minimize the 

increase in the uncertainty of spectral responsivity associated with transfer calibrations. 

2.1. Transfer standard radiometers 

The two transfer standard radiometers contain 1-cm diameter pyroelectric detector elements with gold-black coatings 

used to convert optical power into temperature change and then into current. In Radiometer #2, a domain-engineered 

LiNbO3 detector and in Radiometer #1, a regular LiTaO3 detector without domain engineering were used [5]. Each 

detector was extended to a radiometer. As it is shown in Fig. 1, the detector-case is attached to a thermoelectric (TE) 

cooler/heater and a thermistor, mounted inside of the detector case, is used as a temperature sensor. Using a temperature 
controller, the temperature of the detector is controlled to a constant value slightly above room temperature. The gold 

coated reflecting dome has a hemisphere shape, with an internal diameter of 33 mm. It is mounted above the 20o

 tilted 

pyroelectric detector. The dome has a 4 mm diameter opening at the optical axis. The figure shows how the specular 

components from a parallel incident radiation at the two ends of the input beam diameter are reflected back to the active 

area of the detector. A current-to-voltage converter with multiple signal-gain selections is mounted in an Aluminum 

box. The box is attached to the radiometer Aluminum housing using a connector. The overall housing of the radiometer 

is electrically shielded to minimize 60 Hz pickup. A photo of the radiometer is shown in Fig. 2. 

4 mm diameter

opening

33 mm diameter

gold-coated dome

Incident radiation

Fig. 1. Input scheme of the transfer standard pyroelectric radiometer. 

Fig. 2. Photo of the transfer standard pyroelectric radiometer 

(the top cover is removed) 
2.2. Working standard radiometers 

Four commercial pyroelectric detectors are used as working standards. These working standards propagate the NIST 

infrared responsivity scale to different field applications. All four detectors are mounted in a housing where the detector 

temperature is monitored. The preamplifier is located inside the detector can where a fixed 10 GΩ feedback resistor is 

connected to an operational amplifier to convert the detector current into an output voltage. The detectors are coated 

with a black paint to convert optical radiation changes into temperature changes. 

3. RADIOMETER CHARACTERIZATION 

A set of characterizations were performed on the radiometers to establish the uncertainties associated with the 

radiometer’s responsivity during both calibration and the calibration-transfer to other radiometers. The frequency- and 

temperature-dependent responsivity, signal-gain stability, and noise characteristics were measured in the Ambient 

Infrared Detector Characterization Facility. The Infrared Detector Evaluation Facility (IDEF) was used for measurement 

of the spatial non-uniformity of responsivity, linearity, angular responsivity, absolute responsivity, stability, and 

repeatability. The Infrared Total Integrated Scatter Instrument (ITIS) was used to measure the reflectance at laser 

wavelengths. The Fourier Transform Infrared Spectrophotometry Facility (FTIS) was used to measure the spectral 

reflectance of the coated detectors to determine the relative spectral responsivity. 

3.1. Characterization of the transfer standard radiometers 

The detector-dome combination acts as a trap to provide near unity absorptance across the entire wavelength range of 

use. Accordingly, the spatial uniformity of responsivity at long wavelengths is significantly improved over the bare 

detector case. The spatial scan results obtained for Radiometers #1 and #2 at 10.6 μm are shown in Fig. 3. The size of 

the scanning spot was 0.2 mm. The maximum-to-minimum spatial non-uniformity of responsivity is less than 0.6 % 

within a 1.5 mm diameter center area of both radiometers. Without the reflecting dome, the spatial non-uniformity of 

responsivity was found to be 10 % to 15 % at 10.6 μm. 

1.000

0.997

0.995

0.990

0.981

0.990 0.995

0.992

0.993

0.997

0.997

0.998

0.998

0.996

0.998

0.998

0.999

0.999

0.993

0.993

0.988

0.984

0.998

0.992

0.997 0.997

0.998 0.999

0.982

0.978

0.990

0.986

0.990

0.984

0.992

0.990

0.992

0.992

0.996 0.994

0.992

0.988

0.990

0.994

0.994

0.994

0.994

0.996

0.996

0.996

0.996 0.996

0.996

0.998 0.996

-2 -1 0 1 2

-2

-1

0

1

2

X (mm)

Y (mm)

0.994

0.991

0.994

0.993

0.985

0.983

0.988

0.996

0.993

0.991

0.990

0.989

0.992

0.990

0.997

0.996

0.994

0.983

0.988

0.989

0.990

0.992

0.994

0.993

0.996 0.998

0.989

0.988

0.987

0.990

0.984

0.994

0.997

0.995

0.995

0.994

0.993

0.993

0.993

0.995

0.995

0.995

0.997

0.997

0.997

0.998

0.997

0.996

0.997

0.996

0.994

0.994

0.995

0.993

0.994

0.996

0.997

0.998

0.999

0.999

0.998 0.999

0.994

0.996

0.998

0.997

0.996

-2 -1 0 1 2

-2

-1

0

1

2

X (mm)

Y (mm)

Fig. 3. Spatial (normalized) uniformity of responsivity of the dome-equipped transfer standard 

pyroelectric Radiometers #1 (left plot) and #2 (right plot) at 10.6 μm. 
The noise equivalent power (NEP) is one of the most important characteristics of pyroelectric radiometers that are used 

to measure 1 μW signal levels from monochromators. Therefore, the noise characteristics of the two transfer standard 

radiometers were tested. Fig. 4 shows the measured output total noise of the domain engineered Radiometer (#2) on the 

left Y axis. The 1/f noise of the operational amplifier is the dominating noise up to a gain of 106

 V/A. At higher gain 

levels the resistor (parallel connected detector resistance and feedback resistance) noise dominates the output noise of 

the radiometer. The background produced photocurrent and its noise are negligibly small because of the very low 

responsivity (output photocurrent per input radiant power) of the pyroelectric detector (about six orders of magnitude 

lower than that of silicon photodiodes). This means that pyroelectric detectors do not operate in background limited 

condition as most of the high responsivity infrared detectors do. Because of the very low detector responsivity, the 

signal power to be measured has to be very high. While radiant power levels of 1 pW with a signal-to-noise (S/N) ratio 

of 100 or higher can be measured with silicon photodiodes, the radiant power for pyroelectric detectors must be about 

six orders of magnitude higher to get similar photocurrents and S/N ratios. The noise equivalent current (NEC) is 

calculated as the ratio of the output total noise voltage to the signal gain. The NEC is shown on the right Y axis. The 

noise measurements were made both in the dark and at 1.5 pA signal current originating from the chopped signal of a 

ceramic glower. The chopping frequency was 10.5 Hz and the lock-in time constant was 1 s. Each data point was 

obtained as the standard deviation of the mean from 20 measurements. The same output total noise voltage (as in Fig. 4) 

was measured for both cases with a relative measurement uncertainty of 25 % (k=1). The NEC at a signal gain of 109

V/A is 6.5 fA. An NEP of 20 nW can be calculated as the ratio of the 6.5 μV output total noise (at 109

 V/A) to the 326 

V/W responsivity of this radiometer at 1.32 μm and a 1 s lock-in time constant. The radiometer responsivity was 

measured by substitution against a Ge detector standard in a measurement of total power in the beam from a 1.32 μm 

diode laser. The 1 s time constant corresponds to a frequency bandwidth of 0.16 Hz. The NEP expressed for a 1 Hz 

electrical bandwidth is: 

NEP = 20 nW x (1/0.16)1/2 = 50 nW/Hz1/2. 

10-8

10-7

10-6

10-5

10-14

10-13

10-12

104 105 106 107 108 109

Signal gain [V/A]

Fig. 4. Noise characteristics of the domain engineered LiNbO3 pyroelectric Radiometer #2. 

The change of the NEP at a signal-gain of 109

 V/A versus lock-in time constant is shown in Fig. 5 for the regular 

LiTaO3 Radiometer #1. The graph shows that the NEP decreases from 13 nW at a 1 s lock-in time constant to 3 nW at a 

10 s time constant. The large decrease in the NEP was obtained because of the 766 V/W responsivity of Radiometer #1 

at a gain of 109 V/A, which is more than two times higher than that of the domain engineered Radiometer #2 of 326 

V/W. (The pyroelectric coefficient of LiNbO3 is smaller than that of LiTaO3 and the domain engineered detector is 

about four times thicker than the regular LiTaO3.) 
The frequency dependent responsivity of the radiometers was measured at a gain of 109 V/A. The measured 3 dB upper 

roll-off frequency was 76 Hz for both transfer standards. This frequency was determined by the 2.1 pF stray capacitance 

connected in parallel with the 1 GΩ feedback resistor. In order to have an operating point on the plateau of the 

frequency dependent responsivity curve, the feedback resistor cannot be increased to a higher value than 109 Ω. In this 

case, chopping frequency of about 10 Hz can be used. Fig. 4 shows that the NEC (and hence the NEP) will decrease if 

the feedback resistor can be further increased. A feedback resistor of 10 GΩ could be used if the stray capacitance was 

decreased by an order of magnitude. In this case, sub 10 nW NEPs could be achieved with a 1 s lock-in time constant. 

0

1 10-8

2 10-8

3 10-8

4 10-8

0 2 4 6 810

Lock-in time constant [s]

Fig. 5. NEP of the regular LiTaO3 pyroelectric Radiometer #1 at a signal-gain of 109

 V/A versus lock-in time constant. 

For the two domed pyroelectric transfer standards, the results of the spatial non-uniformity of responsivity 

measurements together with the reflectance measurement results obtained on the ITIS and FTIS facilities are 

summarized in Table 1. The FTIS measurement provides the spectral dependence of the reflectance, whereas the ITIS 

measurement provides a more accurate (absolute reflectance) result, at a single wavelength. The table shows that 0.1 % 

to 0.2 % reflectance levels were measured on the domed detectors at 10.6 μm with the two different methods. The FTIR 

reflectance measurement indicated no wavelength dependence (leading to the spectrally flat responsivity seen in Fig. 

10). The low reflectance of the domed detector in the infrared range results in the low (0.5 % to 0.6 %) spatial nonuniformity of responsivity at 10.6 μm (as can also be seen in Fig. 3) for both domed detectors. 

Table 1. Experimental results of spatial non-uniformity of responsivity and reflectance measurements 

of the regular pyroelectric Radiometer #1 and the domain engineered pyroelectric Radiometer #2 at 10.6 μm 

Transfer standard 

pyroelectric 

radiometers 

Spatial 

non-uniformity 

of responsivity 

Spectral reflectance 

(from FTIS) 

Reflectance 

(from ITIS) 

#1 Bare 15% (max-min) 16% — 

#1 w/Dome < 0.6% — 0.18% 

#2 Bare — 7% — 

#2 w/Dome < 0.5% 0.1% 0.15% 
To obtain the detector element absorptance, we also need to include loss sources other than reflectance: absorption by 

the dome of the detector reflected radiation, and radiation absorbed outside of the detector. We assume that the goldcoated dome reflectance is 98.5 ± 0.5 %. Ray-tracing results indicate that the radiation absorbed outside of the detector 

is < 0.05% and < 0.02 %, for Radiometers #1 and #2, respectively. Using these measurement results, the absorptance at 

10.6 μm is 99.6% and 99.8%, for Radiometers #1 and #2, respectively. 

3.2. Characterization of the working standard radiometers 

All four working standard radiometers have been fully characterized to operate them under application conditions so 

that the measurement uncertainty in use will not be significantly higher than when calibrated. The characterizations help 

the users to determine the optimum spot size of the incident beam, chopping frequency, and temperature dependent 

responsivity corrections for different applications. 

The radiometers were tested for frequency dependent responsivity at the 1010 V/A (fixed) signal-gain. They measured 

the radiation from a ceramic glower from chopper frequencies ranging between 4.5 Hz and 200 Hz. The curve-fit to the 

measured data is shown for one of the test radiometers in Fig. 6. The fit equation is: 

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ ⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

= 2

3

0

2

2

0

2

4

0

1

1 1

1

m

M

m

M

m

M

my

where y is the signal gain (signal output / signal input), M0 is the frequency, m1 is the magnitude (amplitude) of the DC 

output voltage, m4 is a roll-on frequency produced by a differentiating time constant, m2 and m3 are roll-off frequencies 

resulting from integrating time constants. The graph shows that the responsivity roll-on originating from m4 of the black 

paint can cancel the responsivity roll-off produced by m2 of the current-to-voltage converter. The result is a 109 Hz 

upper roll-off frequency originating from the remaining m3 time constant produced by the paint coating. 

20

30

40

50

60

10 100

Frequency (Hz)

curve fit

y = m1*sqrt(1+(M0/m4)^ 2)/sq...

Value Error

m1 51.909 0.10293

m2 16.382 2.4324

m3 109.48 0.74746

m4 15.814 2.3317

Chisq 0.30304 NA

R 0.99988 NA

Fig. 6. Frequency dependent responsivity of a working standard pyroelectric radiometer 

 at a signal (current) gain of 1010 V/A.
The spatial non-uniformity of responsivity was measured at 10.6 μm. The results in Fig. 7 show that the detector has a 

roughly 1 % spatial variation of responsivity in the center area which makes it possible to use it in radiant power 

measurement mode (where the detector is underfilled by the incident radiation) with low uncertainty. The incident 

radiation should avoid the detector corners, where the responsivity is highly non-uniform because of the contacts. 

0.997 1.005

0.981

1.001

0.989

0.981

0.981

0.981

0.989

1.001

1.005

1.005

1.001

0.993

0.989

1.001

0.997

1.005

1.005

1.001

1.005 1.009

1.005

1.005

1.005

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1.005

1.005 0.997

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1.001

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1.001

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1.001

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1.005

1.001 1.001

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0.997

0.993

0.993 0.997

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1.005

1.001

1.001 0.993

1.001

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0.989

1.017 1.017

1.017

1.017

1.017

1.017

1.017

1.017

1.017

1.017

1.017

1.017

1.017 1.017 1.017

1.017

1.017

1.017

1.017

1.017 1.017

1.017

1.017

1.017

1.009

-2 -1 0 1 2

-2

-1

0

1

2

X (mm)

Y (mm)

Fig. 7. Spatial non-uniformity of responsivity of one of the paint coated pyroelectric detectors at 10.6 μm. 

The responsivity is highly non-uniform at the corners because of the contacts. 

In order to determine the correct responsivity of the radiometers for all future applications, the temperature coefficient 

of responsivity (the relative responsivity change versus temperature) was measured for all four working standard 

radiometers. The radiometers were located in a temperature controlled box and measured the stable broad-band 

radiation from a tungsten lamp (located outside of the box) at different detector (box) temperatures. The slope of the 

output voltages versus temperature data points (from a linear fit) was divided by the output voltage at the predicted 

temperature reading of the future absolute responsivity calibration. A 0.19 %/o

C temperature coefficient of responsivity 

was obtained for three detectors and 0.26 %/o

C was obtained for one detector. The relative expanded uncertainty of 

these measurements was 20 % (k=2). 

The noise floor of the working standard radiometers was measured in the dark at a chopping frequency of 10.5 Hz, with 

a lock-in integrating time constant of 2 s. The standard deviation was calculated from 32 data points. The calculated 

noise equivalent photocurrent ranged between 2 fA and 4 fA. With a 10-6 A/W nominal responsivity at 10.6 μm, a noise 

equivalent power (NEP) of 2 to 4 nW was obtained for the working standard radiometers using the 2 s time constant. 

The angular responsivity of the test detectors was measured to obtain quantitative information about responsivity 

changes when the incident radiation geometry is varied. This enables corrections to be made for any specific geometry, 

such as for the converging beam from a monochromator. The 10.6 μm laser beam, in both s and then p polarization 

states, was focused to the working standard radiometers with a biconvex lens. The working standard radiometers were 

rotated about the detector center (coincident with the input beam). The working standard radiometer output signal was 
divided by the signal of the monitor detector. The ratios were recorded versus angle of rotation. Fig. 8 shows the angular 

response for one of the working standard radiometers at 10.6 μm. The angular response change for the average s and p

polarizations was less than 0.5 % within a +/- 15° angular range. 

A radiometer should have constant radiant power responsivity when the power level of the incident radiation changes. 

The working standard radiometers were measured from the maximum allowed radiant power level down to the low end 

limit, determined by the signal-to-noise ratio at the test radiometer output. 

9.7

9.8

9.9

10

10.1

10.2

10.3

10.4

-30 -20 -10 0 10 20 30

S

P

Angle [ o ]

Fig. 8. The angular response of the working standard Radiometer P8 at 10.6 μm. 

The response linearity of two working standard radiometers was measured using a collimated beam from a CO2 laser 

(tuned to 10.6 μm). The linearity measurement results are shown for both working standard radiometers in Fig. 9. The 

beam power was adjusted to different power levels at which measurements were made with the same filter, moved in 

and out of the beam and the ratio or filter transmittance calculated. A constant transmittance (which is proportional to 

the responsivity) indicates the linearity of the detector response versus incident radiant power. The beam power was 

changed using ND filters and a polarizer attenuator. The maximum power with the filter out of the laser beam was 

3 mW (shown in Fig. 9 with the large open circle). The results show that the working standard radiometers had linear 

response (constant responsivity) within a power range larger than three orders of magnitude. The small signal-to-noise 

ratios limited the linearity tests to a minimum incident power of about 0.1 μW. 
0.01

0.1

1

0.01 0.1 1 10 100 1000 10000

P9570

P9532

Sample Power (μW)

Fig. 9. Linearity measurement results of two working standard radiometers at 10.6 μm. 

4. CALIBRATION OF PYROELECTRIC RADIOMETERS 

The spectral power responsivities of the transfer and working standard pyroelectric radiometers were determined using 

the same calibration facilities and similar procedures. 

The facility for Spectral Irradiance and Radiance Responsivity Calibrations using Uniform Sources (SIRCUS) made it 

possible to improve the uncertainty of monochromator-based spectral radiant power responsivity measurements and to 

extend the calibrations from power mode to irradiance [2] and radiance measurement modes [8]. The high beam power 

and stability of the tunable IR lasers of the SIRCUS facility makes it possible to calibrate a wide range of IR detectors 

and radiometers for spectral power, irradiance, and radiance responsivity. 

After determination of the relative spectral responsivities using the ITIS and the FTIS facility results, radiant power 

responsivity tie points were made at a few wavelengths using the IDEF facility to convert the relative spectral 

responsivities into absolute. The tie points have been derived recently from a Si-trap detector and earlier from a single 

element Ge photodiode, both traceable to the NIST reference responsivity scale [9]. During the calibration of the first 

two working standard radiometers, more tie points have been derived from an earlier developed LiNbO3 pyroelectric 

radiometer standard [5] and also from a single element LiTaO3 pyroelectric transfer detector (PD2) calibrated against 

the primary standard cryogenic radiometer at 10.6 μm [10]. 

The responsivity tie points were determined using the detector substitution method. The standard detector, having power 

responsivity sS, is placed into the laser beam, with its output current yS measured. A test detector is then placed into the 

same beam, with its output current yT measured. The power responsivity of the test detector is then given by 

s

s

T

T s

y

y

s ⋅=

The signals yS and yT are corrected for the drift of the source intensity by using the monitor detector signal. All 

measurements were performed at an ambient temperature of 25 °C ± 1 °C. 
4.1. Transfer standard radiometer responsivities 

The spectral power responsivity of the transfer standard pyroelectric Radiometer #2 at a signal gain of 109 V/A is shown 

as an example in Fig. 10 between 1 μm and 18 μm. The relative spectral responsivity function was determined from 

spectral reflectance measurements on the FTIR. The noise at the short wavelength end of each scan was caused by the 

small signal-to-noise ratios. The responsivity tie points are shown with open squares and a dot in the center. The 

absorptances at 10.6 μm (see Section 3.1) were used to determine the 10.6 μm tie point relative to the 785 nm reference 

tie point. The relative expanded (k=2) uncertainties are shown with error bars. The uncertainty of the 785 nm tie point 

propagated to 10.6 μm together with additional uncertainty components, shown in Table 2, increased the relative 

expanded uncertainty from 0.46 % to 0.58 % (k=2). This is the dominating uncertainty component for the overall 

spectral power responsivity function of the pyroelectric transfer standard Radiometer #2. 

4.2. Working standard radiometer responsivities 

As the working standard radiometers propagate the NIST detector responsivity scales to field applications, the increase 

in the responsivity uncertainty during the scale transfer has to be minimized. For the first two radiometers, a redundant 

responsivity scale transfer was developed to obtain low and reliable uncertainty of spectral power responsivity. 

The initial redundant responsivity scale transfer was made prior to the final calibration of the transfer standard 

Radiometers #1 and #2, when the Si-trap detector was not available for a low uncertainty tie point at the short 

wavelength end. The calibration results of the first two working standard pyroelectric radiometers are shown in Fig. 11. 

The plot shows the FTIS and ITIS determined relative spectral responsivity curves and the (absolute) power 

320

322

324

326

328

330

0 5 10 15

Wavelength (μm)

Fig. 10. Spectral power responsivity of the pyroelectric transfer standard Radiometer #2 at 109

 V/A. 
8500

9000

9500

10000

10500

11000

0 5 10 15 20

9570 Mid IR

9532#2 Mid IR

9570 Near IR

9532#2 Near IR

Pyroelectric

Ge

LiTaO3

LiNbO3

Wavelength (μm)

9570

9532#2

Fig. 11. Spectral power responsivities of the previously calibrated working standard 

Radiometers 9570 and 9532#2 at 1010 V/A signal gains.

responsivity (tie) points with error bars (corresponding to the expanded uncertainties) obtained from laser measurements 

at 1.32 μm and 10.6 μm. At 1.32 μm the working standard pyroelectric radiometers were compared to both Ge and 

pyroelectric (LiNbO3) transfer standard radiometers. At 10.6 μm the same working standard radiometers were compared 

to three transfer standard radiometers (pyroelectric LiTaO3, LiNbO3, and another LiTaO3). The spectral curves are 

“tied” to the 1.32 μm and 10.6 μm responsivity points: i.e. they fall within the error bars at the overlap. The error bars 

represent the expanded uncertainties. For the 1 μm to 19 μm spectral range, this was 2.7% (k = 2). 

The other two working standard pyroelectric radiometers have been calibrated recently. These radiometers have tie 

points against a Si-trap detector (at 785 nm) and the transfer standard Radiometers #1 and #2 at 10.6 μm. The spectral 

power responsivity of the pyroelectric working standard Radiometer P8 is shown as an example in Fig. 12. Its 10.6 μm 

tie point was derived from the transfer standard Radiometer #2 using the detector substitution method. The responsivity 

is given in V/W at a signal-gain of 1010 V/A, where the voltage was derived from the DC (un-chopped) responsivity of 

the Si-trap detector. The combined relative expanded uncertainties, that include the relative uncertainty of the spectral 

reflectance measurements of about 0.3 % (k=2), are also shown with error bars in Fig. 12. 
10000

9500

9000

8500

Fig. 12. Spectral power responsivity of the pyroelectric 

working standard Radiometer P8 at a signal-gain of 1010 V/A. 

In applications, where these pyroelectric radiometers are used as working standards, the incident beam power at a given 

wavelength can be calculated from the reading of the lock-in amplifier (attached to the output of the working standard 

radiometer) divided by the responsivity at the given wavelength. This beam power will be measured by the test devices 

in a given application. 

The uncertainty budget of the spectral power responsivity determination (as an example) for the working standard 

Radiometer P8 is included in Table 2 at both 785 nm and 10.6 μm. The relative expanded uncertainty of the working 

standard Radiometer P8 is 0.6 % (k=2) at the 785 nm and 0.8 % (k=2) at the 10.6 μm tie points. As the uncertainties of 

the new responsivity tie points were improved, the combined uncertainties of the two newer working standards are 

about three times lower than the uncertainties of the first two working standards discussed above. 

Table 2. Uncertainty budget as an example for the transfer standard pyroelectric Radiometer #2 

and the working standard pyroelectric Radiometer P8 at 785 nm and 10.6 μm.

Uncertainty component, Transfer Standard Radiometer #2 Working Std. Radiometer P8 

Type 785 nm 10.6 μm 785 nm 10.6 μm 

Si-trap detector, B 0.20% 0.23% 0.20% 0.30% 

Signal variations, A 0.09% 0.05% 0.04% 0.10% 

Spatial non-uniformity, B 0.06% 0.09% 0.20% 0.20% 

Angular (0-8o) resp. change, B 0.10% 0.10% 0.10% 0.10% 

Temperature changes, B 0.02% 0.02% 0.02% 0.02% 

Lock-in measurements, B 0.10% 0.10% 0.10% 0.10% 

TIS and ray-trace, B 0.08% 

Relative combined std. uncertainty 0.23% 0.29% 0.3% 0.4% 

Relative expanded uncertainty 

(k=2) 0.46% 0.58% 0.6% 0.8% 

0 4 8 12 16

Wavelength (μm)
5. CONCLUSIONS 

Two transfer standard pyroelectric radiometers have been developed at NIST. As a result of the enhanced absorption 

from the addition of a reflecting dome above the detector, the Radiometers #1 and #2 have approximately constant 

radiant power responsivities with less than a variation of 0.4 % and 0.2 %, respectively, between 1 μm and 11 μm, and 

estimated to be approximately 0.5% for Radiometer #2 out to 18 μm. Additional radiometers with the same design, 

given knowledge of the bare detector reflectance at longer wavelengths, will not require spectral calibration. One 

responsivity tie point with low uncertainty is enough to perform the radiometer calibration for the above wavelength 

range. Four commercial pyroelectric detectors were also calibrated for spectral power responsivity. These radiometers 

are used as working standards in field applications. They have structured spectral responsivities due to the paint coating. 

Therefore, spectral reflectance measurements are needed to determine their relative spectral responsivities. A Si tunnel 

trap detector with a 0.2 % relative expanded uncertainty (k=2) was the reference radiometer for both the transfer and the 

working standard pyroelectric radiometer calibrations. 

The domed transfer standard pyroelectric radiometers were used to give the 10.6 μm responsivity tie point for the 

second set of working standard pyroelectric radiometers with a relative expanded uncertainty of about 0.6 % (k=2). The 

combined relative expanded uncertainties of the recently calibrated working standard pyroelectric radiometers were 

about 1 % (k=2) between 1 μm and 18 μm. 

6. ACKNOWLEDGEMENT 

The authors thank John Lehman for developing the high performance pyroelectric detectors used in the transfer standard 

radiometers described in this paper. 

REFERENCES 

1. Eppeldauer, G.P., Racz, M., and Hanssen, L.M., Spectral responsivity determination of a transfer-standard 

pyroelectric radiometer. SPIE Proceedings, 2002. 4818: p. 118-126. 

2. Eppeldauer, G.P., et al., Spectral irradiance responsivity measurements between 1 μm and 5 μm. SPIE 

proceedings, 2004. 5543(Society of Photo-Optical Instrumentation Engineers): p. 248-257. 

3. Eppeldauer, G.P. and Racz, M., Spectral Power and irradiance responsivity calibration of InSb working 

standard radiometers. Appl. Opt., 2000. 39(31): p. 5739-5744. 

4. Gong, H., Hanssen, L.M., and Eppeldauer, G.P., Spatial and angular responsivity measurements of 

photoconductive HgCdTe LWIR radiometers. Metrologia, 2004. 41: p. 161-166. 

5. Lehman, J., et al., Domain-engineered pyroelectric radiometer. Appl. Opt., 1999. 38(34): p. 7047-7055. 

6. Day, G.W., Hamilton, A., and Pyatt, K.W., Spectral reference detector for the visible to 12- micrometer 

region; convenient, spectrally flat. Appl. Opt., 1976. 15(7): p. 1865-1868. 

7. Fox, N.P., Prior, T.R., and Theocharous, E., Radiometric calibration of infrared detectors and thermal imaging 

systems. SPIE Proceedings, 1995. 2474: p. 229-237. 

8. Eppeldauer, G.P., et al., Realization of a spectral radiance responsivity scale with a laser-based source and Si 

radiance meters. Metrologia, 2000. 37: p. 531-534. 

9. Larason, T.C., Bruce, S.S., and Parr, A.C. Spectroradiometric detector measurements. NIST Special 

Publication, 1998. 250-41. 

10. Gentile, T.R., et al., Calibration of a pyroelectric detector at 10.6 μm with the NIST High-Accuracy Cryogenic 

Radiometer. Appl. Opt., 1997. 36: p. 3614-3621. 
Extension of the NIST infrared spectral responsivity scale to routine 

monochromator-based calibrations using improved-NEP pyroelectric detectors 

G. P. Eppeldauer, J. Zeng, H. W. Yoon, B. Wilthan, T. C. Larason, and L. M. Hanssen 

National Institute of Standards and Technology 

Gaithersburg, Maryland USA 

Abstract 

Routine NIST spectral responsivity calibrations are needed for the infrared range. Low 

NEP pyroelectric radiometers have been developed for traditional monochromator 

applications to extend the responsivity scale to the infrared. After NEP tests, the best 

pyroelectric detectors were converted to transfer-standard radiometers. The relative 

spectral responsivities were determined from spectral reflectance measurements of the 

organic black detector-coatings. The absolute tie points were measured against a domed 

pyroelectric radiometer standard and a sphere-input extended-InGaAs transfer standard 

radiometer. A single grating monochromator has been adapted to the calibration facility 

and used to characterize and calibrate infrared detectors. 

1. Introduction 

Since responsivity calibrations at the National Institute of Standards and Technology 

(NIST) Spectral Irradiance and Radiance Responsivity Calibrations using Uniform 

Sources (SIRCUS) [1] facility are slow and expensive, a revisit of the traditional 

monochromator source applications was necessary. However, the noise-equivalent-power 

(NEP) of traditionally used pyroelectric detectors is too high for wide-wavelength-range 

measurements at the outputs of regular monochromators. Also, application of low NEP 

cryogenic bolometers is complicated, slow, and expensive [2]. Instead, improved NEP 

pyroelectric detectors with 5 mm detector-diameter have been developed to obtain high 

signal-to-noise ratios (SNR) at the output of regular monochromators [3]. The low-NEP 

pyroelectric detectors were extended to user friendly transfer standard radiometers that 

can extend the responsivity scale to the long-wave IR with low measurement uncertainty. 

Though the improved NEPs are about one order of magnitude lower than that of 

traditional pyroelectric detectors, they are still high enough not to obtain any measurable 

signal contribution from the background radiation and the stray light of the 

monochromator. Traditionally used InSb, HgCdTe, and other IR detectors can be 

calibrated with low responsivity-uncertainty against the new pyroelectric transfer 

standard in the 0.3 μW to ~1 μW output beam of traditional monochromators. While the 

calibrations are performed in this limited power (signal) range, the traditionally used 

(very low-NEP) IR detectors (such as quantum detectors) will extend the spectral 

responsivity calibrations to low signal levels. 

2. Transfer standard pyroelectric radiometer 

For spectral responsivity scale extension and monochromator use, eight, low-NEP 

pyroelectric hybrid detectors have been characterized and selected. They were built from 
100 μm thick LiTaO3 crystals and utilized a frequency compensation method [3]. The 

5 mm diameter active area of the detectors was coated with organic black paint. The paint 

introduced a differentiating time-constant that cancelled the large integrating time 

constant of the photocurrent-to-voltage converter (attached to the pyroelectric detector) 

[3]. The paint also introduced an integrating time-constant which is much smaller than 

the original (cancelled) integrating time-constant. As a result, the upper 3 dB roll-off 

frequency could be extended by a factor of five (to about 100 Hz) at a signal-gain of 

1010 V/A which is an order of magnitude higher than the maximum signal-gain without 

this frequency compensation. Most of the tested pyroelectric detectors were extended to 

radiometers where the temperature of the detectors was monitored. One pyroelectric 

detector was extended to a radiometer where the detector temperature is stabilized at 

26 o

C using thermoelectric heating/cooling. The picture of this transfer standard 

radiometer head is shown in Fig. 1. 

Fig. 1. A temperature-controlled pyroelectric transfer-standard radiometer head. 

3. Tests of the pyroelectric transfer standard radiometer 

The output beam-power of a single-grating monochromator together with the output 

signal-to-noise ratio (SNR) of the pyroelectric transfer-standard radiometer was tested to 

evaluate the achievable responsivity uncertainties. The arrangement of the 

monochromator-based setup is shown in Fig. 2. 

An alignment laser, a blackbody source for single beam operation, a ceramic glower, and 

a tungsten-halogen lamp can be alternately selected with a rotating mirror. The selected 

beam is imaged to the entrance slit of the monochromator though order sorting filters. 

The total power in the output beam of the monochromator is measured by the reference 

and test detector using the detector substitution method. 

The output beam-power of the monochromator changed between 0.3 μW and 1.6 μW 

within the 900 nm to 2600 nm wavelength interval of a grating blazed at 1.25 μm. The 

standard deviation changed between 0.2 % and 0.4 % between 1000 nm and 2500 nm. 

This is equivalent to a signal-to-noise ratio (SNR) between 500 and 250 in the output 

signal of the radiometer [3]. This is the radiant power range where traditionally used InSb, 

MCT and other IR detectors can be calibrated against the pyroelectric transfer standard. 
Fig. 2. Monochromator based detector responsivity calibrator. 

For the best pyroelectric detectors, less than 4 nW/Hz1/2 NEPs were measured which is an 

order of magnitude smaller than the NEP of our earlier developed (traditional) 

pyroelectric detector standard [4]. The NEPs of the eight tested pyroelectric radiometers 

ranged between 3 nW/Hz1/2 and 10 nW/Hz1/2 [3]. The test results of the temperature 

controlled transfer-standard pyroelectric radiometer are shown in Table 1. The NEP was 

calculated as the ratio of the standard deviation (noise) of the output voltage (from twenty 

data points) to the radiometer responsivity. The responsivity value includes the 1010 V/A 

gain of the current meter attached to the pyroelectric detector. A 785 nm responsivity tie 

point was made against a silicon trap detector and a 10.6 μm tie point was derived from 

our previously developed and calibrated dome-input pyroelectric radiometer [4]. These 

tie point derivations were made at a chopping frequency of 10.5 Hz. The frequency 

dependent responsivity of the pyroelectric transfer standard has been measured to 

determine the upper 3 dB roll-off frequency and to apply responsivity corrections for 

different signal frequencies in different applications. The result of the frequency 

dependent responsivity measurement for the transfer standard is shown in Fig. 3. A three 

time-constant curve fit [4] was applied to the measured data after normalizing the data at 

low frequencies. The 3 dB upper roll-off frequency is about 100 Hz, a decade higher than 

the suggested chopping frequency. 

Table 1. 

Test results of the transfer standard pyroelectric radiometer. 

Standard deviation in dark 9.4 x 10-6 V 

NEP (with 1 s time constant) 4.7 nW 

3 dB upper roll-off frequency 100 Hz 

Responsivity, 785 nm, 10.5 Hz 5059 V/W 

Responsivity, 10.6 μm, 10.5 Hz 4995 V/W 

Optical Table

Detectors

Mirror

Single Grating Monochromator

X-Y Translation Stages

Order Sorting 

Filter Wheel

Wavelength 

Drive Motor

Absolute 

Encoder

Chopper

Mirror & 

Rotation Stage 

Blackbody

Glow Bar

QuartzHalogen 

Lamp

Alignment 

Laser
0.4

0.5

0.6

0.7

0.8

0.9

1

1 10 100 1000

Frequency (Hz)

y = m1*sqrt(1+(M0/m4)^ 2)/sq...

Value Error

m1 0.99645 0.0012236

m2 120.29 0.53737

m3 21.598 1.0632

m4 23.354 1.1756

Chisq 0.0002483 NA

R 0.99993 NA

Fig. 3. Frequency dependent responsivity of the pyroelectric transfer standard. 

4. Calibration of the pyroelectric transfer standard radiometer 

The spectral reflectance of the organic black coated transfer standard detector was 

measured on the NIST FTIR Spectrometer Facility. The spectral reflectance of this paintcoated detector is structured versus wavelength. The relative spectral responsivity of the 

detector was determined first. The spectral reflectance measurement results are shown in 

Fig. 4. The reflectance varied from 3.5 % to 5.5 % between 1.5 μm and 14.5 μm. The 

expanded uncertainty (k=2) of the spectral reflectance measurements is shown in the 

same graph. This reflectance uncertainty includes the noise and the signal loss due to the 

detector can. The loss is a systematic uncertainty component which will have a minimal 

contribution to the responsivity uncertainty budget since an absolute tie point to the 

relative spectral reflectance curve will take care of this problem. Since the responsivity is 

proportional to 1-reflectance, the expanded responsivity uncertainty component from the 

relative spectral reflectance is 0.5 % (k=2) between 2.5 μm and 13 μm. 

The 10.6 μm tie point was derived from the previously developed domed pyroelectric 

radiometer [4]. The expanded uncertainty of the 10.6 μm tie points is 0.8 % (k=2). 

The monochromator-based tie point was made against a sphere-input extended-InGaAs 

(EIGA) radiometer. The EIGA radiometer was calibrated against an electrical substitution 

cryogenic radiometer using the detector substitution method [5]. Both radiometers 

measured the same radiant power from intensity stabilized tunable lasers. Since the laser 

power levels were high, the EIGA radiometer was operated in a DC signal measurement 

mode. The calibrations were made between 1 μm and 2.5 μm with an expanded 

uncertainty of 0.4 % (k=2). The tie point at the monochromator-based facility was at 
1790 nm. This tie point calibration was made at 0.5 μW radiant power output-radiation of 

the monochromator. The other (longer wavelength) tie points from the monochromatorbased spectral measurements were not used because of the smaller signal-to-noise ratios. 

The radiation was chopped with 12 Hz and the radiometer (both reference and test) 

output signals were measured by a sine-wave measuring lock-in amplifier. This power 

level was selected to avoid non-linearity errors in the calibrations of the pyroelectric 

detectors. 

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

2 4 6 8 10 12 14

Wavelength [μm]

Expanded uncertainty

Absolute reflectance

Fig. 4. Spectral reflectance of the pyroelectric transfer standard detector. 

Before the tie point calibration, the frequency dependent responsivity of the EIGA 

sphere-detector was measured. Also, the signal attenuation of the pyroelectric transfer 

standard was checked between 12 Hz and 10.5 Hz. The signal attenuation of the EIGA 

sphere-radiometer was 0.3 % over-compensated by the increased signal responsivity of 

the pyroelectric radiometer at 10.5 Hz (compared to 12 Hz) where the spectral 

responsivities are reported. The 0.3 % (k=2) over compensation has been corrected and 

this uncertainty component is not included in the overall uncertainty budget. The reading 

of the sine-wave measuring lock-in amplifier was multiplied by 2.221 to obtain the 

correct responsivity value for the tie point. From three repeats of the absolute tie-point 

measurements of the pyroelectric transfer standard, an expanded measurement 

uncertainty of 0.5 % (k=2) was obtained. This uncertainty component is noise dominated. 

Figure 5 shows the measured spatial uniformities of the pyroelectric transfer standard at 

two different wavelengths. The roughly 2 % maximum-to-minimum non-uniformity in 

the center-area at 785 nm increased by about 50 % at 10.6 μm. The increase in the spatial 

non-uniformity is associated with the ~50 % higher reflectance at 10.6 μm. According to 
Fig. 5, the uncertainty component that originates from the spatial non-uniformity of 

responsivity is wavelength dependent. If the detector center-area is used and the incident 

beam diameter is between 1 mm and 2 mm and positioned into the detector center, the 

spatial non-uniformity uncertainty component can be decreased to 0.5 % (k=2). 

-3

-2

-1

0

1

2

3

Y (mm)

-3 -2 -1 0 1 2 3

X (mm)

0.97

0.99

1.01

Fig. 5. Spatial uniformity plots of the transfer standard at 785 nm and 10.6 μm. 

The responsivity uncertainty budget of the pyroelectric transfer standard radiometer at 

10.5 Hz signal frequency from 2.5 μm to 13 μm is shown in Table 2. The expanded 

uncertainty at 2 μm is 1.3 % (k=2) because of the increased noise in the spectral 

reflectance measurements. Because of the same reason, the expanded uncertainty at 

14 μm increased to 1.2 % (k=2). 

The spectral radiant power responsivity of the pyroelectric transfer standard radiometer is 

shown in Fig. 6. In addition to the 10.6 μm tie point, the tie point of the sphere-input 

EIGA radiometer is also shown in Fig. 6. The individual error bars represent the 

expanded uncertainties (k=2) of the tie points. The sphere-EIGA related error bar (full 

square) illustrates the overall expanded uncertainty summarized in Table 2. 

5. Spectral responsivity propagation from the pyroelectric transfer standard 

The scale from the transfer-standard pyroelectric radiometer can be transferred to other 

infrared test detectors using the detector substitution method. The substitution is 

performed in the 0.3 μW to 1.6 μW radiant power range using a detector-stage at the 

output of the single monochromator in Fig. 2. The monochromator has four gratings to 

continuously cover the spectral range to 24 μm. The total-power in the output beam of 

the monochromator is measured by under-filling both the reference and the test 

detector(s). A stable 1000 Co

 blackbody source is imaged to the entrance slit of the 

monochromator to make wide consecutive wavelength-scans for both the test and the 

reference (transfer standard) detectors. The measurements also can be performed in twobeam mode where the signal of the test or reference detector is simultaneously divided by 

the signal from a monitor detector. 

-2.0

-1.0

0.0

1.0

2.0

Y (mm)

-2.0

-1.0

0.0

1.0

2.0

X (mm)

0.9900

1.0100

1.0300
4950

5000

5050

5100

5150

5200

5250

0 2 4 6 8 10 12 14 16

Relative responsivity

Responsivity vs dome-pyro

Responsivity vs sphere-EIGA

Wavelength (μm)

Fig. 6. Spectral responsivity of the pyroelectric transfer standard radiometer. 

Traditional IR detectors, such as InSb and MCT detectors can be calibrated against the 

pyroelectric transfer standard to extend the radiant power range to low signal levels. All 

infrared responsivity measurements on the monochromator-based facility are performed 

in AC mode using individual lock-in amplifiers for the reference, test, and monitor 

detectors. 

Table 2. Uncertainty budget (k=2) for the spectral responsivity of the 

pyroelectric transfer standard at 10.5 Hz from 2.5 μm to 13 μm. 

Uncertainty factor Type Uncertainty 

(k=2) [%] 

Tie point absolute responsivity calibration:

 Sphere-EIGA radiometer responsivity A 0.4 

 Pyroelectric radiometer gain B 0.04 

 Pyroelectric temperature dependence B 0.04 

 Pyroelectric radiometer frequency dependence B 0.08 

 Pyroelectric spatial non-uniformity of responsivity B 0.5 

 Pyroelectric noise dominated repeatability B 0.5 

Combined expanded uncertainty 0.82 

Relative responsivity calibration:

 Spectral reflectance measurement A 0.5 

Overall expanded uncertainty 0.96 
6. Conclusions 

Traditional pyroelectric detectors need high incident radiant power, such as stabilized 

tunable lasers to obtain high signal-to-noise ratios for low uncertainty measurements. The 

laser-used spectral responsivity measurements are time consuming and expensive. 

Development of low-NEP pyroelectric radiometers was needed to use traditional 

monochromators for routine spectral responsivity calibrations in the infrared. 

Characterizations and calibration of a recently developed low-NEP pyroelectric transfer 

standard radiometer is described in detail. This transfer standard can be used at radiant 

power levels higher than 0.3 μW to obtain 1 % (k=2) responsivity uncertainties. It is 

operated in a limited power range (to a couple of μW) to avoid non-linearity errors in the 

pyroelectric detector. Traditional InSb, HgCdTe, and other very low-NEP infrared 

detectors can be calibrated against the pyroelectric transfer standard at the 

monochromator output to extend the spectral responsivities to sub pW radiant power 

levels. The new monochromator based responsivity scale can be used to 14 μm. 

References 

1. S. W. Brown, G. P. Eppeldauer, and K. R. Lykke, Facility for Spectral Irradiance and 

Radiance Responsivity Calibrations using Uniform Sources, Applied Optics, Vol. 45, No. 

32, p. 8218-8237, 2006. 

2. G. Eppeldauer, A. L. Migdall, and C. L. Cromer, A cryogenic silicon resistance 

bolometer for use as an infrared transfer standard detector, 6th AIAA/ASME 

Thermophysics and Heat Transfer Conference, June 1994, Colorado Springs, CO. Proc. 

HTD-Vol. 277, Thermal Phenomena at Molecular and in Cryogenic Infrared Detectors, p. 

63-67 (Book No. H00908), 1994. 

3. G. P. Eppeldauer, J. Zeng, and H. W. Yoon, Low-NEP pyroelectric radiometer 

standards, SPIE Proc. Vol. 6940, pp. 694036-1 to 694036-8, 2008. 

4. G. P. Eppeldauer, J. Zeng, and L. M. Hanssen, Development and calibration of 

pyroelectric radiometer standards at NIST, SPIE Proc. Vol. 6201, pp. 620119-1 to 

620119-12, 2006. 

5. G. P. Eppeldauer and H. W. Yoon, Short wave infrared radiometers design and 

characterizations, SPIE Proc. Vol. 6542, pp. 65420O-1 to 65420O-9, 2007. 
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RESPONSIVITY CALIBRATION METHODS FOR 365 nm IRRADIANCE METERS 

T. C. Larason, S. W. Brown, G. P. Eppeldauer, and K. R. Lykke 

National Institute of Standards and Technology1

Gaithersburg, MD 20899-8441, USA 

Key Words: detector, irradiance, photodiode, radiometer, spectral responsivity, and ultraviolet 

Abstract

Two detector-based responsivity calibration methods have been compared at the National Institute of Standards and 

Technology (NIST) for ultraviolet (UV) irradiance meters in the 365 nm spectral region. Both methods are based on an 

electrical substitution High Accuracy Cryogenic Radiometer (HACR), but utilize different facilities and transfer 

standards. One facility is a monochromator-based, spectral power responsivity measuring system utilizing an aperture 

scanning method, while the second is a tunable laser and integrating sphere source system using a light-trapping silicon 

transfer detector with a known aperture area. The first reported comparison of these two fundamentally different 

methods agreed to 1 % to 2 % near the peak and long wavelength side of the bandpass curves which is comparable to 

their expanded (k = 2) uncertainties. 

I. INTRODUCTION 

UV irradiance meters have a broad range of industrial applications from semiconductor manufacturing 

(photolithography) to nondestructive testing to curing inks and coatings used in high volume printing. Increasing 

industrial application of UV irradiance measurements has led to a steady increase in the number of calibration requests 

to NIST for UV irradiance meters, particularly those used to measure 365 nm radiation. The measured signal from a 

given irradiance meter is the integral of the source distribution and the meter spectral responsivity, 

i = E(λ) ⋅ S(λ)⋅ dλ

λ

∫ (1) 

where i is the signal, E(λ) is the spectral irradiance from the source measured and S(λ) is the spectral irradiance 

responsivity of the meter. Knowledge of the spectral irradiance responsivity of a meter is critical for high accuracy 

measurements of sources with different spectral power distributions. This is especially critical if more than one model 

of irradiance meter (i.e., different responsivities) is used in the measurement chain. 

NIST currently has two facilities for measuring the spectral responsivity of UV irradiance meters: the Ultraviolet 

Spectral Comparator Facility (UV SCF) [1] and the facility for Spectral Irradiance and Radiance Responsivity 

Calibrations with Uniform Sources (SIRCUS) [2]. Diagrams of these facilities are shown in Figures 1 and 2, 

respectively. The irradiance scale of each facility is based on the High Accuracy Cryogenic Radiometer (HACR), the 

NIST primary standard cryogenic radiometer. While similar methods have been reported elsewhere [3, 4] this is the 

first direct comparison of these two fundamentally different techniques. 

A number of 365 nm irradiance meters with different optical diffusers and spectral responsivities were measured in both 

NIST facilities and their responsivities compared to verify the irradiance calibration uncertainties of the UV SCF and to 

refine the SIRCUS irradiance calibration procedures. The results of this intercomparison are shown here for two 

representative irradiance meters. One irradiance meter, designated IM #1, was a commercial device with an 

approximately 50 nm bandpass (FWHM). The second, IM #2, was a NIST designed transfer standard with an 

approximately 25 nm bandpass (FWHM). 

 

1

 Optical Technology Division, Physics Laboratory, Technology Administration, U.S. Department of Commerce. Official contribution of the National 

Institute of Standards and Technology, not subject to copyright in the United States. 
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Detector

Carousel

Light Tight Enclosure

Monitor

Detector

Sources

Baffle

Alig

n

ment L

aser

Scanning 

Carriage

W

a

velen

gth

Drive

Shutter

OrderSorting

Filter

Beam Splitter

Double Grating 

Monochromator

UV WS

Figure 1. Ultraviolet Spectral Comparator Facility (UV SCF) Diagram. The irradiance meter-under-test is mounted on 

the scanning carriage. Spectral responsivity comparison is accomplished by rotating the detector carousel to place one 

of the UV working standards (WS) into the beam. The order-sorting filter removes 2nd order light beyond 400 nm. 

Figure 2. Spectral Irradiance and Radiance Responsivity Calibrations with Uniform Sources (SIRCUS) Diagram. The 

irradiance meter calibration is performed by direct substitution with the irradiance transfer standard. 

II. UV SCF MEASUREMENTS 

The first facility, the UV SCF, is a monochromator-based system developed in the early 1990s to measure the absolute 

spectral responsivity and uniformity of photodetectors in the 200 nm to 500 nm spectral region. The principal 

component is a computer controlled 1/4 m focal length, f/5, double grating monochromator with a 3 nm bandpass. A 

variety of sources (typically an argon arc) can be selected using a computer controlled turning mirror to align the source 

with the spherical mirror that focuses the light onto the monochromator's entrance slit. The argon arc and 

monochromator operate as a tunable monochromatic source. The typical entrance and exit slits are circular 1.5 mm 

apertures. A shutter is located just after the exit slit. Inside a light tight box, a rotary stage is used to place an irradiance 

meter or silicon working standard at the focal plane. The exit aperture is imaged onto the detectors resulting in an oval 

beam of axis diameters 2.0 mm and 2.5 mm. The beam was centered on, and underfilled the irradiance meter apertures 

and working standard detectors. A pair of orthogonal linear positioning stages translates the irradiance meters for both 
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alignment to the optical axis and scanning for uniformity measurements. The stages’ travel range is 50 mm with a 

manufacturer-specified resolution of 0.1 μm and an accuracy of 0.25 μm per 25 mm. Each detector is mounted to allow 

its position to be adjusted along the optical axis for focusing. A gimbal mount allows for the rotation and tilt of each 

detector to be adjusted for perpendicular alignment to the optical axis. The output current of each detector is converted 

to a voltage by a transimpedance amplifier and measured by a digital voltmeter. A beam splitter directs approximately 

10 % of the beam to a silicon monitor photodiode. Simultaneously measuring the monitor and detector signals 

compensates for any source fluctuations. 

The absolute spectral power responsivity of the irradiance meters was determined from 300 nm to 400 nm in 1 nm 

increments by direct substitution comparisons to the silicon photodiode working standards. The effective aperture area 

of each irradiance meter was determined by scanning the monochromator output beam over the irradiance meter’s 

entrance aperture in 0.2 mm increments to simulate a uniform irradiance. This method has been used by NIST since 

1991 [5]. It has been shown [6] that the effective aperture area is the ratio of the total signal, i, summed over the 

scanned area (total irradiance responsivity) to the product of the total beam power, Φ [W], and the average spectral 

power responsivity, s(λ), within the active area of the aperture, 

A = ∑i(x, y)ΔxΔy

Φ ⋅s(λ) (2) 

where Δx and Δy are the small steps taken to completely overscan the aperture. The spectral irradiance responsivity 

was the product of the effective aperture area and the spectral power responsivity [7]. 

The aperture scanning method can be applied to irradiance meters with non-uniform spatial responsivities. Figure 3 

shows the different spatial responsivity uniformities of the two irradiance meters. The large differences are due to 

different input geometries and diffuser materials. The data are from the UV SCF aperture scans at 0.2 mm steps. 

The expanded uncertainty for the UV SCF measurements varies with wavelength, is a minimum at the peak 

responsivity, and increases at other wavelengths due primarily to wavelength uncertainties and the decreasing signal-tonoise ratio. The expanded uncertainty (k = 2) for both irradiance meters at 365 nm was ≈ 2 %. The uncertainties 

increased in regions of low responsivity to ≈ 10 %. These higher uncertainties do not contribute significantly to the 

overall measurement uncertainty of broadband sources. 

(a)

-4

-2

0

2

4

y [mm]

-4

-2

0

2

4

x [mm]

0.2

0.4

0.6

0.8

1.0

1.2

Relative Responsivity

(b)

-2.50

-1.25

0.00

1.25

2.50

y [mm]

-2.50

-1.25

0.00

1.25

2.50

x [mm]

0.00

0.25

0.50

0.75

1.00

Relative Responsivity

Figure 3. Surface (3D) plot of typical 365 nm detectors having different input geometries and diffuser materials. 

Figure 3a shows Irradiance Meter #1 and Figure 3b is Irradiance Meter #2. 

III. SIRCUS MEASUREMENTS 

Recently a second facility, the SIRCUS, has been developed. The SIRCUS employs a variety of tunable lasers 

(Ti:Sapphire and dye lasers) at both fundamental and frequency doubled wavelengths to cover the spectral range from 

275 nm to 1000 nm. The output of the laser was sent through an intensity stabilizer and a portion into a wavemeter. 

From the intensity stabilizer, the beam was sent through a lens into a 5 cm diameter integrating sphere. The 8 mm 

diameter exit port of the sphere approximated a point source, producing a uniform irradiance on the detectors. A beam 

splitter and monitor silicon photodiode were used to correct for source fluctuations during the measurements. A 
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computer controlled linear positioning stage positioned the detectors in front of the integrating sphere exit port at a 

distance of 25 cm. 

The spectral power responsivity of the silicon trap irradiance transfer standard was measured directly against the 

HACR. The transfer standard was equipped with a known-area aperture. The radiant intensity of the sphere was 

calculated from the transfer standard power responsivity, aperture area, and sphere to transfer standard distance. The 

irradiance meters were substituted for the transfer standard in the uniform irradiance of the integrating sphere source. 

The laser was tuned between 368 nm and 385 nm with roughly 2.5 nm steps. The uncertainty for the SIRCUS results 

was ≈ 1 %, mainly due to the measurement reproducibility. 

IV. RESULTS AND DISCUSSION 

The spectral irradiance responsivity, in A⋅mm2

/W, of the two irradiance meters is presented in Figures 4 and 5. 

0.000

0.005

0.010

0.015

0.020

0

2

4

6

8

10

12

300 320 340 360 380 400

Absolute Irradiance Responsivity [A⋅mm2/W]

Wavelength [nm]

and Relative Expanded Uncertainty ( =2) [%]

UV SCF

Difference [%]

UV SCF Uncertainty [%]

k

SIRCUS

Irradiance Meter #1

Deconvolved Data

-0.2 nm wavelength shift

Figure 4. Plot of irradiance responsivity, UV SCF relative expanded (k = 2) uncertainties, and relative differences for 

the two methods for Irradiance Meter #1. Irradiance Meter #1 is a typical commercial 365 nm detector with an ≈ 50 nm 

bandpass (FWHM). 

0.00000

0.00005

0.00010

0.00015

0.00020

0.00025

0.00030

0.00035

0.00040

0

2

4

6

8

10

12

300 320 340 360 380 400

Absolute Irradiance Responsivity [A⋅mm2/W]

Wavelength [nm]

and Relative Expanded Uncertainty ( =2) [%]

UV SCF

Difference [%]

k

UV SCF Uncertainty [%]

SIRCUS

Irradiance Meter #2

Deconvolved Data

-0.1 nm wavelength shift

Figure 5. Plot of irradiance responsivity, UV SCF relative expanded (k = 2) uncertainties, and relative differences for 

the two methods for Irradiance Meter #2. Irradiance Meter #2 is a NIST designed transfer standard with a ≈ 25 nm 

bandpass (FWHM). 
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The relative expanded uncertainty (k = 2) in the SCF measurements and the relative difference between the SCF and 

SIRCUS measurements are also shown in Figures 4 and 5. The two methods using the UV SCF and SIRCUS agreed to 

the 1 % to 2 % level in the peak portion of the bandpass curves as shown in Figures 4 and 5. This is within the 

expanded (k = 2) uncertainties for the responsivity measurements. The difference increases at the lower values of the 

responsivity to just greater than the expanded uncertainties. The UV SCF wavelength uncertainty is larger than that of 

SIRCUS and may be a factor in the observed differences. Since the UV SCF data were taken in 1 nm intervals and the 

monochromator bandpass is 3 nm, the data were deconvolved using the monochromator slit-function. A 0.1 nm to 

0.2 nm wavelength shift in the deconvoluted UV SCF data brings the measurements between these two facilities into 

agreement on the 1 % to 2 % level over the entire spectral range. The calibration of the monochromator wavelength 

scale was checked with spectral line lamps and showed agreement to better than 0.1 nm over this spectral region. The 

wavelength shift was -0.2 nm for meter #1 and -0.1 nm for meter #2. One would expect the same shift for each 

irradiance meter if the wavelength scale were indeed the cause of the differences observed. A hypothesized cause is 

that the effective aperture area changes with wavelength. Thus, it may be necessary to scan the aperture not only at the 

peak responsivity, but also on either side of the peak. A definitive answer to the observed difference is currently under 

investigation. 

The two independent methods discussed both have advantages and disadvantages. The UV SCF can scan spectrally 

over a wide range easily but is limited by low flux levels, the relatively wide spectral bandwidth for filter cutoff regions, 

and the extremely long time intervals (4 h to 6 h) needed for the spatial scanning of the aperture. The SIRCUS facility 

has better wavelength accuracy, higher flux, faster measurement comparison (only a few minutes per data point since 

there is no spatial scanning), and most importantly, lower uncertainty. The lower uncertainty of the SIRCUS facility 

gives an independent verification of the aperture scanning method. The major disadvantage of the SIRCUS is the 

number of measurements needed to trace the responsivity of an irradiance meter. This is especially true over a broad 

wavelength range where several lasers may be needed. 

Because of the labor-intensive nature of the SIRCUS measurements, a third method is proposed combining the best 

features of the previous two methods. The UV SCF would measure the relative spectral responsivity over a wide 

wavelength range, then the SIRCUS facility would measure a relatively small number of “tie” points at selected 

wavelengths in the center of the irradiance meter bandpass, in the tails, and in the “cut-off” regions. Measurements 

using this method would benefit from the lower uncertainties of the SIRCUS facility measurements and the broad 

spectral coverage of the UV SCF all within a fraction of the time required by the first two methods discussed here. 

V. CONCLUSION 

NIST can provide 365 nm irradiance meter spectral responsivity measurements to support a variety of industrial and 

laboratory applications using either a monochromator-based facility or tunable laser and integrating sphere facility. The 

agreement between these two fundamentally different methods in this first reported comparison is 1 % to 2 % in the 

peak portion of the bandpass curves which is comparable to their expanded (k = 2) uncertainties. The SIRCUS 

uncertainties are lower than the UV SCF with the potential for 0.1 % uncertainties in the future. This will greatly 

reduce the calibration uncertainties NIST provides for UV irradiance meters in the future. 

References

[1] T. C. Larason, S. S. Bruce, and A. C. Parr, Spectroradiometric Detector Measurements: Part I - Ultraviolet Detectors and Part II 

- Visible to Near-Infrared Detectors, Natl. Inst. Stand. Technol., Spec. Publ. 250-41, U.S. Government Printing Office, 

Washington, D.C., 1998. 

[2] S. W. Brown, G. P. Eppeldauer, and K. R. Lykke, “NIST Facility for Spectral Irradiance and Radiance Response Calibrations 

with a Uniform Source,” Metrologia, vol. 37, pp. 579-582, 2000. 

[3] C. A. Schrama and H. Reijn, “Novel calibration method for filter radiometers,” Metrologia, vol. 36, pp. 179-182, 1999. 

[4] T. M. Hunt, N. P. Fox, W. S. Hartree, and N. M. Durant, “Evaluating the performance of filter radiometers as a means of 

improving the uncertainty of ultraviolet measurements,” Metrologia, vol. 35, pp. 345-351, 1998. 

[5] J. M. Bridges and C. L. Cromer, “Final Report on Calibration and Characterization of I-Line Exposure Meters,” SEMATECH, 

2706 Montopolis Drive, Austin, TX 78741, SEMATECH Report 91090678A-ENG, October 17, 1991. 

[6] C. L. Cromer, G. Eppeldauer, J. E. Hardis, T. C. Larason, Y. Ohno, and A. C. Parr, “The NIST detector-based luminous 

intensity scale,” J. Res. Natl. Inst. Stand. Technol., vol. 101, pp. 109-132, 1996. 

[7] G. P. Eppeldauer, M. Racz, and T. C. Larason, “Optical Characterization of Diffuser-Input Standard Irradiance Meters,” in Proc. 

Int. Soc. Opt. Eng., vol. 3573, pp. 220-224, 1998. 
Realization of a spectral radiance responsivity scale 

with a laser-based source and Si radiance meters

George P. Eppeldauer, Steven W. Brown, Thomas C. Larason, Miklos Racz*

, and Keith R. Lykke 

National Institute of Standards and Technology 

Optical Technology Division 

Gaithersburg, Maryland 20899 

*

 Guest researcher from the Hungarian Academy of Sciences 

Research Institute for Technical Physics and Materials Science 

Principal Contact: George P. Eppeldauer 

Phone: 301-975-2338; Fax: 301-869-5700 

Email: geppeldauer@nist.gov 

Abstract 

A spectral radiance responsivity (SRR) scale derived from the spectral irradiance responsivity scale has been 

realized on the newly developed NIST facility for Spectral Irradiance and Radiance Responsivity Calibrations with 

Uniform Sources (SIRCUS). The scales were directly derived from the primary standard cryogenic radiometer 

using transfer standard irradiance trap detectors and laser-based uniform sources. Standards quality silicon radiance 

meters have been developed to hold the SRR scale. The radiance meters were characterized and optimized for sizeof-source effects. The optimized meters were calibrated for SRR against the monochromatic uniform source. In 

addition to the SIRCUS calibrations, preliminary tests were made on the Spectral Comparator Facility (SCF) of 

NIST as well. These relative SRR tests were made in both imaging and non-imaging measurement modes. The 

results of the different SRR calibrations are compared and evaluated. 
1. Introduction 

The high accuracy of primary standard cryogenic radiometers [1] can be utilized only if improved quality 

radiometers are developed and calibrated directly against the primary standard. To achieve this goal, we are 

developing a reference (high accuracy) spectral irradiance and radiance responsivity calibration facility [2]. This 

facility utilizes uniform sources using integrating spheres and lasers [3, 4, 5] to obtain lower scale uncertainties 

compared to traditional monochromators [6]. This paper describes how the irradiance responsivity scale is 

propagated to the radiance responsivity scale on SIRCUS. Design and the basic radiometric characterizations of a 

broad-band working standard Si radiance meter is discussed. This high performance radiance meter will hold the 

high accuracy SRR scale. Arrangements and considerations are discussed for accurate relative and absolute SRR 

measurements. 

2. Radiance responsivity scale derivation

Figure 1 shows the scale propagation from the NIST High Accuracy Cryogenic Radiometer (HACR) to the SRR 

scale level. Si trap detectors are calibrated against the HACR at several laser lines. The response interpolation is 

done between 406 nm and 920 nm based on the physical model of the Hamamatsu 1337 Si photodiodes [7, 8]. The 

aperture area in front of the trap detector is measured with high accuracy using point source geometry [9]. The 

irradiance responsivity of the transfer standard Si trap detector is equal to its power responsivity times the aperture 

area. 

The SRR scale is derived from the spectral irradiance responsivity scale. First, the radiant intensity of the uniform 

source is determined from the detector irradiance responsivity and the distance between detector and source 

apertures. In this case, the distance is large (about 1 m), therefore the source is used as a point source. The radiance 

within the source aperture (at a laser wavelength) is the ratio of the radiant intensity to the source aperture area. 

When calibrating the radiance meter against the Lambertian (uniform) source, its target area (the measured spot) has 
to be within the source aperture (of 5 cm diameter). The radiance responsivity of the meter is the ratio of its 

electrical output signal to the measured source radiance. 

Radiant Power P(λ) [W]

Spectral Radiance L(λ)

Radiance 

detector

HACR

Spectral Irradiance Responsivity 

 Calibrations

SIRCUS

sourcedetector 

distance D

Spectral Radiant Intensity 

 I(λ)=E(λ)*D2 [W/sr]

 Irradiance 

Transfer Standard

Spectral Irradiance Responsivity 

 output current/E(λ) [A*m2/W]

 Spectral Radiance Responsivity 

 output current/L(λ) [A*m2sr/W]

detector 

aperture 

 area

 source 

aperture 

 area

Figure 1. SRR scale derivation. 

3. Si radiance meter design 

Figure 2 shows the design of the transfer standard Si radiance meter. The input optics are attached to the radiometer 

base unit. A beveled aperture in the mirror serves as a field stop and it is positioned into the focus of the camera 
lens. The surroundings of the source target area can be viewed through the eye-piece. The target radiation is imaged 

to the center of the Si photodiode through a second imaging optics producing a well defined field-of-view (FOV) 

and a very efficient out-of-target blocking. The aperture stop in front of the second imaging system keeps the flux 

response of the optics constant for different target distance (lens focus) adjustments. In order to eliminate 

interferences, we replaced the original plane-parallel window of the Si photodiode with a ground glass diffuser of 

high transmittance. 

4. Characterization of the Si radiance meter 

Figure 3 shows the angular responsivity of the Si radiance meter. The measured source was a 1000 W tungsten 

halogen lamp equipped with a 5 mm aperture 4 cm away from the lamp. The distance between the radiometer and 

the source aperture was about 2.5 m. The radiometer was rotated in the horizontal plane around a pivot point in the 

center of its camera lens. This scan was repeated after a 90° rotation of the radiometer around its axis to obtain the 

angular responsivity in the perpendicular (vertical) plane as well. The radiance measurement angle is 0.6° (FWHM) 

and the out-of-target blocking (the signal at zero rotation angle ratioed to the signals at different rotation angles) is 2 

x 103

 at 0.5°, 104 at 1.5° and higher than 105 at 5°. The vertical and horizontal scans resulted in similar results 
CAMERA LENS

EYEPIECE

ADAPTERS

TEMPERATURE 

 CONTROLLED 

 BLOCK

ELECTRONIC

 UNIT

WINDOWLESS 

 SILICON 

PHOTODIODE

 GROUND 

 GLASS 

DIFFUSER

SECOND 

IMAGING 

SYSTEM

APERTURE 

 STOP

 FIELD 

 STOP 

MIRROR

Figure 2. Working standard Si radiance meter. 

0

0.2

0.4

0.6

0.8

1

1.2

10-5

10-4

10-3

10-2

10-1

100

-4 -3 -2 -1 0 1 2 3 4

Relative signal

Relative signal

Angle of rotation [degree]

Figure 3. Angular responsivity of the Si radiance meter. Horizontal response (dashed line, logarithmic scale) 
and vertical response (solid line, linear scale) 

5. Absolute spectral radiance responsivity 

The absolute SRR was measured on the SIRCUS using a 20 cm diameter Spectralon [8] coated integrating sphere. 

The sphere was irradiated by 98 laser lines of different wavelengths between 400 nm and 920 nm. The 

measurement steps followed the scale derivation chart in Figure 1. The solid line in Figure 5 shows the absolute 

SRR of the working standard radiance meter. 

6. Uncertainties 

The uncertainty budget of the SIRCUS radiance responsivity calibrations is summarized in Table 1. Type A and 

Type B uncertainties [10] are shown for both the present (preliminary) and future calibrations. The source radiance 

uncertainties are separated from the uncertainties of the radiance transfer to test radiance meters. We plan to 

decrease the present (uncorrected) relative combined standard uncertainty (k=1) of 0.21 % to about 0.05 % after 

improving the uncertainties as indicated in the Table. 

7. Relative spectral radiance responsivity comparison to the SCF 

Independent relative SRR measurements were made on the SCF. We made two preliminary tests only with two 

different beam geometries. The first one was a simple, non-imaging method which can be used for high quality 

radiance meters where a second imaging optics projects the beam always into the same position on the detector. In 

this case, the target spot of the radiance meter was not defined. These test results are shown in Figure 5 (non-imaged 

SCF curves). With normalization at 705 nm, the obtained relative radiance responsivity curve agrees with the 

results of the absolute (SIRCUS) radiance responsivity measurements within 1 % between 475 nm and 920 nm. The 

repeatability uncertainty was equal to or less than 0.25 % from three relative spectral responsivity scans made with 

different (repeated) alignments. The relative standard uncertainties (k=1) of the SCF measurements are 0.78 % at 
400 nm and 0.11 % from 450 nm to 900 nm in power responsivity mode [6] and 0.94 % at 400 nm and almost 

constant at 0.54 % in the visible up to 925 nm in irradiance responsivity mode [11]. 

Table 1 

Relative combined standard uncertainty (k=1) of the SIRCUS present radiance responsivity calibrations [%] 

(future calibration uncertainties are shown with italic) 

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ 

 Present measurements Planned (future) measurements

Uncertainty origin Type A Type B Type A Type B 

Source radiance:

Trap spectral power responsivity 0.03 0.02 

Trap aperture area 0.01 0.01 

Source to Trap distance squared 0.05 0.02 

Trap repeatibilty 0.05 0.02 

Source aperture area 0.04 0.02 

Amplifier gain 0.04 0.02 

Radiance transfer to test detector:

Source spatial radiance nonuniformity 

(uncorrected) 0.1 

(corrected) 0.02 0.01 

Test detector repeatability 0.05 0.01 

Test detector size-of-source effect 

(uncorrected) 0.15 

(corrected) 0.02 0.01 

Amplifier gain 0.04 0.02 

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ 

Relative combined standard uncertainty:

(uncorrected) 0.21 

(corrected) 0.12 0.054 

Because the non-imaging method is not correct for radiance responsivity measurements, we are suggesting here an 

imaging type test method. We made a preliminary test using this second method where the standard arrangement of 

the SCF was modified to measure simple radiance meters where the detector may have spatially non-uniform 

responsivity and no second imaging optics are used. The modification is shown in Figure 4. The f/9 converging 

beam from the monochromator, before the two lenses, produces a 1.1 mm diameter spot (which is on the surface of 

the power measuring detector in the standard SCF arrangement). In the modification, a camera lens of 35 mm focal 

length is used as a relay lens to magnify this spot into a 15 mm diameter image, inside of an achromatic collector 

lens of 350 mm focal length. The corrected lens collects the radiation exiting from the relay lens and projects it into 

the center of the camera lens of the radiance meter. The distance of the radiance meter from the collector lens has to 
be adjusted until the diameter of the target spot of the radiance meter is equal to the diameter of the reference 

detector which is positioned directly after the collector lens. The reference detector has to be circular (e.g. a 1 cm2

silicon detector). In the eyepiece of the radiance meter, the black (measured) spot has to be in the center of the 15 

mm diameter image inside of the collector lens. The relative radiance responsivity of the meter will be the power 

responsivity of the reference detector times the ratio of the radiance meter output signal to the output signal of the 

reference detector. 

Figure 4. Optical arrangement for radiance meter relative responsivity measurement. 

In our preliminary test, an 18 mm by 18 mm reference Si detector was used and the above described target-spot and 

detector-diameter match was not achieved. Because of lens chromatic abberations, the size of the magnified spot 

inside of the collector lens was wavelength dependent. The lenses were optimized for the visible range. Also, the 

irradiance distribution within the monochromator output spot depends on the wavelength. These problems caused 

relatively large uncertainties for wavelenghts shorter than 420 nm. In Figure 5, where the radiance responsivity 

measurement results are summarized, the normalization was made at 705 nm, the peak responsivity of the 

photodiode, resulting in about 2.5 % discrepancy (relative to the absolute radiance reponsivity) at 450 nm (imaged 

SCF curves). 

The two relative radiance responsivity curves are different not only because of the non-optimized arrangement of 

the imaged SCF measurements (as mentioned above), but also because the transmittance of the anti-reflecting 

coating can be different for the different incident angles of the two cases. A systematic relative radiance 

responsivity uncertainty was measured at 420 nm. This problem, which requires further examination, significantly 
increased the responsivity deviation of the non-imaged SCF measurements relative to the SIRCUS results for 

wavelengths shorter than 475 nm. 

0 100

1 10-4

2 10-4

3 10-4

4 10-4

0.96

0.98

1

1.02

1.04

1.06

500 600 700 800 900

Radiance responsivity [A mm 2 sr/W]

SCF/SIRCUS

Wavelength [nm]

Non-imaged SCF

Imaged SCF

SIRCUS

Figure 5. SRR of the NIST Radiance Meter #303. The relative radiance responsivity curves were measured on the 

SCF in both imaging and non-imaging modes and normalized to the absolute responsivity as measured on the 

SIRCUS. The normalizations were made at 705 nm. The responsivity ratios are shown relative to the SIRCUS 

results. 

8. Conclusion 

SRR calibrations were performed on the preliminary SIRCUS facility. The 0.21 % relative combined standard 

uncertainty (k=1) of the first radiance responsivity measurements (which is 3-4 times better than the SCF irradiance 

responsivity uncertainty in the same wavelength range) showed the dominating uncertainty components. We could 
also estimate the achievable uncertainties and the necessary improvements (finalization) of the facility. Comparison 

of the SIRCUS responsivity measurements to the traditional monochromator based SCF measurements showed that 

systematic errors in the SCF SRR measurements can be verified. The SIRCUS, with the final control and 

measurement system, including a variety of transfer- and working-standard radiometers and improved correction 

and calibration procedures, will serve as a high accuracy reference calibration facility for radiometry, photometry, 

and colorimetry. 

9. Acknowledgements 

The authors thank the Air Force Metrology for funding this project. 

References 

[1] T.R. Gentile, J.M. Houston, J.E. Hardis, C.L. Cromer, and A.C. Parr, “National Institute of Standards and 

Technology high accuracy cryogenic radiometer,” Appl. Opt. 35 (7), 1056-1068, 1996. 

[2] S.W. Brown, G.P. Eppeldauer, and K.R. Lykke, “NIST Facility for Spectral Irradiance and Radiance Response 

Calibrations with a Uniform Source,” Newrad’99, Madrid, Spain. 

[3] K.R. Lykke, P.S. Shaw, L.M. Hanssen, and G.P. Eppeldauer, “ Development of a Monochromatic Uniform 

Source Facility for Calibration of Radiance and Irradiance Detectors from 0.2 μm to 12 μm,” Metrologia, 36, p. 

141-146, 1999. 

[4] K.D. Mielenz, R.D. Saunders, and J.B. Shumaker, “Spectroradiometric determination of the freezing 

temperature of gold,” J. Res. Natl. Stand. Technol. 95, 49-67, 1990. 

[5] V.E. Anderson, N.P. Fox, and D.H. Nettleton, “Highly stable, monochromatic and tunable optical radiation 

source and its application to high accuracy spectrophotometry,” Applied Optics, 31, No. 4, 536-545, 1992. 
[6] T.C. Larason, S.S. Bruce, A.C. Parr, “Spectroradiometric Detector Measurements: Part I-Ultraviolet Detectors 

and Part II-Visible to Near-Infrared Detectors,” National Institute of Standards and Technology Special 

Publication 250-41, 1998. 

[7] T.R. Gentile, J.M. Houston, and C.L. Cromer, “Realization of a scale of absolute spectral response using the 

National Institute of Standards and Technology high-accuracy cryogenic radiometer,” Appl. Opt. 35, No. 22, 

4392-4403, 1996. 

[8] Identification of commercial equipment to specify adequately an experimental problem does not imply 

recommendation or endorsement by the National Institute of Standards and Technology nor does it imply that 

the equipment identified is necessarily the best available for the purpose. 

[9] J.B. Fowler, R.S. Durvasula, and A.C. Parr, “High-accuracy aperture-area measurement facilities at the 

National Institute of Standards and Technology,” Metrologia, 35, No. 4. 497-500, 1998. 

[10]B.N. Taylor and C.E. Kuyatt, “Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement 

Results,” Natl. Inst. Stand. Technol., Tech. Note 1297, 1994. 

[11]G. Eppeldauer, M Racz, and T. Larason, “Optical characterization of diffuser-input standard irradiance meters,” 

SPIE 3573, 220-224, 1998. 
Eppeldauer, et al. Spectral responsivity measurements 

UNCERTAINTIES OF SPECTRAL RESPONSIVITY MEASUREMENTS 

G. P. Eppeldauer, G. Sauter1, and J. L. Gardner2

National Institute of Standards and Technology 

Gaithersburg, Maryland, USA 

1

PTB, Braunschweig, Germany 

2

 National Measurement Institute, Lindfield, Australia 

ABSTRACT 

Uncertainty estimates of detector spectral responsivity measurements are discussed. A model describes independent 

(uncorrelated) uncertainty components at a 

given wavelength based on the measurement equation for test detector calibrations. 

Systematic (correlated) components across 

wavelength are described briefly for spectrally integrated responsivity measurements. 

Propagation of the random and systematic 

components is discussed. 

1. INTRODUCTION 

The uncertainty analysis of spectral responsivity measurements should follow the 

“Guide to the Expression of Uncertainty in 

Measurement” (GUM) [1]. A Technical Report within the TC2-48 Technical Committee 

of the International Committee on Illumination (CIE) is being prepared to make recommendations for spectral responsivity 

measurements of detectors, radiometers, 

and photometers. The goal of the present 

work is to prepare a chapter for the CIE 

TC2-48 Technical Report on the uncertainty 

determination of spectral responsivity measurements using the GUM recommendations. 

Starting with the measurement equation, 

a model is described to evaluate the radiant 

power responsivity determination of a test 

detector at a given wavelength. Uncertainty 

in the measured value arises from the uncertainty of the spectral responsivity of the 

standard (reference) detector, and from uncertainties in the elements of the correction 

factor used to evaluate the radiant power 

responsivity of the test detector from the 

measurement (calibration) transfer. Following the description of contributions that are 

independent of wavelength, systematic (correlated) uncertainty components in the reference detector are described and propagation of the components will be discussed for 

spectrally integrated measurements. 

2. THE MEASUREMENT PROCESS 

The relative standard uncertainty of 

spectral responsivity values can be derived 

from the measurement equation of the detector substitution method. The substitution 

method transfers the radiometric responsivity of a standard detector to a test detector 

that has similar properties to the standard 

detector. When the standard detector measures the constant input flux (the total radiant 

power in the incident beam) Φ, its output 

signal IS is: 

= sI SS ⋅Φ (1)

where is the known responsivity of the 

standard detector. In the following step, the 

test detector is substituted for the standard 

detector and measures the same radiant 

power in the same arrangement: 

s S

= sI TT ⋅Φ (2) 

where is the output signal of the test detector and is the unknown radiant power 

responsivity of the test detector that can be 

calculated from Eqs. (

TI

sT

1) and (2): 

S

T

ST I

I

ss ⋅= (3) 

When a monitor detector is used to decrease fluctuations in the radiant power, the 

modified measurement equation will be: 

S

T

S

MSS

MTT

ST R

R

s

II

II

ss ⋅=⋅= (4) 

where instead of the electrical output signals 

 their ratios to the simultaneously 

measured monitor output signals 

are used: 

ST, II

MSMT, II

MSSSMTTT = , = IIRIIR . 
3. MODEL AT A GIVEN WAVELENGTH 

In Eq. (4) the radiant power responsivity of 

the test detector is calculated as a product 

of at least three factors. If we ignore the 

measurement errors of the electrical signals, 

the relative standard uncertainty in the spectral radiant power responsivity of the test 

detector can be written as 

() () ( ) ( ) [ ] 2/1

S

2

relT

2

relS

2

Trel = rel ++ RuRususu (5) 

In the brackets, the first contribution is the 

relative standard measurement uncertainty 

calculated from the certificate of the reference detector and the operational conditions 

during transfer. The other two contributions 

come from the measurement transfer. 

Note that at present, calibration certificates 

do not report correlation coefficients or uncorrelated and correlated components separately. While measurements at the one 

wavelength do not depend on these correlations, they become important when combining values at different wavelengths in spectrally integrated components; this is discussed in Section 4 below. 

The effective radiant power responsivity 

of the reference detector requires a small 

correction for a possible temperature deviation (relative to the temperature during 

calibration), and for a relative nonuniformity

Ss

∆T

β S : 

( SS 1 S S = ss ′ α ∆⋅+⋅ T + β ) (6)

where αS is the relative temperature coefficient for the responsivity. The relative standard measurement uncertainty of the radiant 

power responsivity of the reference detector is calculated from the expanded 

measurement uncertainty and the 

coverage factor

sS

′

( ) sU S

′

(k = 2) given in the calibration certificate when the responsivity sS

′ was 

measured at temperature TC and is given by 

( ) ( )( ) Srel 2ssUsu SS ′ = ′ ′ . (7) 

The temperature deviation =∆ −TTT CS is 

calculated from the temperature (nominal value, no uncertainty contribution) and 

the measured ambient temperature during use. Often the standard deviation 

TC

TS

( ) Ts S

of repeated thermometer readings is smaller 

than its resolution, which is an interval

( ) ± Tres S with rectangular probability distribution. The temperature is measured with 

the thermometer certified with an (absolute) 

expanded measurement uncertainty 

( S ) = δTTU for a (k = 2) coverage interval 

and gives the standard variance ( )2 δT 2 . 

The standard variance of the temperature 

deviation from the three contributions is:

( ) ( ) ( )

2 3

S

2

S

2

2

2 Tres Ts T Tu ⎟ ++

⎠

⎞ ⎜

⎝

⎛ =∆ δ (8) 

The relative temperature coefficient αS is 

measured separately and the value can be 

determined with an associated relative standard measurement uncertainty ( S u α ) or 

taken from the related literature. 

Finally, the relative non-uniformity β S has a 

zero value (it is included in the responsivity 

value) but its variation contributes to the responsivity measurement uncertainty within 

an interval ±∆sS , having a rectangular probability distribution. Therefore, the standard 

variance is calculated as ( ) 3 2

S S

2 u β ∆= s . 

After these preparations and the two assumptions 1 α S T +∆⋅>> β S and no correlations between the quantities, the relative 

combined variance associated to the responsivity of the standard detector can be 

written: 

( ) = ( ′ ) ususu ( ) ( Tu +∆⋅++ 22

SS

2

S

2

relS

2

rel αβ )

 ( ) 2

S

2 α ∆⋅ Tu (9) 

If the temperature at the time of measurement is the same as that at the time of calibration, ∆T = 0 . In this case, from second 

order terms, the factor 2 ∆T has to be replaced by the associated standard variance 

(∆Tu ) 2 . 

For the test detector, similar contributions 

have to be taken into consideration. The 

corrected value of the radiant power responsivity sT

′ of the test detector can be calculated for the ambient temperature and 

for zero contribution of its own nonuniformity: 

TC

( ) TT 1 α T ∆ + β T = ss ′ ⋅ + ⋅ T (10) 
Similarly to the considerations before, the 

associated relative standard measurement 

uncertainty of sT can be determined assuming small corrections 1 α T T +∆⋅>> β T and 

no correlation. Then the relative variance 

can be written: 

() () ( ) = ′ ususu ( Tu ) +∆⋅++ 22

TT

2

T

2

relT

2

rel αβ

 ( ) (11) 2

T

2 α ∆⋅ Tu

The combination of Eq. (4) with the corrections in Eq. (6) and (10) give a new model 

for the radiant power responsivity evaluation: 

MSS

MTT

T T

S S

ST 1

1

II

II

T

T

ss ⋅ ⎥

⎦

⎤ ⎢

⎣

⎡

+∆⋅+

+∆⋅+ ′ = ′ ⋅ βαβα (12) 

and taking the earlier assumptions into account (first order approach), the bracket is 

simplified to [ ( ) ] 1 α α TS T +∆⋅−+ β − β TS . 

This approach directly shows that for very 

similar test and reference detectors the temperature and spatial uniformity errors will 

cancel out. 

The four photocurrents in Eq. (12), also contribute to the measurement uncertainty. The 

assumptions for the photocurrent measurements are: 

A. The same amplifier and Digital Voltmeter (DVM) are used for both the test and reference detectors assuming that the gain and 

range settings are valid for both photocurrents. 

B. With the test detector in place and shutter 

open, a series of repeated readings 

are taken simultaneously for both the test 

( ) and the monitor ( ) detectors.

n ≥ 20

TI′ MT I′

C. With the above conditions (especially for 

the amplifier gain and DVM range) but with 

the shutter closed, “dark measurements”

( , ) are taken. T0 I′ MT0 I′

D. With the reference detector in place and 

shutter open, repeated readings are 

taken simultaneously for both the reference

( ) and monitor (

n

SI′ MS I′ ) detectors. 

E. Under the same conditions, but with the 

shutter closed, “dark measurements” ( S0 I′ ), 

(IMS0 ′ ) are taken. 

Mean values like TI′ and its related standard 

deviations of the mean ( ) TIs ′ are calculated 

for all the measured quantities and the two 

ratios: MSSSMTTT′ = ′ ′ ; ′ = IIRIIR ′′ . In principle, instead of these ratios, the dark current 

corrected ratios should be averaged. However, if the dark current is small and the 

measurement setup is fairly stable, then the 

measurement uncertainty evaluation can be 

simplified: 

1 1 ′ ′ − ⎛ ⎞ ′ ′ = ≈ ′ ⋅⎜ ⎟ − + ′ − ′ ′ ⎝ ⎠ ∑ i i

i i i

I I I I R R

nI I I I

T, T0, T0 MT0

T T

MT, MT0, T MT′

 (13) 

The ratio for the reference detector readings 

can be calculated similarly. Finally, the double ratio in Eq. (4) will be: 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

′

′ − ′′ + ′′ − ′′ +⋅ ′

′ ≈

MS

MS0

MT

MT0

T

T0

S

S0

S

T

S

T 1

I

I

I

I

I

I

I

I

R

R

R

R (14) 

Usually, there are four contributions to the 

measurement uncertainty from a series of 

repeated readings of a radiometer: the standard deviations of the two mean values for 

light and dark readings; the calibration factor, that cancels out in Eq.(14); and the resolution ±∆I of the DVM. For all photocurrents, the standard measurement uncertainties are calculated similarly: 

( ) ( ) ( )

2

S0

2

S0′ = ′ ∆+ IIsIu 3/ (15) 

If a common amplifier is used for both the 

standard and the test detectors, then the 

currents T0S0,II ′′ for dark (and offset) measurements are the same, as are their measurement uncertainties. As they are determined in a series, one after the other, there 

is no statistical correlation, even if recorded 

by the same amplifier.

Finally, the model to evaluate the radiant 

power responsivity of the test detector is 

calculated from the combination of Eqs. (12) 

and (14) with the higher orders omitted: 

( )

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎣

⎡

′

′ − ′′ + ′′ − ′′

+−+∆⋅−+

=

⋅

′

′ ′ = ′ ⋅

MS

MS0

MT

MT0

T

T0

S

S0

TS TS

S

T

ST

1

I

I

I

I

I

I

I

I

T

corr

corr

R

R

ss

αα ββ (16) 

All the contributions in the brackets are very 

small corrections and the associated relative 

standard measurement uncertainty is often 
negligible. In a reduced form, the relative 

standard measurement uncertainty associated to the radiant power responsivity is 

combined from four dominant contributions: 

() () ( ) ( ) ( ) 22 2 2 u s u s u R u R u corr rel T rel S rel T rel S rel ′ ′′′ = +++

 (17) 

The principles in the measurement equation 

of Eq. (16) are valid for each single wavelength λ . Accordingly, all quantities are 

wavelength dependent: 

() () ( )

( ) ( ) λ

λ

λ λλ corr

R

R

ss ⋅ ′

′ ′ = ′ ⋅

S

T

T S (18) 

The correction factor includes contributions 

(originating from the measurement transfer) 

from temperature deviation , relative 

temperature coefficient of responsivities 

∆T

TS α ,α , relative spatial non-uniformity of 

responsivities TS β ,β , and dark (offset) currents MT0T0S0 MS0 ,,, IIII ′′′′ of the standard, test, 

and monitor detectors, all of which are independent of wavelength (or their changes are 

very small between neighbouring wavelengths where the measurement transfer is 

made). 

The ratios ( ),RR ST

′′ ( ) λλ are formed from 

output signals () () λ , II ST λ with simultaneously measured monitor output signals 

MT () () λ , II MS λ using the correlation between 

the related photocurrents to eliminate noise 

from possible fluctuations of the source. 

Usually this is totally independent of wavelength. 

Typically, the contributions for the determination of any single responsivity value and 

the associated uncertainty, are uncorrelated 

(at the given wavelength where the measurement transfer is made). These significant 

independent uncertainty components are 

added in quadrature. In case of independent 

variables, their covariances are zero. The 

quadrature sum can be applied to all random components at a given wavelength. 

One component that may correlate the test 

and standard measurements is that of wavelength uncertainty. Random wavelength setting errors are correlated between test and 

standard measurements if the wavelength is 

set and the test and standard detectors 

measured; they are not correlated if the 

spectral range is swept independently for 

the test detector and standard detectors. 

4. SPECTRALLY INTEGRATED 

RESPONSIVITY 

The values representing the responsivity 

function (λ) sS

′ listed in a calibration certificate may be calculated from realizations 

totally independent for the different wavelengths. In this case, the uncertainty components may not be correlated. However in 

practice, the responsivity function of the reference detector – usually a trap detector 

calibrated with a laser beam at a limited 

number of wavelengths - is interpolated 

based on the physical knowledge (quantum 

efficiency) or mathematical smoothness and 

results in correlations. Similarly, the responsivity functions of detectors, calibrated with a 

trap detector, are corrected by mathematical 

procedures for wavelength setting, for errors 

due to output slit function or to smooth the 

values from wavelength to wavelength. All 

these procedures produce function values 

with uncertainties that are correlated. The 

correlations do not affect the individual values but become important if spectrally integrated quantities are calculated. Calibration 

transfer from the primary standard radiometer can also introduce correlated uncertainties to a working reference standard, due to 

systematic offsets or scaling factors common to all measurement wavelengths. Calibration certificates usually state the total 

uncertainty at a given wavelength and rarely 

distinguish between effects that are random 

and systematic (correlated) between wavelengths. 

At the highest level (primary or secondary 

calibration laboratory) measurements, when 

combining spectral values over different 

wavelengths, it is usually the systematic 

components that determine the measurement uncertainty. For example. in a photodiode radiant power responsivity calibration, 

such systematic components (at all wavelengths) are the absolute responsivity of the 

reference detector, repeatability with beam 

position, and photodiode amplifier gain. 

The integrated responsivity of a detector 

when it measures a broad-band light-source 

can be written as 
n n

n

R s = ∑ P (19) 

where Pn is the spectral power distribution of 

the light-source and sn is the measured 

spectral power responsivity of the detector 

all at the nth (equally-spaced) wavelength. 

The detector is usually optically filtered to 

obtain a known spectral power responsivity 

function in a well defined wavelength interval. 

The relative uncertainty of R has to be calculated. Uncertainties in sn are independent 

of those in Pn and hence 

( 2 2 2 2 2 () ( ) ( ) n nn n

n

u R su P Pu s = + ∑ ) (20) 

Often the spectral distribution of the source 

is a defined quantity (e.g. CIE Standard Illuminant A) and its values carry no uncertainty. In the following discussion we assume that source uncertainty is negligible; if 

required, the principles used to propagate 

uncertainties from the spectral responsivity 

values to that of the integrated response are 

identical for those of the source uncertainties. 

As seen in Eqs. (3) and (4), determination of 

spectral responsivity is a transfer from a reference standard to the device under test, 

Tn Sn n , , s st = (21) 

where n denotes wavelength and t is the 

transfer ratio at the nth wavelength. Uncertainties in spectral responsivity of the test 

detector arise from those of the standard 

and from the transfer process; these are 

treated independently and then added in 

quadrature. 

4.1 Uncertainties of the standard detector 

From Eq. (21), 

,

, ,

,

() () ( T n

Tn n Sn S n

S n

s

us tus us

s = = , ) (22) 

where the uncertainties in spectral responsivity of the reference detector are obtained 

from the calibration certificate. These may 

be complex, depending on the method of 

generating the primary standard. In such 

cases, a full propagation using covariances 

between the reference values is required 

[1,2] – these must be sought from the supplier of the reference standard. 

Some certificates provide total random component uncertainties and total correlated 

uncertainties at each wavelength. Where the 

ratio (systematic component : total uncertainty) of these components is approximately 

constant through the spectral range of interest, the correlation coefficient r is also approximately constant and given by the 

square of the ratio and effective uncertainties that are random and fully-correlated between wavelengths are readily determined. 

The effective uncertainty in spectral responsivity that is random between wavelengths is 

then given by 

() 1 () u s r us R n = − n (23) 

and the total contribution of random effects 

to the uncertainty in the integrated spectral 

quantity is given by 

( ) 2 2 () 1 ( ) u R r Pu s R n = − 2

∑ n (24) 

The effective uncertainty in spectral responsivity that is fully correlated between wavelengths is given by 

() () u s r us S n = n (25) 

The total contribution of the systematic effects is given by the linear sum: 

() ( ) u R r Pu s S n = ∑ n (26) 

Alternatively, where the systematic and random components are given at each wavelength, or their wavelength dependence is 

given as a scaling of some parameter, each 

systematic component may be propagated 

separately as a linear sum, and the total 

random components propagated in quadrature. 

The total uncertainty contribution of the reference standard is the quadrature sum of 

the systematic and random components. 

A further complication is that spectral responsivity values for the reference standard 

may require interpolation to the wavelength 

values of the measurement. Interpolation 
introduces correlations and these must be 

taken into account when propagating the 

uncertainties of the standard detector. A 

simple process that avoids these complications is to interpolate the transfer ratio to the 

wavelengths at which the reference standard is calibrated and propagate uncertainties in the integral sum (including the change 

in wavelength spacing) using only those values [3]. 

4.2 Uncertainties of transfer process 

Each effect contributing to uncertainty in the 

transfer can be classified as independent 

and either random between wavelengths or 

fully-correlated between wavelengths. These 

effects can also be separately determined 

for the numerator or denominator of the 

transfer ratio, as shown in Eqs. (3) and (4), 

and combined either linearly or in quadrature depending on whether the effects are 

correlated or random between test and reference signals at the one wavelength. 

Once the uncertainty in the transfer ratio and 

hence its uncertainty in spectral responsivity 

, , () ( us s ut e Tn Sn e n = ) (27) 

is determined for each effect at each wavelength, its contribution to the integral sum is 

calculated. For random components, 

2 2 2 () ( ) u R Pu s e n = ∑ e n (28) 

For systematic components, uncertainties in 

the values of spectral responsivity at different wavelengths are generally positively correlated, and the contribution to the integral 

sum is given by 

() ( ) u R Pu s e n = ∑ e n (29) 

However some effects (e.g. wavelength offsets) can produce correlations that are positive or negative between wavelength pairs. 

These effects are properly handled by attaching a sign, that of the sensitivity coefficient for the effect, to the uncertainty in the 

transfer ratio. For example, consider the 

transfer ratio shown in Eq. (21). In the presence of a wavelength uncertainty fully correlated between test and reference, the signed 

uncertainty in the transfer ratio test:standard 

signals at the nth wavelength is given by 

, ,,

, 2

, ,

1 ( ) ( ) Tn Tn Sn

es n

S n S n

R RR

u t u

R R

λ

λ λ

⎛ ⎞ ∂ ∂ = − ⎜ ⎟ ∂ ∂ ⎝ ⎠

 (30) 

The signed uncertainty in spectral responsivity for this effect at the nth wavelength is 

then given by combining Eqs. (27) and (30): 

,, ,

, ,

,

( ) ( Rn Tn S n

es T n n

S n

sR R

u s t u

R

λ) λ λ

⎛ ⎞ ∂ ∂ = − ⎜ ⎟ ⎝ ⎠ ∂ ∂

 (31) 

This expression can be positive or negative 

depending on the slopes of the test and reference signals with respect to wavelength. 

The propagated uncertainty for a wavelength offset applicable at all wavelengths, 

including these mixed correlations, is found 

by the linear sum 

, , () ( ) u R Pu s e n =∑ e s T n (32) 

Detailed discussions and examples for uncertainty contributions of different correlated 

combinations can be found in [2]. 

5. CONCLUSION 

When reporting spectral responsivity measurement uncertainties, the total uncertainty 

contribution of effects systematic over wavelengths should be given at each wavelength, 

instead of the total uncertainty as is the 

usual practice. 

REFERENCES 

1. International Organization for Standardization, “Guide to the Expression of Uncertainty in Measurement”, Geneva 1993 

2. J. L. Gardner, Chapter 6: Uncertainty 

estimates in radiometry, Experimental Methods in the Physical Sciences, 41 291-325, 

Elsevier Inc. 2005. 

3. J. L. Gardner, Uncertainties in interpolated spectral data, J. Res. Natl. Inst. Stand. 

Technol. 108 69-78 (2003) 
Realization of the National Institute of Standards

and Technology detector-based spectral

irradiance scale

Howard W. Yoon, Charles E. Gibson, and Patricia Y. Barnes

A detector-based spectral irradiance scale has been realized at the National Institute of Standards and

Technology NIST. Unlike the previous NIST spectral irradiance scales, the new scale is generated

with filter radiometers calibrated for absolute spectral power responsivity traceable to the NIST highaccuracy cryogenic radiometer instead of with the gold freezing-point blackbody. The calibrated filter

radiometers are then used to establish the radiance temperature of a high-temperature blackbody

HTBBoperating near 3000 K. The spectral irradiance of the HTBB is then determined with knowledge of the geometric factors and is used to assign the spectral irradiances of a group of 1000-W

free-electron laser lamps. The detector-based spectral irradiance scale results in the reduction of the

uncertainties from the previous source-based spectral irradiance scale by at least a factor of 2 in the

ultraviolet and visible wavelength regions. The new detector-based spectral irradiance scale also leads

to a reduction in the uncertainties in the shortwave infrared wavelength region by at least a factor of

2–10, depending on the wavelength. Following the establishment of the spectral irradiance scale in the

early 1960s, the detector-based spectral irradiance scale represents a fundamental change in the way

that the NIST spectral irradiance scale is realized. © 2002 Optical Society of America

OCIS codes: 120.3930, 120.3940, 120.4800, 120.5630.

1. Introduction

The development and use of cryogenic radiometers

have led the trend toward decreasing uncertainties in

the radiometric and the photometric scales because of

improvements in the absolute power measurements.1,2 Furthermore, detector-based scales often

can be maintained with shorter measurement chains

and lower uncertainties than source-based scales.

For example, the photometric scale at the National

Institute of Standards and Technology NISThas

been detector based and traceable to the NIST highaccuracy cryogenic radiometer HACRsince 1993,3

and the implementation of the detector-based photometric scale resulted in a factor of 2 reduction in the

expanded uncertainties compared with the previous

source-based photometric scale.4 Because the radiometric quantities of spectral radiance and spectral

irradiance require measurements at many different

wavelengths compared with the single measurement

in the assignment of a photometric quantity, the establishment of a detector-based spectroradiometric

scale has proven more time-consuming.

The spectral radiance and the radiance temperature scale at NIST have all been based on the absolute radiometric determination of the freezing

temperature of gold,5 and the spectral irradiance

scale is in turn realized from the spectral radiance

scale.6 As shown in Fig. 1a, during the process of

scale realization, the radiance temperature at 655

nm is assigned to a vacuum tungsten-filament lamp

gold-point lampoperated to match the radiance

temperature of the gold freezing-temperature blackbody. The radiance temperature of a tungsten lamp

operated at a higher temperature 1530 Kis in turn

determined with the gold-point lamp, and the radiance temperature of a variable-temperature blackbody VTBBis assigned. The VTBB has a small

2-mm-diameter opening, and the estimated emissivity of the VTBB is 0.9990  0.0005 based on the

geometry and temperature uniformity.7 The spectral radiance of tungsten-filament lamps and integrating sphere sources is assigned by use of the

The authors are with the Division of Optical Technology, National Institute of Standards and Technology, Mail Stop 8441,

Gaithersburg, Maryland 20899. H. W. Yoon’s e-mail address is

hyoon@nist.gov.

Received 7 January 2002; revised manuscript received 6 June

2002.

0003-693502285879-12$15.000

© 2002 Optical Society of America

1 October 2002  Vol. 41, No. 28  APPLIED OPTICS 5879
VTBB; and typically, the temperature of the VTBB is

changed to match the spectral radiance of the sources

to minimize the effects that are due to the nonlinear

responsivities of the detectors. For spectral irradiance realizations, the spectral radiance of an

integrating-sphere source ISSis assigned, and the

ISS is fitted with a precision aperture for use as a

source of known spectral irradiance to calibrate a set

of 1000-W free-electron laser (FEL) lamps.

The source-based spectral irradiance scale realization procedure is long and involves many separate

steps to assign the spectral irradiance of a set of

lamps. The primary reason for the long calibration

chain is the low spectral radiance output of the gold

freezing temperature blackbody at 1337.33 K.8 Because the 1000-W FEL lamps have spectral shapes

similar to that of a 3000 K blackbody, the radiant

output of the intermediate transfer artifacts must be

progressively increased to eventually match the spectral irradiance output of the 1000-W FEL lamp.

Furthermore, a major contribution to the final uncertainties in the spectral irradiance scale is due to the

temporal drift of the ISS and the low signal of the

ISS, especially in the shortwave infrared region.

The temporal drift of the ISS also depended on the

wavelength region, resulting in greater temporal

changes in the ultraviolet wavelength region. The

spectral irradiance scale was difficult to realize at

many different wavelengths because of a possible

temporal drift resulting from the additional time

needed for realizations.

In the past decade, new developments in the construction of high-temperature blackbodies HTBBs

made from pyrolytic graphite have allowed prolonged

100 hoperations at or above 3000 K.9 Furthermore, at NIST the uncertainties in the detector power

responsivity scale were reduced with the advent of

the HACR as the primary standard for spectral power

responsivity calibrations. The advantages of the

new detector-based scale realization are evident in

Fig. 1b, with a much shorter chain from the cryogenic radiometer to the primary working standards

compared with the measurement chain shown in Fig.

1a. In the realization of the detector-based scale,

the filter radiometers FRsare used to determine the

temperature of the HTBB, and then the spectral irradiance output of the HTBB is used to directly calibrate the primary working standard lamps.

In this paper we describe the realization of the

NIST detector-based spectral irradiance scale.

The FRs used to determine the radiance temperature of the HTBB are characterized, and the agreement between the absolute detector-based radiance

temperatures are compared with those found by use

of the International Temperature Scale of 1990

ITS-90.10 The agreement between the detectorbased and the gold freezing-temperature-based

spectral radiances is also shown to verify that the

HTBB spectral radiance does not deviate significantly from a single-temperature Planck radiance

distribution. From the assignment of the radiance

temperature with the FRs, the spectral irradiance

of a set of FEL lamps is determined. The detectorbased and the gold freezing blackbody-based spectral

irradiances are compared, and the uncertainties

of the detector-based spectral irradiance scale are

discussed.

2. Experimental Approach

A. Radiance Temperature Determinations with Filter

Radiometers

A schematic of the measurements is shown in Fig. 2.

Both the spectroradiometer and the FRs reside on a

common moving optical table. The FRs are first

used to determine the radiance temperature of the

HTBB; and thus with knowledge of the radiance temperature, the spectral irradiance responsivity of the

spectroradiometer is assigned by use of a precision

aperture on the integrating-sphere receiver ISR

with the knowledge of the distance between the ISR

and the precision aperture in front of the blackbody.

The spectral irradiance of the 1000-W quartz

tungsten–halogen lamp type FELis then assigned

by use of the spectral irradiance responsivity of the

spectroradiometer.

The FRs are constructed with broadband filters

and silicon detectors that are both temperature stabilized as shown in Fig. 3. A precision aperture is

placed in front of the filter–detector package, and

the aperture area is measured separately in the

NIST High-Accuracy Aperture Measurement Facility

to a relative combined expanded k  2uncertainty

of 0.01%.11 The precision apertures attached to

the FRs range from 4.0 to 4.4 mm in diameter. The

detectors are calibrated for absolute spectral power

responsivity on the NIST Spectral Comparator FaFig. 1. aMeasurement chain used to derive the source-based

spectral irradiance scale used in the 1990 and 1992 scale realizations. bThe measurement chain used in the new detector-based

spectral irradiance scale of 2000.

5880 APPLIED OPTICS  Vol. 41, No. 28  1 October 2002
cility SCF,12 and the power responsivity is converted to spectral irradiance responsivity from

knowledge of the aperture area. A total of three

detectors are used, and the absolute spectral power

responsivities are shown in Fig. 4. Both filter radiometers FR2 and FR4 have photopic response filters resulting in a broad spectral responsivity.

The FR3 has greater spectral responsivity to

shorter wavelengths then the other two radiometers, with a drop in responsivity near 400 nm. The

broadband radiometers were chosen for increased

long-term stability, as compared with narrowband

interference filters.13

The radiance temperature of the HTBB is found

with a measurement equation, which describes the

optical flux transfer with circular and coaxial source

and receiver apertures.14 For a FR, the signal s is

given by

S  GrBB

2

r21 

D2  	 R
L
, Td
, (1)

where  is the emissivity and R is the absolute spectral power responsivity. The geometric factors D

and  are given by D2  d2  r2  rBB2 and  

r2rBB

2

D4, where rBB and r are the radius of the

blackbody aperture and the FR apertures, respectively, and d is the distance between the FR aperture

and the blackbody aperture. G is the preamplifier

gain and L is the spectral radiance found by use of the

Planck radiation law. The radiance temperatures

are found when we iteratively change the blackbody

temperature in Eq. 1until an exact match of the

calculated signal to the measured signal is found.

The uncertainties of the radiance temperatures

found with the FRs are primarily determined by the

uncertainties in the spectral power responsivity.

Figure 5aplots the expanded uncertainties of the

SCF in the spectral power responsivity measurements. The lowest uncertainties are maintained in

the visible wavelength region from 400 to 900 nm

where the spectral power responsivity of the Si-trap

transfer detector can be smoothly interpolated between the discrete laser calibration wavelengths of

the HACR. The uncertainties of the spectral power

responsivity can be converted directly to uncertainties in temperature by use of the derivative of the

Wien approximation with respect to temperature:

L

L  c2


T

T2 (2)

is the relationship between the uncertainty in radiance L and the uncertainty in blackbody temperature

T; c2 is the second Planck’s constant, 1.4387752

cmK; and 
 is the wavelength. The Wien approximation is used to simplify the handling of equations.

Under these experimental conditions, no appreciable

Fig. 2. Schematic of the laboratory setup used for the spectral

irradiance scale realization showing the positions of the HTBB, the

FRs, the spectroradiometer, and the FEL lamp.

Fig. 3. Schematic of the filter radiometers used for the absolute

temperature determination of the HTBB.

Fig. 4. Absolute spectral irradiance responsivities of the FRs

used in the scale realization. Both filter radiometers FR2 and

FR4 are constructed with broadband photopic response filters that

differ in responsivity only slightly below 400 nm.

1 October 2002  Vol. 41, No. 28  APPLIED OPTICS 5881
differences exist between Eq. 2and the similar differential equation found when we use Planck’s radiance law in the wavelength between 250 and 2400

nm. Because of the changes in the shape of the

blackbody radiance with temperature as described in

the Planck radiance law, the temperature uncertainties are both dependent on temperature as well as

wavelength. The corresponding uncertainties in radiance temperatures are plotted in Fig. 5bfor a

blackbody temperature of 3000 K, where the lowest

temperature uncertainties exist in the spectral region between 400 to 900 nm.

B. Description of the Facility for Automated

Spectroradiometric Calibrations

All the experimental research described in this paper

was performed in the Facility for Automated Spectroradiometric Calibrations FASCAL, with the exception of the spectral power responsivity

measurements of the FRs.6 Briefly, the detector system consists of a prism-grating double monochromator with custom-modified entrance and exit optics.

A simplified schematic of FASCAL is shown in Fig. 2.

The light is collected with an off-axis spherical mirror

with either an integrating receiver for spectral irradiance or a flat plane mirror for spectral radiance.

The measurements from 250 to 900 nm were performed with a photomultiplier tube in dc measurement mode. We performed the measurements from

800 to 2400 nm using an InGaAs detector in photovoltaic mode using a mechanical light chopper at 290

Hz with phase-sensitive detection. A significant improvement to the FASCAL detection system is due to

the replacement of the PbS detector 
D*  4  1011

cmHz12

W with the extended InGaAs detector


D*  2  1012 cmHz12W, resulting in a standard deviation of signals 0.05% when a 1000-W

FEL lamp is measured from 800 to 2300 nm. The

spectrometer and the detector enclosure are also continuously purged with air filtered to remove CO2 and

H2O, thus improving the long-term stability of the

detector system.

C. Description of the High-Temperature Blackbody

One of the technological advances that makes possible the realization of the detector-based spectral irradiance scale is the development of pyrolytic

graphite blackbodies, enabling extended operations

near 3000 K without rapid degradation of the cavity.

The HTBB used in this study consists of pyrolytic

graphite rings with an inner diameter of 24 mm

stacked to form a cavity with a depth of 14.5 cm.

The cavity bottom consists of an inverted cone with

an apex angle of approximately 150°, and the radiance at the backside of the cavity bottom is imaged

through an opening at the rear of the cavity by use of

a fused-silica lens onto a temperature-stabilized photometer for operation in closed-loop configuration.

The lens also serves to seal the rear of the blackbody

cavity to atmosphere. The current of the HTBB

power supply is adjusted with a control loop to maintain a constant output from the photometer. Although the spectral irradiance in the ultraviolet

wavelength region could be increased with higher

temperatures, the HTBB was operated near 2950 K

to avoid possible changes in the spectral emissivity of

the blackbody that are due to the sublimation of the

graphite.15 Because the graphite rings expand approximately 10% from room temperature to near

3000 K, the current was increased at 0.1 As to nearly

510 A at 2950 K to allow gradual expansion of the

cavity. The HTBB was also turned off in a similar

manner to avoid thermophysical shocks.

Figure 6 is a plot of the radiance temperatures

measured during a single day of measurements from

9:30 to 14:00 with FR2, FR3, and FR4. The feedback

detector is a temperature-stabilized Si photodiode

with a photopic response filter. The optical feedback

is found to stabilize the HTBB to 0.0004 V at a full

signal of 4.4 V. Figure 6 shows that the HTBB temperature was stable to 0.5 K over the duration of the

5-h measurement. The expanded uncertainties of

the temperatures are shown for the FR2 temperatures that overlap the temperatures measured with

FR3 and FR4. The three FRs agree in radiance temperature determinations to 0.5 K, in agreement

with the combined expanded uncertainty in temperature of 0.86 K at 2950 K.

Each of the FR measurements is an independent

determination of temperature when a primary thermometer is used. A primary thermometer is distinguished from a secondary thermometer in that the

temperature is obtained by use of a primary thermometer without use of any adjustable parameters.16

Fig. 5. aExpanded uncertainties of the NIST SCF for spectral

power responsivity showing the low expanded uncertainties

0.22%between 400 and 900 nm. bThe uncertainties in the

spectral power responsivity converted to temperature uncertainties by use of the derivative of the Wien approximation at 3000 K.

5882 APPLIED OPTICS  Vol. 41, No. 28  1 October 2002
The temperature of the HTBB increased at most by 1

K over 20 h of continuous operation with constant

optical feedback control by use of the optical output

from the rear of the cavity. The slight increase in

temperature over time is possibly attributable to the

opening at the rear of the cavity that gets smaller

from carbon deposits at the edges of the opening.

The HTBB was operated with an open cavity with

continuous 0.5-1min purge of argon from the rear of

the housing and the argon exiting through the front

opening of the cavity.

D. Verification of the High-Temperature Blackbody as a

Planckian Radiator

To determine the spectral emissivity of the HTBB,

the spectral radiance of the HTBB was measured

from 250 to 2400 nm at discrete wavelengths by comparison with a VTBB with a high emissivity. Any

temperature nonuniformity of the cavity would lead

to deviations of the HTBB spectral radiance from a

single-temperature Planck radiance. For these

comparisons, the temperature of the VTBB was set at

2687 K, and the temperature of the HTBB was set at

2950 K. Although the temperatures are different,

the radiance ratios did not differ even at 250 nm,

where the differences are greatest, by more than a

factor of 7. Furthermore, prior to these measurements, the linearity of the spectroradiometer was

measured at various wavelengths with the portable

Beamconjoiner17 and was found to be linear under

these experimental conditions. The spectral radiance determinations were performed before and after

spectral irradiance transfer to a set of 1000-W FEL

lamps. The checks of the HTBB as a Planckian radiator were performed to verify that the HTBB did

not change in the spectral distribution because the

FRs are used to measure over a relatively broad spectral region.

The spectral radiance measurements of the HTBB

were performed with the aperture in front of the

spherical input mirror with the spectroradiometer

reduced to 4 cm in diameter, resulting in F25 focused at the opening of the HTBB at the plane of the

water-cooled aperture. The reduction in the opening of the spherical input mirror resulted in a circular

target of 12 mm in diameter at the bottom of the

HTBB cavity. To keep the same target area constant for the measurements, in both the spectral irradiance and the spectral radiance modes, the HTBB

was mounted on a motorized translation stage for

control of the distance between the HTBB and the

measuring instruments. If possible, the same area

at the rear of the HTBB should be viewed for all

measurements to avoid errors from the possible spatial nonuniformity of the HTBB.

We determined the temperature of the VTBB using

spectral radiance ratios at 655 nm to a vacuum

tungsten-filament lamp maintained at the freezing

temperature of gold as prescribed in the ITS-90.

The spectral radiance of the HTBB was determined

at discrete wavelengths by comparison with the

VTBB and also determined from the radiance temperature found with the FRs. The radiance temperatures of the HTBB found with the FRs were in

agreement with those found with the ITS-90 ratios to

within 0.5 K in all cases in which such comparisons

were performed. We compared the respective blackbodies using spectral radiance ratios:

L
,HTBB  L
,VTBB f


S
,HTBB

S
,VTBB

. (3)

The L
 and the S
 denote the spectral radiance and

the measured spectral radiance response of the

HTBB and the VTBB, and f
 is the possible linearity

correction to the response ratios. The spectral radiances of the HTBB were found to conform to a singletemperature Planck radiance law to within the

combined uncertainties of the measurements as

shown in Fig. 7. Figure 7 shows the percent differences from a single-temperature Planck radiance law

with the temperature of the HTBB determined with

the FRs and the spectral radiances determined with

the VTBB. The errors bars on the individual comparisons correspond to the expanded uncertainty of

0.86 K at 2943.4 K converted to a spectral radiance

uncertainty by use of the derivative of the Wien approximation from Eq. 2. As expected for comparison of two blackbodies, the differences in the spectral

radiance become smaller with increasing wavelength, but there are no discernible increasing spectral differences toward the shorter wavelengths, as

would be expected if either of the temperature assignments of the respective blackbodies were in error.

The differences between the detector-based radiance

temperatures and the source-based determinations

also agree with the previous measurements, which

also showed differences of 0.5% from 250 to 1000

nm.18

E. Spectral Irradiance Transfer to 1000-W FEL Lamps

The spectral irradiance assignment of twelve 1000-W

FEL working standard lamps occurred over a twoFig. 6. Temporal stability measurement of radiance temperatures with the FRs. The expanded uncertainties in temperature

of 0.86 K are shown for FR2. The temporal drift in the HTBB

temperature is less than 0.5 K over the duration of the nearly 5-h

monitoring time.

1 October 2002  Vol. 41, No. 28  APPLIED OPTICS 5883
week period from 28 September to 12 October 2000.

The spectral irradiances of a group of three lamps

were assigned at one time, and the measurements

were separated into the ultraviolet and the visible

wavelength region 250–900 nm, and the shortwave

infrared region 800–2400 nm. Because there are

four separate FEL lamp measurement stations, each

of the measurements of individual lamps was performed in a different station by use of different shunt

resistors, power supplies, and lamp mounts. Each

of the lamp stations was checked for possible position

effects, and no perceptible effects from station-tostation variations were found.

The HTBB was turned on at least 2 h before use

and was temperature-stabilized by the optical feedback. The temperature of the HTBB was assigned

by use of the FRs, and the spectral irradiance responsivity of the spectroradiometer was assigned by use of

the known spectral irradiance of the HTBB. All the

spectral irradiance responsivity transfers to the spectroradiometer were done at a distance of 43.406 cm

0.005 cmfrom the HTBB aperture to the 1-cm2

-

area aperture of the ISR, resulting in a 24.7-mmdiameter circular target area at the cavity bottom.

The spectral irradiance responsivity of the spectroradiometer is assigned by use of the known spectral

irradiance of the HTBB at the input aperture of the

ISR:

E
,HTBB  L
, TrBB

2

D2 , (4)

with the measurement parameters as defined in Eq.

1.

After the spectral irradiance responsivity assignment of the spectroradiometer, the spectral irradiance of a group of three FEL lamps was assigned with

each lamp measured in three separate source positions. The spectral irradiance of each lamp was assigned by

E
,FEL  E
,HTBB f


S
,FEL

S
,HTBB

, (5)

where E
,FELHTBBis the spectral irradiance of the

FEL lamp HTBB, S
,FELHTBBis the net signal from

the FEL lamp HTBBmeasured with the spectroradiometer, and f
 is the linearity correction factor for

the comparison. With use of a shutter, the background signals were subtracted from the total signals

to obtain the net signals. The distance of the HTBB

from the ISR was also chosen such that the same gain

factors could be used to measure both the FEL and

the HTBB. Figure 8 is a plot of the calculated spectral irradiances of the 1000-W FEL along with the

HTBB at 2950 K with the limiting aperture of 9.9933

mm 0.0002 mmin diameter and the ISR aperture

of 11.2838 mm 0.0002 mmin diameter separated

by a distance of 43.406 cm 0.005 cm. At all wavelengths, Fig. 8 shows that the HTBB has a greater

spectral irradiance than the FEL lamp. Although

the spectral irradiance changes by a factor 103 from

250 to 2400 nm, the HTBBFEL signal ratio does not

exceed 2.5. The close match of the irradiances was

chosen to minimize possible errors resulting from

signal-to-noise ratio, nonlinearity, and stray-light effects.

3. Uncertainty Analysis of the Detector-Based Spectral

Irradiance Scale

The discussion of the uncertainties associated with

the detector-based spectral irradiance scale realization is separated into parts. Because the absolute

radiance temperature determination of the HTBB is

performed with FRs with peak spectral responsivities

near 550 nm, the expanded uncertainties in the spectral irradiance measurement at 550 nm is discussed

first. The spectral irradiance uncertainties are converted into temperature uncertainties by use of the

Fig. 7. Spectral radiance differences of the HTBB from a singletemperature Planck radiance as assigned by use of the FRs to the

spectral radiances assigned by use of the VTBB. The error bars

indicate the 0.86 K expanded temperature uncertainty at 2950 K

converted to spectral radiance uncertainties, and the continuous

curves indicate the expanded uncertainties of the spectral radiance

scale.

Fig. 8. Spectral irradiance of the HTBB at 2950 K with the measurement parameters as described with the spectral irradiances of

a typical 1000-W FEL lamp. The measurement parameters were

chosen to closely match the signals of both sources.

5884 APPLIED OPTICS  Vol. 41, No. 28  1 October 2002
derivative of the Wien approximation. The Wien approximation is used because the measurements are

performed at short wavelengths from the peak wavelength of the 3000 K Planck spectral radiance. The

uncertainties of the spectral irradiances of the primary working standards are assigned. Finally, the

expanded uncertainties of the issued standards are

assigned with additional uncertainty added to account for the temporal changes of the working standard lamps.

The uncertainties associated with the detectorbased temperature determinations of the HTBB can

be found from the uncertainty analysis of Eq. 1as

shown in Table 1. The individual components are

listed in descending order of importance, with the

uncertainty that is due to the spectral power responsivity dominating. Additional sources of uncertainty from the alignment and aperture area

measurements are small. The expanded spectral irradiance responsivity uncertainty at 550 nm of 0.26%

leads to an expanded temperature uncertainty of 0.86

K at 2950 K.

Table 2 describes the additional uncertainties associated with the HTBB spectral irradiance including

the components that are due to spectral emissivity,

spatial uniformity, and temporal stability. The first

row shows the expanded uncertainty of the spectral

irradiance that is due to the 0.86 K expanded temperature uncertainty at 2950 K. The uncertainties

that are due to the spectral emissivity and the spatial

uniformity of the HTBB are then assigned. The

temporal stability of the HTBB was measured and

also constantly monitored by use of the optical feedback at the rear of the cavity. The uncertainties in

the alignment of the apertures and in the distance

measurements are included in the geometric factor

uncertainty.

The detectors used in the spectroradiometers have

shown better than 0.1% k  2stability during the

spectral irradiance measurements. However, the

increase of the uncertainty at 2400 nm because the

stability of the spectroradiometer responsivity is due

to the performance of the InGaAs detector. A substantial contribution to the total uncertainty comes

Table 1. Expanded Component Uncertainties in the Spectral Irradiance

Measurement with the FR at 550 nm

Source of Uncertainty

550 nm

Fractional

Uncertainty

Expanded

Uncertainty

%

Spectral power responsivity,

FR

R

R

0.22

Solid-angle factor,

HTBBFR

0.026

Area of detector aperture A

A

0.02

Area of HTBB aperture A

A

0.02

Measurement precision,

HTBBFR

0.006

Amplifier gain G

G

0.006

Combined expanded

uncertainty k  2

0.26

Table 2. Expanded Uncertainties of the Detector-Based 2000 Spectral Irradiance Scales of the Primary Working Standards and the

Issued Standardsa

Component

Wavelength nm

250 350 655 900 1600 2000 2300 2400

HTBB temperature uncertainty

0.86 K at 2950 K

0.57 0.41 0.22 0.16 0.09 0.08 0.07 0.07

HTBB spectral emissivity 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

HTBB spatial uniformity 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

HTBB temporal stability 0.1

Kh

0.07 0.05 0.03 0.02 0.01 0.01 0.01 0.01

Geometric factors in irradiance

transfer

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

Spectroradiometer responsivity

stability

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.5

Wavelength accuracy 0.1 nm0.58 0.38 0.18 0.005 0.011 0.013 0.011 0.011

Lampspectroradiometer

transfer

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

Lamp current stability 0.08 0.06 0.03 0.02 0.02 0.01 0.01 0.01

Uncertainty of the primary

working standards, total

k  2

0.85 0.60 0.36 0.28 0.24 0.24 0.23 0.54

Lamp-to-lamp transfer 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

Long-term stability of working

standards

1.31 0.94 0.50 0.36 0.20 0.16 0.14 0.14

Uncertainty of the issued

standards, total k  2

1.56 1.12 0.63 0.47 0.33 0.31 0.29 0.57

a

Uncertainty k  2%.

1 October 2002  Vol. 41, No. 28  APPLIED OPTICS 5885
from the uncertainty in the absolute wavelength.

The wavelength drive of the prism-grating spectroradiometer has an absolute optical encoder attached to

the shaft, and piecewise continuous polynomial corrections are applied to achieve 0.05-nm standard

uncertainty in the wavelength. For determination

of the uncertainties on the issued standards, additional components arising from the lamp-to-lamp

transfer and long-term stability of the working standards are added. A substantial increase in the total

uncertainties arises from the possible temporal drift

of the working standards. All lamp standards are

subjected to a screening procedure for temporal drift,

and lamps that change by more than 0.5% at 650 nm

over the duration of 24 operational hours are rejected

from further evaluation as possible standards.6 The

temporal drift is found to be inversely proportional to

the wavelength and is accordingly larger at the

shorter wavelengths.

To determine whether the uncertainties were correctly estimated, data from separate independent

scale realizations of a FEL lamp F210were analyzed. Figure 9 shows the percent differences from

the mean in the detector-based spectral irradiance of

the lamp with three independent assignments from

250 to 900 nm and from three other separate assignments from 800 to 2400 nm over four separate days.

The spectral irradiance assignments show that the

three independent scale realizations for a particular

wavelength region are all within the assigned k  2

expanded uncertainties of the 2000 spectral irradiance scale. The temperature of the HTBB was determined on each of the days during the realization,

and the spectral irradiance responsivity was assigned

approximately 30 min after a temperature assignment by use of the FRs. The separate spectral irradiance assignments are all within the expanded

uncertainties. The slight upturn in the uncertainties at 2400 nm is due to the rapidly decreasing spectral responsivity of the InGaAs detector near the

bandgap energy of the material. The spectral shape

of the expanded uncertainty follows the inverse

wavelength dependence expected for a scale based on

a temperature determination of a HTBB.

4. Comparison of the Detector- and Source-Based

Spectral Irradiance Scales

Table 3 shows the total expanded uncertainties of the

spectral irradiance scales from the 1990 and the 2000

realizations. Figure 10 shows that the detectorbased spectral irradiance scale results in the reduction in the uncertainties in the 250–900-nm

wavelength regions by a factor of 2 and a greater

reduction up to a factor of 10 in the uncertainties

from the 900- to 2400-nm wavelength region. The

reduction in the uncertainties is primarily due to the

elimination of the ISS that was used as a transfer

artifact to obtain spectral irradiance from the spectral radiance assignment. The spectral irradiance

of the ISS was lower than that of the 1000-W FEL

and was especially difficult to measure in the infrared

wavelength region with the previous PbS detector,

resulting in the large uncertainties. The detectorbased spectral irradiance utilizes the HTBB, which

has greater spectral irradiance than the 1000-W FEL

lamp at all wavelengths, and the improved InGaAs

detector in the infrared further reduces the measureFig. 9. Percent differences from the mean of three separate spectral irradiance scale realizations performed on four separate days.

The differences are shown with the assigned expanded uncertainties of the working standards for the detector-based spectral irradiance scale.

Table 3. Comparison of the Expanded Uncertainties in the Spectral

Irradiance Scales of the 1990 and 2000 Scale Realizations

Wavelength

nm

Expanded Uncertainties

in Spectral Irradiance

%k  2

1990 2000

250 1.8 1.56

350 1.1 1.12

655 0.9 0.63

900 1.1 0.47

1600 1.4 0.33

2300 3.8 0.29

2400 4.4 0.57

Fig. 10. Comparison of the expanded uncertainties of the 1990

scale realization along with the expanded uncertainties of the 2000

scale realization. The expanded uncertainties of the issued lamps

are greater because of the additional component of the long-term

temporal stability of the working standards.

5886 APPLIED OPTICS  Vol. 41, No. 28  1 October 2002
ment uncertainties. The spectral shape of the uncertainties also has the characteristic 1


dependence of the decrease in uncertainties with increasing wavelength that can be seen in Eq. 2.

The differences in the spectral irradiance between

the source-based and the detector-based spectral irradiance scale are shown in Fig. 11afor a set of

check standard lamps F34, F300, F315in the wavelength region from 250 to 900 nm and in the wavelength region from 800 to 2400 nm in Fig. 11b. At

NIST, a set of lamps working standard lampsare

used for routine calibrations, and another set of

lamps check standard lampsare set aside to verify

that the working standard lamps did not drift. The

check standards were used approximately twice a

year to verify that the working standard lamps did

not changed; thus the total operational hours on the

check standards are typically much less than the operational hours of the working standards.

In Fig. 11athe comparison of the detector-based

scale with the source-based scale shows that the difference of the NIST spectral irradiance assignments

is greater than their assigned expanded uncertainties by 0.5%. The sawtooth oscillations that can be

seen in the source-based spectral irradiance evident

at 400 nm is correlated in all the lamps and is

evident to a lesser extent at longer wavelengths.

The correlated oscillations are attributed to the experimental procedure used in the previous spectral

irradiance scale realization of 1992. In the realization of 1992, the ISS was assigned a spectral radiance

at a particular wavelength, and the spectral irradiance of a set of three lamps was assigned immediately

by use of the spectral irradiance of the ISS. Thus

the spectral irradiance at each wavelength is realized

separately and independently; and especially in the

ultraviolet region, the oscillations could arise from a

possible temporal drift of the ISS. Our ability to

maintain the spectral irradiance over ten years using

a set of stable lamps is shown by the agreement

among lamps F34, F300, and F315 as compared with

the detector-based spectral irradiance scale. The

standard deviation of the mean found when we used

the percent differences of the three lamps from the

detector-based scale is plotted in Fig. 11awith the

open diamonds and shows that the lamps have stayed

together as a group to 0.5% from 1992.

In the shortwave infrared wavelength region, the

source-based spectral irradiance scale from 800 to

2400 nm was last realized from the gold freezingpoint blackbody in 1990. A new spectral irradiance

scale realization was attempted in 1992 from 250 to

2400 nm with a more stable ISS, but the scale realization in the infrared region was not completed because of the insufficient spectral irradiance of the

1992 ISS in the infrared and the low signal-to-noise

ratio from the PbS detector. The discontinuity at

800 and 900 nm for a common lamp is due to the

separate scale realizations performed in 1990 and in

1992. For assignment of spectral irradiance of the

issued lamps, the different spectral irradiance values

were averaged to obtain a single value at those wavelengths. As in the comparisons from 250 to 900 nm,

the check standard lamps remained close together as

a group with their spectral irradiances much better

than 0.5% as shown in Fig. 11bby the open diamonds at the bottom of the figure. Two noticeable

drops in the irradiances are observed at 1600 and

2100 nm in the comparison of the scales. The Consultative Committee on Photometry and Radiometry

CCPRcomparison of 199019 also showed that the

1% drop at 1600 nm and the nearly 2% drop at 2100

nm were seen in all comparisons with the other countries, indicating that the two spectral features were

inherent to the NIST spectral irradiance scale of

1990. The differences of the detector-based spectral

irradiance scale to the source-based scale of 1990

show that the assignment of the spectral irradiances

were within their stated uncertainties since 1990.

These comparisons to the check standards should

reflect the differences between the new detectorbased scale and the scale realized in 1992, and more

Fig. 11. aComparison from 250 to 900 nm of the spectral irradiance assigned to the check standard lamps in 1992 with the

detector-based spectral irradiance assignments. The expanded

uncertainties assigned in 1990 are shown as the dark curve. The

standard deviations of the mean of the three lamps are shown as

open diamonds, indicating the good agreement between the three

lamps. bA comparison from 800 to 2400 nm of the three check

standard lamps of the 1990 spectral irradiance assignment with

the detector-based spectral irradiance assignment. The standard

deviations of the mean of the three lamps are shown as open

diamonds along with the expanded uncertainties of the 1990 scale

shown by the dark curve.

1 October 2002  Vol. 41, No. 28  APPLIED OPTICS 5887
importantly, the scale realized in 1990 before and

after the international comparison of spectral irradiance organized by the CCPR. If the differences seen

can be extrapolated to the CCPR comparisons in

1990, then the NIST spectral irradiance scale for the

comparison would have been approximately 1% low

in the visible and approximately 2% low in the ultraviolet wavelength region. The large variations in

the spectral irradiance scales of the individual countries preclude discerning whether the differences

found between the detector-based scale and the 1990

scale could be detected in the international intercomparison.

5. Discussion

Because of the long history of the spectral irradiance

scale at NIST and the resulting wide usage of the

FEL lamps issued by NIST, the one most important

result is the relationship between the spectral irradiances from the detector-based scale realization of

2000 and the previously assigned spectral irradiances. Figures 12aand 12bshow the means of

the spectral irradiances of the three working standards used to assign FEL lamps to the detector-based

spectral irradiance scale along with the expanded

uncertainties of the 1992 scale realization. In the

wavelength region from 250 to 900 nm, only one

point, at 250 nm, falls beyond the 0.5% of the expanded k  2uncertainties; and if the uncertainties

are increased to 3 k  3, then all the values are

within uncertainties. In the infrared region from

900 to 2400 nm, only three values exceed the expanded uncertainties by more than 0.5%, and again

all the differences fall within the 3 k  3uncertainties.

Because we have shown that the radiance temperature scale and the spectral radiance scale at NIST

are both in agreement with the detector-based scales

within the combined uncertainties, what are the reasons for the observed discrepancies in the spectral

irradiance scales? In the infrared wavelength region from 900 to 2400 nm, the spectral irradiances of

the check standard lamps are within the assigned

expanded uncertainties, although the irradiances

were assigned in 1990. The larger deviations of the

working standards can be attributed to the longer

operational hours and reveal that the spectral irradiances of the working standards should have been

verified against the check standards at shorter time

intervals.

Some of the differences from 250 to 900 nm that

can be seen in Fig. 12acan also be attributed to

temporal drift of the working standards because of

longer operational hours, but the comparison with

the check standards shows that much of the differences between the detector-based scale and the scale

realized in 1992 are also apparent in lamps that have

not been utilized extensively. The spectral irradiance scales of 1990 and 1992 are both dependent on

the radiance temperature and the spectral radiance

scales. Because both the radiance temperature

scales and the spectral radiance scales were found to

be in agreement with the detector-based scale within

the combined uncertainties, possible differences between the source-based and the detector-based spectral irradiances scales could have arisen in the

process of deriving the spectral irradiance scale from

the spectral radiance scale.

The long time period between the spectral irradiance scale realizations of 1992 and 2000 partly

results from the experimental difficulties in the realizations of a spectral irradiance scale with the

gold freezing-point blackbody. The need for numerous transfer artifacts and systematic corrections that are due to the less than optimal

performance of these artifacts prohibited frequent

scale realizations. The new detector-based spectral irradiance scale realization relies only on an

accurate radiance temperature determination of a

HTBB whose adherence to the Planck radiance law

Fig. 12. aComparison from 250 to 900 nm of the difference of

the average of the spectral irradiances assigned in 1992 of three

working standards F234, F302, and F210 to the detector-based

spectral irradiances. The curve indicates the expanded uncertainties of the 1992 spectral irradiance scale. bA comparison

from 800 to 2400 nm of the working standard lamps of the differences of the 1990 spectral irradiance scale to the detector-based

scale. The curve indicates the expanded uncertainties of the 1990

spectral irradiance assignments.

5888 APPLIED OPTICS  Vol. 41, No. 28  1 October 2002
was verified by comparison with a blackbody with a

known high emissivity. Initially, the detectorbased spectral irradiance scale realizations will be

performed on an annual basis in FASCAL. With

sufficient evidence that the spectral irradiance

scale can be maintained on working standard lamps

without increases in the errors that are due to longterm drift, the scale realizations will be performed

on a less frequent basis.

In the past scale realizations, spectral irradiance

assignments at additional wavelengths have been

difficult because of the lengthy procedure needed

for the realizations. The temporal drift of the

transfer artifacts used in the realization resulted in

the limited number of wavelengths of the spectral

irradiance assignments of the working standards.

Because the HTBB used in the detector-based spectral irradiance scale is temporally stable with a

drift of 1 K in 20 h at 3000 K, spectral irradiance

assignments of working standards are possible at

many additional wavelengths if desired by the optical measurement community. These spectral irradiance calibrations at much finer wavelength

intervals can help to resolve issues such as the

optimal interpolation algorithm for use in the calibration of spectroradiometers.20

6. Effect of the Changes That Are Due to the

Detector-Based Spectral Irradiance Scale

The greatest changes of the detector-based spectral

irradiance scale realization result from the lower uncertainties, enabling measurements to be made with

higher accuracy and confidence. However, if the

dominant sources of the total measurement uncertainties were not due to the intrinsic scale uncertainties of the transfer artifact, then it would be difficult

to utilize the lower uncertainties achieved with the

detector-based scale. In addition, the small differences between the detector-based and the sourcebased spectral irradiance scales are within the

expanded uncertainties of many measurement systems, including the spectroradiometers used in the

ultraviolet monitoring of terrestrial solar spectral irradiance.21

In the photometric community, possible changes

could arise in the calibration of sources for color temperature.22 At NIST, color temperatures are assigned in the Photometric Calibration Facility by use

of the relative spectral irradiance of FEL lamps. Because the spectral shapes of the source-based and the

detector-based spectral irradiances in the wavelength region from 350 to 700 nm differ at most by

0.5% 
Fig. 12a, the changes to the color temperature assignments will be negligible.

7. Conclusion

The realization of the NIST detector-based spectral

irradiance scale was described. The realization is

based on the absolute detector-based radiance temperature determinations of a HTBB and is now traceable to the HACR instead of a fixed-point blackbody.

The differences in the spectral irradiances between

the gold-point blackbody-based and the detectorbased scales are discussed, and the differences are

found to agree within the combined uncertainties of

the measurements. The detector-based scale results in the reduction of the uncertainties from 250 to

2400 nm with the greatest reduction occurring in the

spectral range from 1000 to 2400 nm with reductions

by almost a factor of 10. The new detector-based

spectral irradiance scale realization also corrects the

correlated deviations from a smooth Planck radiance

law that existed in the old spectral irradiance scale.

Finally, the differences in the way that the scale is

derived represent a fundamental change in the scale

realization of spectroradiometric sources, and these

results are only the beginning of the implementation

of the detector-based source scales at NIST.

The authors gratefully acknowledge the help and

encouragement of B. Carol Johnson, Robert Saunders, and Al Parr of the Optical Technology Division

at all stages of this project. The authors also acknowledge the assistance of Tom Larason and

George Eppeldauer in the development and characterization of the filter radiometers used in the scale

realization.

References

1. A. C. Parr, “A national measurement system for radiometry,

photometry, and pyrometry based upon absolute detectors,”

NIST Tech. Note 1421 National Institute of Standards and

Technology, Gaithersburg, Md., 1996.

2. T. R. Gentile, J. M. Houston, and C. L. Cromer, “Realization of

a scale of absolute spectral response using the National Institute of Standards and Technology high-accuracy cryogenic radiometer,” Appl. Opt. 35, 4392–4403 1996.

3. C. L. Cromer, G. Eppeldauer, J. E. Hardis, T. C. Larason, and

A. C. Parr, “National Institute of Standards and Technology

detector-based photometric scale,” Appl. Opt. 32, 2936–2948

1993.

4. Y. Ohno, “Improved photometric standards and calibration

procedures at NIST,” J. Res. Natl. Inst. Stand. Technol. 102,

323–331 1997.

5. K. D. Mielenz, R. D. Saunders, A. C. Parr, and J. J. Hsia, “The

1990 NIST scales of thermal radiometry,” J. Res. Natl. Inst.

Stand. Technol. 95, 621–629 1990.

6. J. H. Walker, R. D. Saunders, J. K. Jackson, and D. A. McSparron, “Spectral irradiance calibrations,” NBS Measurement Services SP 250-20 National Bureau of Standards,

Gaithersburg, Md., 1987.

7. H. J. Kostkowski, D. E. Erminy, and A. T. Hattenburg, “Highaccuracy spectral radiance calibration of tungten-strip lamps,”

Adv. Geophys. 14, 111–127 1970.

8. K. D. Mielenz, R. D. Saunders, and J. B. Shumaker, “Spectroradiometric determination of the freezing temperature of

gold,” J. Res. Natl. Inst. Stand. Technol. 95, 49–67 1990.

9. V. I. Sapritsky, “Black-body radiometry,” Metrologia 32, 411–

427 1995–1996.

10. H. Preston-Thomas, “The ITS-90,” Metrologia 27, 3–10 1990.

11. J. B. Fowler, R. D. Saunders, and A. C. Parr, “Summary of the

high-accuracy aperture-area measurement capabilities at the

NIST,” Metrologia 37, 621–623 2000.

12. T. C. Larason, S. S. Bruce, and A. C. Parr, “Spectroradiometric

detector measurements: Part I—Ultraviolet detectors and

Part II—Visible to near-infrared detectors,” NIST Measurement Services SP 250-41 National Institute of Standards and

Technology, Gaithersburg, Md., 1998.

1 October 2002  Vol. 41, No. 28  APPLIED OPTICS 5889
13. P. Sperfeld, J. Metzdorf, S. Gala Yousef, K. D. Stock, and W.

Mo ̈ller, “Improvement and extension of the blackbody-based

spectral irradiance scale,” Metrologia 35, 267–271 1998.

14. H. W. Yoon and C. E. Gibson, “Determination of radiance

temperatures using detectors calibrated for absolute spectral

power response,” in Proceedings of the Seventh International

Symposium on Temperature and Thermal Measurements in Industry and Science, J. Dubbeldam and M. J. de Groot, eds.

Edauw and Johannisen, The Netherlands, 1999, pp. 737–742.

15. P. Sperfeld, S. Galal-Yousef, J. Metzdorf, B. Nawo, and W.

Moller, “The use of self-consistent calibrations to recover absorption bands in the black-body spectrum,” Metrologia 37,

373–376 2000.

16. T. J. Quinn, Temperature Academic, London, 1990.

17. A. Thompson and H. M. Chen, “Beamcon III: a linearity measurement instrument for optical detectors,” J. Res. Natl. Inst.

Stand. Technol. 99, 751–755 1994.

18. H. W. Yoon and C. E. Gibson, “Comparison of the absolute

detector-based spectral radiance assignment with the current

NIST-assigned spectral radiance of tungsten strip lamps,”

Metrologia 37, 429–432 2000.

19. J. H. Walker, R. D. Saunders, J. K. Jackson, and K. D. Mielenz,

“Results of a CCPR intercomparison of spectral irradiance

measurements by national laboratories,” J. Res. Natl. Inst.

Stand. Technol. 96, 647–668 1991.

20. L. K. Huang, R. P. Cebula, and E. Hilsenrath, “New procedure

for interpolating NIST FEL lamp irradiances,” Metrologia 35,

381–386 1998.

21. G. Bernhard and G. Seckmeyer, “Uncertainty of measurements of spectral solar UV irradiance,” J. Geophys. Res. 104,

14321–14345 1999.

22. Y. Ohno, “Photometric calibrations,” NIST Measurement Services SP 250-37 National Institute of Standards and Technology, Gaithersburg, Md., 1997.

5890 APPLIED OPTICS  Vol. 41, No. 28  1 October 2002
Volume 101, Number 2, March–April 1996

Journal of Research of the National Institute of Standards and Technology

[J. Res. Natl. Inst. Stand. Technol. 101, 109 (1996)]

The NIST Detector-Based Luminous

Intensity Scale

Volume 101 Number 2 March–April 1996

C. L. Cromer, G. Eppeldauer,

J. E. Hardis1

, T. C. Larason,

Y. Ohno, and A. C. Parr

National Institute of Standards and

Technology,

Gaithersburg, MD 20899-0001

The Syste`me International des Unite ́s (SI)

base unit for photometry, the candela,

has been realized by using absolute detectors rather than absolute sources. This

change in method permits luminous intensity calibrations of standard lamps to be

carried out with a relative expanded uncertainty (coverage factor k = 2, and thus a

2 standard deviation estimate) of 0.46 %,

almost a factor-of-two improvement. A

group of eight reference photometers has

been constructed with silicon photodiodes, matched with filters to mimic the

spectral luminous efficiency function for

photopic vision. The wide dynamic range

of the photometers aid in their calibration. The components of the photometers

were carefully measured and selected to

reduce the sources of error and to provide

baseline data for aging studies. Periodic

remeasurement of the photometers indicate

that a yearly recalibration is required.

The design, characterization, calibration,

evaluation, and application of the photometers are discussed.

Key words: calibration; candela; illuminance; lumen; luminous intensity; lux;

measurement; photometer; photometry;

scale; standards; units.

Accepted: December 11, 1995

1. Introduction

Traditionally, standardization in photometry was a

discipline driven by primary light sources, first candles,

then flames [1], carbon-filament lamps, and, beginning

in 1948, blackbody radiators operated at the freezingpoint temperature of molten platinum [2]. The latter

marked a turning point, because the platinum-point

blackbody, valued for its reproducibility and universality compared with the earlier alternatives, was the first

standard photometric source with radiometric properties that could be readily calculated, in principle.

Over time, dissatisfaction with platinum-point blackbody standards grew. For the few national laboratories

that had them, they were difficult to maintain. They

operated at a temperature of little technological interest

1 To whom correspondence should be sent, jhardis@nist.gov.

[taken first as 2045 K, later 2042 K, on the International

Practical Temperature Scale of 1968 (IPTS-68)], and the

applicability of this broadband radiation to spectroradiometry was poor. In 1975, Blevin and Steiner [3],

reflecting the mood of the period, made two proposals.

They sought first to redefine the photometric base unit

in a manner to fix its relationship with other Syste`me

International des Unite ́s (SI) base units, such as the

meter and the ampere. Second, they argued that the

photometric base unit should be changed from the candela to the lumen, considering the close relationship

between luminous flux (lumen, lm)2 and radiometric

power measurements (watt, W).

2 As an aid to the reader, the appropriate coherent SI unit in which a

quantity should be expressed is indicated in parenthesis when the

quantity is first introduced.

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After additional study and due consideration, in 1979

the 16th Confe ́rence Ge ́ne ́rale des Poids et Mesures

(CGPM) adopted the first of these proposals. They abrogated the definition of the candela (originally called

the new candle) first adopted by the 8th Confe ́rence

Ge ́ne ́rale in 1948, and redefined it as follows [4]:

The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 3 1012 hertz and that has a

radiant intensity in that direction of (1/683) watt per

steradian.

The 1979 redefinition of the candela permitted diverse methods to be used in deriving luminous intensity

scales. All the methods also rely on the principles governing photometry as compiled by the Bureau International des Poides et Mesures (BIPM) for the Comite ́

Consultatif de Photome ́trie et Radiome ́trie (CCPR) [5].

These include the Commission Internationale de

L’E ́ clairage (CIE) spectral luminous efficiency function

for photopic (cone) vision, V(l), which relates visual

sensitivities at different wavelengths [6]. (The lone frequency of 540 3 1012 Hz mentioned in the definition

has a wavelength of 555.016 nm in standard air, which

for almost all purposes can be taken to be 555 nm

without affecting the accuracy of a real measurement.)

Since the redefinition, national standards laboratories

[7–14] and other research facilities [15] have been free

to realize the candela by use of whatever radiometric

means they found most suitable. Most have used detectors that were equipped with filters that were designed

to match their spectral responsivity to the V(l) function. At NIST [then the National Bureau of Standards

(NBS)] the luminous intensity scale remained based on

a standard source, a blackbody radiator operating at the

freezing-point temperature of molten gold (the gold

point) [7].

As shown in Fig. 1, the blackbody radiation at the

gold point (1337.58 K on IPTS-68) was used to calibrate

a variable temperature blackbody, which provided the

NBS scale of spectral radiance [16]. From this the spectral irradiance scale was derived [17]. The luminous

intensity scale was derived through spectral irradiance

measurements of selected lamps forming a primary reference group, which maintained the candela with respect to the spectral irradiance scale. A secondary reference group of lamps, calibrated against the primary

group, was used for routine candela calibrations.

All the measurements in this lineage compared a light

source with another light source. The final measurement

uncertainty of 0.8 % (2 standard deviation estimate)

[18] contained a relatively large component from the

uncertainty in the gold-point temperature at the top of

Fig. 1. Calibration chain for luminous intensity prior to the present

study.

the chain (comparing IPTS-68 with thermodynamic

temperature), and it was further limited by the longterm behavior of the incandescent lamps that were used.

In 1990, the introduction of the new International

Temperature Scale (ITS-90) caused changes. The gold

point was redefined as 1337.33 K [19], which caused

the NIST luminous intensity scale to shift, depending on

the color temperature of the source, by approximately

0.35 % [20]. More important, NIST revised its procedures to decouple the spectral radiance scale from ITS90. NIST now considers the gold-point temperature to

be a measured rather than a defined quantity. While the

current NIST measurement of 1337.33 K 6 0.23 K (restated from ‘‘3s’’ to k = 2) [21] is in exact agreement

with ITS-90, the new policy allows for the possibility of

future scale revisions as experimental information becomes available. The current NIST gold-point temperature of 1337.33 K is detector based. That is, the result

follows from measurements using absolute radiometric

detectors, a silicon photodiode and an electrically calibrated radiometer.

The purpose of this paper is to describe the considerable simplification that results by realizing the candela

against the detector base directly. We expand upon our

previous reports on this subject [22,23], giving more

details behind the new NIST scale for luminous intensity

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Journal of Research of the National Institute of Standards and Technology

and discussing our experience with it. The benefits of

this conversion include reduced uncertainty in our calibration services and the additional flexibility to provide

new calibration services for detector-based devices.

2. Experimental Approach

2.1 Mathematical Framework

The photometric analog of power in radiometry is

luminous flux, Fv, (lm), where

Fv = Km E

l

Fe(l) V(l) dl, (1)

where Fe(l) is the spectral radiant flux of the light

(W/nm) and Km is the proportionality constant in the

definition of the candela. While a strict reading of the

definition gives Km = 683.002 lm/W [6], for almost all

purposes it is taken to be 683 lm/W without affecting

the accuracy of any real measurement.

A photometer is a device that can be used to help

measure such a flux. Typically, it has an output current3

I (ampere, A), where

I = E

l

Fe(l) s(l) dl, (2)

where s(l) (A/W) is its spectral responsivity. It is advantageous to factor

s(l) = s(555) sn(l), (3)

where s(555) (A/W) is the value of s(l) at 555 nm. This

emphasizes the similarity of sn(l) to V(l), both dimensionless functions that are normalized at 555 nm. It also

permits the overall uncertainty of the spectral responsivity scale to be associated with one number, s(555),

with the function sn(l) consisting of relative measurements only.

The luminous responsivity [24] of the photometer is

sv (A/lm), where

sv = I

Fv

= s(555)

Km

E

l

Fe(l) sn(l) dl

E

l

Fe(l) V(l) dl

. (4)

For a perfect photometer, sn(l) would equal V(l), and

its luminous responsivity would be independent of the

power distribution of the light. In practice, this approach

3 Current is used as an example; the output might be a voltage instead.

requires knowing Fe(l) in order to calculate a spectral

mismatch correction factor

F =

E

l

Fe(l) V(l) dl

E

l

Fe(l) sn(l) dl

. (5)

In general, the closer sn(l) is to V(l), the better F will

be known for the same incertitude about Fe(l).

Figure 2 illustrates the application of such a photometer to luminous intensity measurement. In Fig. 2a, it is

supposed that the photometer intercepts a beam of light,

and that all the light illuminates only a portion of the

active area of the photometer. In this case, the photometer would have an output current I from which the luminous flux of the beam could be determined, presuming

that s(l) is sufficiently invariant from point to point over

the active area:

Fv = Km F I

s(555) . (6)

In Fig. 2b, it is further supposed that the photometer is

fitted with an aperture of precisely known area. Then, if

the light is not confined to a small spot but rather overfills the aperture uniformly, the photometer would have

an output current I that is proportional to the illuminance Ev (lumen per square meter, lux, lx) on the aperture. For an aperture area A (square meter, m2

),

Fig. 2. Application of a photometer to luminous intensity measurement as a progression. (a) When the light beam underfills the entrance

aperture, the photometer measures luminous flux (lm), the photometric analog to radiant power. The responsivities of our detectors were

tested in at least seven positions, as shown. (b) When the light beam

overfills the entrance aperture, the photometer measures illuminance

(lx). (c) When the photometer is used with a point light source at a

distance, the aperture area and the distance to the source combine to

define a solid angle. The photometer then measures the luminous

intensity (cd) of the source.

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Journal of Research of the National Institute of Standards and Technology

Ev = Km F I

s(555)A . (7)

Figure 2c shows the overall geometry for luminous intensity measurement. A point light-source a distance r

from the plane of the aperture and lying on the normal

to its center would have a luminous intensity Iv (lumen

per steradian, candela, cd), where

Iv = Km FIr 2

s(555)A . (8)

The applicability of these geometric prerequisites to

real measurements is explored below.

2.2 Description of the Photometers

To measure photometric quantities and to maintain

the luminous intensity scale at NIST, a group of eight

photometers has been developed. Many laboratories

have used absolute detectors such as electrically calibrated thermal detectors and self-calibrated silicon

photodiodes to realize the candela. We chose to use

calibrated silicon photodiodes because of their wider

dynamic range and simplicity of operation. The photometers contain specially selected silicon photodiodes

with V(l) matching filters, as well as the electronics to

implement the high-sensitivity, wide-dynamic-range

circuit previously described [25]. With an integration

time of 1.67 s, a measurement bandwidth of 0.3 Hz, and

an amplifier gain of 1011 V/A, the output voltage noise

in these devices corresponds to ø 1 fA of photocurrent.

This important feature of the NIST detectors permits

precise measurement of sn(l) even in the regions where

its values are small.

Figure 3 depicts the photometer design. The silicon

photodiode, the V(l) correcting-filter package, and a

precision aperture are mounted in the front piece of a

cylindrical housing. A PTFE4 disk of low electrical conductivity supports the photodiode; small pin-terminals

in the disk form a socket. The V(l) filter is glued to a

holder and is positioned close to the photodiode. On the

front side of the filter, the precision aperture is glued to

a holder. This holder is carefully machined so that its

front surface, the frontmost surface of the photometer, is

3.00 mm from the plane of the aperture knife edge. All

these components are marked in a manner that permits

us to preserve their orientation during disassembly and

reassembly.

4 PTFE, polytetrafluoroethylene, is more commonly known as Teflon,

which is a brand name for such materials.

Fig. 3. Photometer design. A filter modifies the spectral responsivity of a silicon photodiode to replicate as

closely as possible the 1924 CIE spectral luminous efficiency function for phototopic vision.

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Journal of Research of the National Institute of Standards and Technology

The cylindrical housing itself, which extends back

from the front piece shown in Fig. 3, contains an amplifier that also acts as a photocurrent-to-voltage converter.

A switch selects the transimpedance gain of the amplifier, decade values from 104 V through 1010 V. (Photometers 1 and 2 also have 1011 V ranges.) The characteristics of the filter and photodiode change with

temperature, so the operating temperature of the photometer is monitored by a sensor inserted in the front wall

of the housing [26]. The housing contains all additional

components necessary for signal and temperature outputs; it is lighttight and acts as an electrical shield.

2.3 The New Luminous Intensity Scale

It is simpler to realize the candela by this approach,

diagramed in Fig. 4. The luminous intensity scale is

derived by measuring s(l) of each photometer in the

group directly against the NIST spectral responsivity

scale. The spectral responsivity scale is derived from

comparative measurements against absolute radiometric

detectors; at the time of the initial study, 100 % quantum

efficient detectors [27] were the basis of the scale. Today, the scale is based on cryogenic radiometry5 [28].

With the application of the V(l) curve in Eq. (5), and

the application of the geometric definitions in Eq. (8),

the candela is determined. Additionally, since the photometers do not age in use as rapidly as lamps do, an

additional step to form a working group of photometers

for routine use is unnecessary.

Fig. 4. Calibration chain for luminous intensity as revised by the

present study.

5 The photometers cannot be compared directly against the cryogenic

radiometer since the radiometer requires a laser light source. The

parallel surfaces of the optical elements in the photometers might

cause errors due to interference effects with such illumination.

3. Characterization of the Photometers

3.1 Instrumentation and General Procedures

The principal apparatuses used to study the photometers and their components are shown in Fig. 5. They

comprise the Spectral Comparator Facility (SCF),

which holds the NIST spectral responsivity scale referenced in Figs. 1 and 4. An ultraviolet (UV) instrument

spans 200 nm to 400 nm; a visible/near-infrared (IR)

instrument spans 350 nm to 1800 nm. A detector under

test is held in a carriage that can be translated under

computer control. Any point on the active area of the

detector can be positioned at the focus of a nearly circular spot, 1.1 mm or 1.5 mm in diameter for the visible

or UV system, respectively. The carriage also holds reference detectors that serve as secondary standards and

that are measured alternately with the device being

tested. Compensation for changes in the light source

during the course of the measurement is made by using

the signal from a monitor detector. The computer controls the monochromator, which has a bandpass of 4 nm

for this spot size and a spectral standard uncertainty of

6 0.2 nm [29]. The apparatuses typically deliver a few

microwatts of optical power to the detector.

Before the photometers were assembled, the SCF was

used to study their components, both to diagnose systematic effects and as the basis for aging studies. When

the spectral responsivity of an individual photodiode or

a photometer (the photodiode, filter, and aperture together) was measured, the device itself was mounted on

the carriage. For the spectral transmittance of a filter

alone to be determined, the filter was held on the carriage, but a photodiode behind it was not. (Filter transmittance is the ratio of the apparent detector responsivity with and without the filter interposed in the beam.)

In this case, the photodiode was tilted to prevent interreflections.

Care was taken to insulate thermally the devices from

the carriage, which heats up during use because of its

stepping motors. The ambient temperature during measurement was monitored; when applicable, the temperature circuitry of the device under test was used. This

permitted a direct comparison between the temperatures

at calibration and use. Generally, variations in ambient

temperature were held within 6 1 8C during the course

of a measurement.

In addition to the optical calibrations performed at the

SCF, the transimpedance gains of the photometer amplifiers were calibrated electrically. With this procedure,

the photodiode is replaced by a computer-controlled

voltage source, VIN, and a resistor substitution box in

series. Unlike the internal resistors Rf built into the

photometer heads, the external resistors REXT are easily

remeasured. (As explained in Ref. [25], Rf is the trans113
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Fig. 5. Facility used to calibrate the photometric detectors: (a) with visible and IR

radiation, (b) with UV radiation.

impedance gain of the amplifier.) For many combinations of internal and external resistors (as selected by the

photometer gain switch and the substitution box, respectively), the output of the photometer, VOUT, is measured

for a series of VIN. The linear coefficient of this dependence, as obtained from a least-squares fit, is equal to

the corresponding Rf/REXT. This permits the individual

values of Rf to be determined with a relative expanded

uncertainty of < 0.01 % by data fitting. Calibrations on

the SCF, reported in the unit volt per watt for an individual photometer gain-switch setting, can be transferred

between different settings when these data are used.

3.2 Photodiodes

For this project we used Hamamatsu S1226 and

S1227 series photodiodes6 [30]. They were selected for

6 Certain commercial equipment, instruments, or materials are identified in this paper to foster understanding. Such identification does not

imply recommendation or endorsement by the National Institute of

Standards and Technology, nor does it imply that the materials or

equipment identified are necessarily the best available for the purpose.

the largest shunt resistance that the manufacturer could

provide, 2.5 GV to 7.0 GV, in order to minimize noise

and drift in the circuit [25]. This type of photodiode has

less infrared sensitivity than some others, which is advantageous for photometry. As a consequence, their infrared response is more temperature dependent than the

alternatives. We used quartz rather than glass or resin

windows, since we found that the former had less surface scatter. S1227-1010BQ photodiodes having 1 cm2

area were used in Photometers 1 and 2 because they

contained larger V(l) filters. The other six photometers

used S1226-8BQ 0.3 cm2 photodiodes, with the exception of Photometer 4, which contained an S1227-66BQ.

(The only difference was in the case.)

Figure 6 shows the absolute spectral responsivity of

three of these photodiodes, at one spot in their centers,

as measured at the SCF. The dashed curve is the measurement of Photodiode 1. Photodiode 2 behaved similarly. The solid and dotted curves, measurements of

Photodiodes 7 and 8 respectively, bound the responsivity

curves of the remaining photodiodes.

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Fig. 6. Absolute responsivity of the silicon photodiodes used in the

detectors. The dashed curve is Photodiode 1, type S1227-1010BQ.

Photodiode 2, of the same type, matches very closely. The solid curve

is Photodiode 7 and the dotted curve is Photodiode 8, both of type

S1226-8BQ. All other photodiode curves are bounded by the latter

two and are similarly shaped. The relative standard uncertainty of

0.3 % is commensurate with the curve widths.

The eight photodiodes were chosen after screening

many more for uniformity over their active areas, particularly the portion that would be visible through an aperture. Uniformity maps such as the one shown in Fig. 7

for Photodiode 2 were made for each device. To construct a uniformity map, the photodiode responsivity

was measured on the SCF on a grid of points 0.5 mm

apart at three different wavelengths. Mathematica [31]

was used to generate surface plots. Typically, the greatest responsivity was at the edge of the photodiode, as in

Fig. 7 where the most sensitive spot is the lower right

corner. The responsivities over the interior ‘‘bowl’’ of

the selected photodiodes were generally constant to better than 0.2 %.

The change in photodiode responsivity due to a

change in temperature is shown in Fig. 8. Six photodiodes, most of which were included among the final

eight, were tested in a temperature-controlled housing.

At each wavelength, the spectral responsivities of the six

were measured at the SCF at 25 8C, 30 8C, and 35 8C.

Figure 8 shows the average of the six results, the linear

temperature dependence as determined through leastsquares fitting. For the wavelengths of most interest in

photometry, 400 nm to 700 nm, the temperature dependence of the photodiode responsivity was < 0.03 %/8C.

3.3 Filters

We obtained layered, colored glass filters from various sources to benefit from the experience that this

diversity offers. Filters 1 and 2 were provided through

the courtesy of the National Research Council of

Canada (NRC), Filter 3 was provided courtesy of the

National Physical Laboratory of the U.K. (NPL), and

Filters 4 to 8 were manufactured by PRC Krochmann

(PRC)[32]. Such filters are individually made to achieve

a good realization of the V(l) function. First, the

glasses are carefully chosen [8,33], and then the thicknesses of the individual glass layers are determined

Fig. 7. Responsivity map of a typical photodiode used in this study. The responsivity of a photodiode (A/W) was measured while scanning a

monochromatic probe beam over the surface. This photodiode, which was used in Photometer 2, is 1 cm on a side. The grey scale shows the

responsivity at a point, referenced to the greatest value on the device (100 %). The contours indicate changes of 0.05 % in responsivity.

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Fig. 8. Temperature dependence of the silicon photodiodes at 30 8C. Responsivities of six

photodiodes of the types used in this work were measured at 25 8C, 30 8C, and 35 8C. The

plot shows the linear change in responsivity, as a fraction of their nominal values, averaged

over the six photodiodes. Individual variations among the six generally agreed within the

measurement noise. The error bars represent the statistically estimated standard deviation,

from the sample of six.

through an iterative procedure including repeated polishing and transmittance measurements. Filters 1 and 2

were originally designed to match QED-200 trap detectors; Filter 3 was designed to match Centronics OSD

300-5 photodiodes. Filters 4 to 8 were optimized to

match our type of silicon photodiode.

While spectral match is important, so that Eq. (5) is

insensitive to Fe(l), other important filter properties

include the spatial uniformity, birefringence, and temperature dependence. Filters 4 to 8 were selected from

among 24 candidates after visual inspection. Filters with

obvious dislocations, scratches, bubbles, and other optical defects were rejected. The remaining filters were

screened for uniformity by scanning them with a whitelight spot 1.5 mm to 2.0 mm in diameter. Those with the

sharpest and largest changes were eliminated.

Since the filters are composed of dissimilar layers

cemented together, any resulting strains might cause

birefringence or a polarization-dependent transmittance. (The light from a monochromator during calibration is partially polarized.) To verify the absence of such

a problem, representative filters were tested. A plane

polarizer was interposed between the photometers and a

lamp operating at approximately 2856 K. No change in

signal above noise was noted as the photometer was

rotated, limiting the potential error to 0.01 %. Nevertheless, candidate filters that showed the greatest birefringence were also rejected.

After selecting the most promising filters, more detailed diagnostics were performed. Transmittance measurements were made in 5 nm intervals, and at many

positions on the filters to determine their spatial uniformity. Hexagonal patterns were used, consisting of 37

spots for the larger filters (1 and 2), and 7 spots for the

smaller (3 to 7). Figure 9 shows the average transmittances of all spots measured on representative filters,

using the SCF. Figure 9a compares representative filters

from the different sources; others from a common

source would be indistinguishable on the graph. However, Filter 8 was from a different batch and provided a

better spectral match than the other PRC filters. The

small difference between it and the others is highlighted

in Fig. 9b.

Figure 10 shows the variation among the measurements at the different spots, expressed as the scatter of

the measurements. Scatter in excess of the measurement

noise (the heavy curves) represents non-uniformity in

the filter transmittance. Figure 10b provides a striking

illustration of how the individual layers in these filters

contribute differently at different wavelengths. Below

525 nm, the change in transmittance between Filters 5

and 8 (seen in Fig. 9b) is well correlated with the improved uniformity of Filter 8.

Of particular concern is the temperature dependence

of the filter transmittance. Figure 11 shows representative data obtained by using a commercial spectrophotometer equipped with a sample heater. A 3 mm by 10 mm

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Fig. 9a. Transmittance of the matching filters used in the detectors.

The standard deviation of the measurements, as the percent of the

signal, is shown. Representative samples of the filters from the three

sources: Filter 2, NRC, dashed curve; Filter 3, NPL, dotted curve;

Filter 5, PRC, solid curve.

Fig. 9b. Transmittance of the matching filters used in the detectors.

The standard deviation of the measurements, as the percent of the

signal, is shown. Comparison of the two batches of PRC filters: Filter

6, first batch, solid curve; Filter 8, second batch, dotted curve.

probe beam was used. For Filter 3, this data is consistent

with the filters discussed in Ref. [8]. This data is also

consistent with the broadband temperature dependence

of the complete photometers, which is discussed in detail below.

Fig. 10a. Transmittance uniformity of the matching filters, comparing several positions on the filters. The variation between the measurements is given by their standard deviations from their means. NRC and

NPL filters. The heavy curves are the limiting measurement noise:

solid for NRC, broken for NPL. Filter 1 (NRC) is the light solid curve;

Filter 2 (NRC) is the light dashed curve; Filter 3 (NPL) is the light

dotted curve.

Fig. 10b. Transmittance uniformity of the matching filters, comparing several positions on the filters. The variation between the measurements is given by their standard deviations from their means. PRC

filters. The heavy curve is the measurement noise. Filter 6 (first batch)

is the light solid curve, and is typical of the others in the batch. Filter

8 (second batch) is the light dashed curve.

3.4 Apertures

The photometers were fitted with precision apertures,

nominally 0.5 cm2 for Photometers 1 and 2, and 0.1 cm2

for Photometers 3 to 8. They were electroformed out of

nickel-clad copper and given a black, nickel finish. The

fabrication and properties of similar apertures are discussed in Ref. [34]. Most important to us is the resultant

knife-edge from this process, sharp and without burrs.

However, such apertures may depart from circularity.

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Fig. 11. Temperature dependence of the V(l) matching filters. Transmittances at 23 8C and 33 8C were measured using a Cary 2390

spectrophotometer. The small differences plotted are of the same

magnitude as the uncertainties in the measurements—this data is

shown to illustrate the overall trend. n, Filter 2 (NRC); u, Filter 3

(NPL); s, Filter 5 (PRC).

The Precision Engineering Division at NIST measured and certified the areas using a View Engineering

Precis 3000 vision-based measuring machine [35]. After a pass was made to find the approximate center of the

aperture, 720 radii were measured from the center to the

lip at 0.58 angular intervals. The measurements were not

sensitive to the method of lighting the aperture (i.e.,

different forms of front and back lighting). The area was

estimated from these radii by a polygonal approximation. The combined standard uncertainties of the radii

measurement and the area estimation were given as

0.02 % for the larger apertures and 0.05 % for the

smaller. Since the coefficient of linear thermal expansion for copper is ø 0.0017 %/8C, temperature corrections were unnecessary.

3.5 Assembled Photometers

After the photodiode, filter, and apertures were individually tested, they were assembled into photometers as

shown in Fig. 3. The advantage to calibrating the components assembled is that internal reflections and scattering have similar effects during both calibration and

use. The essential role of the SCF is to calibrate the

spectral responsivity s(l) of the photometers to determine s(555) [Eq. (3)] and F [Eq. (5)]. The small output

spot from the SCF can be positioned at various places

within the aperture.

The first attempt at calibrating the photometers was

to measure s(l) at seven positions within the aperture,

comprising the vertices and center of a regular hexagon.

(Photometers 1 and 2 were measured at 37 positions,

which formed a larger, regular hexagonal pattern.) The

average over these positions was taken to be s(l) for the

photometer as a whole. However, consistency among the

photometer calibrations was improved by a factor of two

by using the following method.

s(l) was first measured at 5 nm intervals at one

position near the center of the aperture of each photometer. Data from representative photometers are shown

in Fig. 12a. Of particular importance in these data is the

degree of IR and UV suppression, the latter including

both transmission and fluorescence signals.

However, a correction was needed because s(l)

varied over the aperture area. The spectral responsivity

of each photometer, relative to the center point, was

determined at 50 nm intervals on a fine, rectangular

mesh of points. For the larger apertures (Photometers 1

and 2) the step size was 0.25 mm; for the smaller apertures (Photometers 3 to 8) the step size was 0.2 mm.

Measurements that were not affected by the aperture

edge were averaged.

Figure 12b shows such data, the ratio of the average

responsivity to the responsivity of the center spot. Polynomial fits are made to these data in order to interpolate

between them. This permits us to estimate the average

responsivity, given the center point responsivity, at all

wavelengths. After application to the data in Fig. 12a,

the final spectral responsivities for representative photometers are shown in Fig. 12c. The scatter given in the

lower part of the figure is only the statistical noise of

measuring s(l) at the center. Additional uncertainties

also apply, and they are discussed below. During the

calibration process the temperature of a photometer was

monitored using its built-in thermometer. Variations

were generally held to 6 1 8C. The average temperature

was recorded for each photometer to be used for temperature dependence corrections.

Fig. 12a. Responsivity of the filtered photodiode packages with emphasis on their behavior in the UV and IR. One spot in the center of

the aperture is probed. The measurement uncertainty at this spot is

commensurate with the width of the curve in the visible, with the

apparent scatter of the data in the IR, and shown by error bars in the

UV. Representative packages: Photometer 2, NRC, dashed curve; Photometer 3, NPL, dotted curve; Photometer 5, PRC, solid curve.

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Fig. 12b. Comparison of responsivity at the center spot with the

average of many spots over the face of the aperture. Data taken at 50

nm intervals are interpolated by polynomial fits. The correction factor

converts the responsivity at the center to the average responsivity over

the face of the aperture. The curves are as in Fig. 12a.

Fig. 12c. Responsivity of the filtered photodiode packages. The

curves are as in Fig. 12a, after the corrections in Fig. 12b have been

applied. The standard deviation of the measurements is shown below.

Figure 13 shows the mesh of spectral responsivity

measurements in more detail. Photometer 3 provides a

striking illustration of how spatial nonuniformities may

be associated with the individual glass layers in a filter,

each affecting a particular wavelength band. This data

also helps to estimate the systematic error that might

arise if the aperture is not fully and uniformly illuminated during a measurement.

s(l) varies with the temperature of the photodiode

and the filter, as shown in Figs. 8 and 11. We measured

the overall temperature effect by operating representative photometers at elevated temperatures. Figure 14

diagrams the experimental setup. A photometer was

placed in a heated, plastic foam box and left to reach

thermal equilibrium overnight. It was illuminated in the

normal manner by an inside-frosted lamp of the type

formerly used at NIST for luminous intensity calibrations. The lamp had a color temperature ø 2856 K. A

temperature-controlled monitor detector with a V(l)

filter was used to compensate for the variation in lamp

output from lighting to lighting.

Figure 15 shows the results. The luminous responsivity of the photometers decreased with increasing temperature, as measured with each photometer’s built-in

thermometer. As expected, the data form clusters that

depend on the filter construction. Therefore, all data

concerning filters from the same source are considered

together and fit to a common line. Compared with the

value when the photometer was unheated, the responsivity of Photometer 3 decreased by 0.049 %/8C, the

responsivities of Photometers 1 and 2 decreased by

0.063 %/8C, and the rest decreased by 0.088 %/8C. The

standard uncertainty of these results is < 0.002 %/8C.

The temperature effect would be different when measuring sources with other spectral compositions.

Direct comparison of these results with the data of

Fig. 11 is difficult because of the large uncertainties in

the latter. Nevertheless, the spectral temperature dependence presented in Figs. 8 and 11 corresponds to broadband changes (as above) of 0.08 %/8C, 0.06 %/8C, and

0.10 %/8C, respectively. The largest discrepancy is for

Photometer 3. Ref. [8] gives an independent measurement of 0.12 %/8C for a similar photometer.

Pertinent aspects of the photometers are summarized

in Table 1. As explained in Ref. [25], the higher the

shunt resistance of the photodiode, the better can be the

signal-to-noise ratio of the circuit. A limiting photocurrent noise ø 1 fA in Photometers 1 and 2 corresponds to

a sensitivity limit ø 1027 lx. Besides the spectral correction factor F, a traditional metric of the match of

sn(l) to V(l) is f1' [24], which is also shown in the table.

3.6 Illuminance Uncertainty

Following Eq. (7), the relative combined standard uncertainty, uc,r, of the illuminance responsivity I/Ev of the

photometers arises from the standard uncertainties of

s(555), F, and A. They are summarized in Table 2. By

adopting the terminology of the BIPM [36] and ISO

[18], the uncertainties are categorized as Type A, meaning those that were evaluated from the statistics of repeated measurements; and Type B, meaning those that

were not (such as estimates of possible systematic effects based on scientific judgment). These uncertainties

are reported in relative (that is, fractional) form, as percentages, because of the way the uncertainties scale and

combine in Eq. (7).

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Fig. 13. Responsivity map of representative photometers. The responsivities (A/W) of the photometers were measured while scanning a monochromatic probe beam over the aperture area. Photometer 2 had an aperture diameter of 7.98 mm; the others had a diameter of 3.57 mm. The grey

scale shows the responsivity at a point, referenced to the greatest value measured (100 %). The contours indicate changes of 0.05 % in responsivity.

Fig. 14. Arrangement to determine the overall temperature dependence of the photometers. The photometer was allowed to reach thermal equilibrium overnight in an insulated box also containing a resistance heater. The photometric responsivity of the photometer was

then measured, using a temperature-controlled detector to compensate

for variations in the reference lamp.

The principal uncertainty in s(555) is that of the

NIST spectral responsivity scale. The currently accepted relative standard uncertainty of 0.11 % [37]

arises largely from the uncertainty in the absolute spectral responsivity of silicon photodiode trap detectors,

with smaller additional contributions resulting from

comparisons between the trap detectors and the working

standards. The uncertainty that arose from random effects in comparing the photometers with the scale, obtained by averaging the standard uncertainties shown in

Fig. 12c for the eight photometers, is 0.04 %.

Calculation of F [Eq. (5)] requires knowledge or presumption of the spectral distribution of the source,

Fe(l). Since the photometers are normally illuminated

by an incandescent lamp operating with a color temper120
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Fig. 15. Temperature dependence of photometer luminous responsivity when viewing a broadband source at 2856 K. Photometer number

(filter source): n, 3 (NPL); 3, 1 (NRC); +, 2 (NRC); j, 5 (PRC); ◆,

6 (PRC); m, 8 (PRC). Linear fits include all data from each filter

source.

ature of 2856 K (CIE Source-A), we begin by presuming Planckian distributions. Following Eq. (3), only the

uncertainty of sn(l) relative to the NIST scale matters.

The statistical noise of the responsivity measurements is

shown in Fig. 12c. After adding their effects in quadrature, the resultant uncertainty of the Fe(l)-weighted

integral in F is 0.01 %. (This result presumes that the

possible error that is accounted for under the 0.11 %

spectral responsivity scale uncertainty is uniform for all

wavelengths. If it varies with wavelength, the possible

error in F may be greater than 0.01 %. Nevertheless, for

the purpose of analysis of the combined uncertainty in

illuminance calibration, this effect is accounted for by

the spectral responsivity scale uncertainty already in the

budget.)

An uncertainty is also introduced from the correction

polynomials, which do not pass directly through the data

points in Fig. 12b, and which slightly differ in additional

ways from the exact correction functions. This is, at

worst, a 0.01 % effect. Further, there is an uncertainty

as to how well the aperture averages are computed.

Patches of area within the apertures that were near the

center were covered approximately five times by the

probe beam. Portions near the rim of the aperture were

covered no more than once. This center-weighting

would tend to bias the average if the responsivity varied

radially, which Fig. 13 shows to be the case at 500 nm

for Photometers 2 and 3. While the uncertainties due to

nonuniform responsivity are difficult to quantify, given

the typical magnitudes shown in Figs. 12b and 13, we

estimate that the nonuniformity causes an additional

0.02 % relative standard uncertainty in determining

s(l).

When an actual lamp is used, its color temperature

may be other than the desired 2856 K or its spectrum

may be other than true Planckian. Figure 16 shows the

sensitivity of F to variations in blackbody temperature

for the different types of filters used. For an uncertainty

in the temperature of 6 10 K, the uncertainty in F

amounts to no more than 0.02 %. To quantify the nonPlanckian effect, we measured the spectral irradiance of

five inside-frosted lamps of the type formerly issued by

NIST for luminous intensity standards. While their correlated color temperatures were ø 2850 K, their distribution temperatures were within 3 K. Equation (5) was

evaluated for each photometer and for each lamp using

its actual spectra, and the results were no more than

0.02 % greater than when presuming a 2856 K blackbody.

The evaluation of F does not include infrared and

ultraviolet response beyond the domain of V(l). However, each is a potential problem. Evaluation of Eq. (2)

using the spectral responsivity data of Fig. 12a shows

that the infrared response (800 nm to 1100 nm) is less

than 0.003 % of the signal for a 2856 K radiator. Ultraviolet response (200 nm to 400 nm) is less than 0.002 %.

Two experimental factors characteristic of the SCF

affect the responsivity calibration through both s(555)

and F. First, the integral in Eq. (2) is dependent on the

wavelength calibration of the SCF. Numerical simulation using the responsivities of the photometers (Fig.

12c) and 2856 K blackbody sources shows that F/s(555)

Table 1. Summary of the photometers

Shunt resistance Calibration F f1'

Photometer Photodiode (GV) Filter source (nA/lx) (2856 K) (%)

1 S1227-1010BQ 5 NRC 10.116 1.002 6.00

2 S1227-1010BQ 5.2 NRC 10.067 1.003 5.97

3 S1226-8BQ 7 NPL 2.821 0.954 7.26

4 S1227-66BQ 6.6 PRC 2.350 0.990 2.55

5 S1226-8BQ 7 PRC 2.335 0.989 2.35

6 S1226-8BQ 7 PRC 2.331 0.990 2.37

7 S1226-8BQ 7 PRC 2.341 0.987 2.79

8 S1226-8BQ 4.3 PRC 2.334 1.000 1.43

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Table 2. Uncertainty budget for illuminance calibration

Relative

standard uncertainty (%)

Source of uncertainty Type A Type B

s(555)

Spectral responsivity scale 0.11

Comparison of photometer with scale 0.04

F

Measurement scatter (noise) 0.01

Data fitting procedure 0.01

Residual non-uniformity within aperture 0.02

Color temperature of lamp(6 10 K) 0.02

Planckian approximation for lamp 0.02

Infrared leakage 0.003

Ultraviolet leakage and fluorescence 0.002

Correlated s(555) and F

Wavelength calibration 0.04

Numerical aperture 0.05

A

Aperture area (as certified, small apertures) 0.05

Additional

Temperature variation 0.03

Polarization sensitivity 0.01

Electrical current-to-voltage conversion 0.003

Responsivity nonlinearity 0.001

Other 0.12

Combined standard uncertainty 0.19

Expanded uncertainty (k = 2) 0.39

Fig. 16. Effect on photometer calibration when sources at different

temperatures T are viewed. The required correction is reported as

F(T)/F(2856 K). Representative packages: Photometer 2, dashed

curve; Photometer 3, dotted curve; Photometer 5, solid curve; Photometer 8, dash-dot curve.

varies by 0.69 %/nm of offset. The wavelength calibration uncertainty of 0.2 nm leads to an uncertainty of

0.14 % in the calibration of the photometer.

Second, s(l) measurements can be affected by the

angular convergence (to a focus) of the probe spot. The

optical density of the filter would appear too large when

a light ray from the monochromator intersects it

obliquely, giving an erroneously low value of s(l).

While the photometer is aligned normal to the beam axis

within a few milliradians by retroreflecting the alignment laser shown in Fig. 5, the lamp sources are focused

using f/9 optics, which have a maximal angle of incidence of 55 mrad. Presuming the sole effect of the filter

is absorption, excluding front-surface reflection, the

proportionately longer path length at that angle for the

data in Fig. 9 would bias the integral in Eq. (2) by

0.20 % (Photometers 1 and 2, the worst case). The actual bias would be less, considering the distribution of

angles within the ray bundle and the reflection that was

ignored. Since the bias varies as u2

, a uniform distribution of rays would give an overall bias of 0.10 %.

To mitigate these two effects and to improve accuracy,

we used both the SCF and the NIST Reference Spectrophotometer [38] to measure the transmittance of the

V(l) filters. Comparison of the data, matching peak

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position and shape, indicated that the two sources of

bias on the SCF fortuitously canceled each other. The

residual uncertainty in the responsivity caused by the

wavelength scale is 0.04 %, and that caused by the SCF

optics is 0.05 %.

The Precis 3000 aperture area measurements, for Eq.

(7), are given in Table 3, and their uncertainty is included in Table 2. While these measurements were made

while the apertures were detached, we also sought to

confirm their behavior when they were installed in the

photometers. For this, we used the SCF. Consider the

output light beam from the monochromator as having a

principle axis and an irradiance B(x', y') (W/m2

) in a

plane more-or-less perpendicular to this axis, its coordinate origin at the intersection point. The photometers

were mounted on the x -y carriage, in order to position

the probe beam axis at point (x , y ) in the aperture plane.

If s(x , y ) is the responsivity s(l) of the photometer at

(x , y ) with a wavelength setting l of the monochromator, the total signal from the photometer

I(x, y ) =EE`

2 `

s(x + x', y + y') B(x', y') dx' dy'. (9)

Using the x-y carriage, the probe beam can be scanned

over the photometer in fine steps, and the output

summed, approximating

EE`

2 `

I(x , y ) dx dy =

EEEE`

2 `

s(x + x', y + y') B(x', y') dx' dy' dx dy

=EE`

2 `

FEE`

2 `

s(x + x', y + y') dx dyG B(x', y') dx' dy'

=EE`

2 `

s(x , y ) dx dy EE`

2 `

B(x', y') dx' dy'. (10)

(The separation follows after transforming the inner integral, x→x 2 x'.) The first integral on the right is the

product of the aperture area and the average photometer

responsivity within that area. It is the important quantity

for any sort of irradiance measurement instrument, including the photometer described in Eq. (7). The second

integral is just the total beam power B(W). Given an

independent determination of the average s(l) within

the active area of the aperture, by completely overscanning the aperture with small step size Dx and Dy, the

aperture area A is given by

A =

OI(x , y ) Dx Dy

B s(l) . (11)

This fine scanning was, in fact, the exercise reported

in connection with Figs. 12b and 13. Such area computations, averaged over wavelength, are also shown in

Table 3. The uncertainty due to the scatter of the data of

different wavelengths is shown as well.

It is clear that there is an unresolved discrepancy

between the two methods. It cannot be accounted for

solely by temperature variations, the residual uncertainty in the average responsivity, or the reliability of the

displacement measurements Dx and Dy . Numerical

modeling indicates that a small portion of it may arise

from reflections and scattering within the photometer,

where the back side of the aperture traps light that

would otherwise escape. The discrepancy does not cast

doubt on the actual aperture areas, as the Precis 3000

measurements differed on average by only 0.01 % from

independent measurements made by the aperture manufacturer. Either the problem lies in this second method

of determining areas, or there may be an unaccounted

aspect of the photometers themselves. An additional

uncertainty component of 0.12 % is included in the

uncertainty budget to account for this and other possible

influences.

Table 3. Aperture area measurements

Photometer Precis 3000 SCF Ratio

number (cm2

) (cm2) SCF/Precis

1 0.500044 (1 6 0.02 %) 0.500492 (1 6 0.03 %) 1.0009

2 0.499756 (1 6 0.02 %) 0.501015 (1 6 0.04 %) 1.0025

3 0.099964 (1 6 0.05 %) 0.100298 (1 6 0.08 %) 1.0033

4 0.100065 (1 6 0.05 %) 0.100534 (1 6 0.05 %) 1.0047

5 0.100042 (1 6 0.05 %) 0.100375 (1 6 0.02 %) 1.0033

6 0.099969 (1 6 0.05 %) 0.100345 (1 6 0.05 %) 1.0038

7 0.100065 (1 6 0.05 %) 0.100399 (1 6 0.06 %) 1.0033

8 0.099857 (1 6 0.05 %) 0.100206 (1 6 0.06 %) 1.0035

Average (3 to 8) 1.0037

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Additional small uncertainties arise from the method

of temperature-correcting the photometers (0.03 %),

from potential polarization selectivity of the photometers (0.01 %), and from the electrical calibration of the

amplifier (0.003 %). There is also an uncertainty in the

calibration due to a potential nonlinear response of the

photometers, that is, whether the output voltage remains

proportional to the illuminance for disparate values of

the same. We presume that the answer is spectrally

independent, or at least insensitive to the color temperature of an incandescent lamp that is attenuated by ‘‘neutral’’ density filters. Figure 17 shows the results of a

linearity test on a typical photometer using the beam

conjoiner method previously described [39]. During

calibration, the photocurrent peak (at 555 nm) is typically 1026 to 1027 A. Clearly, nonlinearity effects contribute an error of less than 0.001 %.

4. Realization of the Candela

4.1 Photometry Bench

The application of a photometer, measuring illuminance, to the luminous intensity determination of a light

source [Eq. (8)] is facilitated by the optical bench shown

in Fig. 18. The base consists of three 1.8 m (6 ft) long,

46 cm (18 in) thick, steel optical tables with a regular

array of tapped holes. Upon it, rigid telescope mounts

and upright, marked fiducial plates define the reference

axes. The longitudinal axis runs parallel to rails upon

which a carriage glides, holding a photometer. A support with cross hairs is substituted for the photometer to

align the carriage and rails; lateral alignment within 6 2

mm is achieved at the end opposite the telescope. By

substituting a flat mirror for the photometer and by

viewing the telescope in itself, orthogonality is ensured

to within 5 mrad. A lamp being measured is mounted on

another carriage, which permits it to be placed at the

intersection of the reference axes. With a side-viewing

telescope, the lamp filament is aligned to the plane defined in combination with the vertical fiducial mark.

(When frosted lamps are measured, such as the type

previously issued by NIST as luminous intensity standards, a model is aligned rather than the lamp itself. The

model contains additional fiducial marks both to set the

filament plane and to locate the filament within that

plane [7].)

The lamp is powered by a constant-current source,

which is set under computer control with a resolution of

0.15 mA. The current is independently monitored across

an air-cooled, Leeds & Northrup 4360, 0.1 V precision

shunt resistor [40], which is calibrated at NIST under

operating conditions with a standard uncertainty of

0.002 %. The proper operating current for the color temperature of interest is determined by repeated measurements using a diode-array-type spectroradiometer. Additionally, the computer monitors the lamp voltage and

the photometer signal and temperature, and it operates

the shutter under programmed control.

The apparatus in Fig. 18 is covered by a plastic box

lined with black velvet. Surfaces within the box, to the

maximum extent possible, are either painted black or

covered with black cloth. A baffled chimney above the

lamp permits convective cooling without introducing

Fig. 17. Relative responsivities of Photometer 2 as measured with the beam conjoiner at various

input powers.

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Fig. 18. New NIST photometry bench.

stray light. A light trap is interposed in front of the

longitudinal telescope during operation to minimize the

light that is reflected back at the photometer. (The side

telescope is blocked by black cloth.)

To estimate the magnitude of stray light resulting

from reflections and scattering, an additional photometer was used concurrently during testing and evaluation.

It was placed outside the area illuminated through the

baffles, but near, and oriented in the same general manner as, the photometer being used for measurement.

With various arrangements, the stray light was consistently < 0.03 % of the signal. To estimate the stray light

originating near the lamp, we covered the side of the

lamp towards the photometer. This signal was

< 0.001 % of the original. The box attenuated the ambient light from the laboratory by a factor on the order of

106

.

4.2 Lamp-to-Photometer Distance

The position of the photometer carriage is monitored

by a computer-readable, absolute linear encoder with a

resolution of 0.013 mm. The distance r between the

photometer and the transverse reference axis, and a

lamp filament, is fixed by sliding an attachment on the

photometer carriage into the view of the telescope so

that the zero position can be noted. The accuracy of the

encoder was checked with a 2.75 m (9 ft) vernier caliper

by moving the photometer carriage to various positions

and measuring its distance mechanically from the telescope mount as well as electronically. These repeated

measurements had a consistency between the methods

of 0.18 mm, which we take to be the uncertainty in

determining the distance. In actuality most of this scatter was associated with the use of the large caliper, and

it will not affect photometric measurements. A standard

uncertainty of 0.18 mm in separation corresponds to a

relative standard uncertainty in luminous intensity of

0.01 % when the photometer is 3.6 m from the lamp at

the far end of the bench.

More significantly, a lamp is not the point source

envisioned in Fig. 2c. The size of the radiating volume

requires that Iv in Eq. (8) be taken as the asymptotic

value at large r. Typical inside-frosted lamps calibrated

at NIST are tubular with a radius of 5 cm and extend 10

cm below the center of the filament, which is 5 cm

below the top of the lamp. Less important is the transverse extent of the radiating and scattering surfaces,

away from the longitudinal axis. At a distance of 2 m to

the photometer, a lateral displacement of 10 cm by a

point source would decrease its reading by only 0.38 %

(0.25 % because of the increased distance and 0.13 %

because of the increased angle of incidence). In comparison, a 5 cm longitudinal displacement of a point

source would affect the reading by 5 %. Clearly the

model is most sensitive to the longitudinal location of

the origin of the light.

For this study, the automation afforded by computerized instrumentation and data analysis permitted us to

make rapid measurements with the photometer at many

distances from the lamp. In this way, an effective origin

of the light was found as the best-fit offset ro in the

expression

Ev = Iv

(r 2 ro)

2 , (12)

given the measured illuminance Ev as a function of r.

(Similarly, the best-fit luminous intensity Iv can be

derived.)

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Five inside-frosted lamps were measured in this fashion, each with two randomly chosen photometers. The

intensity of the lamp was monitored during these measurements by a stationary, unfiltered, temperature-controlled silicon photodiode. It was exposed to the lamp

through a fiber-optic cable, the other end of which was

mounted on the second baffle where shown in Fig. 18.

The photodiode assembly itself was shadowed from direct radiation from the lamp. This data was used to

compensate the output of the moving photometer for

variations in the lamp intensity. Equation (12) was best

fit by including only data taken with r between 270 cm

and 370 cm, the maximum of the apparatus.

Typical offsets of 0.50 cm 6 0.15 cm were found for

NIST inside-frosted lamps, with a systematic tendency

for the offset to decrease by ø 0.15 cm after a lamp had

been burning for ø 1 h. This may be attributed in part

to imperfect compensation by the monitor if the spectral

distribution of the lamp was changing, particularly in

the infrared. Surprisingly, similar offsets of 0.3 cm 6

0.2 cm were found in a set of five, unfrosted Osram WI

41/G lamps. However, part of this (< 0.2 cm) can be

attributed to the shape and thickness of the glass envelope, which, acting as a diverging lens, displaces the

apparent position of the filament.

The uncertainty of r in Eq. (8) is dependent both on

the physical measurement of distance and on the applicability of the model Eq. (8) represents, that is, on how

one wishes to treat the issue of the effective origin of the

light. To ignore it means including a potential systematic

error in r; to measure it means using up precious hours

of a standard lamp’s life. For the purpose of defining the

new NIST scale of luminous intensity, we presume that

the offset is determined and applied, either for the lamp

being measured or from a collection of lamps of similar

construction. The relative combined standard uncertainty of r, uc,r(r), is then dominated by the uncertainty

in the offset distance, typically 0.11 cm in our measurements. At r = 3.7 m, the corresponding relative uncertainty in luminous intensity is 0.06 %.

4.3 Self-Consistency of Photometer Group

The calibration errors due to random causes can be

established for the photometers by measuring the same

luminous intensities with all of them, under the same

conditions. This was done with a group of five insidefrosted standard lamps, and the results are shown in

Table 4. Some photometers gave results consistently

above or below the group average for every lamp. This

is because what were random effects during calibration

become ‘‘frozen’’ into the responsivity assignment for

each photometer. However, we can average out this variation by applying correction factors to the original calibrations in order to bring the set of calibrations into

self-consistency. Such correction factors are given in the

table.

The correction factors are calculated by modeling

each entry in Table 4 as the product of a true luminous

intensity for the lamp in that column (five unknowns)

and a correction factor for the true photometer responsivity in that row (eight unknowns). These 13 values are

derived by data fitting; the full procedure will be published separately. In effect, each photometer calibration

is compared with the average of them all, and each is

slightly adjusted such that the adjusted values do not

bias the group average. Strictly, the normalization condition for the correction factors is that their product must

be 1. The results show that the random effects that arose

during the calibration of the photometer responsivities

affected the calibrations, on average, by 0.15 %. The

residuals after the data fit show that the random error in

making each luminous intensity measurements for the

table had a relative standard deviation of 0.02 %.

Table 4. Self-consistency check of photometer group. The luminous intensity (cd) of five lamps are determined with

the eight photometers built to realize the scale. Each value was measured three times; the typical scatter was 0.02 %

of the mean. The experimental standard deviations of the eight measurements of the lamps, with the different

photometers, are given at the bottom. The correction coefficient is explained in the text.

Lamp identification number

Photometer 4975 4976 4977 4978 4979 Correction coefficient

1 705.94 707.29 680.34 708.69 708.67 0.9980

2 706.56 707.53 680.92 709.28 709.04 0.9987

3 707.60 709.08 681.70 710.42 710.48 1.0004

4 708.37 709.74 682.66 711.02 711.02 1.0014

5 707.25 708.40 681.27 709.74 709.99 0.9997

6 708.20 709.78 682.85 711.11 710.63 1.0012

7 706.32 707.52 680.39 708.75 708.94 0.9984

8 708.79 710.31 683.22 711.46 711.53 1.0021

s 0.15 % 0.17 % 0.17 % 0.15 % 0.15 % 0.15 %

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The scatter in Table 4 can be reduced to 0.11 % by

using the aperture areas measured by the SCF found in

Table 3 for Eq. (8), but this may be deceiving. Photometers 1 and 2 not only have the larger (hence better

known) aperture areas, they also require the most severe

uniformity corrections (Fig. 12b); this indicates a potential bias in this alternative.

The same experiment was repeated with a set of five

Osram WI 41/G lamps. The correction factors were

found to be the same within 0.05 %, except for Photometer 6, which was different by 0.1 %. The residuals

had a relative standard deviation of 0.06 %. Since the

inside-frosted lamps appeared to be better behaved, we

henceforth apply the correction factors in Table 4 to the

calibrations in Table 1 for routine use of individual photometers. The additional consistency between the

groups of two different types of lamps was most encouraging.

The result that the calibrations of a set of photometers

had an actual random standard deviation of 0.15 % may

be compared with Table 2. Random influences noted in

the Table 2 uncertainty budget (those of Type A, and

some fraction of the uncertainties in aperture area and

temperature) together amount to a relative standard uncertainty ø 0.06 %. The difference is surprising, and is

perhaps the result of 1/f noise in one of the measurement

steps. However, in the end the conclusion of Table 2 is

still meaningful. The random component of each photometer after averaging (the self-consistency correction)

would have a relative standard deviation of (0.15/Ï8) %,

which is also ø 0.06 %. That is, the combined relative

standard uncertainty in Table 2 should be taken as applicable following the self-consistency step just described.

4.4 Uncertainty Budget for Luminous Intensity

Measurements

In Table 5 the uncertainties for luminous intensity

measurements of inside-frosted lamps are summarized.

The starting point is the uncertainty budget in Table 2;

uc,r for the illuminance responsivity of a photometer,

0.19 %, carries over directly and becomes the dominant

uncertainty in this budget. The measurement noise contributes 0.02 %, as explained in Sec. 4.3.

The photometers are operated through three cycles of

exposure and darkness. Each period of exposure or

darkness is ø 3 s, including settling time and an integration time of 1.67 s for the output voltage measurement.

This provides sufficient noise reduction, yet is sufficiently quick to obviate worry about heating the filter

because of optical absorption, a mechanism that would

not be detected by the temperature probe. While a precise model would depend on detailed knowledge about

the construction of the filters, we can demonstrate an

order-of-magnitude estimate. Presuming that all power

dissipated from a 500 W lamp is radiated, at a distance

> 2 m the irradiance is < 4 mW/cm2

. Taking a typical

specific heat of glass to be ø 1700 mJ/(K ? cm3

) and an

optical depth of a temperature sensitive, thermally insulated, totally adsorbing layer to be ø 0.1 cm, a 3 s

Table 5. Uncertainty budget for luminous intensity measurements

Relative

standard uncertainty (%)

Source of uncertainty Type A Type B

Illuminance Responsivity

Scale uncertainty from Table 2 0.19

Measurement noise 0.02

Filter absorption 0.006

Lamp to Photometer Distance

Size and construction of lamp 0.06

Physical distance measurement 0.01

Geometrical

Photometer transverse placement a

Photometer orthogonality 0.002

Lamp Operation

Current regulation 0.03

Aging (per hour) 0.1

Combined standard uncertainty 0.23

Expanded uncertainty (k = 2) 0.46

a Too small to list.

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exposure would raise the temperature of this layer by

ø 0.07 K. These severe assumptions show that the

influence of absorption on one measurement is

< 0.006 %. While any short-term drift of the photometer cannot be attributed to absorption by the filter at

these power levels, errors might arise at higher irradiances or with longer integration times. (Possible tracking errors of the thermometer in an environment with a

slowly changing ambient temperature were taken into

account in the Table 2 uncertainty budget.)

The uncertainties of the photometer to lamp distance,

r in Eq. (8), are discussed in detail in Sec. 4.2. There is

a 0.06 % relative standard uncertainty in luminous intensity measurements resulting from the difference between the geometric and effective position of the lamp

filament. The relative standard uncertainty caused by

the electronic ruler is < 0.01 %.

The various geometrical uncertainties make negligible contributions to the overall uncertainty. A transverse

misalignment of the photometer by 6 2 mm would affect the measurement by only a few parts in 107

. A

nonorthogonality to the longitudinal axis of 5 mrad

would affect the measurement by < 0.002 %. Clearly the

geometrical prerequisites of Eq. (8) are met. The angles

of incidence on the photometer from the extended

source are much less than those encountered during

illuminance calibration, and this would tend only to reduce the possible systematic error in numerical aperture

already accounted for.

NIST originally elected to use inside-frosted lamps as

luminous intensity standards because measurement results were less affected by small changes in the orientation of the lamps [41]. Variations of < 0.2 % were reported for misorientations in pitch (about the vertical

lamp axis) of less than 6 28. Similarly, the fine-grained

frosting aids in generating uniform illuminance in the

far field, in the neighborhood of the photometer. We

believe that any remaining local variations in illuminance will not contribute to possible measurement error

beyond those already accounted for in connection with

the spatial averaging of the responsivity of the photometers. Errors that may arise because of the differences in

lamp orientation between NIST and other laboratories

are beyond the scope of this paper.

At the operating point, marginal fractional changes in

lamp current cause magnified fractional changes in

lamp output by factors of 6 to 8 [42,8]. Since the nominal current of an inside-frosted lamp is 3 A, the 0.15

mA resolution in the current control implies a luminous

stability of 0.02 %. The 0.002 % calibration relative

standard uncertainty of the shunt resistor implies a reproducibility in output of 0.016 %. Together these imply

a relative standard uncertainty component resulting

from lamp current measurement of 0.03 %.

Before luminous intensity measurements were made,

the lamp currents were ramped slowly up to the operating point, and the lamps were allowed an equilibration

time of at least 10 min. Nevertheless, it is important to

remember that lamps change with age rather than reach

a stable equilibrium. Figure 19a shows the behavior of

three types of lamps over the course of 2 h of operation.

The scatter in the data, or noise, was discussed in connection with Table 4. Figure 19b demonstrates that the

effect spans separate lamp lightings. The gaps in the

data correspond to ramping and equilibration periods

during which no data were taken. While Fig. 19a shows

that the lamps changed most rapidly for an additional 20

min to 30 min after the initial warm-up period (as noted

above in connection with the determination of ro), permanent changes in luminous intensity of 0.1 %/h contraindicate long equilibration times and are a severe

limitation on a calibration service requiring lamps as

transfer standards. More recently, modified FEL 1000

W quartz-halogen lamps were further tested for suitability as photometric transfer standards, and they were

shown to be stable to within 0.2 % 2 0.6 % over 60 h of

operation [43].

4.5 Comparison of New and Old Scales

Before this study the last full realization of the old

luminous intensity scale (Fig. 1) occurred in 1985 in

connection with the international intercomparison of

such scales [44]. At that time the NBS candela was

found to be 0.58 % smaller than the world mean. (That

is, lamps calibrated at NBS were given higher candela

values than the average.) Of this, 0.35 % was later removed with the adoption of ITS-90 [20], making the

NIST scale 0.23 % smaller than the world mean.

Encouraging early results by Andor and Zalewski in

1988 [45] showed that a detector-based candela gave

results 0.07 % larger than the world mean. This was

determined by measuring the primary lamp group with

the prototype photometers similar to those reported in

this study. Based on this and other indirect evidence, in

Ref. [22] we concluded that the new scale realization

described in this study did not cause a significant scale

shift in comparison with the uncertainty of the old scale,

and that it was perhaps on the order of 0.3 %.

While studies continue at NIST to validate this result,

additional confirming evidence has recently become

available. In 1985, the luminous intensity scale of Germany maintained at the Physikalisch-Technische Bundesanstalt (PTB) was found to be 0.32 % larger than the

world mean [44]. A comparison of the new NIST scale

with the PTB scale [46] showed that the scale difference

narrowed from 0.9 % in 1985 to 0.2 % in 1993. This

implies that the new NIST scale is 0.12 % larger than the

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Fig. 19a. Drift and noise in the output of representative standard lamps during one lighting

of an: Osram Wi 41/G lamp, ●; FEL lamp, ❍; and Inside-frosted T-20 lamp, ▲.

Fig. 19b. Drift and noise in the output of representative standard lamps during five

consecutive lightings of the Osram lamp.

1985 world mean, a 0.35 % shift from the old NIST

scale with the ITS-90 correction applied. Additionally,

the Orsza ́gos Me ́re ́su ̈gyi Hivatal (OMH) in Hungary has

maintained a scale based on the BIPM lamp group that

holds the 1985 world mean. Preliminary data from a

comparison of the new NIST scale with the OMH scale

implies that the NIST scale is 0.03 % smaller than the

world mean, a 0.2 % shift from the old NIST scale.

Another international intercomparison is planned for

1995 [47].

4.6 Long-Term Stability of the Standard

Photometers

The calibration procedure described in Secs. 3.5 and

4.3 has been repeated twice to test the stability of the

calibration result shown in Table 1. The results are

shown in Table 6. For the purpose of comparison, the

data are adjusted to correspond to a uniform temperature of 298 K and normalized to the calibration values

in Table 1. The data shows that the group average

changed by < 0.1 % in their first year, and then by an

additional 0.4 % in the subsequent 2 years.

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Table 6. Photometer calibration stability

Relative illuminance responsivity

Photometer Nov. 1991 Nov. 1992 Dec. 1994 After cleaning

1 1.0000 0.9998 0.9939 1.0032

2 1.0000 0.9996 0.9875 1.0056

3 1.0000 0.9960 0.9926

4 1.0000 0.9991 0.9964

5 1.0000 0.9988 0.9976

6 1.0000 0.9999 0.9977

7 1.0000 1.0010 0.9987

8 1.0000 0.9997 0.9969

Average 1.0000 0.9992 0.9952

One reason for this change appeared to be a surface

film that had developed on the exterior side of the glass

filters on Photometers 1 and 2. These filters were wiped

gently with dry lens tissue, and their photometers were

recalibrated. Indeed, their values shifted significantly.

The average drift of Photometers 3 to 8 remained

ø 0.11%/yr.

5. Conclusion

Two major goals have been reached. A luminous

intensity scale has been derived with detectors, and in a

simpler and more direct manner than before. In the

process the uncertainty of lamp calibration has been

reduced.

This change also puts NIST on good footing for future improvements. The principal uncertainties in the

illuminance calibration, the uncertainty of the spectral

responsivity scale and the uncertainty in the aperture

area, will be reduced significantly by ongoing research

and development in our Division. We can expect to reduce the smaller uncertainties as well by improvements

in measurement technique. A 0.2 % relative expanded

uncertainty (k = 2) in illuminance measurement appears

to be achievable.

Based on our experience, we believe that the detectorbased scale will prove more durable and stable than the

lamp-based scale. Nevertheless, yearly recalibration of

the standard photometers will be required to maintain

the accuracy of the scale, and frosted FEL lamps hold

promise as an improved vehicle for disseminating the

scale.

This study is of particular benefit for those many

applications where illuminance needs to be measured

directly, including imaging (such as photography) and

ergonomics, where the effects of lighting rather than the

light sources themselves matter. The standard photometers have enabled NIST to expand its range of services to

include the calibration of luminance meters and illuminance meters [48]. In the field, secondary-standard illuminance meters can be used to calibrate other illuminance meters by substitution, eliminating the need for a

long optical bench. Further, the standard photometers

have been applied to realize a detector-based geometrically total luminous flux scale for the measurement of

lamps [49]. This important development brings the benefits of this study to the lighting industry, for which total

luminous flux is perhaps the most important measurable

quantity.

While traditional photometry has always involved

standard light sources, e.g., lamps in recent decades,

detector-based standardization permits smaller uncertainties and often simpler procedures. Unlike lamps the

photometers require no large power supplies, and they

are useful over a wide dynamic range. Photometry

benches need not be long to provide for 1/r 2 attenuations. Well-characterized photometers should prove especially useful for the calibration of modern, nonincandescent light sources, including self-luminous displays.

(Care needs to be taken to know the spectrum of the

source.) Stable photometers also permit the incidental

use of lamps during calibration procedures without regard to their long-term stability. With standards-quality

lamps difficult to procure, this alternate technology

merits particular attention.

Acknowledgments

Many people, staff and visitors, contributed much to

this project. We thank Ronald Wilkinson for many

skilled photometric measurements, Joel Fowler and

Patrick Tobin for much assistance in the design and

construction of the new bench, H. Sun for many filter

characterizations and extensive study of the temperature

dependence of the photometers, Ambler Thompson and

Sally Bruce for stewardship and operation of the beam

conjoiner, John Jackson for measuring the spectral irra130
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Journal of Research of the National Institute of Standards and Technology

diance of lamps at FASCAL, Gyula De ́zsi and Georg

Sauter for hospitality and fellowship in the tasks of

comparing the luminous intensity scales, Donna Bell

and Jason Hoffman for able assistance in many respects,

Robert Saunders for many helpful discussions, and

Klaus Mielenz for support and encouragement throughout the project.

6. References

[1] J. W. T. Walsh, Chap. 1 in Photometry, 3rd Ed., Constable &

Company, London (1958).

[2] Comptes Rendus des Se ́ances de la Neuvie`me Confe ́rence Ge ́ne ́rale des Poids et Mesures (Bureau International des Poids et

Mesures, Paris, 1948), session 9, p. 53.

[3] W. R. Blevin and B. Steiner, Redefinition of the Candela and the

Lumen, Metrologia 11, 97–104 (1975).

[4] Comptes Rendus des Se ́ances de la 16e Confe ́rence Ge ́ne ́rale des

Poids et Mesures (Bureau International des Poids et Mesures,

F-92312 Se`vres, Cedex, France, 1979), session 16, p. 100; see

also P. Giacomo, News from the BIPM, Metrologia 16, 55–61

(1980). (Corrected English translation: Metrologia 17, 74

(1981).)

[5] G. Wyszecki, W. R. Blevin, K. G. Kessler, and K. D. Mielenz,

Principles Governing Photometry (Bureau International des

Poids et Mesures, F-92312 Se`vres, Cedex, France, 1983); see

also Principles Governing Photometry, Metrologia 19, 97–101

(1983).

[6] The Basis of Physical Photometry, Publ. 18.2 (Commission Internationale de L’E ́ clairage, Paris, 1983). (Currently available

through the U. S. National Committee of the CIE, c/o Mr.

Thomas M. Lemons, TLA-Lighting Consultants, Inc., 7 Pond

Street, Salem, MA 01970-4819.)

[7] R. L. Booker and D. A. McSparron, Photometric Calibrations,

Natl. Bur. Stand. (U.S.), Spec. Publ. 250-15 (1987).

[8] T. M. Goodman and P. J. Key, A radiometric realization of the

candela, NPL Report QU 75 (National Physical Laboratory, Teddington, UK, February 1986); T. M. Goodman and P. J. Key, The

NPL Radiometric Realization of the Candela, Metrologia 25,

29–40 (1988).

[9] L. P. Boivin, A. A. Gaertner, and D. S. Gignac, Realization of the

New Candela (1979) at NRC, Metrologia 24, 139–152 (1987).

[10] C. Carreras and A. Corrons, Absolute spectroradiometric and

photometric scales based on an electrically calibrated pyroelectric radiometer, Appl. Opt. 20, 1174–1177 (1981).

[11] Z. Gao, Z. Wang, D. Piao, S. Mao, and C. Yang, Realization of

the Candela by Electrically Calibrated Radiometers, Metrologia

19, 85–92 (1983).

[12] J. L. Gardner, Recent International Intercomparison of Basic

Lighting Standards, Lighting in Australia 7(4), 21–24 (1987).

[13] V. I. Sapritski, A New Standard for the Candela in the USSR,

Metrologia 24, 53–59 (1987); V. I. Sapritskii, National Primary

Radiometric Standards of the USSR, Metrologia 27, 53–60

(1990).

[14] V. Jediny, J. Krempasky, J. Zatkovic, and P. Nemecek, Luminous

intensity measurement according to the new definition of the

candela, Cesk. Cas. Fyz. A 38(6), 601–611 (1988).

[15] G. Eppeldauer, Longterm changes of silicon photodiodes and

their use for photometric standardization, Appl. Opt. 29, 2289–

2294 (1990).

[16] J. H. Walker, R. D. Saunders, and A. T. Hattenburg, The NBS

Scale of Spectral Radiance, Metrologia 24, 79–88 (1987); J. H.

Walker, R. D. Saunders, and A. T. Hattenburg, Spectral Radiance

Calibrations, Natl. Bur. Stand. (U.S.), Spec. Publ. 250-1 (1987).

[17] J. H. Walker, R. D. Saunders, J. K. Jackson, and D. A. McSparron, Spectral Irradiance Calibrations, Natl. Bur. Stand. (U.S.),

Spec. Publ. 250-1 (1987).

[18] The present study follows, to the extent possible, the ISO Guide

to the Expression of Uncertainty in Measurement, International

Organization for Standardization, Geneva, Switzerland (1993).

Since 1994, NIST policy has been to conform to the Guide in

reporting its activities, using an expanded uncertainty coverage

factor (as defined in the Guide) of k = 2. Prior work at NIST was

generally reported with ‘‘3 s’’ uncertainties. For consistency in

this paper, when a standard uncertainty of the present study is

compared with an earlier result, the latter is restated to a ‘‘1 s’’

basis. Earlier results are restated to a ‘‘2 s’’ basis when the

context calls for an expanded uncertainty; see also B. N. Taylor

and C. E. Kuyatt, Guidelines for Evaluating and Expressing the

Uncertainty of NIST Measurement Results, Natl. Inst. Stand.

Technol. Note 1297, 2nd ed. (1994).

[19] H. Preston-Thomas, The International Temperature Scale of

1990 (ITS-90), Metrologia 27, 3–10 (1990). (Erratum, ibid. p.

107.)

[20] K. D. Mielenz, R. D. Saunders, A. C. Parr, and J. J. Hsia, The

1990 NIST Scales of Thermal Radiometry, J. Res. Natl. Inst.

Stand. Technol. 95, 621–629 (1990).

[21] K. D. Mielenz, R. D. Saunders, and J. B. Shumaker, Spectroradiometric Determination of the Freezing Temperature of Gold,

J. Res. Natl. Inst. Stand. Technol. 95, 49–67 (1990).

[22] C. L. Cromer, G. Eppeldauer, J. E. Hardis, T. C. Larason, and

A. C. Parr, National Institute of Standards and Technology Detector-Based Photometric Scale, Appl. Opt. 32(16), 2936–2948

(1993).

[23] Y. Ohno, C. L. Cromer, J. E. Hardis, and G. Eppeldauer, The

Detector-Based Candela Scale and Related Photometric Calibration Procedures at NIST, J. Illum. Eng. Soc. 23(1), 89–98 (1994).

[24] Methods of Characterizing the Performance of Radiometers

and Photometers, Publ. 53, Commission Internationale de

L’E ́ clairage, Paris (1982). (See Ref. [6] for availability.)

[25] G. Eppeldauer and J. E. Hardis, Fourteen-decade photocurrent

measurements with large-area silicon photodiodes at room temperature, Appl. Opt. 30, 3091–3099 (1991).

[26] G. Eppeldauer, Temperature Monitored/Controlled Silicon

Photodiodes for Standardization, in Surveillance Technologies,

S. Gowrinathan, R. J. Mataloni, and S. J. Schwartz, eds., Proc.

Soc. Photo-Opt. Instrum. Eng. 1479, 71–77 (1991).

[27] E. F. Zalewski and C. R. Duda, Silicon photodiode device with

100 % external quantum efficiency, Appl. Opt. 22, 2867–2873

(1983).

[28] J. M. Houston, C. L. Cromer, J. E. Hardis, and T. C. Larason,

Comparison of the NIST High Accuracy Cryogenic Radiometer

and the NIST Scale of Detector Spectral Response, Metrologia

30, 285–290 (1993). T. C. Larason, S. S. Bruce, and C. L.

Cromer, The NIST High Accuracy Scale for Absolute Spectral

Response from 406 nm to 920 nm, J. Res. Natl. Inst. Stand.

Technol. 101, 133 (1996).

[29] The characteristics of the same model of monochromator are

described in R. D. Saunders and J. B. Shumaker, Apparatus

function of a prism-grating double monochromator, Appl. Opt.

25, 3710–3714 (1986).

[30] Hamamatsu Corporation, 360 Foothill Road, P. O. Box 6910,

Bridgewater, NJ 08807-0910.

[31] Mathematica software is a product of Wolfram Research, 100

Trade Center Dr., Champaign, IL 61820-7237.

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Journal of Research of the National Institute of Standards and Technology

[32] The authors extend special thanks to Phil Boivin, National Research Council of Canada, and David Nettleton, National Physical Laboratory of Great Britain, for kindness and generosity in

supplying some of the filters used in this project. We also thank

G. Czibula, PRC Krochmann (Geneststrasse, 6, D-1000 Berlin

62, Germany), for cooperation and assistance in developing the

additional filters.

[33] G. Czibula, Producing a Detector with Predetermined Spectral

Responsivity, presented at the International Measurement Confederation 10th International Symposium of the Technical Committee on Photon-Detectors, 20–22 Sept. 1982, Berlin (OMIKK

Technionform, Budapest, 1983) pp. 189–199.

[34] T. M. Goodman, J. E. Martin, B. D. Shipp, and N. P. Turner, The

Manufacture and Measurement of Precision Apertures, in Proceedings of the Second International Conference on New Developments and Applications in Optical Radiometry, M. P. Fox and

D. H. Nettleton, eds., Vol. 92 of Institute of Physics Conference

Series, Institute of Physics, Bristol, UK (1989) pp. 121–128.

[35] View Engineering, 1650 N. Voyager Ave., Simi Valley, CA

93063-3385.

[36] P. Giacomo, News from the BIPM, Metrologia 17, 69–74 (1981);

see also H. H. Ku, Uncertainty and Accuracy in Physical Measurements, Natl. Inst. Stand. Technol. Spec. Publ. 805 (1990).

[37] C. L. Cromer, A New Spectral Response Calibration Method

using a Silicon Photodiode Trap Detector, presented at the 1991

Measurement Science Conference.

[38] K. L. Eckerle, J. J. Hsia, K. D. Mielenz, and V. R. Weidner,

Regular Spectral Transmittance, Natl. Bur. Stand. (U.S.), Spec.

Publ. 250-6 (1987).

[39] R. D. Saunders and J. B. Shumaker, Automated radiometric

linearity tester, Appl. Opt. 23, 3504–3506 (1984).

[40] Leeds & Northrup, 351 N. Sumneytown Pike, North Wales, PA

19454-2531.

[41] E. F. Zalewski, A. R. Schaefer, K. Mohan, and D. A. McSparron,

Optical Radiation Measurements: Photometric Instrumentation

and Research (1970 to 1971), Natl. Bur. Stand. (U.S.), Tech.

Note 594-2 (1972) pp. 22–33.

[42] Incandescent Lamps, Publ. TP-110, General Electric Company,

Nela Park, Cleveland, OH (1964).

[43] Y. Ohno and J. K. Jackson, Characteristics of Modified FEL

Quartz-Halogen Lamps for Photometric Standards, Metrologia

(in press).

[44] J. Bonhoure, Metrologia 24, 157–162 (1987); see also Rapport

de la 11e Session, Comite ́ Consultatif de Photome ́trie et Radiome ́trie, Bureau International des Poids et Mesures, F-92312

Se`vres Cedex, France (1986).

[45] G. Andor and E. F. Zalewski, (personal communication).

[46] Y. Ohno and G. Sauter, 1993 Intercomparison of Photometric

Units Maintained at NIST (USA) and PTB (Germany), J. Res.

Natl. Inst. Stand. Technol. 100, 227–239 (1995).

[47] Rapport de la 12e Session, Comite ́ Consultatif de Photome ́trie

et Radiome ́trie, Bureau International des Poids et Mesures,

F-92312 Se`vres Cedex, France (1990).

[48] NIST Calibration Services Users Guide 1995, Natl. Inst. Stand.

Technol. Spec. Publ. 250 (1995).

[49] Y. Ohno, Realization of NIST 1995 Luminous Flux Scale using

Integrating Sphere Method, J. Illum. Eng. Soc. 25(1), 13–22

(1996).

About the authors: Albert Parr serves as Chief of the

Optical Technology Division of the NIST Physics Laboratory. Christopher Cromer manages the Optical Sensor

Group in the Optical Technology Division. Yoshihiro

Ohno is the project leader in the Optical Technology

Division for photometry and provides luminous intensity

and other photometric calibrations. G. Eppeldauer, J. E.

Hardis, and T. C. Larason are scientists in the Optical

Technology Division. The National Institute of Standards and Technology is an agency of the Technology

Administration, U. S. Department of Commerce.

132
Volume 103, Number 6, November–December 1998

Journal of Research of the National Institute of Standards and Technology

[J. Res. Natl. Inst. Stand. Technol. 103, 615 (1998)]

Spectral Response Based Calibration Method

of Tristimulus Colorimeters

Volume 103 Number 6 November–December 1998

George Eppeldauer

National Institute of Standards and

Technology,

Gaithersburg, MD 20899-0001

A new method is described to calibrate

tristimulus colorimeters for high accuracy

color measurements. Instead of traditional

lamp standards, modern, high accuracy

detector standards are suggested for calibration. After high accuracy absolute spectral response determination of the tristimulus receivers, color (spectral) correction

and peak (amplitude) normalization can

minimize uncertainties caused by imperfect realizations of the Commission Internationale de l’Eclairage (CIE) color matching functions. As a result of the corrections,

stable light sources of different spectral

power distributions can be measured with

an accuracy dominated by the sub tenths

of a percent uncertainty of novel spectral

response determinations.

Key words: chromaticity coordinates;

color calibration; color temperature; colorimetry; detector standard; photometry;

spectral response; tristimulus values.

Accepted: August 19, 1998

Available online: http://www.nist.gov/jres

1. Introduction

Tristimulus colorimetry is based on light measurement using three or more receivers with spectral responsivities matched to the Commission Internationale de

l’Eclairage (CIE) x ̄(l), y ̄(l), and z ̄(l) color matching

functions [1]. To achieve accurate measurements for a

large variety of light sources, the spectral matches

should be as close as possible to the color matching

functions. The receivers are usually realized with silicon

photodiodes and attached filter packages [2]. Usually,

the spectral mismatch between the realized and the color

matching functions give the dominant uncertainties in

tristimulus color measurements.

At present, tristimulus colorimeters are calibrated

with standard lamps. The calibration of the most frequently used color temperature standard lamps is

derived from source-based spectral irradiance scales.

NIST reported a 0.67 % relative expanded uncertainty

(k = 2)1 for the disseminated spectral irradiance standard lamps in the visible range and a relative 0.59 %

long-term reproducibility [3]. Research is being conducted at NIST to decrease the 0.67 % uncertainty by a

factor of three still using standard lamps [4]. The accuracy of the standard lamp influences the photometric

[receiver matched to y ̄(l)] accuracy of the tristimulus

colorimeter. The wavelength dependent (e.g., burning

time caused) changes of the standard lamp influence the

colorimetric accuracy of the tristimulus meter.

Several commercially available colorimeters were

compared for accuracy by measuring nine different

laser lines (saturated colors) by Berns et al. [6]. The

differences between the theoretical and the measured

chromaticity coordinates were reported. The lowest rms

1 Throughout this paper uncertainties are given as relative expanded

uncertainties with a coverage factor k = 2 unless otherwise stated [5].

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errors in x and y (0.0042 and 0.0051, respectively) were

observed on a tristimulus colorimeter employing partial

(mosaic) filters. The errors are expected to decrease to

a large extent for white light sources, such as tungsten

lamps. The reported errors were dominated by spectral

response deviations (mismatch) of the receivers relative

to the CIE recommended color matching functions. The

uncertainties of the calibrating standard lamps also contributed to the results.

In contrast to source standards, primary standard detectors (cryogenic radiometers) can measure optical (radiant) power with an uncertainty of 1024 [7, 8]. Certain

type silicon detectors, in a light-trap arrangement, can

be calibrated against primary standard radiometers using several intensity stabilized lasers [9]. With interpolation between the laser lines, a 0.06 % uncertainty in

spectral responsivity was reported on light-trap Si detectors between 406 nm and 920 nm [10]. This uncertainty is about one fourth of the uncertainties reported

for traditional monochromator based detector spectral

response measurements [11].

Achievable total uncertainty of spectral transmittance

measurements on high quality color filters is reported to

be 2 3 1024 [12].

A narrow-band filter-radiometer was calibrated for

spectral irradiance response in the visible region against

a trap detector with an uncertainty of 0.07 % [13] for

measured irradiance. In that report, the dominant uncertainty components were the uncertainties of the trap

detector response, 0.036 %, the area of the trap aperture, 0.034 %, and the wavelength reproducibility,

0.026 %.

If the uncertainties of the receiver response measurements are very small, the spatial response non-uniformities of the filter-detector packages could limit the accuracy of the tristimulus measurements. This problem can

be avoided if apertures are used in front of the filter-detector packages and the apertures are overfilled with the

uniform field of the (point) source to be measured. The

area of the apertures can be measured with an uncertainty of 0.026 % [14].

The motivation behind the development of a detectorbased calibration method for tristimulus colorimeters

was to utilize the significantly lower uncertainty of new

detector standards compared with traditional lamp standards. The goal of the method described in this paper is

to determine broad-band calibration factors for all receivers in a tristimulus colorimeter to minimize measurement uncertainty. If the spectral response determination of the receivers is accurate, application of the

calibration factors for different source distributions will

result in high colorimetric accuracy. This multiple receiver method is an extension of the single receiver

spectral mismatch correction used in our detector-based

illuminance scale realization [15, 16].

2. Theoretical Basis

In order to determine x , y chromaticity coordinates of

a light source, the CIE tristimulus values of the source

are to be obtained by

X = kelS(l) x ̄(l) dl

Y = kelS(l) y ̄(l) dl (1)

Z = kelS(l) z ̄(l) dl,

where S(l) is the spectral power distribution of the

source to be measured; x ̄(l), y ̄(l), and z ̄(l) are the 1931

CIE color-matching functions; and k is a normalization

factor. In practice, x ̄(l) is realized by two receivers,

x ̄L(l) and x ̄S(l):

x ̄S(l) = 0 and x ̄L(l) = x ̄(l) if the wavelength is

longer than 504 nm, and

x ̄L(l) = 0 and x ̄S(l) = x ̄(l) if the wavelength is

shorter than 504 nm.

(Note that the subscripts L and S mean long and short,

respectively.)

The CIE tristimulus value X can be written as:

X = X1 + X2, (2)

where

X1 = kelS(l) x ̄L(l) dl, and

X2 = kelS(l) x ̄S(l) dl.

Y in Eq. (1) will give an absolute photometric quantity

(e.g., in lux) [15] if

k = Km = 683 lm/W. (3)

The measured photodiode output currents of the four

separate receivers are

IX1 = elS(l) sXL(l) dl

IX2 = elS(l) sXS(l) dl

IY = elS(l) sY (l) dl

IZ = elS(l) sZ (l) dl. (4)

where sXL(l), sXS(l), sY (l), and sZ (l) are the absolute

spectral responsivities of the receivers.

When measuring a light source of known spectral

power distribution S(l), the receiver calibration factors

can be determined from the ratio of Eq. (1) to Eq. (4):

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kX1 = X1

IX1

= KmelS(l) x ̄L(l) dl

elS(l) sXL(l) dl

kX2 = X2

IX2

= KmelS(l) x ̄S(l) dl

elS(l) sXS(l) dl

(5)

kY = Y

IY

= KmelS(l) y ̄(l) dl

elS(l) sY (l) dl

kZ = Z

IZ

= KmelS(l) z ̄(l) dl

elS(l) sZ (l) dl .

By normalizing the color matching functions to their

peak values, the receiver calibration factors can be written as:

kX1 = 1.06291 Km FX1

sXL(599)

kX2 = 0.3501 Km FX2

sXS(442)

(6)

kY = Km FY

sY (555)

kZ = 1.78297 Km FZ

sZ (446)

by introducing the color correction factors:

FX1 = elS(l) x ̄Ln(l) dl

elS(l) sXLn(l) dl

FX2 = elS(l) x ̄Sn(l) dl

elS(l) sXSn(l) dl

(7)

FY = elS(l) V(l) dl

elS(l) sYn(l) dl

FZ = elS(l) z ̄n(l) dl

elS(l) sZn(l) dl ,

where sXL(599), sXS(442), sY (555), and sZ (446) are the

absolute responses of the realized receivers at the peak

wavelengths of the color matching functions; and

sXLn(l), sXSn(l), sYn(l), and sZn(l) are the relative responses of the realized receivers normalized also at the

peak wavelengths of the color matching functions. The

peak wavelengths of the realized receivers are not necessarily equal to the peak wavelengths of the color matching functions.

A color correction factor will be unity if the normalized channel response is equal to the normalized CIE

color matching function.

Once the tristimulus colorimeter is calibrated for kX1,

kX2, kY , and kZ , the tristimulus values of a test light

source can be measured as

X' = X1' + X2' where X1' = kX1IX1' and X2' = kX2 IX2'

Y' = kY IY' (8)

Z' = kZ IZ'

where IXl', IX2', IY', and IZ' are the measured output

currents of the receivers.

The calibration procedure can be applied to various

measurement geometries (e.g., illuminance, luminance,

luminous flux, or luminous intensity) depending on the

units in which sXL(599), sXS(442), sY (555), and sZ (446)

are expressed.

3. Achievable Accuracy

In order to obtain the highest color measurement accuracy, the receiver calibration factors are to be redetermined for all S(l) source distributions to be measured.

The spectral mismatch of the receivers, relative to the

CIE functions, should be small to allow for relatively

large uncertainties when determining S(l). It was

shown in an earlier work [16] that the change of FY with

a high quality spectral match of f1' = 1.43 % [2], was

0.1 % for a color temperature change from 2600 K to

3200 K of a Planckian radiator. With a lower quality

spectral match of f1' = 3.4 %, which is typical for the red

and blue receivers, the change in FY would be larger, still

allowing for a large enough uncertainty of S(l). The

final S(l) for tungsten lamps, which are more or less

similar to Planckian radiators [17], can be obtained by

iterating the Planckian function (at different temperatures) and the tristimulus measurements, until the

highest color measurement accuracy is reached. For

other types of sources with smoothly varying spectral

power distribution (e.g., many kinds of paints, color

tiles, etc.), S(l) can be measured with a low accuracy

spectroradiometer, and the color measurement accuracy

still remains high.

According to the references in the Introduction, the

presently achievable relative expanded uncertainty of

absolute spectral response determinations is on the order of 0.1 %. The uncertainty of relative spectral response measurements can be lower because of the

smaller number of uncertainty components. The uncertainties of the tristimulus values propagate to the uncertainties of the chromaticity coordinates. The chromaticity coordinates can be calculated from the tristimulus

values via

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x = X

X + Y + Z , y = YX + Y + Z . (9)

Now, assume that the relative uncertainties of X, Y, and

Z are all 0.1 %. For a Standard Illuminant A, where

x = 0.4476 and y = 0.4074, the worst case scenario

(DX = + 0.1 %, DY = 2 0.1 %, and DZ = 0 %) shows a

chromaticity coordinate change of ≅0.0004 for both x

and y , resulting in a ≅10 K change in the correlated

color temperature. These expanded uncertainties are

similar to those reported for the source-based NIST

color temperature scale [18]. With improvements of

spectral response determinations (as suggested below),

the accuracy of detector-based tristimulus color measurements can be further increased.

4. Suggested Realizations

The described detector-based calibration method can

be applied to the calibration of existing tristimulus colorimeters where the spectral response of the receivers

can be measured. The achievable color measurement

accuracy will depend on the uncertainty of the spectral

response measurements.

Standard quality tristimulus colorimeters can be constructed using high accuracy detector standards such as

trap detectors. The advantage of using silicon trap detector standards is that the spectral response of the trap

detector can be determined directly against a primary

standard cryogenic radiometer [10]. Further advantages

of trap detectors are relative response non-uniformities

of less than 0.02 % [19] and very low reflectance in the

visible wavelength range [9], especially for transmission

type versions [20, 21]. The filter packages can be measured separately if they are used with transmission-type

trap detectors because of zero back reflection from

these detectors.

We have started developing a new facility to calibrate

illuminance measuring photometers and tristimulus colorimeters against irradiance measuring trap detectors.

These trap detectors will be calibrated against the cryogenic radiometer in the power (detector is underfilled by

the laser beam) measurement mode. The trap detectors

are equipped with precision apertures and will measure

the well-collimated radiation (within the aperture) from

point sources to obtain the highest accuracy. The point

sources are being realized with small integrating

spheres illuminated by tunable lasers. The aperture areas are also measured with point sources. The accuracy

of our cryogenic radiometer is being improved to

achieve radiant power measurements with an uncertainty of between 0.01 % and 0.02 %. The expected

spectral irradiance response uncertainty of the irradiance trap detectors (for point sources) is about 0.03 %.

All of our existing illuminance-type meters can be calibrated against the irradiance trap detectors with substitution in the uniform field of the tunable monochromatic

point source. After spectral response calibrations, the

described correction method will be applied. A tristimulus colorimeter calibrated this way will have a chromaticity coordinate measurement uncertainty (expanded but not relative) of about 0.0003. The accuracy

of matrix corrected tristimulus colorimeters [22, 23, 24]

can also be improved if they are calibrated against the

suggested response corrected reference tristimulus colorimeters. Further analysis is suggested to establish a

relationship between the f1' of the receivers and the colorimetric accuracy when spectrally structured and

changing source spectral power distributions (e.g., color

TV monitors) are measured.

5. Conclusion

The significant decrease of uncertainties in detector

spectral response measurements in the past 5 years motivated the development of a detector-based calibration

method for tristimulus colorimeters.

A method for color (spectral mismatch) correction

and peak (amplitude) normalization of color measuring

tristimulus receivers has been developed. Broad-band

calibration factors, based on spectral response measurements of the receivers, can be determined to minimize

the color measurement uncertainties caused by the imperfect receiver response realizations. The method utilizes the lower uncertainty of new detector standards

relative to traditional lamp standards. The calibration

factors can be determined for sources of different spectral power distributions.

Application of the described detector-based calibration method will result in chromaticity coordinate expanded uncertainties (not relative) of less than 0.001.

This corresponds to a color temperature measurement

accuracy equal to or better than that of presently used

primary lamp standards.

Acknowledgments

The author thanks Y. Ohno and M. Racz for their

helpful advice.

6. References

[1] Publication CIE No 15.2 (1986). Central Bureau of the CIE,

A-1033 Vienna, P.O. Box 169, Austria.

[2] Publication CIE No 69 (1987). Central Bureau of the CIE, A1033 Vienna, P.O.Box 169, Austria, pp. 5, 9.

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Journal of Research of the National Institute of Standards and Technology

[3] J. H. Walker, R. D. Saunders, J. K. Jackson, and D. A. McSparron, Spectral irradiance calibrations. NBS Special Publication

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[10] T. R. Gentile, J. M. Houston, and C. L. Cromer, Realization of

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[11] T. C. Larason, S. S. Bruce, and C. L. Cromer, The NIST High

Accuracy Scale for Absolute Spectral Response from 406 nm to

920 nm, J. Res. Natl. Inst. Stand. Technol. 101(2), 133–140

(1996).

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[13] R. Friedrich, J. Fischer, and M. Stock, Accurate calibration of

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(1993).

[16] C. L. Cromer, G. Eppeldauer, J. E. Hardis, T. C. Larason, Y.

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Intensity Scale, J. Res. Natl. Inst. Stand. Technol. 101, 109–132

(1996).

[17] Y. Ohno and M. Navarro, Improved Photometric and Colorimetric Calibrations at NIST, Proc. of the NCSL Workshop and

Symposium, Session 1E (1997) pp. 99–110.

[18] Y. Ohno, Photometric Calibrations, NIST Special Publication

250-37 (1997).

[19] R. Kohler, R. Goebel, M. Stock, and R. Pello, An international

comparison of cryogenic radiometers, in Optical Radiation Measurements III, J. M. Palmer, ed., Proc. SPIE2815 (1996) pp.

22–30.

[20] J. L. Gardner, Transmission trap detectors, Appl. Opt. 33(25),

5914–5918 (1994).

[21] T. Kubarsepp, P. Karha, and E. Ikonen, Characterization of a

polarization-independent transmission trap detector, Appl. Opt.

36(13), 2807–2812 (1997).

[22] G. Eppeldauer and J. Schanda, Colorimeter with matrix transformation, AIC Conference on Color Dynamics, Budapest, Hungary, Proc. (1976) pp. 403–413.

[23] E 1455-92, Standard Practice for Obtaining Colorimetric Data

from a Visual Display Unit Using Tristimulus Colorimeters,

ASTM Standards on Color and Appearance Measurement, 4th

Ed. (Available from ASTM, 100 Barr Harbor Dr., Wet Conshohocken, PA 19428-2959.)

[24] Y. Ohno and J. E. Hardis, Improved Matrix Method for Tristimulus Colorimetry of Displays, AIC Color’97, Kyoto, May 26-30,

1997.

About the author: George Eppeldauer is a Ph.D. Electronics Engineer in the Optical Technology Division of

the NIST Physics Laboratory. The National Institute of

Standards and Technology is an agency of the Technology Administration, U.S. Department of Commerce.

619
Design and characterization of a

photometer–colorimeter standard

George P. Eppeldauer and Miklo ́ s Ra ́ cz

A photometer and tristimulus colorimeter has been developed at the National Institute of Standards and

Technology NISTto realize a color scale. A novel construction was developed to implement the

spectral-responsivity-based scale with small uncertainty. The new device can be used as a reference

illuminance and luminance meter as well. Temperature-controlled filter combinations, with 5–8 layers

in one package, are used to match the responsivity of a silicon tunnel-trap detector to the CIE colormatching functions with small spectral mismatch values  f1. Design considerations to extend the

tunnel-trap detector with replaceable single and double apertures and changeable filter combinations are

described. The design and fabrication of the filter packages and the dependence of the f1 values on the

thickness of the filter layers are discussed. The colorimeter was characterized for angular, spatial, and

spectral responsivity. An improved preamplifier can convert current to voltage in an 11-decade dynamic

range with 0.01% uncertainty. © 2004 Optical Society of America

OCIS codes: 040.5160, 330.1730, 120.4800, 120.5240.

1. Introduction

In our earlier publication1 a method was suggested

for calibrating tristimulus colorimeters against detector standards instead of traditional lamp standards. In this new calibration method, spectral

corrections are applied to the broadband calibration

factors of the tristimulus channels of a colorimeter.

As a result of the spectral and amplitude corrections,

the imperfect realizations of the Commission Internationale de l’Eclairage CIEx, y, and z

color-matching functions can be compensated. It is

the uncertainty of the spectral responsivity measurement of the channels that will dominate the uncertainty of tristimulus color measurements. The

present paper describes the design considerations

and characterizations of a special tristimulus colorimeter construction with which the spectral responsivity of the colorimeter channels can be determined

with extremely low uncertainty.

To make it possible to measure a light source with

a known spectral power distribution S, the channel calibration factors can be determined from the

ratio of the CIE tristimulus values to the measured

output currents of the four channels:

kX1  X1

IX1

 Km  Sx 1d

 SsX1d  1.06291Km FX1sX1599,

kX2  X2

IX2

 Km  Sx 2d

 SsX2d  0.3501Km FX2sX2442,

kY  Y

IY

 Km  Syd 

 SsYd  Km FYsY555

,

kZ  Z

IZ

 Km  Szd

 SsZd  1.78297Km FZsZ446.

(1)

As xhas two lobes, it is realized by two channels,

x1and x2. The right-hand side of the equations

was obtained by normalizing the color-matching

G. P. Eppeldauer george.eppeldauer@nist.govis with the National Institute of Standards and Technology, Optical Technology

Division, Gaithersburg, Maryland 20899. M. Ra ́cz is with the

Konkoly Observatory, Hungarian Academy of Sciences, P.O. Box

67, 1525 Budapest, Hungary, and the Hungarian Academy of Sciences, Research Institute for Technical Physics and Materials Science, Magyar Tudomanyos Akademia Hungarian Academy of

Sciences, Muszaki Fizikai es Anyagtudomanyi Kutatointezet Research Institute for Technical Physics and Material Science, P.O.

Box 49, 1525 Budapest, Hungary, and was a National Institute of

Standards and Technology guest researcher when this research

was begun.

Received 30 July 2003; revised manuscript received 17 February

2004; accepted 18 February 2004.

0003-693504132621-11$15.000

© 2004 Optical Society of America

1 May 2004  Vol. 43, No. 13  APPLIED OPTICS 2621
functions to their peak values and introducing the

color correction factors:

FX1   Sx 1nd

 SsX1nd ,

FX2   Sx 2nd

 SsX2nd ,

FY   SVd

 SsYnd ,

FZ   Sz nd

 SsZnd , (2)

where sX1

599, sX2442, sY555, and sZ446are the

absolute responsivities of the realized channels at the

peak wavelengths of the color-matching functions,

x1n, x2n, and znare the color-matching functions normalized to one at their peaks, Vis the

spectral luminous efficiency function for photopic vision also normalized to one at its peak, and sX1n

,

sX2n

, sYn, and sZnare the relative spectral

responsivities of the realized channels normalized to

one at their peak wavelengths.

After the tristimulus colorimeter is calibrated for

kX1

, kX2, kY, and kZ, the tristimulus values of a test

light source can be measured as

X  X1 X2, where X1  kX1

IX1, X2  kX2IX2,

Y  kY IY,

Z  kZ IZ, (3)

where IX1

, IX2, IY, and IZ are the measured output

currents of the tristimulus channels.

This calibration procedure can be applied to either

illuminance or luminance measurement geometry by

use of the relevant units of sX1

599, sX2442, sY555,

and sZ446in the equations.

According to the above procedure, the photometric

and colorimetric measurement uncertainties will depend only on the uncertainty of the spectral responsivity determination of the colorimeter channels.

An advantage of the method is that accurate color

and photometric measurements can be made even if

the CIE functions are poorly realized with large

spectral mismatchin the channels of a colorimeter.

For perfect realizations, the color of any source distributions could be measured accurately with one set

of calibration factors shown in Eq. 1. In this case,

all the color correction factors in Eq. 2would become

unity. We have decided to keep the CIE f1 spectral

mismatchvalues2 of the realized channels small so

that one set of calibration factors can be used for

sources with similar spectral distributions. Also,

rough knowledge of the source distribution is enough

to perform accurate color measurements. Even with

small f1 values, an additional set of calibration factors will be needed to measure very different source

distributions, such as gas discharge lamps or display

monitors.

Our goal was to design and fabricate a photometer–

colorimeter for which the spectral responsivity of the

channels can be determined with an expanded uncertainty k  2of 0.1% or less.3 A 0.1% change in the

spectral irradiance responsivity of any one channel

will result in a chromaticity coordinate change of

0.0002 for both x and y for a Planckian radiatorand

a change in the illuminance responsivity of 0.1%.

These expected colorimeter uncertainties are equivalent to the uncertainties of current primary lamp

standards. While intensity and spectral distribution of lamp standards may change significantly with

burning time, the responsivity change of colorimeter

channels can be much smaller versus time.

In order to satisfy the above expectations, a silicon

tunnel-trap detector is used in our colorimeter standard. This detector does not have back reflections to

the filters, and its spectral responsivity can be determined with an uncertainty of 0.1%. The four filter

combinations that modify the spectral responsivity of

the trap detector to be similar to the CIE functions

needed individual design and fabrication to achieve

small f1 values. The small f1 values make it possible to avoid frequent change redeterminationof

the channel calibration factors even for significant

changes in the measured source distribution. Temperature stabilization of the filter combinations

packagesis necessary to eliminate changes in their

spectral transmittances.

The photometric and tristimulus color scale realizations have been studied.4 The photometer–

colorimeter, when equipped with different filters, can

be used as a radiometric standard as well. We have

also studied the application of the filter-trap radiometer for ultraviolet and visible calibrations.5

2. Trap-Detector-Based Photometer–Colorimeter

The silicon tunnel-trap detector we developed recently6 was extended by a temperature-controlled filter

wheel with four selectable filter combinations, a removable luminance measuring tube, and an improved current-to-voltage converter. The details of

the trap-detector extension are discussed below.

The goal was to develop a versatile tunnel-trapdetector-based photometer–colorimeter for which the

channel spectral responsivities can be determined

with low uncertainties.

A. Silicon Tunnel-Trap Detector

A significant advantage of a tunnel-trap detector is

that no light is reflected back from the detector to the

input optics such as filters and aperture. Consequently, the filter combinations and the trap detector

can be calibrated either separately or as a combined

package. The nonabsorbed light i.e., light transmitted through the trapcan be easily measured to

apply the physical model of internal quantum efficiency for responsivity determination.7 The other

advantage of a trap detector is that the uniformity of

spatial responsivity can be high if the internal quantum efficiency of the photodiodes is uniform over the

active area. These features can make well-designed

2622 APPLIED OPTICS  Vol. 43, No. 13  1 May 2004
and precisely fabricated trap detectors suitable for

accurate measurement of beam power.

The scheme of a recently designed tunnel-trap detector is shown in Fig. 1. Two 10 mm  10 mm and

four 18 mm  18 mm silicon photodiodes, equivalent

to the Hamamatsu S1337 model,8 were packed in a

light-trapping arrangement. We used this photodiode type to utilize the physical model of internal

quantum efficiency for spectral responsivity extrapolation and interpolation.7 This photodiode model

has a high close to unityand spatially uniform internal quantum efficiency. The beam propagates in

the tunnel-trap detector from the first photodiode behind the apertureto the last sixthphotodiode.

Photodiodes 3 and 6 are not shown for better illustration. The output beam from the trap detector can

be utilized for alignment or for detector transmittance measurements in spectral responsivity determination. A second light trap can be attached to the

trap-detector output to absorb transmitted radiation

and to minimize ambient stray light.

The implementation of the scheme of Fig. 1 is

shown in Fig. 2. The photodiodes are mounted in a

triangular tunnel. Choosing different size of photodiodes allowed the aperture area and the field of view

FOVto be maximized. Temperature control for

the photodiodes was not needed because the temperature coefficient of responsivity of the photodiodes is

close to zero in the visible range.

This trap detector is suitable for both radiant

power and irradiance measurements. In power

mode measurements, the aperture is underfilled, and

in irradiance mode measurements the aperture is

overfilled by the incident radiation. In power mode

measurements, the incident beam must be focused to

the front surface of the aperture. Radiance or luminance can be measured by attaching a radiance–

luminance measuring tube see belowto the front of

the trap detector.

B. Trap Detector Extended with a Filter Wheel

The inside arrangement of the extended trap detector

is illustrated in Fig. 3. The incident beam originating from a baffled point sourceoverfills the common

aperture mounted on the front panel of the cover box.

The aperture front surface and the front surface of

the cover box are in the same plane. This is the

reference plane of the photometer–colorimeter for illuminance mode measurements. The replaceable

filter combinations packagesare mounted in a

temperature-controlled filter wheel. The wheel can

be heated slightly above room temperature with a

thermoelectric cooler–heater. This regulated temperature will ensure stable spectral transmittances

for the filters without condensation. The wheel has

five well-defined positions with filter-mounting holes.

The filter combinations are mounted in the first four

holes. The last hole in the fifth position is empty for

Fig. 1. Beam propagation in the triangular tunnel-trap detector.

The converging incident beam is focused to the aperture.

Fig. 2. Construction of the triangular tunnel-trap detector. The

aperture is drawn to be semitransparent in the figure.

Fig. 3. Filter wheel between the aperture and the trap detector.

The outside edge of the aperture can be seen where the incident

beam from a baffled point source overfills the aperture.

1 May 2004  Vol. 43, No. 13  APPLIED OPTICS 2623
spectral responsivity determination of the trap detector itself.

The filter wheel is located between the aperture

and the front end of the tunnel-trap detector. A rotating knob is mounted on the shaft of the wheel and

located on the back of the cover box. The length of

the filter combinations is limited to 10 mm by the

thickness of the filter wheel. The space for the

wheel, between the aperture and the trap detector, is

12 mm. This separation did not decrease the FOV

of the meter.

C. Radiance–Luminance Measuring Tube

While illuminance or irradiancecan be measured

with one aperture, luminance or radiancemode

measurements need two apertures. An input tube

with two baffles between the apertures can be attached to the front of the photometer–colorimeter for

radiance and luminance mode measurements. The

aperture in the front plate of the housing and the

front aperture of the tube will determine the radiance

luminancemeasurement angle. Figure 4 shows

the picture of the photometer–colorimeter when it is

equipped with the radiance–luminance measuring

tube.

The FOV scheme of the radiance–luminance measuring tube is shown in Fig. 5. The diameter of the

trap-detector illuminance measuringaperture is d.

The diameter of the front aperture is D.

The radiant power 	d entering the trap detector in

radiance measurement mode is

	d  Lt
m Ad, (4)

where Lt is the radiance of the target surface measured by the meter, 
m is the viewing solid angle

measurement angleof the meter, and Ad is the acceptancearea of the trap-detector aperture. Using

the symbols of Fig. 5,

Ad  d2

4, (5)


m  21  cos
2. (6)

When D  11.29 mm, and the separation between the

two apertures is s  165 mm, the nominal or effectiveviewing angle can be calculated:


  2 tan1

D2s 3.919°. (7)

From the above values and for d  5 mm,

Ad  0.1964 cm2

,


m  0.003674 sr.

When the trap detector calibrated for power responsivitymeasures radiant power, the radiance of the

target surface can be calculated from Eq. 4. Determination of 
m from the nominal viewing angle 
 is

an accurate approximation when Ad is small. If we

integrate the radiant power reaching the detector

from a uniform source of Lt  constant radiancefor

an ideal 
 angle d  0and the real case d  0,

using the same detector aperture Ad, the integrated

difference ideal radiance minus real radiancewill

be 0.012% for d  5 mm and 0.006% for d  3.5

mm. These systematic radiance luminancemeasurement errors are very small. For a detector aperture of d  5 mm, the integrated difference can be

utilized as a correction factor for the measured radiance luminance. A detailed analysis with the

achievable uncertainties of radiance measuring tubes

Fig. 4. Picture of the photometer–colorimeter equipped with a

radiance–luminance measuring tube.

Fig. 5. FOV design of radiance–luminance measurement.

2624 APPLIED OPTICS  Vol. 43, No. 13  1 May 2004
with different input geometries will be discussed in a

following paper.

The unvignetted FOV of the radiance luminance

measuring tube is

  2 tan1 D  d

2s .

For the above geometry with d  5 mm,  is 2.18°.

The full radiance-measurement angle is

  2 tan1 D d

2s .

For the above tube design,   5.65°, which is smaller

than the 8° FOV of the trap detector discussed below. With this design, the unvignetted target spot

diameter the plateau of the output signalwill be

40% of the full spot diameter seen by the radiance–

luminance meter.

The design of the baffle arrangement inside the

tube is shown separately in Fig. 6 to illustrate the

separation of rays from an extended source. Baffles

B1 and B2 minimize the effect of stray light and reject

radiation from light sources outside the FOV. For

simplicity, three rays are shown outside the two FOV

rays producing to illustrate this situation for a

large extended source.

For the above tube design, B1 had a diameter of 8.0

mm, and it was located at a distance not too far from

the detector aperture to avoid any decrease by clippingin the FOV. This baffle was fabricated with

the same procedure as the other two FOV-limiting

apertures. They were all made of copper, coated

with black nickel. The aperture thickness is 0.15

mm. The position of B2 is not critical. It has a

larger diameter and stops radiation entering the

front aperture at large incidence angles.

As an alternative to the geometrical radiance or

radiance responsivitydetermination described

above, the radiance responsivity of the photometer–

colorimeter can be determined from radiance measurement of a calibrated sphere source. The radiant

intensity of the sphere source can be determined

against an irradiance meter standard such as another trap detectorwhen the trap detector and

source separation is large enough to take the source

as a point source. The source radiance measured by

the photometer–colorimeter will be equal to the ratio

of the radiant intensity and the output area of the

source.9 The radiance responsivity will be the ratio

of the output signal of the photometer–colorimeter

and the source radiance.

The above tube design can be utilized in measurements for which the target spot determined by the

full radiance measurement angleof the photometer–

colorimeter can be positioned within the radiating

surface of the source to be measured. A calibration

source should be spatially uniform such as a sphere

exit portto yield low measurement uncertainties.

3. Spatial Characteristics

Three spatial characteristics were measured to verify

the design expectations in the three measurement

modes. The uniformity of spatial responsivity was

measured in flux powermode with the trap detector

underfilled by an incident beam scanned over the

aperture. The angular responsivity was measured

in illuminance mode with the aperture of the trap

detector overfilled by the incident radiation. The

FOV was measured in radiance mode to determine

the measurement angle and the out-of-target blocking of the photometer–colorimeter for luminance

measurements.

A. Spatial Uniformity of Responsivity

To minimize uncertainty in flux measurement mode,

a good spatial uniformity of responsivity is needed

from the trap detector. The spatial uniformity was

tested by scanning the incident beam over the active

area of the tunnel-trap detector. The f9 output

beam 6.4° full angleof a monochromator was focused on the plane of the removed aperture. The

diameter of the beam spot was 1.1 mm. The beam

was not clipped by any of the six photodiodes inside

the trap detector. The scan was made with 0.5-mm

step increments. The wavelength of the beam was

500 nm. The 0.05% nonuniformity contours are

shown in Fig. 7. The real acceptance area is at least

0.55 mm but not more than 1.05 mmlarger than the

measured uniform area shown in the plot. Accordingly, the maximum diameter of the trap detector

aperture is 5 mm.

Fig. 6. Baffle B1, B2arrangement inside the radiance–luminance tube and FOV and out-of-FOV rays of an extended source measurement.

1 May 2004  Vol. 43, No. 13  APPLIED OPTICS 2625
B. Angular Responsivity

The normalized angular responsivities of the tunneltrap detector, when equipped with a 3.5-mm diameter aperture, were measured in two perpendicular

planes. The results are shown in Fig. 8.6 During

the horizontal scan, the trap detector was rotated in

the horizontal plane around its aperture center. It

measured the radiation from a luminous intensity

lamp considered a point sourceat a separation of

3 m. Thereafter, the radiometer was rotated 90°

around its optical axis and the vertical scan was done

in the same way as the horizontal one. The graph

shows that the deviation of the realized angular responsivities from the expected cosine function is less

than 0.02% within a 5° FOV and 0.05% at 8° FOV.

Accordingly, the allowed maximum convergence full

angle of an incident beam is 8°. In Subsection 2.C,

the largest beam convergence angle is   5.65°.

The measurement results discussed above verified

the optical and mechanical design expectations for

the tunnel trap detector.

C. Radiance–Luminance Measurement FOV

The point-spread function of the trap detector with

the radiance–luminance tube was measured with a

small incandescent lamp of 5-mm diameter at a

distance of 1 m. The lamp was mounted in an optical axis and the photometer–colorimeter was moved

in a plane perpendicular to that optical axis. The

filter combinations were moved away from the input

of the trap detector, and the open channel was measured. The measurement results are shown in Fig.

9 on both linear and logarithmic scales. As a result

of the optimized input geometry of the radiance–

luminance tube, an out-of-field blocking of more than

4 orders of magnitude was measured.

4. Tristimulus Filters

The four channels of the photometer–colorimeter are

spectrally matched to the x1, x2, y, and z

color-matching functions by individually realizing

four filter combinations that are alternately used

with the tunnel-trap detector. The responsivity of a

channel is the trap-detector spectral responsivity

multiplied by the spectral transmittance of the selected filter combination.

A. Design of the Filter Combinations

Different spectral transmittances were needed from

the filter combinations to modify the spectral responsivity of the trap detector according to the CIE colormatching functions. Our goal was to achieve the

smallest possible CIE f1 values discussed in Subsection 4.Cfor the realized tristimulus channels. The

achievable f1 value is limited by several factors, such

as the availability of certain filter types, the thickness

limit of the filter combination package, the thickFig. 7. Nonuniformity of spatial responsivity of the tunnel trap

detector. The 0.05% contours are shown at a wavelength of 500

nm. The detector was moved by 0.5-mmstep increments, and

the beam spot diameter was 1.1 mm.

Fig. 8. Normalized angular responsivities of the tunnel-trap detector when equipped with a 3.5-mm diameter aperture. The

expected cosineresponsivity is shown as well.

Fig. 9. Point-spread response of the radiance measuring trap

detector on both linear and logarithmic scales.

2626 APPLIED OPTICS  Vol. 43, No. 13  1 May 2004
ness uncertainty of the individual layers during fabrication, temperature differences between design and

applications, and the uncertainty of the spectral

transmittance determinations.

All possible color filters that seemed to be promising for the realization of the four filter combinations

were purchased. Unfortunately, the number of commercially available filter types is decreasing. The

fabrication of many filter types has been discontinued

because of the decreasing demand in the market. A

database was generated from the spectral transmittance measurements of the collected filters. The

most suitable filter types modelswere chosen for the

tristimulus filter combinations. Filters were purchased only from Schott and Hoya.8

The thicker longerthe filter combination, the

lower the transmittance. The maximum thickness

of a filter combination was limited to 10 mm because

of the space available between the aperture and the

front end of the trap detector. The peak transmittance maximization of the individual filter combinations was a secondary concern because of the wide

signal dynamicrange of the trap detector. The

peak transmittance of each filter combination was

limited to a minimum of 1.5%.

In each filter combination, after optimization for

the spectral transmittance, five to eight filter disks

layerswere cemented together. The ends of all

combinations were evenly aligned to the front surface

of the filter wheel facing the aperture. All filterdisk diameters were 9.5 mm. This diameter, with

the 10 mm maximum thickness of a combination, was

a good compromise to avoid limiting the original FOV

acceptance angleof the trap detector.

The optimum thickness of all filters within a filter

combination was calculated with an interactive program. A similar optimization method, to obtain the

best spectral fit, has already been published.10 After

the initial filter type and thickness selections, the

program finds a local minimum of the f1 value by

individually changing the thickness of the other filter

layers inside of the same package. The f1 optimization is an iterative method where the filters are

remeasured several times for spectral transmittance

after they are polished to the desired thickness calculated by the computer program. As the uncertainty of our filter thickness realization was 3 m, the

fabrication of the filter combination the first filter

realizationstarted with the thinnest filter. Several

pieces of the thinnest filters were made polished

and then the thickness of each piece was measured.

The filter that gave the best results was selected for

the combination, and the thickness of the other layers

in the same combinationwas recalculated. The

less critical filter of the combination was calculated

last. The program continuously displayed the peak

transmittance and the total thickness of the filter

combination being optimized. The uncertainty of

the spectral transmittance measurements was 0.2%.

The spectral responsivity of the filter–detector

combination was calculated with the following equation:

Sn 1  explog10Sdi

ti

log10

i

m

1  

ti

m  ,

(8)

where

 is wavelength,

 is the surface reflection,

Sdis the spectral responsivity of the detector,

i is the filter index,

ti is the thickness of the ith filter in the package,

i

mis the measured spectral transmittance of

the ith filter,

ti

m is the measured thickness of the ith filter,

m superscript shows that the value was measured.

The surface Fresnelreflection depends on the refractive index of the filter material. The refractive

indices of the filters are similar to one another with a

significant wavelength dependence in the visible

range. The internal transmittance of the filter layers dominates the spectral transmittance of the realized filter combination. For all separate filters and

cemented filter combinations, a   0.08 was used in

the calculations. Ultraviolet and infrared blocking

filters were used to attenuate the incident radiation

for wavelengths shorter than 360 nm and longer than

830 nm. The blocking was necessary for all filter

combinations because of the broad sensitivity range

of the silicon trap detector.

To yield optical-quality filter combinations, both

sides of the individually made filters were polished.

The individual filters were glued together with optical cement that has constant spectral transmittance

in the visible range Lens Bond Optical Cement, Type

F65, Modified RD3-74 from Summers Laboratories,

Inc.. The refractive index of the optical cement is

very similar to that of the glass filters and should

almost eliminate internal reflections.

B. Responsivity of the Realized Filter Combinations

The spectral power responsivities of the colorimeter

channels were determined to characterize the filter

combinations for f1 values. The spectral irradiance

responsivity calibrations of the channels will be performed later on the combined filter–detector channels. The four channels with a common aperture at

the front will be calibrated against an irradiance

mode reference trap detector when both measure the

same irradiance from a monochromatic point

source. Irradiance measuring reference trap detectors are available with 0.1% responsivity uncertainty.

The calibrations will be made at the National Institute of Standards and Technology NISTSpectral

Irradiance and Radiance Responsivity Calibrations

with Uniform Sources SIRCUSfacility with an irradiance responsivity uncertainty of close to 0.1%.

1 May 2004  Vol. 43, No. 13  APPLIED OPTICS 2627
The photometer–colorimeter calibrations will be described in a future publication.

The absolute spectral responsivities of the realized

channels are shown in Fig. 10aon a linear scale and

Fig. 10bon a logarithmic scale. The logarithmic

graph shows the sharp cutoff of the filters at the sides

of the responsivity curves. These spectral responsivities were determined from piecewise measurements. The filter transmittances were measured

separately in the 360–830 nm wavelength range

with 5-nm increments. The measurements were

made with a prism-grating spectrometer. The spectral responsivity of the trap detector was derived

from another trap detector calibrated against the primary standard cryogenic radiometer.7 The CIEdefined color-matching functions and the realized

and then normalized channel responsivities are

shown in Fig. 11.

C. Spectral Mismatch of the Channels

The spectral mismatch of the realized channel responsivities relative to the CIE standard functions

can be calculated from the above determined channel responsivities. The spectral responsivity mismatch of a realized channel relative to the CIE

defined function can be described by the CIEdefined spectral mismatch index2 f1. According to

the definition, f1 can be used to define the degree of

spectral mismatch of photometers when the goal is

to equalize the realized spectral responsivity curve

to the Vfunction.

According to the definition,

f1  o

 s*rel  Vd

o

 Vd

 100%, (9)

s*rel  o

 SA Vd

o

 SA sreld

srel, (10)

where s*rel is called the normalized relative spectral responsivity, SA is the spectral distribution of

the Standard Illuminant A11 used in the measurement, Vis the spectral luminous efficiency of photopic vision, and srel is the relative spectral

responsivity of the realized channel. Here we extended the CIE f1 definition from the original photometric channel to all four tristimulus channels by

substituting the x1, x2, y, and zcolormatching functions for the Vfunction.

A mismatch of f1  1.39% has been reported12 for

a Vfunction realization fabricated with a similar

sandwich layermethod. This f1 can be misleading, because the wavelength increments were 10 nm

Fig. 10. Absolute responsivities of the realized tristimulus channels. Spectral responsivity on aa linear scale and ba logarithmic scale.

Fig. 11. CIE x, y, and zcolor-matching functions solid

curvesand the realized and then normalized channel responsivities dashed curves.

2628 APPLIED OPTICS  Vol. 43, No. 13  1 May 2004
in a shorter wavelength range of 400–750 nm. In

the present work the design-related transmittance

measurements and the f1 optimizations were made

between 360 and 830 nm with 5-nm increments.

These measurements followed the CIE definitions for

the color-matching functions. However, our final filter combination measurements were made between

380 and 780 nm with 5-nm increments.

D. Analysis of the f1 Values for Fabrication

It was an important design criterion to understand

how the f1 values of the realized channels depend

on the thickness changes of the individual filter

layers inside of a filter combination. Figure 12

shows the changes of the f1 values for partial thickness changes of the layers for all of the realized

channels. The graphs show that the fabrication of

the thinnest filters is the most critical see Table 1.

This was the reason that we started the layer fabrications within a filter combination with the thinnest filters.

The filter models of the four realized filter combinations with the designed calculatedand realized

thickness of the layers and combinations are summarized in Table 1. Table 1 shows that the fabricated

thickness of the filter layers can be equal to or very

different from the calculated designedvalues. The

allowed thickness deviation was dependent on filter

type and filter combination. We controlled the layer

polishing tolerances according to the results of Fig.

12. The calculated designedand realized f1 and

peak transmittance maxvalues are also shown in

the table. The f1 values were calculated from the

spectral responsivities of the channels after the realization of the filter combinations. The channel responsivities were determined from separate

transmittance for the filter combinationsand responsivity for the trap-detectormeasurements.

Fig. 12. f1 value dependence of the four channels as functions of the thickness change of the filter layers.

1 May 2004  Vol. 43, No. 13  APPLIED OPTICS 2629
E. Spectral Transmittance Differences

As a result of our rigorous filter fabrication procedure, the relative transmittance curves of the filter

combinations are very similar to the designed transmittance curves. However, the differences between

the realized and designedcurves and the CIE functions are significantly larger. The performed transmittance differences are illustrated in Fig. 13 for the

photometric channel. The calculated transmittance

was normalized to the measured values. The CIE

function is shown to illustrate where the significant

differences are. A highest transmittance difference

between the realized function and the CIE function

of 0.07 was obtained at 535 nm. The spectral transmittance differences relative to the CIE functions

were dominated by the availability of filter components. Table 1 shows that the maximum peak

transmittance, max, values after the realizations

were randomly different for the four filter combinations. This variation was caused by the fabrication

thickness tolerance that we allowed for the thick filter layers.

The Table also shows that the f1 values of the

fabricated filter combinations are all somewhat

higher than the designed values. The increase was

obtained for a few reasons. The largest change was

caused by the temperature difference between the

design and final transmittance measurements. The

f1 values depend on the temperature because the

cut-on edges of the filters, used on the shortwavelength sides of the transmittance curves, are

temperature dependent. During the design measurements the temperature of the filters was not controlled. The lack of temperature-controlled filter

holders made the design measurements simpler and

faster. The transmittance of the realized filter combinations was measured at 26 °C in the temperaturecontrolled filter wheel. Here temperature

stabilization was necessary to achieve high stability.

The temperature of the filter wheel was controlled to

3 °C above room temperature to avoid condensation. The increase in the f1 values can be less if the

filters are measured and used at the same temperature for both design and applications.

Also, significant f1 changes were obtained because

of the limited sensitivity of the transmittancemeasuring spectrophotometer. Sometimes filter

transmittances had to be calculated from transmittances measured with different filter thicknesses and

limited signal resolution. The thin filters needed

special attention. The transmittance of a thin filter

has to be measured, because it cannot be calculated

from the transmittance measurement of the same

thick filter. Also, when thin filters of large diameter

are to be made, they should be cemented to a transparent glass substrate before polishing. The thick

substrate with spectrally constant transmittance

helps avoid cracks and can make polishing and thickness measurements easier. The final transmittance

of a filter combination will be a product of the spectral

transmittances of the five to eight individual layers,

the glass substrate, and the optical cement between

the layers.

Without careful filter combination design and fabrication, the f1 can be several percent or higher.

With the careful design and fabrication procedure

described above, the f1 of the yand x1channels

was less than 2% for the 380–780 nm wavelength

range with 5-nm increments. The implementation

of the blue channels is more difficult because of the

Fig. 13. Transmittance differences left Y axisof the realized

photometric channel relative to the CIE and designed normalized

spectral transmittances. The CIE function is shown to illustrate

where the significant differences are.

Table 1. Filter Types with Designed Calculatedand Realized

Thickness of Layers, Spectral Mismatch Values, and Maximum

Transmittances for the Four Filter Combinations

Filter

Thickness m

Filter

Thickness m

Calculated Realized Calculated Realized

X1 X2

BG 40a 3100 3093 BG 1a 3120 3149

OG 570a 54 60 BG 39a 2028 2031

RG 610a 42 42 FG 15a 4236 4250

UG 3a 1215 1143 GG 435a 170 169

LA 120b 1556 1728 UG 3a 162 148

Y 52b 2850 2531 Total 9716 9747

Total 8817 8597 f1 3.83% 4.12%

f1 1.55% 1.63% max 3.41% 3.36%

max 8.15% 8.93%

Y Z

BG 7Aa 288 297 BG 4a 376 375

BG 40a 2623 2585 BG 7Aa 644 433

FG 3a 63 63 BG 24a 1945 1857

FG 13a 1506 1563 BG 39a 2028 2028

OG 515a 43 44 FG 13a 676 654

Y 52b 120 115 GG 435a 153 156

Total 4643 4667 LA 120b 2820 2969

f1 1.47% 1.58% LB 200b 1226 1265

max 38.04% 36.43% Total 9868 9737

f1 3.31% 3.57%

max 1.65% 1.79%

a

Schott filter. b

Hoya filter.

2630 APPLIED OPTICS  Vol. 43, No. 13  1 May 2004
smaller number of suitable filters available for this

range. Eight filters were needed for the zchannel

to achieve an f1  3.57%. An f1 of 4% seems to be

the best realization for the x2channel.

5. Photocurrent Measurement Uncertainty

The design of the photocurrent-to-voltage converter for

the silicon tunnel-trap detector has already been published.6 The improvement introduced in the present

design resulted in an uncertainty reduction in the

current-to-voltage conversion for all signal gains. We

used feedback resistors with 0.01% uncertainties of

their decadic nominal values and temperature coefficients of 10 parts in 106

°C. Accordingly, calibrations

for the individual signal gains were not necessary anymore. The dynamic signal range of the photometer–

colorimeter is 11 decades in dc measurement mode

with a noise-equivalent photocurrent of 32 fA at a

bandwidth of 0.3 Hz.

6. Conclusion

A new photometer and tristimulus colorimeter has

been developed to implement the first detector-based

tristimulus color scale we published recently.1 The

design considerations of a silicon tunnel-trap detector

that was extended by a temperature-controlled filter

wheel, an aperture, a removable luminance measuring tube, and an improved current-to-voltage converter have been described. Four filter

combinations were made to implement the CIE colormatching functions with f1 values whose small size

constitutes a benchmark for subsequent work. The

main goal was to realize a colorimeter in which the

channel spectral responsivities could be determined

with uncertainties of 0.1%.

The characterization results on the uniformity of

spatial responsivity, angular responsivity, FOV, and

out-of-field blocking verified the optical and mechanical design expectations. Photocurrents from the

trap detector could be measured with an uncertainty

of 0.01% in a dynamic range of 11 decades. The

spectral transmittance of the realized filter combinations and the spectral responsivity of the trap detector were measured to determine the f1 values of the

realized channels. An analysis showed the f1 dependence on the thickness change of the filter layers

inside of a filter combination. As a result of the

rigorous filter realization procedure, the f1 values of

the realized channels were dominated by the limited

number and availability of suitable filter components. Very small f1 values were realized to allow

us to use the same set of calibration factors for the

colorimeter channels and to obtain small color measuring uncertainties even when the spectral distribution of the measured source is different e.g., when it

changesfrom the distribution used to determine the

calibration factors. The colorimeter can measure

sources with all kinds of spectral distribution. A

new set of calibration factors will be needed only for

very different source distributions, such as discharge

lamps or displays cathode ray tube or liquid crystal.

The described design and realization considerations, the results of measurements and characterizations, and the planned and available calibration

methods, devices, and setup promise a real possibility

for determining the spectral irradiance and radiance

responsivities of the colorimeter channels with the

expected 0.1% uncertainty. After calibration, the

reference photometer–colorimeter will be used to

propagate NIST realized detector-based scales to

field-level applications. We hope to discuss the spectral irradiance responsivity calibration of the channels and the determination of the calibration factors

for different source distributions in a future paper.

The authors thank Don Lynch of Reyer Corporation for the mechanical fabrication and filter wheel

design, Thomas Larason for the detector spatial response uniformity test, Steve Brown for the pointspread response test, Edward Early for measuring

the spectral transmittance of the filter packages, and

David Wilmering and John Fuller for fabricating the

filter packages.

References and Notes

1. G. Eppeldauer, “Spectral response based calibration method of

tristimulus colorimeters,” J. Res. Natl. Inst. Stand. Technol.

103, 615 1998.

2. Publication CIE No. 69 Central Bureau of the CIE, Vienna,

1987.

3. All uncertainties discussed in this paper are relative expanded

uncertainties with a coverage factor of two.

4. G. P. Eppeldauer, S. W. Brown, C. C. Miller, and K.R. Lykke,

“Improved accuracy photometric and tristimulus-color scales

based on spectral irradiance responsivity,” in Proceedings of

the Twenty-Fifth Session of the CIE Central Bureau of the

CIE, Vienna, 2003, Vol. 1, pp. D2-30–D2-33.

5. D. W. Allen, G. P. Eppeldauer, S. W. Brown, E. A. Early, B. C.

Johnson, and K. R. Lykke, “Calibration and characterization of

trap detector filter radiometers,” in Earth Observing Systems

VIII, W. L. Barnes, ed., Proc. SPIE 5151, 471–479 2003.

6. G. P. Eppeldauer and D. C. Lynch, “Opto-mechanical and electronic design of a tunnel-trap Si-radiometer,” J. Res. Natl. Inst.

Stand. Technol. 105, 813–828 2000.

7. T. R. Gentile, J. M. Houston, and C. L. Cromer, “Realization of

a scale of absolute spectral response using the NIST high accuracy cryogenic radiometer,” Appl. Opt. 35, 4392–4403 1996.

8. The mention of certain commercial products in this paper is for

information purposes only and does not constitute an endorsement of the product by the authors or their institutions.

9. G. P. Eppeldauer, S. W. Brown, T. C. Larason, M. Racz, and

K. R. Lykke, “Realization of a spectral radiance responsivity

scale with a laser-based source and Si radiance meters,” Metrologia 37, 531–534 2000.

10. G. Czibula, “Producing a detector with predetermined spectral

responsivity,” in Proceedings of the International Measurement

Confederation IMEKO10th International Symposium of the

Technical Committee on Photon Detectors IMEKO Secretariat, Budapest, 1982, Vol. 1, pp. 189–199.

11. Publication CIE No. 15.2 Central Bureau of the CIE, Vienna,

1986.

12. J. P. Makai, G. Czibula, and J. Schanda, “The importance of

the spectral responsivity correction in case of photoelectrical

elements,” in Proceedings of the International Measurement

Confederation IMEKO11th International Symposium of the

Technical Committee on Photon Detectors IMEKO Secretariat, Budapest1984, pp. 215–225.

1 May 2004  Vol. 43, No. 13  APPLIED OPTICS 2631
NEW PHOTOMETER STANDARDS FOR LOW UNCERTAINTY 

ILLUMINANCE SCALE REALIZATION 

G. P. Eppeldauer, C. C. Miller, and Y. Ohno 

National Institute of Standards and Technology, USA 

ABSTRACT 

Improved performance photometers have been developed at the National Institute of Standards 

and Technology (NIST) to utilize the low spectral responsivity uncertainty of spectral irradiance 

responsivity measurements performed on the facility of Spectral Irradiance and Radiance 

Responsivity Calibrations using Uniform Sources (SIRCUS). Based on the improved design of 

the transfer standard photometers, a lower uncertainty detector-based photometric scale is being 

realized with an uncertainty goal of 0.1 % (k=2). The existing photometer standards that maintain 

the present NIST illuminance unit can be calibrated against the new transfer standards. In 

addition, new generation working standard photometers have been developed to utilize the 

extended group policy to better monitor and correct responsivity changes. The working standards 

propagate the new reference scales from the transfer standards with a minimal increase in 

measurement uncertainty. Design issues of the new photometers and the improved scale 

realization and transfer are discussed. 

Keywords: detector-based calibration, illuminance, photometry, spectral responsivity, standard 

1. INTRODUCTION 

The present NIST illuminance unit is maintained on a group of eight photometer standards with a 

relative expanded uncertainty (k=2) of 0.39 % [1]. Several components in the uncertainty budget 

are related to the determination of the photometer relative spectral responsivities using the 

traditional lamp/monochromator system of the NIST Spectral Comparator Facility (SCF). The 

dominant uncertainties originate from the converging beam geometry, the small spot size on the 

photometers, wavelength errors, aperture area measurement error, and the spatial non-uniformity 

of the detector and filter combination. A significant long-term uncertainty component originates 

from stain settlement (build-up of a layer) on the front surface of a filter package that decreases 

the responsivity of the photometer. The standard photometers, built in 1990, cannot be calibrated 

on the SIRCUS facility because the coherence in the laser-based sphere sources results in 10 % 

level interference fringes in the output signals. Instead, new generation transfer standard 

photometers with optimized optical, photometric, and electronic characteristics have been 

developed. The improved scale is realized on the new transfer standard photometers. The old 

photometer standards, together with the new generation working standard photometers, can be 

calibrated against the new transfer standard photometers by measuring the illuminance from a 

2856 K color temperature standard lamp. The working standard photometers will be recalibrated 

yearly against the transfer standards and their long term stability will be monitored. The extended 

group of working standards is used for routine photometer calibrations and photometric scale 

dissemination. 

2. TRANSFER STANDARDS 

The transfer standards were designed such that it is the uncertainty of the spectral irradiance 

responsivity calibrations that determines the photometric scale uncertainty and not limitations in 

the performance of the photometers themselves. New filter combinations have been designed 

with a minimum allowed thickness of 4.5 mm to avoid interference fringes. They are individually 

fabricated to closely match the responsivity of the silicon detector to the CIE V(λ) function [2]. The 

filter combinations are in a filter wheel located between the common detector and aperture. The 

wheel temperature is controlled at 25 o

C where the spectral mismatch errors were minimized. 

Two types of transfer standard photometers were designed and built. The first type, as shown 

in Fig. 1, uses windowless silicon photodiodes in a tunnel trap configuration [3]. The cut-outs 

were made for better illustration. The long-term stability of this photometer is regularly monitored 

to see if any responsivity changes happen due to either stain settlement on the filter surfaces or 
because the photodiodes are exposed to the ambient air. A few tenths of a percent changes have 

been observed by us earlier on open Si trap detectors at 400 nm. The changes gradually 

decreased and became negligibly small at 500 nm. In this tunnel-trap detector, light is not 

reflected back to the filters. 

In the improved (newer) transfer standard, a single-element silicon photodiode is used which 

has a sealed wedged-window to avoid fringes. The picture of the new transfer standard (with the 

front panels removed) is shown in Fig. 2. The front panels are removed for better illustration. The 

photo shows the light tight box with the detector and the filter-wheel inside. The photocurrent 

meter is attached to the side of the box. The current measuring electronics are matched to the 

electronic characteristics of the photodiode for low-noise performance over a signal dynamic 

range of 12 decades. The uncertainty of the current-to-voltage conversion is 0.02 % (k=2). 

 Fig. 1. The filter-trap transfer standard. Fig. 2. The new generation transfer standard 

3. WORKING STANDARDS 

The illuminance responsivities of the present working standard photometers have been 

determined yearly based on their spectral power responsivity measurements at the SCF. Figure 3 

shows the long-term changes normalized to unity in 1991. Yearly scale realizations were made to 

determine the actual responsivities based on the SCF scale realizations. The thick line shows a 

0.3 % maximum responsivity change for the group average of photometers 4, 6, and 8. The front 

surfaces of the filters in photometers 1 and 2 were cleaned first in 1994. The other photometers 

were not cleaned until 2006, when the front surfaces of all photometer filters were cleaned. The 

results show that the long term stability of the individual photometers can be improved to +/- 

0.1 % if the front surfaces of the filters are cleaned on a regular basis. Change of photometer 5 

after 2003 is due to repairs. 

Ten-year long changes of 0.02 % were 

measured at the SCF on silicon photodiodes 

sealed with fused silica windows used in 

these working standards. It can be 

concluded that change-free photometer 

standards can be made if the photometer 

head is sealed with a fused silica window. 

The stability of the working standards should 

be matched to the lower uncertainty of the 

SIRCUS-based scale to obtain an overall 

uncertainty improvement in the disseminated 

scale. A package design was applied for 

both the old and the new working standard 

photometers to obtain a uniform temperature 

distribution for the filter combination and the 

silicon photodiode. The spectral 

transmittance of the V(λ) curve is 

temperature dependent. Also, the applied 

infrared-suppressed silicon photodiode has 

a significant temperature coefficient of 

0.97

0.975

0.98

0.985

0.99

0.995

1

1.005

1.01

1991 1993 1995 1997 1999 2001 2003 2005

Ph.1

Ph.2

Ph.3

Ph.4

Ph.5

Ph.6

Ph.7

Ph.8

Avg of 4,6,8

Year

Fig. 3. Long-term changes of the old photometers. 

All photometers were cleaned in 2006 and Ph.1 

and Ph.2 were cleaned in 1994 and 1997. 
responsivity at wavelengths longer than 630 nm. These two components are mounted in a metal 

housing, and the uniform temperature is monitored in the existing (old) photometers [1], and 

stabilized in the new working standards. As shown in Fig. 4, the aperture (1), the filter 

combination (2), and the photodiode (3) are close to each other inside of a Copper pot (4). While 

there is a small gap between the photodiode and the filter, the very thin aperture is mounted on 

the front surface of the filter to avoid inter-reflections. In order to simplify cleaning the front 

surface of the filter, the aperture is fixed in a holder (5) that can be easily removed and relocated 

into the same position using an asymmetric screw arrangement. A temperature sensor (6) is 

plugged into the copper pot. A ring shape thermoelectric cooler (7) is mounted to the bottom of 

the copper pot in the new working standards to keep the temperature constant, just above the 

ambient. 

Fig. 4. Structure of a photometer package Fig. 5. A new generation working standard. 

The field-of-view (FOV) of the illuminance meter depends on the diameter of the aperture and 

the photodiode active area. It is always kept small (e.g. 11o

) to reject ambient light as well as 

reflections and stray light from a test source. The base unit, as shown on the right side of Fig. 5, 

can be equipped with a bayonet mount at the front to attach an input optic for luminance 

measurement. In this example, the filter can be removed; therefore its temperature is 

independently controlled from the temperature of the photodiode. The photocurrent meter is 

located inside of another cylindrical housing attached to the bottom of the base unit. The 

electronic characteristics of the current-to-voltage converter are matched to the high shunt 

resistance of the silicon photodiode to obtain low output noise and wide signal range. 

4. RESPONSIVITIES 

The spectral irradiance responsivities of the transfer standards were determined against two 

irradiance-measuring reference trap detectors. 

As an example, the spectral irradiance 

responsivity of one of the transfer standards, as 

measured on the SIRCUS, is shown in Fig. 6. 

The left-Y axis shows the measured data on a 

linear scale. The right-Y axis is a logarithmic 

scale to show the out-of-band responsivity of 

the realized V(λ) curve. 

The illuminance responsivity se, which is the 

ratio of the photometer output current to the 

illuminance measured by the photometer, was 

determined from the SIRCUS measured 

spectral irradiance responsivity sE(λ) and the 

incident irradiance E(λ) from a CIE Standard 

Illuminant A source: 

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

10-6

10-5

10-4

10-3

10-2

10-1

400 500 600 700 800

Fig. 6. Spectral irradiance responsivity of 

the filter-trap transfer standard. 
( ) ( )

()() λλλ

λλλ

dEVK

dEs

s ∫

∫ =

m

E

e

where Km is the maximum spectral luminous efficacy, 683 lm/W and λ is the wavelength. 

The illuminance responsivity has also been measured against the SCF-based scale. The 

illuminance responsivity of the new generation transfer standard was measured against the 

average illuminance responsivity of a selected group of the old photometer standards. The 

photometers measured the same illuminance from a 2856 K color temperature lamp. The 

preliminary ratio of the SIRCUS-based illuminance responsivity to the SCF-based illuminance 

responsivity at gain 108 V/A is ≈1.004. The relative expanded uncertainty of the SIRCUS-based 

illuminance responsivity is estimated to be 0.1 % (k=2). This preliminary uncertainty is dominated 

by a constant 0.08 % irradiance responsivity difference in the visible wavelength range between 

the two reference trap detectors used to calibrate the transfer standards. Also, the ratio obtained 

at the previous photometric scale comparison in 2003, using the filter-trap transfer standard, was 

1.0038. At present, the data evaluation for the filter-trap transfer standard is still being done. 

There will be further comparisons of the two scales after the annual SCF-based calibration of the 

old photometers. 

5. CONCLUSIONS 

The results of a research work to improve the uncertainty of the NIST detector-based photometric 

scale are presented. Transfer standard illuminance meters have been developed and calibrated 

on the SIRCUS facility with decreased spectral irradiance responsivity uncertainty. In order to 

decrease the long-term responsivity changes of the old (presently used) working standard 

photometers that maintain the NIST photometric scale, the old group has been extended with 

new-generation photometers. The extended group can be calibrated against the new transfer 

standards. Repeated scale realizations since 1991 verified that the long term responsivity 

changes of the photometers are caused by the development of stain layers at the front surface of 

the V(λ) filter packages. The instabilities of the old photometer standards could be decreased to 

within +/- 0.1 % of their original (clean) responsivities after the front surfaces of the filters were 

cleaned. It was suggested that photometer working standards, free of responsivity changes 

(without any cleaning), can be made if the front of the photometer head is sealed with a fused 

silica window. The working standard group policy was utilized to determine and then to minimize 

the long term responsivity changes. Using the SIRCUS-based lower scale uncertainty and the 

minimized long-term change in the average responsivity of a selected working standard group, 

the uncertainty of routine illuminance meter calibrations can be reduced by about a factor of two. 

ACKNOWLEDGEMENTS 

The authors thank R. Bousquet, S. Brown, and K. Lykke for help with the SIRCUS 

measurements. 

REFERENCES 

1. Cromer, C.L., et al., The NIST detector-based luminous intensity scale. J. Res. NIST, 1996. 

101(2): p. 109-132. 

2. CIE, The Basis of Physical Photometry. Publication CIE Central Bureau, A-1033 Vienna, P. O. 

Box 169, Austria, 1983. 18.2. 

3. Eppeldauer, G.P. and D.C. Lynch, Opto-mechanical and electronic design of a tunnel-trap Siradiometer. J. Res. Nat'l. Inst. Stand. Technol., 2000. 105(6): p. 813-828. 

Authors: 

George Eppeldauer Cameron Miller 

National Institute of Standards and Technology National Institute of Standards and Technology 

Gaithersburg, Maryland 20899 USA Gaithersburg, Maryland 20899 USA 

Phone: 301-975-2338 Phone: 301-975-4713 

e-mail: george.eppeldauer@nist.gov e-mail: ccmiller@nist.gov 

Yoshi Ohno 
Eppeldauer, et al. New photometer standards... 

5 

National Institute of Standards and Technology 

Gaithersburg, Maryland 20899 USA 

Phone: 301-975-2321 

e-mail: ohno@nist.gov 
IMPROVED ACCURACY PHOTOMETRIC AND TRISTIMULUS-COLOR 

SCALES BASED ON SPECTRAL IRRADIANCE RESPONSIVITY 

George P. Eppeldauer, Steven W. Brown, C. Cameron Miller, and Keith R. Lykke 

National Institute of Standards and Technology 

Optical Technology Division 

Gaithersburg, Maryland, 20899 USA

ABSTRACT 

A new spectral irradiance and radiance responsivity calibration with uniform sources (SIRCUS) facility has 

been developed at the National Institute of Standards and Technology (NIST) that can calibrate radiometers in 

irradiance measurement mode with expanded uncertainties (k=2) of 0.15 %. A reference tristimulus 

colorimeter/photometer has been developed to reduce the uncertainty in the NIST photometric units and to 

realize a detector-based color scale. A novel, spectrally tunable, solid-state source has also been developed 

to transfer the illuminance responsivity and tristimulus color scales from the reference colorimeter/photometer 

to test photometers and colorimeters that measure light sources with specific spectral distributions. By setting 

the transfer source distribution to approximate a particular target distribution, test photometers and 

colorimeters, without knowing their relative spectral responsivities, can be calibrated against the reference 

instrument with almost no spectral mismatch errors resulting in low photometric and color measurement 

uncertainties. 

Keywords: colorimetry, detector-based calibration, illuminance, irradiance, photometry, spectral responsivity, 

standard, transfer-source, tristimulus 

1. INTRODUCTION 

Improvements in detector technology over the past decade have opened a new era in the field of radiometric 

and photometric calibrations. Lower measurement uncertainties can be achieved with modern detector 

standards than with traditionally used source standards. Consequently, fundamental photometric and 

radiometric scales at NIST are currently realized and maintained using detector-based standards [1, 2]. The 

detector-based approach is being extended to colorimetry as well [3]. In the present NIST photometric units, a 

major source of uncertainty is the spectral responsivity measurements of the photometers using the NIST 

Spectral Comparator Facility (SCF) [4] that utilizes a monochromator and a lamp. 

A calibration facility for Spectral Irradiance and Radiance Responsivity Calibrations using Uniform Sources 

(SIRCUS) has been developed at NIST to overcome the limitations of the SCF, in particular for calibrating 

irradiance and radiance meters [5, 6]. The facility introduces the output from tunable lasers into integrating 

spheres, producing a monochromatic, high-power uniform source. The responsivity scale is transferred from 

the NIST High-Accuracy Cryogenic Radiometer [7] and maintained on irradiance standard 6-element 

transmission trap detectors [8]. Their spectral power responsivity is determined using a cryogenic electrical 

substitution radiometer, and their irradiance responsivity is derived by placing a calibrated aperture at the input 

plane. The SIRCUS facility has several advantages over conventional lamp-monochromator systems to 

realize photometric and colorimetric scales. It provides high-power, low wavelength uncertainty, and the ability 

to produce a monochromatic Lambertian radiation that enables calibration of instruments directly for irradiance 

or radiance responsivity. 

The overall relative combined expanded (k=2) uncertainty for the NIST illuminance unit realization using the 

SCF is currently 0.39 % [1]. There are several components in the uncertainty budget related to the 

determination of the photometer spectral responsivity in the SCF [1]. These uncertainty components can be 

significantly reduced or eliminated by realizing the illuminance scale on SIRCUS. 

It is expected that the standard uncertainty in the spectral responsivity scale will be reduced from 0.11 % 

(measured on the SCF) to 0.075 % due to the reduction of transfer steps from the absolute cryogenic 

radiometer. The CIE spectral luminous efficiency, V(λ), is a strong function of wavelength. The SIRCUS 

wavelength scale, with uncertainties reduced to 0.001 nm from the current SCF’s wavelength uncertainty of 

0.1 nm, will reduce the relative standard uncertainty for this component from 0.04 % to less than 0.001 %. A 

significant set of uncertainty components results from the geometry of the SCF output beam. The SCF uses 

f/9 optics to focus the light to a 1 mm spot that is used to calibrate the photometers. The photometers are 

used in a far field condition. SIRCUS can calibrate photometers in a geometrical configuration identical to the 

application geometry. In addition, since SIRCUS calibrates the detector in irradiance mode instead of power 

mode, the uncertainty of the aperture area and the uncertainty due to the non-uniform spatial response of the 

photometer will be eliminated. The combined uncertainty from these components related to measurement 

geometry can be reduced from 0.12 % [1] to less than 0.01 %. The overall relative expanded uncertainty (k=2) 

for the NIST illuminance unit realization is expected to be reduced to 0.24 %, a 40 % reduction in the 
uncertainty in the current scale, when the new illuminance scale is realized. The new illuminance scale will 

lead to an expected overall relative expanded uncertainty of 0.27 % (k=2) for the NIST candela. 

Similar reductions in the uncertainty of the color scale may be expected as well. Typically, a 0.1 % 

uncertainty in the spectral irradiance responsivity of any one channel of the tristimulus colorimeter will result in 

a change of 0.0004 in the x, y chromaticity coordinates (for a Planckian radiator). These expected colorimeter 

uncertainties are equivalent to the uncertainties of the current primary lamp standards. Though it may be 

challenging to further reduce color uncertainties with the detector-based calibration, it leaves future possibility 

with further improvement of the spectral irradiance responsivity uncertainty. 

The SIRCUS facility is used to calibrate primary photometers and colorimeters spectrally. Generally, the 

scale is transferred from the primary reference instruments to test photometers and colorimeters by direct 

substitution against incandescent lamp sources (typically operated at 2856 K). Test instruments are often 

used to measure sources with markedly different spectral distributions, e.g. discharge lamps, displays, light 

emitting diodes (LEDs), etc. Because the instrument’s responsivity does not exactly match the V(λ) or the 

color-matching functions, correction factors need to be applied to the instruments to maintain low uncertainty 

[9]. For such a spectral mismatch correction, however, the relative spectral responsivity of the test instruments 

must be known. In many cases, such data are not available and it would be often too costly for users to 

measure them. To avoid such difficulties, test instruments with unknown relative spectral responsivity can be 

calibrated with standard photometers/colorimeters (with known relative spectral responsivity) using the 

particular light source to be measured by the test instrument. It is not practical to maintain artifacts of all 

possible types of specialty sources at NIST. To solve this problem, we have developed a spectrally tunable 

transfer source based on light emitting diodes (LEDs) [10]. This source is designed to mimic the spectral 

distributions of both traditional and special test sources. It will be used to propagate the NIST reference scales 

to field level photometers and colorimeters with small increases in the uncertainties. 

2. REFERENCE TRISTIMULUS COLORIMETER/PHOTOMETER 

Improved performance photometer and tristimulus colorimeter standards were developed using temperaturestabilized, filtered single-element and tunnel-trap silicon detectors to utilize the very low uncertainties of the 

new SIRCUS spectral responsivity scales [5]. Four filter combinations with the trap detector implement the 

CIE color matching functions [11]. The spectral mismatch of the realized channels is characterized by the CIE 

f1

’

 values [12]. The realized f1

’

 values are 1.6 % for the x 1(λ) and V(λ), 3.6 % for the z (λ), and 4.1 % for the 

 x 2(λ) channels. The filter combinations are mounted in a temperature controlled (heated) filter wheel placed 

between the trap detector and the front aperture. The aperture plane is the reference plane of the illuminance 

mode photometer/colorimeter. A current-to-voltage converter can be plugged to the top of the light tight box of 

the photometer/colorimeter. Electronic and radiometric characterizations, including current-to-voltage 

conversion uncertainty and spatial, angular, and spectral responsivity, showed that the prototype 

photometer/colorimeter had satisfied the design expectations and it will be possible to determine the channel 

spectral irradiance responsivities with 0.1 % relative standard uncertainty. 

A single photometer has also been developed where the photodiode and the filter combination are mounted 

inside of a temperature-controlled copper block. Care was taken in the design - and the front surface of the 

V(λ) filter was sanded - to avoid interference fringes in the SIRCUS calibrations. The f1

’

 was 1.85 %. An 

aperture mounted in front of the filters gives the reference plane of irradiance and illuminance measurements. 

3. SPECTRAL RESPONSIVITY MEASUREMENTS 

Depending on the application, a variety of different integrating spheres are used on SIRCUS. For irradiance 

responsivity calibrations, the source is a 2.5 cm diameter sphere with variable precision exit-apertures that 

mimics the beam geometry of luminous intensity lamp measurements. In this case, the interreflection effects 

within a photometer will not change from calibration to application. Also, because of the uniform irradiance, 

the non-uniformity of spatial responsivity of detectors, filters, and diffusers will not contribute to the uncertainty 

of measurements. Corrections for bandpass will not be necessary, as the bandwidth from the lasers is 

negligible. Comparisons of the spectral responsivities determined on the SIRCUS and the SCF are done on a 

regular basis to minimize uncertainties. 

4. ILLUMINANCE RESPONSIVITY 

The photometer illuminance responsivity is the ratio of the photometer output current to the illuminance 

measured by the photometer: 

sEi = E(λ)sE(λ)dλ λ∫

Km E(λ)V(λ)dλ λ∫ (1) 
where E(λ) is the incident spectral irradiance on the photometer, V(λ) is the CIE spectral luminous efficiency,

Km is the maximum spectral luminous efficacy, 683 lm/W, sE(λ) is the spectral irradiance responsivity of the 

photometer as measured on the SIRCUS, and λ is the wavelength.

The broad-band (illuminance) calibration factor of the photometer is: 

 

 

Ccal = 1

sEi

, [lx/A] (2) 

5. CALIBRATION FACTORS FOR THE TRISTIMULUS COLORIMETER 

Similar to the above illuminance responsivity calibration of a single photometer, the channel calibration factors 

of the tristimulus colorimeter can be determined from the ratio of the CIE tristimulus values to the measured 

output currents of the four channels: 

 

kX1 = X1

I

X 1

= Km E(λ)x 1(λ)dλ λ∫

E(λ)sX1

(λ)dλ ∫λ

= 1.06291Km FX1

sX1(599) kX2 = X2

IX2

= Km ∫λE(λ)x2 (λ)dλ

E(λ)sX2 (λ)dλ λ∫ = 0.3501Km FX2sX2(442)

 

kY = Y

I

Y

= Km ∫λE(λ)V(λ)dλ

E(λ)sY (λ)dλ λ∫ = Km FYsY (555) kZ = Z

IZ

= Km ∫λE(λ)z(λ)dλ

E(λ)sZ (λ)dλ λ∫ = 1.78297Km FZsZ (446) (3) 

The right side of the equations was obtained by normalizing the x1(λ), x2(λ), V(λ), and 

z(λ) functions to 

their peak values and introducing the color correction factors for all tristimulus channels: 

 

FX1 = ∫λE(λ)x1n (λ)dλ

E(λ)sX1n (λ)dλ λ∫ FX2 = ∫λE(λ)x2n (λ)dλE(λ)sX2n (λ)dλ λ∫

 

FY = ∫λE(λ)V(λ)dλ

E(λ)sYn (λ)dλ λ∫ FZ = ∫λE(λ)zn (λ)dλE(λ)sZn (λ)dλ λ∫ (4)

where sX1(599), sX2(442), sY(555), and sZ(446) are the absolute irradiance responsivities of the realized 

channels at the peak wavelengths of the color matching functions, x 1n(λ), x 2n(λ), and z n(λ) are the color 

matching functions normalized to one at their peaks, sX1n(λ), sX2n(λ), sYn(λ), and sZn(λ) are the relative spectral 

irradiance responsivities of the realized channels normalized to one at their peak wavelengths. 

After the tristimulus colorimeter is calibrated for kX1, kX2, kY, and kZ, the tristimulus values of a test light 

source can be measured as 

 X'=X1'+X2', where X1'= k I X1 ' and X ' = k I ' Xl 2 X2 X2

 Y' = kY IY', and Z' = kZ IZ' (5) 

where I Xl

', IX2', IY', and IZ' are the measured output currents of the tristimulus channels. This calibration 

procedure can be applied to either illuminance or luminance measurement geometry using the relevant units 

of sX1(599), sX2(442), sY(555), and sZ(446) in the equations. 

From the procedures described above, the photometric and colorimetric measurement uncertainties will 

depend only on the uncertainty of the spectral responsivity determination of the channels. An advantage of 

the method is that accurate color and photometric measurements can be made even if the CIE functions are 

poorly realized (with large spectral mismatch in the channels). 

If the CIE f1

’

 (spectral mismatch) values of the realized channels are small, the color correction factors can 

be kept very close to unity even if the source distribution changes (between the calibration source and the test 

source) are significant. However, even with small f1

’

 values, an additional set of calibration factors may be 

needed to accurately measure very different source distributions, such as gas discharge lamps or display 

monitors. In this case, rough knowledge of the source distribution is enough to derive correction factors 

enabling accurate photometric and color measurements. This is the principle behind the development of a 

spectrally tunable source. 

6. SCALE DERIVATIONS USING A TUNABLE OUTPUT LED TRANSFER SOURCE 

By setting the transfer source distribution equal, or very similar, to that of the test source to be measured, the 

photometric and color scales can be transferred from the primary standard photometers and colorimeters 

calibrated on SIRCUS to field meters with minimal increase in uncertainties. In our recently developed 
4

spectrally tunable solid-state source [10] the radiant flux from a sufficient number of light emitting diodes 

(LEDs) with different spectral distributions is introduced into an integrating sphere. A reference 

spectroradiometer is mounted on the sphere that measures the radiance (luminance) at the sphere exit port. 

The LEDs are individually controlled by adjustable current sources and are tuned - according to the 

spectroradiometer reading – to approximate a target source distribution. Standard and test photometers and 

colorimeters then measure the irradiance from the source at a given distance. The source can be rapidly 

tuned to match any desired spectral distribution. Customers no longer need to send the source artifact (e.g. 

discharge lamp or display), only its spectral distribution(s). Knowledge of the relative spectral responsivity of 

the test instruments is not needed when they are calibrated against the reference instruments by measuring 

the transfer source tuned to the source distribution to be measured. In this case, the spectral mismatch errors 

are very small resulting in low measurement uncertainties. 

 

The initial prototype source was built using a total of 40 LED’s, 4 LED’s each with 10 different spectral 

distributions. While this is a transfer source, in principle only requiring that the radiance be stable over the 

course of a measurement, it is desirable to know and understand the radiometric characteristics of the LEDs. 

This knowledge will impact the ultimate design of the source. LED’s were tested for stability and dependence 

on drive current. The effect of LED seasoning for luminance and chromaticity was studied. Also, the 

luminance, chromaticity, and spectral distribution changes versus LED drive current were analyzed for 

representative red, green, and blue LEDs [10]. The prototype source demonstrated the feasibility of a 

spectrally tunable LED-based source. 

Simulations showed that a 40-channel source could approximate the CIE standard illuminant A within 0.1 % 

and the D65 within 5 % deviation over the visible spectral range from 380 nm to 780 nm. Consequently, we 

have started the development of a 40-channel source. The source has 4 LED heads, with 10 channels per 

head. There are typically 3 LEDs per channel, though for certain spectral regions only low power LEDs are 

available and in those cases additional LEDs are added to the channel.

7. SUMMARY 

Recently performed irradiance responsivity calibrations with expanded uncertainties (k=2) of 0.15 % motivated 

the development of a detector-based tristimulus colorimetric scale and the improvement of the present NIST 

photometric units. A reference tristimulus colorimeter/photometer has been developed to implement the first 

detector-based color scale and to study the uncertainty decrease of illuminance responsivity calibrations on 

the new SIRCUS facility. A novel, spectrally tunable, solid-state source was developed to transfer the high 

accuracy illuminance responsivity and tristimulus color scales from the reference tristimulus 

colorimeter/photometer to working standard and field photometers and tristimulus meters. By setting the 

transfer source distribution to approximate a particular target distribution, the photometric and color scales can 

be transferred to field meters with minimal increase in uncertainties. 

REFERENCES 

[1] Cromer, C. L., Eppeldauer, G., Hardis, J. E., Larason, T. C., Ohno, Y., and Parr, A. C., The NIST DetectorBased Luminous Intensity Scale, J. Res. of the NIST, Vol. 101, No 2, p.109-132, 1996. 

[2] Yoon, H. W., Gibson, C. E., and Barnes, P. Y., Realization of the National Institute of Standards and 

Technology detector-based spectral irradiance scale, Appl. Opt. Vol. 41, No. 28, 5879-5890, 2002. 

[3] Eppeldauer G., Spectral Response Based Calibration Method of Tristimulus Colorimeters, J. Res. of the 

NIST Vol. 103, No. 6. 615-619, 1998. 

[4] Larason, T. C., Bruce, S. S., and Parr, A. C., Spectroradiometric Detector Measurements: Part I-Ultraviolet 

Detectors and Part II-Visible to Near-Infrared Detectors, NIST Special Publ. 250-41, 1998. 

[5] Brown, S. W., Eppeldauer, G. P., and Lykke, K. R., NIST Facility for Spectral Irradiance and Radiance 

Response Calibrations with a Uniform Source, Metrologia, Vol. 37, 579-582, 2000. 

[6] Eppeldauer, G. P., Brown, S. W., Larason, T. C., Racz, M., and Lykke, K. R., Realization of a spectral 

radiance responsivity scale with a laser-based source and Si radiance meters, Metrologia, Vol. 37, 531-534, 

2000. 

[7] Gentile, T. R., Houston, J. M., Hardis, J. E., Cromer, C. L., and Parr, A. C., National Institute of Standards 

and Technology high-accuracy cryogenic radiometer, App. Opt. Vol. 35, No. 7, 1056-1068, 1996. [8] Eppeldauer, G. P. and Lynch, D. C., Opto-mechanical and electronic design of a tunnel-trap Si-radiometer, J. 

Res. Natl. Inst. Stand. Technol. Vol. 105, No. 6, p. 813-828, 2000. 

[9] Brown, S. W., Zong, Y., and Ohno, Y., NIST Calibrations of Colorimeters for Display Measurements, 

Information Display, Vol. 15, 30-34, 1999. 

[10] Brown, S. W., Santana, C., and Eppeldauer, G. P., Development of a Tunable LED-based Colorimetric 

Source, J. Res. NIST, Vol. 107, No. 4, 363-371, 2002. 

[11] Publication CIE No. 15. 2 (1986), Central Bureau of the CIE, A-1033 Vienna, P.O. Box 169, Austria. 

[12] Publication CIE No. 69 (1987), Central Bureau of the CIE, A-1033 Vienna, P.O. Box 169, Austria. 
Realization and application of a detector-based tristimulus color scale 

at the National Institute of Standards and Technology, USA 

G. P. Eppeldauer, S. W. Brown, K. R. Lykke, and Y. Ohno 

National Institute of Standards and Technology, Optical Technology Division 

Gaithersburg, Maryland (USA) 

Corresponding author: G. P. Eppeldauer (george.eppeldauer@nist.gov) 

ABSTRACT 

The recently introduced detector-based calibration method for tristimulus colorimeters has 

been realized. The NIST reference colorimeter has been calibrated for spectral irradiance responsivity 

with an uncertainty of 0.15 % (coverage factor k=2) resulting in a chromaticity uncertainty of 0.0004 

(k=2) in the x and y chromaticity coordinates when a CIE Illuminant A source is measured. The color 

scale is realized and maintained by reference colorimeters rather than reference lamps. The color 

measurement uncertainty increases when sources other than Illuminant A are measured due to spectral 

mismatch errors of the channels. Variable reference source models have been developed so that the 

reference source for the colorimeter can be automatically matched to the measured test source of 

certain types. A model using Planckian radiation with a variable temperature has been tested and 

proved to be effective in eliminating the mismatch errors for incandescent lamps. Another model 

based on primary colors of a display has also been tested and shown to be effective. 

1. INTRODUCTION 

A reference tristimulus colorimeter has been developed at the National Institute of Standards 

and Technology (NIST) to implement the recently developed tristimulus colorimeter calibration 

method based on detector standards [1, 2]. The reference tristimulus colorimeter was designed such 

that the combined uncertainty of the color and photometric measurements is dominated by the 

uncertainty of the spectral responsivity calibrations. The spectral responsivities of the four colorimeter 

channels are closely matched to the CIE color matching functions (the f1’ values are 1.6 % for the Y 

and X1, 3.6 % for the Z, and 4.1 % for the X2 channels) to minimize additional uncertainties in color 

measurement. The channel spectral irradiance responsivities were determined with the lowest possible 

uncertainty using our laser-based facility to produce uniform monochromatic irradiance [3]. 

Based on the spectral irradiance responsivity of the channels, a colorimetric scale has been 

realized and maintained by the reference colorimeters instead of standard lamps. The detector-based 

color scale can be calculated for any given spectral distribution of a reference source, which can be 

either theoretical or real. Generally, CIE Illuminant A is used as the reference source. In this case, the 

uncertainty of measurement increases when sources other than Illuminant A are measured due to 

inherent spectral mismatch of the colorimeter channels (to the CIE functions). To avoid spectral 

mismatch errors, an approximate spectral distribution of the test source is needed. A need for a 

spectroradiometer for this purpose would negate the benefit of tristimulus colorimeters. 

To solve this problem, a variable reference source model has been developed. This method, 

applied to certain types of source, avoids or reduces the spectral mismatch errors without knowledge 

of the spectral distribution of the test source. The spectral distribution of a model, used as the 

reference source in the colorimeter calibration equation (see below), is adjusted based on the color 

temperature or tristimulus values of the test source as measured by the colorimeter. A model using 

Planckian radiation at a variable temperature has been tested and shown to be effective for the 

measurement of incandescent lamps. A model based on the spectral distribution of each primary 

color of a liquid crystal display (LCD) has also been tested and shown to be effective for display color 

measurements. 
2. DETECTOR-BASED CALIBRATION OF TRISTIMULUS COLORIMETERS 

The spectral irradiance responsivities of the four colorimeter channels were determined on the 

new NIST facility for Spectral Irradiance and Radiance Responsivity Calibrations using Uniform 

Sources (SIRCUS) [3]. The measurement is traceable to an absolute cryogenic radiometer that 

maintains the NIST primary unit for optical power. 

The continuously tunable output from 

several different tunable lasers was consecutively 

introduced into a small integrating sphere to 

produce uniform, monochromatic irradiance [3] at 

the reference planes of the tristimulus colorimeter 

and the reference trap detector. The spectral 

irradiance responsivity scale from the trap detector 

was transferred to the channels of the tristimulus 

colorimeter using the detector substitution method. 

The colorimeter signal gain was 108

 V/A for all 

channels. The results are shown in Fig. 1; cubicspline fits were applied for interpolation between 

the laser-measured data points. 

0

5 106

1 107

1.5 107

2 107

2.5 107

3 107

0

5 107

1 108

1.5 108

2 108

2.5 108

3 108

3.5 108

400 450 500 550 600 650 700 750

Wavelength [nm]

X1

Y

Z

X2

The responsivity transfer in the uniform 

monochromatic irradiance makes the calibration 

and application beam geometries equal. 

Furthermore, the uncertainty components caused by the changing internal reflectance patterns in the 

colorimeter (between calibration and applications) and spatial non-uniformities of the channel 

responsivities are reduced compared to lamp-monochromator-based calibrations. The relative 

combined expanded uncertainty (k=2) of the spectral irradiance responsivity transfer to the 

colorimeter was 0.15 %. 

Figure 1: SIRCUS measured spectral irradiance 

responsivities of the reference tristimulus meter. 

The low responsivity uncertainty made it possible to accurately calibrate the colorimeter 

channels for responsivity to tristimulus values. The channel broad-band (spectrally integrated) 

calibration factors have been calculated [2]:

∫

∫ ==

λ

λ

λλλ

λλλ

dsE

dxE

I

X k

)()(

)()(K

1X

m 1

1X

1

1X 

∫

∫ ==

λ

λ

λλλ

λλλ

dsE

dxE

I

X k

)()(

)()(K

2X

m 2

2X

2

2X

∫

∫ ==

λ

λ

λλλ

λ λ λ

dsE

dVE

I

Y k

)()(

)()(K

Y

m

Y

Y 

∫

∫ ==

λ

λ

λλλ

λλλ

dsE

dzE

I

Z k

)()(

)()(K

Z

m

Z

Z (1) 

where E(λ) is the relative spectral distribution of the reference source, x1 λ)( , x 2 λ)( , V λ)( , 

and z λ)( are the CIE color matching functions, Km is the maximum spectral luminous efficacy, 

683 lm/W, sX1(λ), sX2(λ), sY(λ), and sZ(λ) are the channel spectral irradiance responsivities, and λ is 

the wavelength. Both the responsivity measurements and the integrals were made between 360 nm 

and 1000 nm (the responsivity limit of silicon detectors). The calibration factors obtained for CIE 

Illuminant A are: 036.2 lx/V, kY = 359.8 k 1X = , 769.8 k 2X = , and 96.108 kZ = . The tristimulus 

values of test light sources were determined using these calibration factors: 

X'=X1'+X2', where X1'= kX1I Xl' and X2' = kX2 IX2', Y' = kY IY', and Z' = kZ IZ' (2) 

where I Xl', IX2', IY', and IZ' are the output signals of the channels for a given test source. 

The 0.15 % responsivity uncertainty propagates to the tristimulus values of the measured test 

sources and result in uncertainties in the x, y chromaticity coordinates of 0.0004 when a CIE 

Illuminant A source is measured. 
3. VARIABLE REFERENCE SOURCE MODEL 

The low uncertainty of spectral responsivity measurements and the small spectral mismatch 

of the channel responsivities to the CIE color matching functions makes it possible to provide an 

accurate color scale to a tungsten lamp realizing CIE Illuminant A. However, when sources other than 

Illuminant A are measured, spectral mismatch errors are inevitable even with well-matched channel 

spectral responsivities. With the developed NIST colorimeter, the chromaticity errors for Planckian 

radiation from 2300 K to 3200 K are within 0.001. The errors for light sources other than tungsten 

lamps are estimated to be within 0.003 in x, y. 

An advantage of the detector-based calibration method is that the calibration factors of the 

colorimeter can be determined for any spectral distribution including theoretical models. The error 

will be significantly reduced if an approximate spectral distribution of the test source is used as E(λ) 

in Eqs. (1). However, use of a spectroradiometer for this purpose will negate the benefit of tristimulus 

colorimeters. An attempt has been made to use spectral distribution models to reduce or eliminate 

spectral mismatch errors with no prior information of the spectrum of the test source. 

A model using Planckian radiation with a variable temperature T [K] has been introduced and 

tested. E(λ) in Eqs. (1) is given by 

[ 1

2

5 )( 1)/exp( − − = λλ λTckE − ] (c2=1.4388×10

-2

m·K, k: normalization constant) (3) 

The calibration factors in Eqs. (1) are initially calculated for T=2856 K (CIE Illuminant A). Then a 

test lamp is measured with the colorimeter and the color temperature T1 is obtained. Next, T1 is 

replaced in Eqs. (1) and the calibration factors in Eqs. (1) are recalculated, and the color quantities of 

the test source are recalculated. With this recalculation, the CCT (and thus the spectral distribution) of 

the reference source is nearly equal to that of the test source, realizing the condition of strict 

substitution. One time recalculation removes most of the errors for incandescent lamps, but two or 

three iterations can remove the mismatch error completely. There are only small remaining errors due 

to the small deviation of the spectral distribution of the test source from the theoretical Planckian 

curve. The residual errors for a quartz halogen lamp at color temperatures of 2300 K to 3200 K were 

found to be negligible (< 0.00002 in x,y) for our NIST reference colorimeter. 

This model works perfectly for Planckian sources, and is also effective to some extent for 

other general sources, depending on the relative spectral responsivity of the channels. 

Another model has been tested for display calibration. The spectral distribution of displays 

are very similar within each type of display, 

therefore their spectral distribution can be modeled. 

A model for a display is prepared as: 

 

)()()()(λ BB λ += GG λ + SkSkSkE RR λ (4) 

where 

SB(λ), SG(λ), SR(λ) are the relative spectral 

distribution of each primary color in a typical LCD 

or CRT. The mixing factors are initially 

determined so that E(λ) gives a white point at 

6500 K and a test display is measured with the 

colorimeter. Based on the first tristimulus values 

measured, the mixing factors k are 

recalculated to give E(λ) the same chromaticity 

coordinates as the measured values of the test 

source. Based on the new E(λ), the color quantities 

of the test source are recalculated. A single iteration 

is sufficient. Additional iterations did not converge 

in our test. Using this process, the spectral 

distribution of the reference source E(λ) is adjusted 

to be nearly equal to the test source. Although the 

kB, kG, kR

B, kG, kR

0

0.001

0.002

0.003

0.004

0.005

0.006 CIE Illuminant A

6500 K white

variable LCD model

Figure 2: Chromaticity error Δxy = Δx

2 + Δy2

in the measurement of various display colors due 

to spectral mismatch of the NIST colorimeter, 

with various reference sources including the 

variable LCD model. 
spectral distribution of each primary color of the measured display may not be exactly the same, they 

are very similar within each type of display, and most of the spectral mismatch errors are removed for 

a given type of display, regardless of the color measured. As a demonstration, Fig. 2. shows a 

simulation of measurements of three different LCD displays and one CRT, where the reference source 

model is based on the primary color spectra of LCD1. The results are shown for three cases where 

displays are measured with colorimeter calibration using Illuminant A, LCD1 white (6500 K), and the 

variable LCD model. The results for LCD1, shown as zero for all colors, are for verification. The 

results for LCD2 and LCD3, having slightly different spectra from LCD1, show that errors are 

reduced by an order of magnitude and kept within 0.001 in Δxy. The results for CRT, having very 

different spectra, are not improved as much. 

4. TRANSFER CALIBRATION 

Test colorimeters can be calibrated against the detector-based reference colorimeter under 

illumination by a reference (transfer) source. For a simple case, a CIE illuminant A source is used, 

but when the test colorimeter is used to measure other various sources, the spectral mismatch error 

can be significant. To avoid such errors, the transfer calibration needs to be done with the same type 

of source that is to be measured by the test colorimeter (strict substitution). If the source is one of the 

types described in the reference source models above (incandescent lamp, display), then such a real 

source can be used for calibration transfer. For other source types, the transfer calibration needs to be 

performed with a known approximate spectral distribution Ea(λ) of the source to be measured. The 

reference colorimeter is calibrated with Ea(λ) replaced in Eqs. (1), and determines the tristimuls 

values Xr, Yr, Zr of the source. The test colorimeter is calibrated against the Xr, Yr, Zr values. Such 

transfer calibrations for various sources can be done effectively by using a spectrally tunable source 

(STS) as reported in Ref. 4. The STS is set to simulate a given test source spectrum Em(λ), and the 

test colorimeter is calibrated against the reference colorimeter under that illumination. The STS can 

produce as many spectra as needed, and transfer calibration can be done for each type of source with 

small spectral mismatch errors, without knowing the spectral responsivity of the test colorimeter.

5. CONCLUSIONS 

The NIST reference tristimulus colorimeter has been calibrated for absolute spectral 

irradiance responsivity on our tunable-laser-based spectral calibration facility. The four channels of 

the colorimeter were calibrated with an uncertainty of 0.15 % (coverage factor k=2), which results in 

an uncertainty of 0.0004 (k=2) in the x, y chromaticity when measuring a CIE Illuminant A source. 

The color scale is realized and maintained by the reference colorimeters. For measurement of sources 

other than Illuminant A, variable reference source models have been developed to avoid or reduce 

spectral mismatch errors. The model using Planckian radiation at a variable temperature has been 

introduced and tested. Using this model, the spectral mismatch errors for incandescent lamps are 

practically eliminated. Another model based on the primary colors of a display has also been tested 

and shown to be effective. Other models are being explored to measure LEDs and other sources. The 

transfer calibration to test colorimeters can be performed with real sources used in the variable 

reference source models or by using a spectrally tunable source to avoid spectral mismatch errors. 

 

References 

1. Eppeldauer, G. P. and Racz, M., Design and characterization of a photometer-colorimeter 

standard. Applied Optics, 2004. 43(13) p. 2621-2631. 

2. Eppeldauer, G. P., Spectral response based calibration method of tristimulus colorimeters. J. Res. 

NIST, 1998. 103(6): p. 615-619. 

3. Brown, S. W., Eppeldauer, G. P., and Lykke, K. R., NIST Facility for spectral irradiance and 

radiance responsivity calibrations with uniform sources. Metrologia, 2000. 37: p. 579-582. 

4. Fryc, I., Brown, S. W., Eppeldauer, G. P., and Ohno, Y., A spectrally tunable solid-state source 

for radiometric, photometric, and colorimetric applications, Proc. SPIE, 2004. 5530, p. 150-159. 
Eppeldauer, et al. Detector-based calibration procedures for tristimulus 

DETECTOR-BASED CALIBRATION PROCEDURES FOR 

TRISTIMULUS COLORIMETER STANDARDS 

G. P. Eppeldauer, C. C. Miller, and Y. Ohno 

National Institute of Standards and Technology 

Gaithersburg, Maryland, USA 

ABSTRACT 

Two reference and three working standard 

tristimulus colorimeters have been developed at the National Institute of Standards 

and Technology (NIST) to utilize the recently 

introduced detector-based colorimeter calibration method [1]. The tristimulus colorimeters are calibrated on three reference calibration facilities of NIST. The preliminary 

calibration procedures are described and 

the obtained results are evaluated. Future 

work to improve the uncertainty of detectorbased tristimulus color measurements is 

discussed. 

Keywords: calibration, colorimetry, color 

temperature, spectral responsivity, tristimulus 

1. INTRODUCTION 

At present, routine calibrations of tristimulus 

colorimeters are performed against lamp 

standards. The expanded uncertainty using 

the NIST primary standard color temperature lamp standards is 8 K (k=2). This 

source-based calibration uncertainty can 

increase with the burning hours of the lamp 

standards. Both the long-term stability and 

the spectral distribution of the lamps can 

significantly change versus burning time. 

When the tristimulus colorimeter calibrations 

are performed against detector standards 

the uncertainty of the spectral responsivity 

calibrations of the colorimeter channels can 

dominate the color measurement uncertainty 

[2]. Also, long-term changes in the measurement uncertainty can be significantly decreased. The goal of this work is to utilize 

the advantages of the detector-based calibrations and to improve the present sourcebased color calibration uncertainty by at 

least a factor of two. 

2. NIST TRISTIMULUS COLORIMETERS 

First, a silicon trap-detector based reference 

tristimulus colorimeter was developed [2] 

with a temperature controlled filter-wheel for 

the NIST developed four filter combinations. 

The second reference tristimulus colorimeter, Model F100, was a similar design but 

the detector was a large area single-element 

silicon photodiode [2]. The picture of this 

colorimeter, with the front cover (where the 

aperture is mounted) removed, is shown in 

Fig. 1. Five equally designed and fabricated 

sets of filter combinations were purchased 

and installed in a temperature controlled 

copper filter-wheel. Since the blue filter 

combinations (Xs and Z) had significant 

leakage in the near-IR, they have recently 

been replaced with improved-blocking filter 

packages. One filter set was installed in the 

second reference tristimulus colorimeter and 

three sets have been installed in three additionally fabricated working standard colorimeters of the same design. 

Figure 1. Picture of the prototype singleelement-Si based colorimeter 
3. NIST CALIBRATION FACILITIES 

Both reference colorimeters were calibrated 

at the Spectral Irradiance and Radiance Responsivity Calibrations using Uniform 

Sources (SIRCUS) facility. The colorimeter 

channels were calibrated for spectral irradiance responsivity. The expanded responsivity uncertainty goal is 0.1 % (k=2) or less. 

The monochromator-based Spectral Comparator Facility (SCF) was used to measure 

the channels of the second reference tristimulus colorimeter and the three working 

standard colorimeters for spectral power 

responsivity. These measurements were 

needed to check if the relative spectral responsivities of the corresponding channels 

of the four colorimeters agree. This spectral 

comparison is needed because the three 

working standard colorimeters will be calibrated against the second reference colorimeter in broad-band mode. The SCF measurements were made with an expanded 

relative uncertainty of 0.2 % (k=2). The SCF 

measured the near-IR leakage of the filter 

packages to 1300 nm. 

The NIST Photometry Facility was used to 

measure the illuminance from lamp standards with the two reference tristimulus colorimeters. 

4. SPECTRAL RESPONSIVITIES 

After measuring the channel spectral responsivities on the SIRCUS and SCF, the 

results were evaluated. 

In the channel-responsivities of the trapdetector based colorimeter, the rejection for 

near-infrared radiation was about four orders of magnitude and no fluorescence 

could be measured. 

The spectral irradiance responsivity curves 

of the four channels of the second reference 

tristimuls colorimeter with the leaky blue filter combinations are shown in Fig. 2. The 

spectral irradiance responsivity measurements on the SIRCUS were made between 

360 nm and 960 nm. The SCF spectral 

power responsivity measurements were 

used to extend the responsivity curves to 

1300 nm, the sensitivity limit of the applied 

silicon detector. The logarithmic scale 

shows that the blue (Xs and Z) filter combinations have significant leakage in the nearIR range. 

The wavelength shift of the monochromator 

was less than 0.1 nm. 

The relative spectral responsivities measured on the SIRCUS and SCF were compared. As an example, Fig. 3 shows the percent differences between the SIRCUS and 

SCF measured and then normalized spectral responses for the Y channel. The left-Y 

axis shows the normalized response at the 

peak wavelength of 555 nm. The right-Y axis 

shows the percent difference between the 

SIRCUS and SCF normalized responses. 

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

400 600 800 1000 1200

Xs

Z 

Xl

Y

Wavelength [nm]

Figure 2. Spectral irradiance responsivities 

of the single-element-Si based colorimeter 

(F100) with the leaky blue filters. 

0

0.2

0.4

0.6

0.8

1

-1

-0.5

0

0.5

1

450 500 550 600 650

Wavelength [nm]

Y-channel

Figure 3. Percent differences between the 

SIRCUS and SCF measured and then normalized F100 spectral responses. 
The difference curve has structures. The 

differences around the peak are at the 0.1 % 

level. However, at the sides of the curve, the 

structures are larger but their effect is lower. 

The structures originate from the SIRCUS 

calibrations and are caused by laser fluctuations and calibration protocol errors. Recent 

SIRCUS calibration procedures have been 

improved and results verified that spectral 

responsivity measurements can be performed with 0.05 % (k=2) uncertainty. 

The SIRCUS measured a 0.08 % higher 

absolute responsivity value at the 555 nm 

peak of the Y-channel than the SCF. 

The spectral responsivity of the Y-channel 

was re-measured at the SCF after the Y filter package was flipped over (the front surface became the back surface) in the temperature controlled filter wheel. Figure 4 

shows the normalized spectral responsivities before and after the flip on a log scale. 

An increased responsivity was measured in 

the blue between 380 nm and 450 nm. The 

responsivity increase was caused by the 

fluorescence of the thin cut-on filter-layer. 

The change in the fluorescent signal, after 

reversing the filter package in the filterwheel, indicates that the exciting blue-light 

(producing the fluorescence) is attenuated 

differently at the two different orientations of 

the Y filter package. An f1’ of 1.4 % was calculated with the lower fluorescence and 

1.7 % with the higher fluorescence for the Y 

channel. 

10-5

10-4

10-3

10-2

10-1

100

400 450 500 550 600 650 700

Wavelength [nm]

after flipping Y-filter

before flipping Y-filter

CIE Y 1931

f1'=1.7

f1'=1.4

Figure 4. Fluorescence caused responsivity 

change in the F100 Y-channel before and 

after reversing the filter in its holder. 

Figure 5 shows the fluorescence caused 

responsivity changes in the Y-channel in a 

linear scale. The magnitude of the fluorescence caused contribution to the responsivity increase is not known. The increased 

responsivity at the original filter orientation, 

relative to the CIE Y 1931 function, can also 

be caused by the realized filter transmittance. The responsivity of the Y-channel is 

about 0.4 % higher (relative to the unity 

peak responsivity of the Y-channel) with the 

turned over filter compared to the original 

filter orientation at 410 nm. At 400 nm, at the 

original filter orientation, the responsivity is 

about 0.4 % higher than the target (Y 1931) 

responsivity. 

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

400 450

Wavelength [nm]

0.4 % difference

Y 1931

Y channel with

 original filter mount

Y channel responsivity

after reversing filter

Figure 5. Fluorescence caused responsivity 

change in the F100 Y-channel on a linear 

scale at two different filter orientations. 

Similar, but smaller, responsivity changes 

were measured in the Xs and Z channels 

below 400 nm. These changes were also 

caused by the fluorescence inside of the 

blue filter packages. The responsivity, after 

reversing the filter-package, changed from 

0.1 % to close to 1 % (relative to the peakresponsivity at 445 nm) at 390 nm. After the 

flip, the f1’ of the Z channel decreased from 

3.9 % to 3.8 %. The f1’ of the Xs channel, 

after the flip, increased from 2.9 % to 3 %. 

The reason of the responsivity changes is 

again the different attenuation of the excitation light between the two (starting and reversed) filter positions. All filter packages 

were used at the orientations where the responsivity increase was smaller (lower fluorescence). The f1’ of the Xl

 channel was 

4.3 % and no fluorescence could be measured. 

After eliminating the near-IR leakages in the 

blue filter combinations, the goal to achieve 

a 0.1 % (k=2) expanded relative uncertainty 
for the channel spectral responsivity measurements is feasible. 

5. COLORIMETER CALIBRATIONS 

5.1 Reference colorimeters 

The spectral irradiance responsivities of the 

channels of the F100 reference colorimeter 

(shown in Fig. 2) were determined against 

two silicon tunnel-trap detectors [3]. The picture of the calibration arrangement at the 

SIRCUS is shown in Fig. 6. The trapdetector reference standards were calibrated previously against the primarystandard electrical-substitution cryogenicradiometer in radiant power measurement 

mode. The aperture areas were determined 

at the NIST aperture measurement facility 

[4]. The aperture area times the power responsivity is equal to the irradiance responsivity of the trap detector. The two reference 

colorimeters were calibrated against the two 

trap detectors in irradiance measurement 

mode using the detector substitution 

method. 

The (broad-band) calibration factor of a colorimeter channel can be calculated as the 

ratio of the CIE tristimulus value to the 

measured output signal (current) of the 

same (realized) channel [1]: 

∫

∫ == λ

λ

λλλ

λλλ

dsE

dxEK

I

X k

)()(

)()(

1X

m 1

1X

1

1X

∫

∫ == λ

λ

λλλ

λλλ

dsE

dxEK

I

X k

)()(

)()(

2X

m 2

2X

2

2X

∫

∫ == λ

λ

λλλ

λλλ

dsE

dVEK

I

Y k

)()(

)()(

Y

m

Y

Y

∫

∫ == λ

λ

λλλ

λλλ

dsE

dzEK

I

Z k

)()(

)()(

Z

m

Z

Z (1) 

where E(λ) is the relative spectral distribution of the reference source (which is not a 

standard in this detector-based calibration), 

x1 λ)( , x2 λ)( , V λ)( , and z λ)( are the CIE 

color matching functions, Km is the maximum spectral luminous efficacy, 683 lm/W, 

sX1(λ), sX2(λ), sY(λ), and sZ(λ) are the measured spectral responsivities of the realized 

channels (shown in Fig. 2), and λ is the 

wavelength. The integrals were made from 

360 nm to 1300 nm (involving the near-IR 

leakage) to correct for spectral mismatch 

and amplitude errors. As an example, the 

channel calibration factors calculated for the 

F100 reference colorimeter using E(λ ) = 

2300 K, 2856 K, and 3200 K Planckian reference distributions are shown in Table 1. 

The detector-based calibration factors in the 

Table were calculated with Planckian temperatures that are close to the color temperatures of the lamp-standard also measured by the F100 reference colorimeter. 

Figure 6. Arrangement of the two reference 

tristimulus colorimeters (right) and the two 

silicon trap-detectors (left) at the SIRCUS. 

Table 1. Channel calibration factors of the 

F100 reference tristimulus colorimeter 

Temp. 

[K] 

kX1 kX2 kY kZ

2300 27082

6 

5568 19225 54720 

2856 27182

9 

9310 19247 59072 

3200 27216

3 

10315 19252 59719 

Table 1 shows that kX2 of the XS blue channel, where the near-IR leakage is the highest, changed almost a factor of two for a 

900 K temperature change. The change in 

the leaky Z channel is close to 10 % for the 

same temperature change. The change of 

kX1 for the Xl

 channel is 0.5 % and kY of the 

Y channel is only 0.14 % for the 900 K 

change of the lamp. 

It is expected that after eliminating the nearIR leakage of the blue filter packages, the 

large changes in kX2 and kZ will dramatically 
decrease and one set of calibration factors, 

calculated with the 2856 K reference source 

distribution, will be enough to make wide 

temperature-range measurements of tungsten lamps. 

In order to compare the detector-based and 

source-based color temperature calibrations, the F100 colorimeter measured a 

color-temperature lamp-standard. The 

measurements were made inside of a lighttight photometer bench, with two baffles between the lamp standard and the F100 colorimeter. From the measured output signals 

of the four channels, using the above calibration factors, the tristimulus values were 

calculated for all four channels: 

r

XX

r

1 = IkX 11

r

XX

r

2 = IkX 22

r

YY

r = IkY

r

ZZ

r = IkZ (2) 

where superscript r indicates that the measurements were made with the F100 reference colorimeter. 

From the tristimulus values the color temperatures are calculated using iterations. 

First, the u’,v’ chromaticity coordinates are 

calculated for a range a blackbody temperatures from 1000 K to 20000 K. From the 

chromaticity coordinates of the test source, 

the distance is calculated to the blackbody 

curve (coordinates). The closest distance is 

chosen along with its neighbors. In a second 

step, the set of blackbody temperatures are 

extended to 20 points centered on the previous closest point and bounded by the 

neighbors. Again, the smallest distance is 

chosen along with its neighbors. This process is repeated four more times. The last 

step will calculate the correlated color temperature to within 0.01 K of the F100 measured chromaticity coordinate. 

The color temperatures were also determined from spectral irradiance measurements (of the same lamp) at the Facility for 

Automated Spectral Calibrations (FASCAL). 

The expanded relative uncertainty of the 

FASCAL color-temperature calibrations at 

2856 K is 2 K (k=2). 

The color temperature values obtained with 

the source-based lamp and detector-based 

F100 calibrations are shown in Table 2. The 

last column shows the differences at three 

different temperatures. The difference at 

2300 K is higher than at higher lamp temperatures because the near-IR leakage of 

the blue filter-combinations plays a more 

significant role at the low temperature 

(2300 K) color measurement. 

The color temperature uncertainty when 

propagated from the FASCAL calibrated 

lamp standard to the F100 on the photometer bench (at 2856 K) increases to 8 K (k=2). 

The lamp was calibrated on the FASCAL at 

a distance of 0.5 m. When it is used in the 

photometer bench with a 2 m separation 

from the F100 colorimeter, the spatial nonTable 2. Color temperature measurements 

(in K) using detector-based (F100) and 

source-based (FASCAL) calibrations. 

Source 

Based 

FASCAL

F100 

ref = 

2300K 

F100 

ref = 

2856K 

F100 

ref = 

3200K 

F10

0 

- 

FASCAL 

2292.9 2304.4 11.5 

2857.2 2862.2 5.0 

3198.4 3201.7 3.3 

uniformity of the irradiance (in the reference 

plane of the colorimeter) significantly 

changes versus lamp alignment. This spatial 

non-uniformity causes the large uncertainty 

increase in the source-based calibration of 

the F100 colorimeter. 

The uncertainty goal for the detector-based 

reference colorimeter calibrations is 4 K 

(k=2).

5.2 Working standard colorimeters 

The three working standard colorimeters are 

not calibrated at the SIRCUS facility to save 

the long and expensive calibration time. 

Their channels will be measured for spectral 

power responsivity at the SCF and then 

compared to the channels of the reference 

colorimeter. All the filter combinations and 

the Si detectors were taken from the same 

batches. Before the SCF spectral responsivity measurements, it is important to check 

the wavelength accuracy of the monochromator to avoid responsivity errors when 
measuring the steep sides of the channel 

responsivity curves. 

The working standard colorimeters will be 

calibrated against the reference colorimeter 

(of the same type) in broad-band mode using the illumination from a stable 2856 K 

lamp. The calibration factors can be transferred from the channels of the reference 

colorimeter to the equivalent channels of the 

working standard (test) colorimeters by 

measuring the signal-ratios. The ratios give 

the corrections to the calibration factors of 

the reference colorimeter to obtain the channel calibration factors for the working standard colorimeter. The working standard colorimeters are used as test colorimeters in 

this calibration transfer. Since a working 

standard colorimeter should measure the 

same tristimulus values for a CIE Illuminant 

A as the reference colorimeter, it can be 

written for the X1 channel: 

t

X

t

X

r

XX

r t

1 1 11 === IkIkXX 11 (3) 

t

X

r

t XX

X

I

Ik k

1

11

1 = (4) 

where superscript t indicates testcolorimeter which is the working standard in 

this case. The other three calibration factors 

of the test-colorimeter can be derived in the 

same way. These calibration factors also 

include the spectral mismatch and channelamplitude corrections. However, this scale 

transfer will result in low color-temperature 

measurement uncertainty for different 

source distributions if the relative spectral 

responsivities of the corresponding channels 

are very similar to each other. 

6. CONCLUSIONS 

The above described reference colorimeters 

and calibration considerations, with the obtained preliminary measurement results indicate that tristimulus color calibrations of 

tungsten lamps on a detector-base can decrease the 8 K (k=2) uncertainty of traditional source-based calibrations. The 

achievable small f1’ values are also promising to apply the detector-based calibration 

method for special test sources with spectral 

distributions other than tungsten. In order to 

achieve these goals, the infrared leakage of 

the blue filters must be dramatically decreased and the uncertainty of the measured spectral responsivity data should be 

improved by about a factor of two. 

ACKNOWLEDGEMENTS 

The authors thank the US Air Force 

AFMETCAL for funding this project, and also 

Steve Brown, Thomas Larason, and Jeanne 

Houston for participating in the responsivity 

data evaluations. 

REFERENCES 

1. G. Eppeldauer, Spectral Response 

Based Calibration Method of Tristimulus 

Colorimeters, J. Res. Natl. Inst. Stand. 

Technol. Vol. 103, No. 6. p. 615, 1998. 

2. G. Eppeldauer and Y. Ohno, Development of the NIST Detector-based Color 

Temperature Scale, Proc. ISCC/CIE Expert Symposium ’06 “75 Years of CIE 

Standard Colorimetric Observer”, p. 55-

58, CIE Central Bureau, 27, Kegelgasse, A-1030, Vienna, Austria, 2006. 

3. S. W. Brown, G. P. Eppeldauer, and K. 

R. Lykke, Facility for Spectral Irradiance 

and Radiance Responsivity Calibrations 

using Uniform Sources, Applied Optics, 

Vol. 45, No. 32, p. 8218-8237, 2006.

4. J. Fowler and M. Litorja, Geometric area 

measurements of circular apertures for 

radiometry at NIST, Metrologia, Vol. 40, 

No. 1, S9-S12, 2003.

AUTHORS 

G. P. Eppeldauer, C. C. Miller, and Y. Ohno 

National Institute of Standards and Technology 

100 Bureau Drive 

Gaithersburg, Maryland 20899, USA 

Phone: 301-975-2338, FAX: 301-869-5700, 

Email: george.eppeldauer @nist.gov 
Directional error correction of 

radiometric and photometric standard detectors 

Miklós Rácz 

Hungarian Academy of Sciences Research Institute for Technical Physics and Materials Science 

H-1525 Budapest-114, P.O.Box 49, Hungary 

George Eppeldauer 

National Institute of Standards and Technology, Optical Technology Division 

Gaithersburg, MD 20899 

Abstract 

Changes in beam geometry during the calibration and subsequent testing of optical detector standards can cause errors 

which appear as uncertainties in the responsivities of the detectors. These uncertainties, caused by non-ideal detector 

input characteristics and changes in input beam geometry, can be decreased significantly if the detector response is 

always corrected to a reference beam geometry such as a collimated beam normally incident on the detector surface. 

An integral directional error can be determined for radiant power, luminous flux, irradiance and illuminance detectors 

by calculating the weighted integral of the product of the measured source radiance and the directional error over the 

solid angle produced by the light source. A conical directional error is introduced, and used to describe the case of 

circular and uniform radiant sources (e.g. exit port of an integrating sphere) and circularly symmetric detectors. 

Evaluation of the conical directional error and the directional response correction factor, the results of directional 

response measurements, and directional response correction factors for practical standard detectors (such as 

diffuser-input InGaAs and integrating-sphere-input silicon irradiance meters, silicon photodiode, and pyroelectric 

radiant power and irradiance measuring detectors) are presented. 

Keywords: calibration, directional error, f2 error, conical directional error, standard detector 

1. Introduction 

The accuracy of primary standard radiometers has significantly improved in the last few years [1, 2, 3]. In order to 

benefit fully from these improvements, the accuracy of the derived radiometric scales needs to be improved. Greater 

accuracy in the scales means that some effects, formerly negligible, have become more important. One such effect is 

the directional response error of the detectors. At calibration the directional distribution of optical radiation (beam 

geometry) from a source may differ from that in subsequent tests of optical detector standards. These changes in beam 

geometry can be significant: here they are treated as equivalent to uncertainties in detector responsivity. Such 

uncertainties can be reduced by correcting the detector response to a reference input beam geometry. A collimated 

beam normally incident on the detectorsurface makes a practical choice for reference geometry. This paper introduces 

a conical directional error, fd(α), and a directional response correction factor, Cd, which can easily be derived from the 

directional error, f2(ε,φ), as defined by the International Commission on Illumination (CIE), for spatially uniform and 

circularly symmetric calibration sources. [4]. 

2. Calculation of directional response correction factor 

The directional response correction factor Cd of a radiometric detector is a quantity that corrects the detector response 

measured for the beam geometry Sb to the collimated beam response Sc: 

S SC c b = d . (1) 

An integral directional error quantity f2 (defined in the CIE Publ. No 53) is given by: 

f SS 2 = − b c 1. (2) 
It follows from Eqs. (1) and (2) that 

C f d = +1 2 . (3) 

References [4] and [5] describe a method for determining the directional characteristics of irradiance, illuminance, and 

radiance meters by the directional error f2(ε,φ). For irradiance and illuminance meters, the CIE defined directional 

error is: 

f

E

E

reading

reading

2 0 (, ) 1

(, )

( ) cos ε φ

ε φ

ε ε = = °⋅ − , (4a) 

where φ is the azimuth angle (rotation around the detector axis), and ε is the angle of incidence. Ereading(ε,φ) and 

Ereading(ε=0°) are the readings for an irradiance or illuminance, E, arriving at the angles of incidence ε and 0°, 

respectively. 

As the denominator shows, the response of an ideal irradiance or illuminance meter follows the cosine function. For 

radiant power and directional luminous flux meters, where ideally the response is independent of the direction, the 

directional error f2(ε,φ) is: 

f

E

E

reading

reading

2 0 (, ) 1 (, )

( ) ε φ

ε φ

ε = = ° − . (4b) 

References [4] and [5] describe how to calculate the integral directional error f2 from the directional error f2(ε,φ). The 

integral directional error f2 describes the response measurement error originating from the directional error of the 

detector. The CIE defined integral directional error f2 for irradiance and illuminance meters is: 

f f L dL d 2 2 = ⋅ ⋅⋅ ⋅⋅ ∫ ∫ ( , ) ( , ) cos ( , ) cos εφ εφ ε εφ ε Ω Ω

Ω Ω

, (5a) 

where L(ε,φ) is the source radiance, dΩ is the elementary solid angle, and Ω is the total acceptance solid angle (field 

of view) of the detector. 

For radiant power and directional luminous flux meters, where ideally the response is independent of the direction, the 

error f2 is: 

f f L dL d 2 2 = ⋅⋅ ∫ ∫ (, ) (, ) (, ) εφ εφ εφ Ω Ω

Ω Ω

⋅ . (5b) 

Using only angles ε and φ, Eq (5a) can be written as: 

f f L dd L d 2 2

0

2

0

2

0

2

0

2

= ⋅ ⋅ ⋅⋅ ⋅ 2 2

⎡

⎣

⎢ ⎤

⎦

⎥⋅ ⋅ ⋅ ⋅ ⋅ ⎡

⎣

⎢ ⎤

⎦

⎥⋅ ∫ ∫ ∫ ∫ ( , ) ( , ) cos sin ( , ) cos sin

/ /

εφ εφ ε π ε φ ε εφ ε π ε φ ε

ππ ππ

d . (6) 

References [4] and [5] describe the cases where the irradiation comes from the Ω=2π hemisphere or the total Ω=4π

sphere. For detector calibrations, spatially uniform and circularly symmetrical calibration sources should be used 

where the source center is on the optical axis of the detector. For irradiance and illuminance meter calibrations, such 

radiation sources can be realized with integrating spheres. The radiance or luminance of the exit port of a high-quality 

integrating sphere can be considered spatially uniform. In this case L(ε,φ)=L, for ε<α, and L(ε,φ)=0 for ε>α, where α

is the half viewing angle determined by the radius of the light source (the exit port of the integrating sphere) and the 

distance to the aperture center of the detector. 

In case of spatially uniform and circularly symmetrical calibration sources, the integral directional error f2 depends on 

the viewing half angle α of the radiation (extended) source, that is, f2=f2(α). To avoid confusion with the CIE f2(ε,φ) 

(and later f2(ε)), we introduce the conical directional error fd(α) instead of f2(α). 

The conical directional error fd(α), using spatially uniform and circularly symmetrical sources, for irradiance and 

illuminance meters is: 
f f d ( ) α εφ ε π ε φ ε ε π ε φ d d d d

α π π α

= ⋅ ⋅⋅ ⋅ ⎡

⎣

⎢ ⎤

⎦

⎥⋅ ⋅⋅ ⋅ ⎡

⎣

⎢ ⎤

⎦

⎥⋅ ∫ ∫ ∫ 2 ∫

0

2

0 0

2

0

( , ) cos sin 2 2 cos sin ε . (7) 

The calculation becomes simpler if the detector directional response is also circularly symmetrical (i.e. the response is 

independent of azimuth angle φ) resulting in f2(ε,φ)=f2(ε). In this case, the conical directional error for irradiance and 

illuminance meters is: 

ff d ( ) d α ε εε ε d

α α

= ⋅⋅ ⋅ ∫ ∫ 2

0 0

( ) sin sin 2 2 ε . (8a) 

Similar evaluation of Eq. (5b) will result in the conical directional error for radiant power and directional luminous 

flux meters: 

ff d ( ) d α ε εε ε

α α

= ⋅⋅ ∫ ∫ 2

0 0

( ) sin sin ⋅dε . (8b) 

For radiant power and directional luminous flux meter calibrations, where the incident beam underfills the detector 

aperture, the uniform source can be realized by projecting a point source onto the detector entrance with a lens. 

In accordance with Eq. (3), the conical directional error can be compensated for all kinds of radiometers by applying 

the directional response correction factor Cd: 

C f d d = +1 ( ) α (9) 

3. Application of conical directional error and directional response correction factor 

At NIST, determination of detector directional response characteristics is done on a regular basis. Several of our 

measurements have been published by Eppeldauer et al. [6] and Lehman et al. [7]. 

For practical applications, the directional response correction factor Cd is used to correct the detector response for the 

reference beam geometry, which is the axially incident parallel beam. Because the directional response correction 

factor Cd is close to unity, the conical directional error fd(α) gives better visual information. 

The CIE f2(ε) directional errors were measured, the conical directional errors fd(α), and the directional response 

correction factors Cd were calculated for a number of detector standards. The results of four tested detectors are 

summarized in table . Here, directional error curves are shown as an example for a diffuser-input InGaAs irradiance 

meter only. This radiometer has an InGaAs photodiode with input optics consisting of a flashed opal glass diffuser, a 

precision aperture, and a field-of-view limiter. The characterization of the input optics and the directional response 

measurement results of this irradiance standard have been published by Eppeldauer et al. [6]. The detector directional 

response characteristics were measured with an incandescent lamp irradiation. The CIE directional error f2(ε) and the 

conical directional error fd(α) of the detector can be seen in figure . 

figure can be used to determine the directional response correction factor Cd. If the viewing half angle α of the source 

from the detector center is known, the value of the conical directional error fd(α) can be read from the right vertical 

axis. Thereafter, the directional response correction factor can be calculated using Eq. (9). The corrected detector 

response can be calculated from Eq. (1). 
f 2 ( ε )

f d (α)

-0,4%

-0,3%

-0,2%

-0,1%

0,0%

0,1%

0,2%

0 2 4 6 8 10 12

 Incidence angle ε and source half viewing angle α [degree]

CIE directional error f 2 ( ε )

-0,20%

-0,15%

-0,10%

-0,05%

0,00%

0,05%

0,10%

Conical directional error 

f d (α)

Figure 1. The directional error f2(ε) (dotted line with open circles) and the conical directional error fd(α) (solid line 

with black diamonds) of a diffuser input InGaAs irradiance meter. The uncertainties are less than 0.025 % for f2(ε) 

when ε≤6° and less than 0.023 % for fd(α) when α≤9° (k=1). 

Table 1. Conical directional errors fd(α) and directional response correction factors Cd of several irradiance and 

radiant power detector standards for f/9 and f/4 incidence beam geometry. The relative uncertainties of the error 

determinations are also given, k=1. 

Irradiance mode Radiant flux (power) mode 

Detector type f/9 beam, α=3.18o f/4 beam, α=7.13o f/9 beam, α=3.18o f/4 beam, α=7.13o 

fd Cd fd Cd fd Cd fd Cd

Sphere-input Si 

(1) 

+0.033 % 

±0.007 % 

1.00033 +0.166 %

±0.005 %

1.00166 

Diffuser-input 

InGaAs 

+0.055 % 

±0.010 % 

1.00055 +0.081 %

±0.016 %

1.00081 

Gold-black coated 

pyroelectric (2) 

+0.036 % 

±0.046 % 

1.00036 +0.022 %

±0.033 %

1.00022 -0.003 % 

±0.005 %

0.99997 -0.006 % 

±0.004 % 

0.99994 

Si photodiode with 

window (3) 

+0.076 % 

±0.033 % 

1.00076 +0.175 %

±0.026 %

1.00175 -0.009 % 

±0.038 %

0.99991 +0.037 % 

±0.026 % 

1.00037 

In addition to the InGaAs radiometer, the test results of the following detectors are summarized in table : 

(1) Integrating-sphere-input silicon irradiance meter. A Si photodiode was attached to the exit port of a 50 mm 

diameter integrating sphere. An early design of this irradiance meter has been published by Eppeldauer [8]. In the 

present version, a smaller (3.5 mm diameter) input aperture is used, and an additional light-tight cover is added to 

the housing. The directional characteristics were measured with an incandescent lamp. 

(2) Pyroelectric radiant power and irradiance measuring detector. A gold black coated LiNbO3 pyroelectric detector, 

published by Lehman et al. [7], was further tested here. The detector has an 8 mm diameter aperture with 1 mm 

separation from the detector surface. The power-mode directional measurements were performed with a laser 

beam focused onto the detector. The irradiance-mode directional characteristics were measured with an 

incandescent lamp source. 

(3) Silicon photodiode. The most frequently used transfer standards are silicon photodiodes for the near UV, visible, 

and near IR spectral ranges, as described by Larason et al. [9]. The directional characteristics were measured on a 

widely used standard photodiode. This device has a window in front of the circular, 1 cm2

 area photodiode. The 

tests were made with incandescent lamp irradiation. 

The results show that even for well-designed (optimized) radiometer standards, the conical directional error fd(α) can 
exceed the 0.1 % level (k=1). In order to achieve uncertainties below 0.1 %, application of the directional response 

correction factors can be necessary even for high-performance radiometer standards. In some cases, the uncertainties 

of our directional response measurements were too high to determine the directional response correction factors with 

the desired low uncertainty. 

4. Conclusions 

The conical directional error, fd(α), has been introduced and used to evaluate the effect of the CIE defined directional 

error, f2(ε,φ), for transfer standard radiometers. For a given incident beam geometry, fd(α), can be determined as a 

weighted integral of the CIE f2(ε,φ) directional error. A directional response correction factor, Cd, has also been 

calculated. The uncertainty budget of detector response measurements can be decreased by applying this response 

correction. The CIE directional error can thus be replaced by the directional response correction factor determination, 

which has a smaller uncertainty. The suggested calculation can be applied to all irradiance, illuminance, power, and 

directional luminance flux meters. For the most frequently used beam geometries at the NIST, the conical directional 

error fd(α) ranged between +0.022 % and +0.175 % for irradiance meters, and from -0.003 % to +0.037 % for radiant 

power meters. In order to simplify the calculation of Cd, circularly symmetric radiometers should be designed for 

standardization. A high-accuracy measurement setup is required to determine the directional response correction 

factor with a small enough uncertainty for the needs of standards-quality detectors. The described response correction 

method can be applied for medium-performance detector standards as well. 

Acknowledgements 

The authors thank Eric L. Shirley of the NIST Optical Technology Division and Jack J. Hsia of the NIST Office of 

International and Academic Affairs for their valuable advices, and Yuqin Zong of the NIST Optical Technology 

Division for helping in the directional response measurements. 

References 

1. Gentile T. R., Houston J. M., Hardis J. E., Cromer C. L., and Parr A. C., National Institute of Standards and 

Technology high-accuracy cryogenic radiometer, Applied Optics Vol. 35, No. 7, 1 March 1996. p. 1056-1068. 

2. Goebel R., Pello R., Stock K. D. and Hofer H., Direct comparison of cryogenic radiometers from the BIPM and 

the PTB, Metrologia, 1997, 34, p. 257-259. 

3. Köhler R, Goebel R and Pello R., Experimental procedures for the comparison of cryogenic radiometers at the 

highest accuracy, Metrologia, 1996, 33, p. 549-554. 

4. Publication CIE 53-1982 Methods of Characterizing the Performance of Radiometers and Photometers.

5. Publication CIE 69-1987 Methods of Characterizing Illuminance Meters and Luminance Meters.

6. Eppeldauer G., Rácz M., and Larason T., Optical characterization of diffuser-input standard irradiance and 

illuminance meters, Optika’98, 14-17 Sep. 1998, Budapest, Hungary, SPIE 3573, p. 220-224, 1998. 

7. Lehman J., Eppeldauer G., Aust J. A., and Rácz M., Domain-engineered pyroelectric radiometer, 1999, In press. 

8. Eppeldauer G., Near Infrared Radiometer Standards, Optical Radiation Measurements, 8-9 Aug. 1996, Denver, 

Colorado, SPIE Vol. 2815, p. 42-54, 1996. 

9. Larason T. C., Bruce S. S., and Parr A. C., Spectroradiometric Detector Measurements: Part I-Ultraviolet 

Detectors and Part II-Visible to Near-Infrared Detectors, NIST Special Publication 250-41. 
THE REALIZATION AND THE DISSEMINATION OF THE 

DETECTOR-BASED KELVIN 

Howard W. Yoon, Charles E. Gibson, David W. Allen, Robert D. Saunders, Maritoni Litorja, 

Steven W. Brown, George P. Eppeldauer, Keith R. Lykke 

Optical Technology Division 

National Institute of Standards and Technology 

Gaithersburg, MD 20899 

USA

ABSTRACT 

In the International Temperature Scale of 1990 (ITS-90), temperatures above the freezing temperature of silver 

are determined with radiation thermometers calibrated using spectral radiance ratios to one of the Ag-, Au- or 

Cu-freezing temperature blackbodies and the Planck radiance law. However, due to the use of spectral radiance 

ratios, the temperature uncertainties of the ITS-90 increase as the square of the temperature ratios, and recent 

acoustic-gas thermometry measurements have also shown that the underlying thermodynamic temperatures used 

in the radiance ratios in determining the Ag- and Au-fixed point temperatures could be in error. Since the 

establishment of ITS-90, much progress has been made in the development of radiation thermometers and 

blackbody sources. Cryogenic electrical-substitution radiometry is widely used in detector and radiometer 

calibrations, and stable, high-temperature metal-carbon eutectic blackbodies are under development. Radiation 

thermometers can be calibrated for absolute radiance responsivity, and blackbody temperatures determined from 

the amount of optical power without the use of any fixed points thus making possible direct dissemination of 

thermodynamic temperatures. We show that these temperatures can be measured with lower final uncertainties 

than the ITS-90 derived temperatures. We have shown that these “Absolute Pyrometers” can be used to 

determine the thermodynamic temperatures of the ITS-90 fixed points as well as also being used in bilateral 

comparisons of temperature scales. Many leading national measurement institutes are already utilizing detectorbased temperatures in establishing spectroradiometric source scales. We believe, that due to these developments, 

the international temperature scale should be revised so that a thermodynamic temperature scale can be directly 

disseminated. 

1. INTRODUCTION 

The development of an international temperature scale and the periodic adjustments of the scale are 

attempts to disseminate and best reproduce thermodynamic temperatures. Thermodynamic 

temperatures can be determined by primary thermometry using equations of state which relate 

temperatures with measurable quantities without any temperature-dependent parameters such as in 

pressure-volume and acoustic gas thermometry, noise thermometry and detector-based radiation 

thermometry [1]. Due to the difficulties in developing facilities and performing experiments for 

primary thermometry, various phase transitions of material have been assigned temperatures based 

upon available thermodynamic temperature measurements, and these fixed-points cells and 

blackbodies are in-turn used to calibrate secondary thermometers or sensors whose output changes in 

response to temperature. Almost all the national measurement institutes (NMI) rely upon a set of these 

fixed-points to generate the international temperature scale instead of performing their own primary 

thermometry, and thus the current International Temperature Scale of 1990 (ITS-90) with its system of 

fixed-points and defining instruments is an attempt at achieving closest agreement with the 

thermodynamic temperature scale [2]. 

Although there are no fundamental, inherent temperature limitations in the equations describing the 

relationship between measurables and thermodynamic temperatures in primary thermometry, in 

practice, experimental concerns limit these primary thermometers to a range of temperatures. Since 
the experimental upper temperature limit for the lowest uncertainty constant-volume gas thermometry 

and acoustic-gas thermometry is < 900 K, these temperature limitations have impacted the higher 

temperatures uncertainties of the ITS-90 [3]. Due to the conflicting results of two constant-volume 

gas thermometry measurements, the mean of the two results were used as reference values at 743 K 

for radiation thermometry in determining the Al-, Ag- and Au-freezing temperatures used in the ITS90 [1]. The latest acoustic-gas thermometry measurements have been found to be consistent with the 

work of Edsinger and Schooley that would conclude that the current ITS-90 assignments for the each 

of the high-temperature fixed-points have inherent temperature biases [4]. There have also been 

recent efforts in noise-thermometry in measurements of the Ag- and Pd-freezing temperatures, but the 

uncertainties of the noise-thermometry determinations are comparable to those assigned to the ITS-90 

values of these fixed points [5]. Even with new efforts in noise thermometry using super-conducting 

junctions to generate noise standards, the thermodynamic temperature uncertainties above the Agpoint are not expected to be greatly reduced below the present uncertainties [6]. 

Detector-based radiation thermometry can used for thermodynamic temperature determinations which 

are applicable over a wide range of temperatures from 60 K to > 3000 K. With the development of 

cryogenic electrical substitution radiometers (ESR), accurate measurements of optical power by 

comparison to electrical power resulted in the determinations of the Stefan-Boltzmann constant from 

total radiation thermometry [7]. As the temperatures of blackbodies are increased, spectrally-selective 

radiation thermometers calibrated using ESR-based radiometry can be used to determine the 

thermodynamic temperatures with low uncertainties using Si-diode based radiation thermometers [8]. 

Recognizing that these detector-based radiation thermometers be used to obtain lower temperature 

uncertainties than ITS-90 based radiation thermometers, many leading national measurement institutes 

have developed calibration facilities for detector-based temperatures [9]. The needs for the lowest 

uncertainties in temperature > 900 K arise chiefly from the spectroradiometric community where 

sources are used to calibrate remote-sensing instruments. 

With the development of high-temperature metal-carbon and metal carbide-carbon eutectics, these 

stable sources can be used as fixed points for redefinition of the ITS [10]. However, for the lowest 

thermodynamic uncertainties needed for the scale, detector-based radiation thermometry should be 

used to determine the transition temperatures of the eutectics since the any practical temperature scale 

should be in agreement with the thermodynamic scale. 

Although detector-based radiation thermometry is increasingly being used in the international 

radiometric community, the international temperature community still utilizes the source-based ITS-90 

derived temperatures, leading to a possible inconsistency in the disseminated radiometric and 

temperature scales from a common NMI. The situation is analogous to that in the photometry with the 

transition from the platinum-point based candela to the redefinition of the candela based upon optical 

power in 1979 [11]. If a general redefinition of the ITS-90 over all temperatures is not feasible or 

needed at the present time, then the ITS-90 above the Ag-point or perhaps above the Al-point should 

be redefined to reflect the maturity of detector-based radiation thermometry. 

In this paper, we describe the facilities and the experimental procedures in calibrating detector-based 

radiation thermometer traceable to a cryogenic electrical substitution radiometer. The radiation 

thermometer, Absolute Pyrometer 1 (AP1), has been constructed at NIST to be temporally stable and 

is characterized for linearity, size-of-source effect (SSE) and detector-based radiance responsivity. 

The AP1 was used to determine the thermodynamic temperatures of the Ag- and Au-freezing 

temperatures and was also used for a bilateral comparison of temperature scales with the National 

Physical Laboratory (United Kingdom) using high-temperature metal-carbon eutectic blackbodies. 

With these measurements, we demonstrate that primary thermometers such as the AP1 can be used to 

directly disseminate thermodynamic temperatures with lower uncertainties that any ITS-90 based 

thermometer. We describe improvements to radiation thermometer designs to reduce the SSE to 

< 5x10-5 with long-term stability of the responsivity from the use of graphite reference rods in the 
construction. We believe that these results along with further advances at other NMIs will result in the 

adoption of detector-based thermodynamic temperature scale above the Ag-freezing temperature with 

possible extension down to the Al-freezing temperature. 

2. DETECTOR-BASED RADIANCE RESPONSIVITY CALIBRATIONS 

Without the development of facilities to derive radiance and irradiance responsivity from electrical 

substitution radiometers, detector-based radiation thermometry would not be possible. Radiation 

thermometers can be constructed to measure irradiance or radiance, and simple filter radiometers with 

a precision aperture can be used to measure the irradiance of the source if the source also has a 

defining aperture. If the spatial uniformity of the filter radiometer is quantified, then power 

responsivity measurements along with the aperture area will provide the irradiance responsivity. 

However, typical radiation thermometers are constructed using lenses to define a target area to 

measure in radiance mode, and blackbody temperatures can be determined using the detector-based 

radiance responsivities and Planck’s law by the use of 

( )dTLSi λλε Lc ⋅⋅= , ∫ , (1) 

where ic is the calculated photocurrent, SL is the radiance responsivity, and L(λ,T) is the Planck 

radiance law, ε is the emissivity of the blackbody. With the use Eq. 1, blackbody temperatures can be 

determined directly with no adjustable parameters in the measurement equation relating the radiance 

responsivity to the thermodynamic temperature. Since there is a unique relationship between the 

calculated current and the blackbody temperatures in Eq. 1, then integrations can be performed to find 

a match between the calculated and the measured photocurrents to determine blackbody temperatures. 

At NIST, the radiance and irradiance responsivities of radiometers are calibrated using the NIST 

Spectral Irradiance and Radiance responsivity Calibrations using Uniform Sources (SIRCUS) 

facility [12]. Briefly, the 6-element trap detectors used in this facility are calibrated for power 

responsivity using the NIST High-Accuracy Cryogenic Radiometer (HACR) [13], and from the 

knowledge of the spatial uniformity and the precision aperture area of the trap detectors [14], the 

detector-based spectral irradiance responsivity is determined as shown in Fig. 1. 

HACR 

Si-trap Detectors 

Filter Radiometer, 

Radiation T hermo me ter 

Blackbody 

Temperatures 

Length S ta ndards 

Aperture Area, 

Distance 

Inte gra ting Sphere 

Source 

Figure 1. The realization chain for thermodynamic temperatures based upon detector-based radiation thermometry. 
With the irradiance responsivity of the Si-trap detectors calibrated from the power responsivity, the 

. THE DESIGN AND CHARACTERIZATION OF THE AP1 

ith very few exceptions, the performances of commercial radiation thermometers are quite limited in 

spectral irradiance of the laser-illuminated integrating sphere source (ISS) can be determined. 

Knowing the distance between the Si-trap detector and the precision aperture of the ISS determines the 

detector-based spectral radiance of the ISS. The above procedure is repeated with changing laser 

wavelengths, and thus the radiance or the irradiance responsivity of the filter radiometer or the 

radiation thermometer can be determined. Since the radiation thermometer is calibrated as a system, 

knowledge of the lens transmittances in not needed, and complex radiation thermometers with many 

optical elements can also be calibrated in the SIRCUS facility. 

3

W

the temporal stability, size-of-source and optical imaging so that new types of radiation thermometers 

need to be constructed. A schematic of the AP1 in front of the gold-point blackbody is shown in 

Fig. 2. The dimension of the AP1 from outside of the front plate to the back plate is 53 cm. The 

optical elements are attached to three 50 cm long, 12.5 mm diameter invar rods for stability. A 

gradient-index singlet lens is chosen for the objective to minimize the possible scattered light from the 

lens interfaces and to improve the image quality. The objective distance is set at 50 cm using a fixedFigure 2. The schematic of the AP1 in front of the gold-point blackbody.

cus singlet lens distance of 33.3 cm. A 0.5 mm diameter, blackened bi-metal pinhole is used as the 

he re-imaging of the field stop is performed using an achromatic lens, which collimates the light. 

fo

field stop, which results in a nominal target size of 0.75 mm diameter. The size of the target area was 

chosen such that tungsten-strip lamps and fixed-point blackbodies could be compared to variabletemperature blackbodies with larger cavity apertures. 

T

The collimated light passes through the interference filters and is incident on the 5.8 mm by 5.8 mm 

square Si photodiode. The spot size on the diode is estimated to be 5 mm diameter from ray-trace 

analysis. The spectral selection is performed using an ion-assisted deposited interference filter with 

center wavelength at 650 nm. The spectral selection filter is temperature stabilized near room 

temperature, and the hermetically sealed Si photodiode has a 2-stage thermo-electric cooler for 

operation at –15 °C to achieve a noise-equivalent power of 10 fW. The entire pyrometer can be 

purged with dry air or nitrogen to reduce effects due to humidity on the optical elements. 
3.1 RADIANCE RESPONSIVITY CALIBRATION OF THE AP1 

The AP1 was calibrated for radiance responsivity using the NIST SIRCUS facility. The detectorbased radiance responsivity of the AP1 is shown in Fig. 3. The interference filter used in the AP1 

400 500 600 700 800 900 1000

10-14

10-12

10-10

10-8

10-6

10-4

10-14

10-12

10-10

10-8

10-6

10-4

1337.33 K

 Spectral Radiance, L [ W/(cm2sr) nm ]

Radiance Responsivity, 

SL [ A/W/(cm2sr) ]

Wavelength [ nm ]

Figure 3: The radiance responsivity of the AP1 measured in the SIRCUS facility plotted with the Planck radiance at 

13 ed 

as < 1x10-7 suppression in the out-of-band region from the peak value of the responsivity. The full3.2 DETERMINATION OF DETECTOR-BASED TEMPERATURES 

The calculated photocurrents from the use of Eq. 1 and the responsivity in Fig. 3 are plotted versus the 

37.33 K. The center wavelength is 650 nm with a FWHM of 10 nm. The out-of-band suppression of < 1x10-7 is achiev

in the wavelength region from 700 nm to 1000 nm. 

h

width at half-maximum (FWHM) of the radiance responsivity is 10 nm. The calibration of the 

detector-based radiance responsivity is performed with the AP1 as a system and thus any other 

radiation thermometer can be calibrated similarly. The total expanded uncertainty of the radiance 

responsivity is 0.15 % (k=2). 

respective blackbody temperatures in Fig. 4 and shows that the photocurrents range from < 10-10 A to

1000 1500 2000 2500 3000 10-12

10-11

10-10

10-9

10-8

10-7

10-6

10-5

Photocurrent [ A ]

Temperature [ K ]

Figure 4. The calculated photocurrent from the use of Eq. 1 with emissivity of 1. The temp ature of the blackbody is er

determined using the relationship between the calculated photocurrent and the temperature. 
> 10-6 A from the Ag- and Au-point temperatures to 3000 K. The range in photocurrent from the AgLINEARITY CHARACTERIZATION OF THE

ince the measurement of the radiance responsivity was performed in SIRCUS using gain 8, the 

able 1: AP1 preamplifier gains determined by reference to NIST Precision Preamplifier with 0.01 % precision resistors 

Gain Gain factors [V/A] Uncertainty (k=2) [%] Ratios Normalization factors to gain108

freezing temperature to > 3000 K is in the linear photocurrent region for Si diodes if the radiation is 

not incident on the edges of the photodiode [15]. The photocurrent of < 10-10 A near the Ag-freezing 

temperatures indicates the need for low noise photodiodes and preamplifiers for these measurements.

3.3 AP1 

S

normalization factors to the other gains are needed if the AP1 is used at different gain settings. Instead 

of the traditional determination of radiometer linearity using radiation sources, the preamplifier was 

measured separately with a programmable constant-current source and compared to the current-tovoltage conversions using the NIST Precision Preamplifier (NPP) as shown in Table 1. The NPP is a 

current meter whose the nominal decade values of the feedback resistors have a tolerance of 0.01 %. 

The temperature coefficients of the resistances are 10x10-6/ °C. The AP1 preamplifier was calibrated 

against the NPP using an input-current on/off switch to eliminate the output offset voltages of the test 

and standard preamplifiers. As the noise and ripple pickup was minimized in the preamplifier 

standard, the test preamplifier could be calibrated with 0.022 % (k=1) uncertainty even at gain 10.

T

used as feedback resistors. 

6 1.00010E+06 0.02 108/106= 9.95920E+01 

7 1.00008E+07 0.014 108/107= 9.95940E+00 

8 9.96020E+07 0.014 108/108= 1.00000E+00 

9 9.94820E+08 0.022 108/109= 1.00121E-01 

10 9.94330E+09 0.022 108/1010= 1.00170E-02 

. DETERMINATION OF THE AG- AND AU-FREEZING TEMPERAT RES 

ne of the most critical tests of the detector-based radiation thermometer is the comparison of the 

able 2. Summary of the Ag- and Au-freezing temperature determinations with the ITS-90 assignments. 

Freezing T (AP1) [ K ] Uncertainty T 

(A

T90 [ K ] Uncertainty T T-T90 [ K ] 

4 U

O

thermodynamic temperatures of the Ag- and Au-freezing temperatures to the ITS-90 [16]. If the 

detector-based measurements are not within the combined uncertainties of the experiment then some 

unknown systematic uncertainty component could be improperly assigned. The AP1 was used to 

compare the thermodynamic Ag- and Au-freezing temperatures to the ITS-90 assigned values [17]. A 

summary of the measurements is listed in Table 2. 

T

Material P1) [ K ] (k=2) (ITS-90) [ K ] 

(k=2) 

Ag 1234.956 0.106 1234.93 0.080 0.026 

Au 1337.344 0.121 1337.33 0.100 0.014 

From Table 2, the dominant uncertainty component is from the radiance responsivity uncertainty of 

0.15 % (k=2) which corresponds to an expanded temperature uncertainty of 0.121 K and 0.106 K at 

the Ag- and Au-freezing temperatures, respectively. Since the center wavelength of the AP1 is in the 

wavelength and temperature region where the Wien approximation is applicable, the uncertainty of the 

temperature from the uncertainty of radiance is found from the derivative of the Wien approximation, 

and the differences, T-T90, are found to be within the combined uncertainties. 
5. COMPARISON OF NPL ITS-90 AND NIST THERMODYNAMIC TEMPERATURES 

The NIST thermodynamic temperature scale based on the AP1 was also used for bi-lateral comparison 

of temperature scales with the National Physical Laboratory (NPL), United Kingdom, using a set of 

metal-carbon eutectics [18]. The temperatures of the eutectics were assigned at the NPL using ITS-90 

temperatures and then compared by transporting the crucibles to NIST for measurements with the 

AP1. The results are shown Fig. 5. The solid lines are the combined uncertainties of the 

measurements and the dotted lines are the uncertainties of the AP1 measurements. The differences are 

1600 1800 2000 2200 2400 2600 2800

-1.0

-0.5

0.0

0.5

1.0

TNPL-TNIST, AP1 [ K ]

Temperature [ K ]

 Combined uncertainties (k=2)

 AP1 uncertainties (k=2)

Figure 5. The differences between the NPL (ITS-90) assigned temperatures and the NIST thermodynamic temperatures of 

t

ithin the combined uncertainties of the comparison and within the uncertainties of the detector-based 

. NEW DESIGNS FOR RADIATION THERMOMETERS 

ur experience with the AP1 and further analysis of the contributions to the SSE in radiation 

he optical design of the radiometer has been influenced by our studies of the contributions to the 

SSE [19]. The main source of the SSE has been determined to be the scatter from the objective lens. 

The scatter can be reduced by the placement of the Lyot stop or the aperture stop behind the field stop 

he metal-carbon eutectics. The solid line is the combined temperature uncertainties and the dotted line denotes only the AP1 

uncertainties. 

w

temperatures as well. The uncertainties of the NIST detector-based temperature scale is about x2 

smaller than the ITS-90 based scale of NPL. 

6

O

thermometers have lead to new designs for future NIST radiation thermometers. These radiometers 

will be used for detector-based radiation thermometry and for ratio radiation thermometry to obtain the 

lowest uncertainties at temperatures to the Sn-point. A design to be used for detector-based radiation 

thermometry from 350 nm to 2500 nm utilizing different detectors and lenses is shown in Fig. 6. The 

outer case is constructed with 25 cm diameter anodized aluminum, and the large outer case is for 

suppression of scatter from internal reflections. The internal walls are covered with low-reflective 

black appliqué, and the field stop is tilted to avoid direct reflections back onto the objective lens. For 

temporal stability, the optical elements are attached to graphite reference rods which have low 

coefficient of thermal expansion. If the mechanical stability of the graphite rods are not deemed 

adequate, then the reference rods can be exchanged with those constructed from invar. The radiometer 

is also designed for removal of the objective lens from the outside for easy cleaning and replacement if 

the objective lens becomes damaged. Our goal for the uncertainty due to long-term stability of the 

radiance responsivity is 0.01 % or 100 ppm. 

T
such that the image of the objective lens is formed on the Lyot stop by the collimating lens. The 

optical 

Figure 6. A side-view schematic of the graphite-rod referenced radiation thermometer. The outer diameter of the radiation 

thermometer is 25 cm. 

i

co

objective lens design leads to the lowest SSE as shown in Fig. 7. 

maging and chromatic aberrations have been assessed for various different types of lenses using a

mmercial optical modeling software. We have found that for radiation thermometry, the simplest 

6.0x10-4

0 10 20 30 40 50 60

0.0

1.0x10-4

2.0x10-4

3.0x10-4

4.0x10-4

5.0x10-4

SSE

Diameter [ mm ]

 LP3

 NIST

Figure 7. A comparison of the SSE between the NIST radiation thermometer design and the LP3. 

In Figure 7, the optical design utilized in the NIST radiation thermometers is co pared against the 

SSE from t ion in the 

SE. Custom lens designs are being assessed to obtain both optical performance as well as low 

m

he Linear Pyrometer 3 (LP3)*. The simpler objective lens can lead to > 10 reduct

S

surface scatter. 
8. THE DEVELOPMENT OF A FUTURE TEMPERATURE SCALE 

One of the dominant factors in the increase in the ITS-90 temperature uncertainties above the Agfreezing point is the lack of higher-temperature fixed points above 1400 K. Recent developments in 

high-temperature metal-carbon and metal-carbide-carbon eutectic blackbodies could lead to lower 

temperature uncertainties if the eutectic blackbodies are determined to be suitable for use as high 

temperature fixed-points [20]. Spectral radiances of the new metal- carbon and metal carbide-carbon 

eutectic blackbodies are shown along with the Au- and the Ag-fixed points in Fig. 8. For any future 

temperature scale to be closely in agreement with the thermodynamic scale, the temperatures of the 

high temperature eutectic blackbodies must be determined using absolute detector-based techniques. 

If radiance ratios from the Au-point temperature are used to determine the temperatures of the 

eutectics then the uncertainties would be unacceptably large, since the uncertainties are found by using 

( ) ( ) 2

2 BB

REF

REF

BB T

T

Tu Tu = , (2) 

with TREF denoting the fixed point blackbody, and TBB the unknown temperature of the eutectic-point 

blackbody. 

300 400 500 600 700 800 900 1000 1100

10-2

10-1

100

101

102

103

104

105

106

900 nm

Al (933 K)

TiC-C (3034 K)

Ag (1235 K)

Au (1337 K)

Re-C (2747 K)

365 nm

650 nm

 Spectral Radiance [ μW / cm2 nm / sr ]

 Wavelength [ nm ]

Figure 8. The spectral radiances of the blackbodies at the respective temperatures. The measurements of the Au- and the 

Ag-freezing points at 650 nm are compared with the planned measurements of the eutectic points at shorter wavelengths. 

However, there is still a role for ratio radiometry in the new temperature scale. If the temperature of 

the reference fixed-point blackbody described in Eq. 2 is greater than the temperatures of the 

blackbodies under measurement, then the temperature uncertainties of the lower temperature 

blackbodies become smaller by the ratio of the squares of the respective temperatures. A possible 

future temperature scale could be based upon an absolute temperature determination of several hightemperature metal-carbon eutectic blackbodies ~ 3000 K with the temperatures of the lowertemperature fixed point determined using radiance ratios. 

Table 5 shows the temperature uncertainties both using absolute detector-based techniques and 

radiance ratios to the TiC-C blackbody, and the uncertainties of the detector-based temperature 

determinations can be estimated from the derivative of the Wien approximation to Planck’s radiance 

law, 
2

2 c

T

ΔΔ TL (3) 

able 5. A comparison of the temperature uncertainties found using absolute detector-based techniques and radiance ratios. 

Wavelength 

Radiance 

Uncertainty 

(%) 

Temperature 

Uncertainty (K) 

Ratio Pyrometry 

(K) 

L = λ , 

which shows the relationship between the uncertainty in radiance, L, to the uncertainty in blackbody 

temperature, T, where c2 is the second Planck’s constant, and λ is the wavelength. If the temperatures 

of the respective blackbodies are measured at the wavelengths shown in Col. 3, then the radiance 

uncertainties shown in Col. 4 lead to the uncertainties in Col. 5 as found using Eq. 3. However, if the 

temperatures of the lower temperature fixed points are determined using radiance ratios to the TiC-C, 

then the temperature uncertainties decrease as in Eq. 2 thus leading to lower uncertainties as shown in 

Col. 6. For the lowest uncertainties in the temperature scale, both types of temperature determinations 

are needed to verify the assigned uncertainties in addition to the ratio radiometry based on the lowertemperature acoustic-gas thermometry. 

T

Detector-based Ratio to TiC-C 

Material Temperature (K) (nm) (k = 2) (k = 2) (k = 2) 

TiC-C 3034 365 0.1 0.234 --- 

Re-C 2748 400 0.1 0.210 0.172 

Cu 1357.77 650 0.1 0.083 0.042 

Au 1337.33 650 0.1 0.081 0.041 

Ag 1234.93 800 0.1 0.069 0.035 

Al 933.473 900 0.1 0.055 0.020 

Zn 692.677 1250 0.3 0.125 0.011 

9. DISCUSSION 

With the improvements in radiation thermometer designs for long-term stability and low SSE, the total 

radiance responsivity uncertainty in detector-based thermometry is expected to decrease to 0.1 % 

(k=2) in the wavelength region from 350 nm to 1000 nm. Although, even with the current design of 

the AP1, the detector-based determinations of the Ag- and Au-freezing temperature are in agreement 

with the combined uncertainties, further reduced uncertainties will lead to the thermodynamic 

uncertainties as shown in Table 6. The present thermodynamic uncertainties in the ITS-90 assigned 

temperatures are listed. Although the uncertainties appear comparable, the limiting uncertainties in 

n

h

[mK] (k = 2) uncertainties [mK] 

(k = 2) 

oise-thermometry are due to random uncertainties, while the dominant uncertainties in detector-based

t ermometry are due to systematic uncertainties, indicating that even lower total uncertainties are

achievable with detector-based thermometry. 

Table 6. A comparison of the thermodynamic temperature uncertainties obtained using noise and detector-based 

thermometry with the current uncertainties in the ITS-90 assignments. The detector-based thermometry is determined using 

0.1 % (k = 2) uncertainty in the radiance responsivity at 650 nm. 

Metal T90 [K] T90, Thermodynamic 

temperature uncertainty 

[mK] (k = 2) 

Noise thermometry 

uncertainty 

Detector-based 

thermometry 

Al 933.473 50 -- 55 

Ag 1234.93 80 80 68 

Au 1337.33 100 -- 81 

Cu 1357.77 120 126 83 

Pd 1827.95 200 212 151 
We have shown that detector-based thermometry can

uncertainties near the Ag- and Au-freezing temperat

S-90 based radiation thermometry at higher temperatures. The promise of lower uncertainties and 

oints will not remain as fixed points but will be allowed to vary within the uncertainty of the 

 higher temperature uncertainties than is possible with a detector-based scale, and NIST has already 

recognized the restrictions that a fixed-point scale pon re uncertainties. The 

current situation is analogous to th od IPT iz -90. 

Althou via h ic te ure scale of the IPTS-68 was recognized, 

restrictions of a fixed-point based scale at the discrepancies without 

new tem res assig o the fix oints. R nizing the trictions, NIST has been 

detector-based since 199 h a separa dependent, thermodynam perature d

the Au-fre per 1], and with the new generation of radiation thermometers, will soon be 

completel tector-ba he ITS-9 le is desired, then correction factors can be applied to the 

NIST det r-based s interna l compari and to c with mutual recognition 

arrangeme . 

0. CONCLUSION 

e show that much progress has been made toward an implementation of a detector-based 

imply that the material or equipment are necessarily 

est availa or the p

[1] Quinn T. J., Temperature, 2 nd ic Pre

[2] Preston-Thomas H., “The International Temperature Scale of 1990 (ITS-90)”, Metrol , 1990, 

. 3-10. 

[3] f [1] pp

[4] ouse G. Mo er M. R., Ripple D. C., ”Progress in primary acoustic 

ome 273 K to 50 TMCSI, Vol. 7, Chicago, edited by Ripple D. C 003, 

 achieve comparable uncertainties to the ITS-90 

ures and can attain lower uncertainties than any 

IT

the requirements for determining the metal-carbon eutectic transitions with the lowest uncertainties 

have led to efforts at NPL, PTB, NMIJ/BIPM, CSIRO and HUT, among others, to set up similar 

detector-based radiance responsivity calibration facilities, and with such facilities, direct 

disseminations of thermodynamic temperatures are possible with either calibrated radiation 

thermometers or secondary transfer standard sources. 

We believe that these developments will lead to a reassessment of the ITS-90 and the future 

international temperature scale. Since it is possible, with detector-based radiation thermometry, to 

directly disseminate thermodynamic temperatures, the present Ag-, Au-, Cu- and even the Al-freezing

p

thermodynamic temperature determinations. Remaining within the framework of ITS-90 could result 

in

 places u

 when the 

the temperatu

e time-peri S-68 was util

ermodynam

ed prior to ITS

gh the de tions from the t mperat

meant th

ed p

could not be resolved

peratu ned t ecog se res

0 wit te, in ic tem etermination of

ezing tem ature [2

y de sed. If t 0 sca

ecto cale for tiona sons omply

nts

1

W

thermodynamic temperature scale. The impetus for such progress has arisen from the 

spectroradiometric community and the need for the lowest-uncertainty temperature measurements of 

the new metal-carbon eutectic blackbodies. These detector-based primary radiation thermometers 

have been used to determine the Ag- and Au-freezing temperatures and even for bilateral comparison 

of temperature scales. With continuing efforts at many different NMIs, direct dissemination of 

thermodynamic temperatures will be possible in the near future. We believe that a reassessment of the 

ITS-90 is needed to reflect the developments in detector-based radiation thermometry. 

REFERENCES 

* Certain commercial equipment, instruments, or materials are identified in this paper to foster 

understanding. Such identification does not imply recommendation or endorsement by the National 

Institute of Standards and Technology, nor does it 

the b ble f urpose.

ed., London, Academ ss Ltd., 1990.

ogia 27

pp

Re . 56-57. 

Str F., Defibaugh D. R., ldov

therm try at NIST: 5 K”, ., 2
pp. 31-36. 

[5] Edler F., Kühne M., Tegeler E., ”Noise Thermometry above 960 °C”, Proceedings of TEMPMEKO 

1999

00 °C”, Philosophical Transactions of the Royal 

Metrologia 40, 2003, pp. S9-S12. 

 Battuello M., Bloembergen P., Girard F., Ricolfi, “A Comparison of Two Methods for Measuring the 

Nonlinearity of Infrared Radiation Thermometers”, Temperature: Its Measurement and Control in 

l. ed by D. C. Ripple, 2003, pp. 613-618. 

C. E., Litorja M., Saunders R. D., Brown S. W., Eppeldauer G. P., 

ture Part of a 

Future ITS with the Aid of Eutectic Metal-Carbon Fixed Points”, Temperature: Its Measurement and 

Control in Science and Industry, Vol. 7, edited by D. C. Ripple, 2003, pp. 291-296. 

. D., Saunders R. D., Shumaker J. B., “Spectroradiometric Determination of the Freezing 

Gold”, J. Res. Natl. Inst. Stand. Technol. 95, 1990, pp. 45-67. 

dress rive 

Gaithers

, Delft, edited by Dubbeldam J. F., de Groot, M. J., 1999, pp. 394 -399. 

[6] Nam S. W., Benz S. P., Martinis J. M., Dresselhaus P., Tew W. L., White D. R., ”A Ratiometric 

Method for Johnson Noise Thermometry Using a Quantized Voltage Noise Source”, TMCSI, Vol. 7, 

Chicago, edited by Ripple D. C., 2003, pp. 37 -42. 

[7] Quinn T. J., Martin, J. E., ”A radiometric determination of the Stefan-Boltzmann constant and 

thermodynamic temperatures between -40 °C and +1

Society of London A 316, 1985, pp. 85 -189. [8] Allen D. W., Saunders R. D., Johnson B. C., Gibson C. E., Yoon H. W., “The Development and 

Characterization of an Absolute Pyrometer Calibrated for Radiance Responsivity”, TMCSI, Vol. 7, 

Chicago, edited by Ripple D. C., 2003, pp. 577 -582 

[9] Fox N. P., Metrologia 32, 1995/1996, pp. 535 -543.; Taubert D. R., Hartmann J., Hollandt J., Fischer J., 

”Investigation of the Accuracy of the ITS-90 with Reference to Thermodynamic Temperature in the 

Range from 400 °C up to 600 °C”, TMCSI, Vol. 7, Chicago, edited by Ripple D. C., 2003, pp. 7 –12. 

[10] Yamada Y., Sakate H., Sakuma F., Ono A., “A Possibility of Practical High Temperature Fixed Points 

above the Copper Point, Proceedings of TEMPMEKO1999, Delft, edited by Dubbeldam J. F., de Groot, 

M. J., 1999, pp. 535 -540. 

[11] Blevin W. R., and Steiner B., “Redefinition of the Candela and Lumen”, Metrologia 11, 1975, pp. 97-

104. 

[12] Brown S. W., Eppeldauer G. P., Lykke K. R., “NIST Facility for Spectral Irradiance and Radiance 

Responsivity Calibrations with Uniform Sources”, Metrologia 37, 2000, pp. 579-582. 

[13] Gentile T. R., Houston J. M., Cromer C. L., “National Institute of Standards and Technology Highaccuracy Cryogenic Radiometer”, Appl. Opt. 35, 1996, pp. 4392-4403. 

[14] Fowler J. and Litorja M., “Geometric Area Measurements of Circular Apertures for Radiometry at 

NIST”, 

[15]

Science and Industry, Vo 7, edit

[16] Yoon H. W., Allen D. W., Gibson 

Lykke K. R., “Temperature Determination of the Ag- and Au-freezing points using a Detector-based 

Radiation Thermometer”, submitted to the Proceedings of Tempmeko 2004, Croatia, 2004. 

[17] Ref. [1] p. 59. 

[18] Machin G., Gibson C. E., Low D., Allen D.W., Yoon H.W., “A Comparison of ITS-90 and Detectorbased Scales between NPL and NIST Using Metal-carbon Eutectics ”, submitted to the Proceedings of 

Tempmeko 2004, Croatia, 2004. 

[19] Yoon H.W., Allen D.W. Saunders R.D., “Methods to reduce the size-of-source effect in radiation 

thermometers”, submitted to the Proceedings of Tempmeko 2004, Croatia, 2004. 

[21] Bloembergen P., Yamada Y., Yamamoto N., Hartmann J., “Realizing the High-tempera

[21] Mielenz K

Temperature of 

Ad of the Principal Author: Howard W. Yoon, Optical Technology Division, NIST, 100 Bureau D

burg, MD 20899-8441, USA, tel. (301) 610-0094, fax (301) 869-5700, e-mail: hyoon@nist.gov
Thermodynamic-temperature determinations of the Ag

and Au freezing temperatures using a detector-based

radiation thermometer

Howard W. Yoon, David W. Allen, Charles E. Gibson, Maritoni Litorja, Robert D. Saunders,

Steven W. Brown, George P. Eppeldauer, and Keith R. Lykke

The development of a radiation thermometer calibrated for spectral radiance responsivity using cryogenic,

electrical-substitution radiometry to determine the thermodynamic temperatures of the Ag- and Aufreezing temperatures is described. The absolute spectral radiance responsivity of the radiation thermometer is measured in the NIST Spectral Irradiance and Radiance Responsivity Calibrations using Uniform

Sources (SIRCUS) facility with a total uncertainty of 0.15% k  2and is traceable to the electrical watt,

and thus the thermodynamic temperature of any blackbody can be determined by using Planck radiation

law and the measured optical power. The thermodynamic temperatures of the Ag- and Au-freezing

temperatures are determined to be 1234.956 K 0.110 Kk  2and 1337.344 K 0.129 Kk  2

differing from the International Temperature Scale of 1990 (ITS-90) assignments by 26 mK and 14 mK,

respectively, within the stated uncertainties. The temperatures were systematically corrected for the

size-of-source effect, the nonlinearity of the preamplifier and the emissivity of the blackbody. The

ultimate goal of these thermodynamic temperature measurements is to disseminate temperature scales

with lower uncertainties than those of the ITS-90. These results indicate that direct disseminations of

thermodynamic temperature scales are possible. © 2007 Optical Society of America

OCIS codes: 120.6780, 120.3940.

1. Introduction

The measurements of temperature can be classified

into primary and secondary thermometry.1 Primary

thermometry is defined as determining thermodynamic

temperatures using equations of state and physical constants without any adjustable temperature-dependent

parameters; some examples are constant-volume gas

thermometry,2 speed-of-sound measurements in

gases,3 or noise thermometry.4 Primary measurements based on the measurements using gases, however, are limited in temperature range owing to the

deviation of the gas from ideal behavior and other

experimental limitations,5 and noise thermometry is

limited by the need for long measurement times required for sufficient statistical precision.6

Since primary thermometers are not easily transportable and are difficult to use, secondary thermometers are used as transfer devices. Because of the

difficulties in maintaining primary thermometers for

routine calibrations, the International Temperature

Scale of 1990 (ITS-90) assigns fixed values for the

phase-transition temperatures of various pure materials based upon the best thermodynamic temperature determinations available at the time of

specifying the scale.7 Secondary interpolating thermometers are based upon these fixed points, and

the assigned temperatures are ultimately traceable

to primary thermometers through the fixed points.

Some examples of secondary thermometers are standard platinum resistance thermometers and thermocouples.

Another type of primary thermometer is the total

and the spectral radiometer, calibrated using electrical substitution radiometry and used in conjunction

with a blackbody. Such total radiometers in the past

have determined the Stefan–Boltzmann constant using the wavelength integrated Planck’s radiance law

to a relative combined uncertainty of 0.013%.8 If only

a narrow spectral region is selected by the use of

spectral filters, then the spectral radiometer can be

The authors are with the Optical Technology Division, National

Institute of Standards and Technology, Gaithersburg, Maryland

20899-8441, USA. H. Yoon’s e-mail address is hyoon@nist.gov.

Received 14 November 2006; accepted 18 December 2006; posted

17 January 2007 (Doc. ID 77061); published 1 May 2007.

0003-6935/07/152870-11$15.00/0

© 2007 Optical Society of America

2870 APPLIED OPTICS  Vol. 46, No. 15  20 May 2007
used to determine the temperatures of blackbodies

with the use of Planck’s radiation law within the

spectrally selected region.

In the past, detector-based radiance temperature

measurements have been performed using filter

radiometers calibrated for spectral irradiance responsivity.9 These filter radiometers with precision

apertures are typically used in nonimaging applications to measure the temperatures of blackbodies,

but such optical flux techniques are difficult to use

to measure the fixed-point blackbodies with subcentimeter diameter cavity openings. The nonimaging

radiometers are used to measure spectral irradiance

using double-aperture flux transfer techniques, and

the small, 1 cm internal apertures of fixed-point blackbodies make it difficult to define a source aperture.

Such techniques can also result in large uncertainties

in the diffraction corrections needed from the use of the

small defining apertures. However, small aperture

blackbodies can be measured by using imaging radiometers in which the field stop defines the area of

measurement. In the past, absolute imaging radiometers or pyrometers have been constructed from filter

radiometers by using a lens with a measured transmittance,10 but similar component-based calibrations

cannot be used with low final uncertainties if a number

of optical elements such as lenses and filters are introduced into the optical path.

The ultimate goal of detector-based radiance temperatures is the direct dissemination of thermodynamic temperatures without the use of physical

artifacts such as fixed-point blackbodies. Such a transition occurred for the definition of the candela in

1979 when it was changed from being derived from

the Pt-freezing point to that of optical power,11 and

the uncertainties in the realization of the candela can

be improved with the development of new detectors

and procedures.

In this work, measurements of the thermodynamic

temperatures of the Ag- and Au-freezing points using

the NIST Absolute Pyrometer (AP1) are described in

which the radiation thermometer is calibrated at the

system level. The AP1 is designed and constructed at

the NIST and is calibrated for radiance responsivity

as a system using a cryogenic, electrical-substitution

radiometer-based method. The characterization of

the AP1 for size-of-source effect and linearity are described, and the measured temperatures are corrected

for these systematic effects. The thermodynamic temperatures are compared to the previous temperature

measurements and found to be in agreement within

the combined uncertainties. This work demonstrates

that the thermodynamic temperatures can be directly

disseminated in this range using detector-based calibrations with comparable or lower uncertainties than

that of the ITS-90.

2. Experimental Section

A. Description of the Absolute Pyrometer

A schematic of the AP1 in front of the gold-point

blackbody is shown in Fig. 1. The dimension of the

AP1 from outside of the front plate to the back plate

is 53 cm. The optical elements are attached to three,

50 cm long, 12.5 mm diameter Invar rods for structural stability with a low-temperature coefficient of

expansion. The radiometer uses an on-axis design with

a plano–convex singlet lens focal length  20 cmfor

the front objective with the aperture stop (AS) in

front of the lens. For the objective lens, a gradientindex singlet lens was chosen to minimize the possible scattered light from the lens interfaces and to

improve the image quality. The 50 mm diameter objective lens is set at a fixed object distance of 50.0 cm

with the field stop (FS) at an image distance of

33.3 cm. A 0.5 mm diameter blackened bimetal aperture is used as the field stop, which results in a

nominal target size of 0.75 mm diameter. The actual

field of view was measured by raster scanning a

source with a small 10 m pinhole aperture. The size

of the target area was chosen such that tungsten-strip

lamps and fixed-point blackbodies could be compared

to variable-temperature blackbodies with larger cavity

opening apertures.

The reimaging of the field stop is performed using

a gradient-index achromatic lens (RL), which collimates the light. The light passing through the interference filters (IF) is collimated, and no further lenses

are used between the filters and the 5.8 mm by

5.8 mm square Si photodiode (PD) with the diode

suppression of the near-infrared power responsivity.

The spot size on the diode is estimated to be 5 mm

diameter from the ray-trace analysis. The spectral

selection is performed using ion-assisted-deposited

Fig. 1. (Color online) Schematic of the AP1 placed in front of the gold-point blackbody. The aperture stop (AS), field stop (FS), relay lens

(RL), interference filter (IF), and the photodiode (PD) are shown.

20 May 2007  Vol. 46, No. 15  APPLIED OPTICS 2871
interference filters12 with the center wavelengths at

650 nm for at least 107 suppression of the responsivity in the out-of-band region to 1100 nm. The spectral selection filter is temperature stabilized using a

thermoelectric (TE) cooler near room temperature,

and the hermetically sealed Si photodiode has a twostage TE cooler for operation at 15 °C to achieve a

noise-equivalent power (NEP) of 10 fW. The AP1

can be purged with dry air or nitrogen to reduce

effects attributable to humidity on the interference

filters.

B. Radiance Responsivity Calibration of the Absolute

Pyrometer

The AP1 was calibrated for absolute radiance responsivity using the NIST Spectral Irradiance and Radiance Responsivity Calibrations using Uniform Sources

(SIRCUS) facility13 as illustrated in the sequence of

measurements in Figs. 2(a)–2(d). The optical power of

the power-stabilized and collimated laser source is

measured using a cryogenic electrical substitution radiometer, the NIST Primary Optical Power Radiometer (POWR) in Fig. 2(a). Since the POWR is difficult to

use on a daily basis, the power responsivity is transferred to six-element Si-trap detectors in Fig. 2(b).

From the knowledge of the spatial uniformity and the

area of the precision defining aperture on the trap

detectors, the detector-based spectral irradiance responsivity is determined. The laser is input into an

integrating sphere to obtain a spatially uniform and

Lambertian source in Fig. 2(c), and the spectral irradiance of the source is determined using the Si-trap

detector. The spatial uniformity at the exit aperture of

the integrating sphere is mapped to determine the

uncertainties attributable to the nonuniformity of

the sphere. The power-stabilized laser is transmitted

through a fiber, which is agitated in a water-filled ultrasonic bath. The rapid vibrations in the ultrasonic

bath remove the laser speckle in the sphere output

since the integration times of the detectors are much

longer than the time duration of the speckle pattern. A

small 38.1 mm diameter integrating sphere is used to

increase the throughput of the sphere, and the 5 mm

diameter exit port of the integrating sphere source is

chosen to approximate the 6 mm diameter opening of

the fixed-point blackbody cavities. With precision apertures on both the output port of the integrating

sphere and the entrance of the Si-trap detector combined with the knowledge of the distance separating

the sphere and the trap detector, the monochromatic

spectral radiance of the integrating sphere can be

assigned from the detector-calibrated irradiance responsivity of the trap detector. The aperture area and

the distance measurement device are traceable to

length standards. The AP1 is then calibrated for spectral radiance responsivity by substitution with the

trap detector as shown in Fig. 2(d). Once the monochromatic, spectral radiance of the integrating-sphere

source is known, any radiometer or radiation thermometer can be calibrated at the system level. The

procedure is repeated at other wavelengths until the

full spectrum of the radiance responsivity is obtained.

The detector-based radiance responsivity of the

AP1 is shown along with the spectral radiance of

the gold-point blackbody in Fig. 3. The interference

filter used in the AP1 shows 1  107 suppression

in the out-of-band region relative to the peak value

of the responsivity. The FWHM of the radiance responsivity is 10 nm with the centroid wavelength of

649.115 nm. The total expanded uncertainty of the

radiance responsivity at a single wavelength is

0.15% k  2.

Fig. 2. (Color online) Procedure for detector-based spectral radiance responsivity calibrations with the use of the electrical substitution

radiometer. (a) Measurement of the spectral power of the laser with the cryogenic electrical substitution radiometer; (b) determination of

the spectral power responsivity of the Si-trap detector; (c) measurement of the spectral irradiance of the integrating sphere source; (d)

determination of the radiance responsivity of the radiation thermometer as a system.

2872 APPLIED OPTICS  Vol. 46, No. 15  20 May 2007
The wavelength spacing between calibrations was

decreased near the peak of the spectral responsivity

since interference effects from interreflections can

lead to oscillations in the spectral responsivity, which

are wavelength dependent, as seen in Fig. 4. The

sources of the interference effects are from the remaining coherence of the laser through the integrating sphere source combined with the interreflections

between the optical elements in the radiation thermometer. Although an effort was made to reduce the

interference effects by designing the optical filter

with a 5° tilt of one of the surfaces from the optical

axis, the interference effects are evident as 1% peak

oscillations of the responsivity. Since the radiation

thermometer is used to measure the radiance from a

blackbody, which is an incoherent source, the convolved radiance will not exhibit the interference effects, and the interference effects in the radiance

responsivity will depend on the spatial coherence of

the incident radiation. The increase in the uncertainties attributable to the interference effects can be

minimized by performing measurements at closely

spaced wavelength intervals.

The thermodynamic temperatures of blackbodies

are found from the radiance responsivity and Planck’s

law by the use of

ic   SLL, Td, (1)

where ic is the calculated photocurrent, SL is the absolute radiance responsivity, and L, Tis the spectral radiance given by Planck radiance law. Planck

radiance law is

L, T c1L

n25

1

expc2nT  1, (2)

Fig. 3. (Color online) Radiance responsivity of the AP1 measured in the SIRCUS facility plotted with the Planck radiance at 1337.33 K.

The center wavelength is 650 nm with a FWHM of 10 nm. The out-of-band suppression of 1  107 is achieved in the wavelength region

from 700 to 1000 nm.

Fig. 4. (Color online) Spectral radiance responsivity near the peak

of the responsivity function showing the interference fringes. The

fringes arise from the interference of the radiation with the planar

reflective surfaces in the AP1. The presences of the fringes require

measurements at sufficient wavelength intervals to resolve them.

20 May 2007  Vol. 46, No. 15  APPLIED OPTICS 2873
where c1L and c2 are the first and second radiation

constants, T is the thermodynamic temperature, is

the wavelength of the radiation in air, and n is the

refractive index. For these calculations, the CODATA

values14 for the radiation constants and the refractive

index of air of n  1.00029 were utilized.

There are no adjustable parameters in the measurement equation relating the radiance responsivity

of the AP1 to the thermodynamic temperature, and

Eq. (2) can be used to generate a curve of photocurrent to blackbody temperatures. The one-to-one relationship is shown in Fig. 5. The photodiode used in

the AP1 is operated in the photovoltaic mode without

any bias voltages, and this type of photodiode in the

photovoltaic mode has been shown to be linear over a

wide dynamic range.15 The range of calculated photocurrents of the AP1 are from 1  1011 A at the Ag

point to 1  106 A near 3000 K, which is in the linear

regime for photodiodes. The plot in Fig. 5 also indicates

the need for low-noise current-to-voltage amplifiers to

measure the low photocurrents near the Ag- and Aufreezing temperatures. Other corrections such as the

size-of-source effect, the nonlinearity of the preamplifier, and the emissivity of the blackbody will be applied

as corrections to the measured photocurrents before

comparison to the calculated photocurrents in Fig. 5.

The relationship between photocurrent and blackbody

temperatures can be fit with an interpolation function16 to facilitate conversions from signals to temperatures.

3. Instrumental Characterizations of the Absolute

Pyrometer

A. Gain Linearity

To reduce the uncertainties in the linearity corrections, the same preamplifier was used for both AP1

calibrations and the temperature determinations.

The SIRCUS calibrations were performed at a gain of

108 VA. If the AP1 is used with any other gain setting on the preamplifier, then the gain normalization

factors to the 108 VA gain are needed to compare

the measurements at the different gains. These gain

factors were measured at the beginning of the study

and the values used through the measurements.

Since the gain factor nonlinearities primarily arise

from the deviation of the feedback resistance values

from their precision stated values, the resistances

values are not expected to change during the operational lifetime of the radiation thermometer. The

gain factors for the AP1 preamplifier were determined by comparison to the NIST Precision Preamplifier (NPP) with 0.01% precision resistors used as

feedback resistors, and the gain correction factors are

listed in Table 1. These gain factors can also be obtained by the use of a stable radiation source such as

a light-emitting diode whose intensity can be varied

by neutral density filters. A programmable-current

source was used to provide constant current for the

ratio measurements between the AP1 preamplifier

and the NPP. The linearity of the NPP and the AP1

preamplifier depends upon the accuracy of the electrical resistance measurements as compared to the

optical linearity characterizations used for other radiation thermometers. Since the AP1 is used at gain

1010 VA to 108 VA, the normalization factors are

found by using ratios of gains and are found to be

1.00170  102 0.022% k  2. The linearity of

the Si diode in the AP1 was not measured separately

since the Si diode has been demonstrated to have

linear response over a 14-decade ratio of photocurrents.15

B. Size-of-Source Effect Characterization

Since the integrating sphere source used for the

detector-based spectral radiance responsivity calibration and the Ag- and Au-freezing temperature blackbody have different spatial distributions, systematic

corrections are needed. The size-of-source effect was

characterized by using two different techniques. First,

the point-spread function of the AP1 was measured

using a 10 m diameter pinhole aperture, which was

illuminated by a laser diode centered at 650 nm. A

microscope objective was used to collect the collimated radiation from the laser diode and made incident on the pinhole. The 10 m source was translated

on the x and y axis stages in 100 m steps at the

object plane of the AP1, and the point-spread function

determined, as shown in Fig. 6. The FWHM was

Fig. 5. (Color online) Calculated photocurrent as a function of the

blackbody temperature. The calculation is performed with no adjustable parameters.

Table 1. AP1 Preamplifier Gain Corrections Measured 11 June 2002

Gain

Gain Factors

[VA]

Uncertainty

(k  2)

[%] Ratios

Normalization

Factors to Gain

108

6 1.00010  106 0.02 108106 9.9592  101

7 1.00008  107 0.014 108107 9.9594

8 9.96020  107 0.014 108

108 1.0000

9 9.94820  108 0.022 108

109 1.0012  101

10 9.94330  109 0.022 1081010 1.0017  102

2874 APPLIED OPTICS  Vol. 46, No. 15  20 May 2007
determined to be 0.78 mm 0.01 mmwith a difference between 10% and 90% of the peak value of

0.11 mm 0.01 mm. The measured spot size is in

agreement with the expected spot size based on geometric optics.

Since the point-spread function determines only

the optical imaging quality of the AP1, a large-area,

radiance source was used to determine the size-ofsource effect (SSE). The AP1 was characterized for

SSE using a LED illuminated radiance source with a

5 mm diameter conical, central obscuration using the

so-called indirect technique. The outer diameter of

the source was changed with a variable-diameter iris.

The SSE is plotted in Fig. 7 using

	d, do vL, d vL, do

vL, (3)

where d is the diameter of the uniform radiance

source, do is the diameter of the central obscuration,

and L is the radiance of the source. The signal measured while viewing the unobstructed radiance source

is vL, and the signal measured while viewing the

central obscuration with the diameter of the radiance source, d, is vL, d. The signal measured with

the diameter of the variable aperture at the diameter

of the central obscuration, do, is vL, do.

With knowledge of the SSE using a uniform source,

the SSE must be corrected for the nonuniform blackbody source by spatial scans during the freeze. The

spatial scans of the Au-freezing temperature blackbody is shown in Fig. 8. The scans were performed

with the AP1 on a motorized stage while the Au-point

blackbody was in the freeze plateau. Since the electrical heating is reduced during the freeze, there is

contrast observed between the central cavity and the

surrounding graphite crucible seen as a reduction in

the signal past 7 mm.

The SSE corrections for the Ag and Au freezes were

determined using the spatial distribution of the radiance from Fig. 8 measured by scanning the AP1

convolved with the SSE measurements shown in Fig.

7 along with Eq. (3) according to

	r, ro i

L


Lo 

	i
, ro


 	
, (4)

where a modified SSE, 	, is found from the product

of the differential increase in the SSE, 	i, and the

measured relative radiance distribution as a function

of the radius, L
. Since the Ag and Au furnaces

utilize the same designs and components, the spatial

scans of the Au-point furnace was also used to correct

the Ag-point furnace.

4. Blackbody Design

The physical diagram of the blackbody and the furnace is shown in Fig. 9. The graphite crucible is held

in an alumina tube with an argon purge at the rear.

The alumina tube is placed in a Na-heatpipe liner

constructed from Inconel 601 for temperature uniformity and is sealed except for the front opening. The

Fig. 6. (Color online) Spatial responsivity of the AP1 measured

using an illuminated 10 m pinhole scanned across the object

plane.

Fig. 7. (Color online) SSE measured for the AP1 using an LED

radiance source with a 5 mm diameter central obscuration.

Fig. 8. (Color online) Spatial scans of the Au-freezing temperature blackbody during the freeze for use in SSE corrections.

20 May 2007  Vol. 46, No. 15  APPLIED OPTICS 2875
heatpipe is heated using two cylindrical heaters that

surround the heatpipe, and the alumina tube separates the crucible from the heatpipe to avoid possible

contamination of the pure metal in the crucible from

the Inconel heatpipe liner. The remaining space in

the furnace is filled with fiberglass-insulation material, and the outer jacket is water cooled. Both the Agand Au-freezing points utilize the same furnace and

crucible designs. The temperature uniformity of the

crucible is increased with the use of graphite spacer

rings, which restrict the field of view to f6. The temperature of the crucible is monitored for electrical

heating with a thermocouple encased in a fused-silica

holder in contact with the rear of the crucible. The

furnace is operated as a two-level power control with

different constant-current levels to either initiate the

melt from the solid or to initiate the freeze from the

melt.

A detailed view of the crucible is shown in Fig. 10.

The crucible is constructed of graphite and filled with

1.3 kg of high-purity (99.999% mass fraction) gold.

Although the opening of the blackbody can be made

smaller than a 6 mm diameter with graphite apertures, none were used during these measurements.

The emissivity of the blackbody was determined using Monte Carlo calculations17 based upon the geometry shown in Fig. 10, and the calculated emissivities

are listed in Table 2 for graphite emissivity of 0.86

(col. 2) and 0.80 (col. 3), showing the relative insensitivity of the emissivity calculation with initial conditions. The graphite surface is expected to increase

in emissivity with increasing operational hours owing to surface roughening, and thus the higher

graphite emissivity value was used for this study. A

uniform temperature distribution was assumed for

the calculations with the emissivity of graphite of

0.86 at room temperature.18 These calculated emissivities are in agreement with experimental measurements19 and with other calculations.20

5. Summary of Systematic Corrections to Absolute

Pyrometer

The correction factors listing the dominant systematic corrections to the AP1 signals are listed in Table

3. The AP1 signals were corrected prior to the application of Eq. (1) by using

i  G 	

 im, (5)

where im is the measured photocurrent, i is the corrected photocurrent, G is the gain correction,  is the

emissivity, and 	 is the SSE correction. The corrected

photocurrent can then be directly compared to the

calculated photocurrents in Fig. 5. The gain correction factor is the normalization factor of gain 1010 to

gain 108 as shown in Table 1 since the responsivity

calibrations were performed at gain 108 while the Agand Au-freezing temperatures were measured at gain

1010. The SSE correction will have the effect of reducFig. 9. Schematic of the NIST furnace showing the (1) graphite cavity and the (2) crucible, which is surrounded by the (3) cylindrical heat

pipe, which is heated by the (4) semicylindrical heater elements. The alumina tube separates the crucible from the Inconel liner, and the

argon purge enters from the rear and exits at the front opening of the furnace to reduce oxidation of the graphite elements.

Fig. 10. (Color online) Design of the Ag- and Au-freezing temperature crucibles. The graphite crucible is operated inside a furnace

with Na-heatpipe liner for temperature uniformity. The conical

cavity has an apex angle of 57°.

Table 2. Calculated Emissivity of the Graphite Blackbody Cavity with

50 mm Depth and 57° Conical Bottom and  650 nm with Two

Different Initial Conditions for the Graphite Emissivity

Aperture

Diameter

[mm]

Emissivity with

Graphite Emissivity

  0.86

Emissivity with

Graphite Emissivity

  0.80

6.0 0.99964 0.99943

2.0 0.99996 0.99993

1.5 0.99998 0.99996

1.0 0.99999 0.99998

2876 APPLIED OPTICS  Vol. 46, No. 15  20 May 2007
ing the measured signal since the responsivity calibration was used with a 5 mm diameter opening of

the integrating sphere source with no other source

of radiation outside the opening. The emissivity of

blackbodies will also reduce the radiance, and thus

compensation can be made using Eq. (5).

6. Measurements of the Ag and Au Melts and Freezes

The Au-freezing temperatures were measured over a

2 week period from 15 May 2003 to 28 May 2003.

Since the blackbody power supply can be operated

under computer control, measurements were made

over a 24 h period for each of the runs listed in Tables

4 and 5. A representative Au melt and freeze temperature measurement is shown in Fig. 11. Here the

operation of the furnace is briefly described. Since the

heatpipe furnace liner provides temperature uniformity over the length of the blackbody cavity, the

furnace is operated with two-level constant-current

control of the furnace power supply for inducing either

the melting or the freezing transition. The temperature of the blackbody is held initially at approximately

15 K below the melting temperature, and then the

melting transition is induced by ramping the current

to approximately 9 A and then holding the current at

that level. The time response of the furnace is much

slower than the change in the current due to the thermal capacity of the furnace. The temperature rises up

to the melting temperature and then is made constant

until all the metal is melted. If there are temperature

gradients in the furnace or impurities in the pure

metal, then the rapid temperature rise above the melting temperature is expected to be rounded or less

sharp. After the metal has completely melted with the

temperature of the molten metal at approximately

20 K above the transition temperature, the current is

lowered to approximately 5 A, inducing the freeze. The

temperature of the molten metal decreases until the

supercool, and the freezing transition occurs at slightly

higher temperatures from the supercool. The time duration of the freeze plateau is typically 20 min, and the

duration of the freeze plateau depends on the amount

of the metal, the furnace parameters, and the power

supply setting, among other parameters.

A more detailed view of the melts and freezes with

an expanded temperature scale is shown in Fig. 12.

The melts and freezes are plotted with the thermodynamic temperature scale from the AP1, and a line

at the ITS-90 temperature shows the agreement between the detector-based scale and the ITS-90. Slight

temperature differences of 20 mK are observed between the melting and the freezing temperatures. We

believe that these differences are attributable to the

temperature gradients in the furnace since the differences between the melting and freezing temperatures became 2 mK with a new heatpipe liner and

heating elements. The gradual increase in the freezing temperatures is attributable to the drift in the

dark current in the preamplifier of the AP1 and is not

caused by changes in the Au-freezing temperature.

The dark current correction to the signal was measured only at the beginning of the cycles, and the same

correction was applied to the following melt and freeze

cycles. At the high gains of 1010 VA used for these

measurements, the circuit in the transimpedance amplifier could be susceptible to room-temperature drift

or humidity changes, and dark-current corrections for

each melt and freeze transition led to a reduction in the

temperature drift of less than 10 mK in later studies.

For each freeze, as shown in Fig. 13, a mean temperature was determined with the uncertainties attributable to the averaging process estimated to be less than

5 mK. The noise-equivalent temperature at the Aufreezing temperature is less than 3 mK leading to a

noise-equivalent power of 4 fW. The summaries of

Fig. 11. (Color online) Repeat temperature cycle of melts and

freezes of the Au-point blackbody measured with the AP1 showing

the melt, slight supercool, and the freeze.

Table 3. Systematic Correction Factors to the AP1 Signal

Type of Correction Gain, G Emissivity,  SSE, 	

Signal correction factor 1.0017 0.99964 0.99963

Uncertainty (k  2) 0.022% 0.02% 0.02%

Table 5. Summary of the Ag-Freezing Temperature Measurements

Date No. of Freezes

Temperature

[K]

T-T90

[K]

3 June 2003 9 1235.010 0.080

9 June 2003 8 1234.901 0.029

Average 1234.956 0.026

Table 4. Summary of the Au-Freezing Temperature Measurements

Date No. of Freezes

Temperature

[K]

T-T90

[K]

15 May 2003 12 1337.372 0.042

23 May 2003 12 1337.329 0.001

28 May 2003 10 1337.332 0.002

Average 1337.344 0.014

20 May 2007  Vol. 46, No. 15  APPLIED OPTICS 2877
the all the Ag- and Au-freezing temperature measurements are shown in Figs. 14 and 15, respectively, along

with the ITS-90 temperatures and associated uncertainties.

The discussion of the uncertainties of the measurements must start from the initial uncertainties

arising from the initial realization to the cryogenic electrical substitution radiometer in the NIST

SIRCUS facility, and the component uncertainties

are listed in Table 6. The component uncertainties

arise from the individual transfers and steps as

shown in Fig. 2. The two largest components, lines 4

and 7, are attributable to the spatial uniformity and

the uniformity of the angular output of the integrating sphere and the long-term stability of the trap

detectors. Since the windows in the multielement diode trap detectors are removed to above the multiple

reflections between the windows and the diode surfaces, the power responsivities of the diodes can

change owing to contamination or surface damage.

The final total uncertainty leads to the uncertainties

in Table 7. Additional information on the uncertainties in the detector-based realizations can be found in

Ref. 13.

The individual uncertainties are listed in Table 7 as

a percentage of the signals and then converted to temperature uncertainties. The dominant contribution to

the expanded temperature uncertainties is the uncertainty in the radiance responsivity of 0.15% k  2.

Since the center wavelength of the AP1 is in the

wavelength and temperature region where the Wien

approximation is applicable, the uncertainty of the

temperature from the uncertainty of radiance is

found from the derivative of the Wien approximation

dL

L  c2

dT

T2 , (6)

Fig. 12. (Color online) Plot of the melts and freezes of the Au point on an expanded temperature scale. The slight drift in the temperatures

is attributable to the changes in the dark signal of the AP1.

Fig. 13. (Color online) Representative Au melt and freeze temperatures measured using the AP1. The slight positive slope in the

melt and the negative slope in the freeze is likely attributable to

the size-of-source effect of the AP1.

Fig. 14. (Color online) Summary of the Au-point measurements

with the AP1 with the line indicating the ITS-90 assigned

temperature.

2878 APPLIED OPTICS  Vol. 46, No. 15  20 May 2007
where L is the radiance, is the centroid wavelength,

T is the temperature, and c2 is the second radiation

constant.

7. Discussion

Our detector-based Ag- and Au-freezing temperatures

are in agreement with the measurements of Fox

et al.21 who also used a detector-based filter radiometer

to measure the Ag- and Au-freezing temperatures to be

1235.009 K 0.088 Kand 1337.330 K 0.098 K

respectively. The differences between our temperature determinations and the earlier results by Fox

et al.21 are within the combined uncertainties. The

Au-freezing temperature is also in agreement with

the detector-based measurements of Mielenz et al.22

Our results are also in agreement with the ITS-90

temperatures. The ITS-90 temperature assignments of

the respective freezing temperatures are primarily

from the ratio pyrometry work of Jung and Fischer23

with radiance ratios taken from a lower temperature

blackbody at 730 K. The thermodynamic temperature

of the blackbody was assigned from two conflicting

constant-volume gas thermometry measurements24

with differences of 30 mK at 730 K. Since the difference could not be resolved at the assignments of the

ITS-90 fixed points, a decision was made to compromise between the two results and agree upon a compromise of 15 mK at 730 K, or half the value of the

30 mK difference. Since the uncertainties in temperature increase as

Ta  Ta

2

Tb

2 Tb, (7)

where Ta and Tb are the uncertainties of the blackbody at temperatures Ta and Tb, the resulting thermodynamic temperature offset at 1337 K resulting

from ratio pyrometry is expected to be 50 mK.

In addition to the thermodynamic temperature

uncertainties, the uncertainties in realizing a temperature scale using fixed points include uncertainties due to material purity, emissivity of the cavity,

furnace-temperature uniformity, and furnace operation. Even if the fixed point is filled initially with

ultrapure 99.999%metal, the metal in the blackbody can become contaminated due to operations at

high temperatures, and any contamination will suppress the freezing temperature. To have reproducible

and stable freeze plateaus, the furnace should have

a uniform temperature distribution. The electrical

power heating of the furnace also has to be optimized

to achieve reproducible and flat freeze plateaus. The

dependence of the freezing temperature on the impurities and the operational parameters can lead to

realization uncertainties of 50 mK k  2,24 and temperature scale comparisons can require side-by-side

operation of the respective fixed points to achieve

lower temperature uncertainties.

The transition to detector-based radiance temperatures would lead to better agreement with thermodynamic temperatures and lead to direct dissemination

of thermodynamic temperatures. This transition would

be in accordance with the movement to having defined quantities or fixed values for the fundamental

constants as the basis for the SI units instead of fixed

artifacts as has already occurred for the candela in

1979. The dissemination of detector-based temperatures would also result in having a common basis, the

electrical watt and length units, for photometric, raTable 7. Uncertainty Components for the Ag- and Au-Freezing

Temperature Measurements

Signal Uncertainty Component

[%] (k  2) Ag Au

1 Spectral radiance responsivity 0.15 0.15

2 Temporal stability of

responsivity

0.03 0.03

3 Plateau identification 0.01 0.01

4 Emissivity 0.02 0.02

5 Nonlinearity 0.022 0.022

6 Dark current drift 0.03 0.03

7 Size-of-source effect 0.02 0.02

Total uncertainty in signal 0.16 0.16

Temperature uncertainty

[K] (k  2)

0.110 0.129

Fig. 15. (Color online) Summary of AP1 measurements of the Ag

point along with the ITS-90 assigned temperature.

Table 6. Total Uncertainty of the Spectral Radiance Responsivity

Calibrations in the NIST SIRCUS Facility Broken Down into the

Component Uncertainties

SIRCUS Uncertainty Components (k  1) Type

1 Trapa responsivity B 0.025%

2 Aperture areas B 0.004%

3 Distance B 0.010%

4 Sphere spatial and angular uniformity B 0.050%

5 Amplifier gain A 0.010%

6 Temperature coefficient of trap B 0.003%

7 Temporal stability of trap B 0.050%

Combined standard uncertainty (k  1) 0.076%

Expanded total uncertainty (k  2) 0.153%

a

Trap refers to the Si-diode trap detector used for the realization.

20 May 2007  Vol. 46, No. 15  APPLIED OPTICS 2879
diometric, and temperature scales possibly leading to

a resolution of any inconsistencies in the national

scales. The uncertainties in the SIRCUS-based radiance responsivity calibrations are expected to be near

0.05% k  2in the near future with more frequent

cryogenic radiometer realizations and finer wavelength intervals in the realized wavelengths. The resulting temperature uncertainty at the Au-freezing

temperatures from such improvements is expected to

result in 
50 mK k  2uncertainties.

8. Conclusions

The thermodynamic temperatures of the Ag- and

Au-freezing temperatures are determined to be

1234.956 K 0.110 K k  2 and 1337.344 K

0.129 K k  2 differing from the ITS-90 assigned values of 1234.93 K 80 mK k  2 and

1337.33 K 90 mK k  2 by 26 mK and 14 mK,

respectively. The temperatures are in agreement

with the thermodynamic temperature uncertainties

of the ITS-90 assigned values. The temperatures

were systematically corrected for the size-of-source

effect, the linearity of the preamplifier, and the emissivity of the blackbody. The ultimate goal of these

thermodynamic temperature measurements is to disseminate temperature scales with lower uncertainties than those of the ITS-90. These results indicate

that direct disseminations of thermodynamic temperature scales are possible.

Certain commercial equipment, instruments, or

materials are identified in this paper to foster understanding. Such identification does not imply recommendation or endorsement by the National Institute

of Standards and Technology nor does it imply that

the material or equipment are necessarily the best

available for the purpose.

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Inst. Stand. Technol. 104, 11– 46 (1999).

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10. N. P. Fox, J. E. Martin, and D. H. Nettleton, “Radiometric

aspects of an experiment to determine the meltingfreezing

temperature of gold,” Metrologia 28, 221–227 (1991).

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lumen,” Metrologia 11, 97–104 (1975).

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W. G. Sainty, “Ion-beam-assisted deposition of thin films,”

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2880 APPLIED OPTICS  Vol. 46, No. 15  20 May 2007
29 4A Vol. 29, No 4A 

2008 10 ACTA METROLOGICA SINICA October, 2008 

Uncertainty Analysis and Maintenance of the NIST Detectorbased Temperature Scale 

H. W. Yoon, C. E. Gibson, G. P. Eppeldauer, A. W. Smith, 

S. W. Brown, K. R. Lykke 

 (Optical Technology Division 

National Institute of Standards and Technology 

Gaithersburg, MD 20899 USA) 

Abstract: Thermodynamic temperatures can be directly determined using the Planck radiance law and detector-based 

radiation thermometers. Although the final uncertainties in the detector-based radiation thermometry can be lower than 

in the ITS-90 based temperatures, detailed uncertainty analyses for each step of the detector-based realization are needed 

to validate these low uncertainties. We list the measurement steps in the detector-based temperatures and also describe 

the characterizations in determining the measurement uncertainties for each of the steps. We further describe measures 

to maintain the low uncertainties obtained from the radiometric calibrations. 

Key words: Thermodynamic temperature; Temperature measurement; Radiation Thermometry; Uncertainty Analysis

CLC number: TB94 Document code: A Article ID: 1000-1158(2008)04A-0000-00 

 Received: 2008-00-00 

Corresponding e-mail address: hyoon@nist.gov

1. Introduction 

A fundamental goal in the establishment of the 

Système International d'Unités (SI) is to base the SI 

units on constants which are invariant in space and 

time. The movement to define the SI units based upon 

fundamental physical constants and, in particular, to 

adopt a fixed Boltzmann constant as the basis of the 

unit of temperature, the kelvin, is in pursuit of this 

goal [1]. With the redefinition of the kelvin, work is 

underway in the Consultative Committee on Thermometry (CCT) to give guidance on the practical realization of the kelvin or the mise en practique (MeP). 

The new MeP will include descriptions and references 

to all primary thermometry techniques including, 

among others, constant-volume gas thermometry, 

acoustic thermometry, noise thermometry, dielectricconstant gas thermometry, and detector-based radiation thermometry [2]. The MeP will also list the uncertainties associated with each of these primary 

thermometry techniques. The common value linking 

these different methods is the fixed Boltzmann constant which also fixes the kelvin temperature scale. 

Presently, the International Temperature Scale of 

1990 (ITS-90) defines the kelvin scale and is used 

successfully in most applications. However, the 

greatest weakness of the ITS-90 is recognized to be at 

temperatures above the Ag freezing temperatures 

where temperatures are defined by the use of Planck 

radiance ratios from either the Ag-, Au- or the Cufreezing temperature blackbodies [3]. This weakness 

is due to the use of extrapolations to higher temperatures from the defining fixed point using radiation 

thermometers which can have many systematic biases 

which, in turn, can lead to large temperature differ-
ences. Detector-based radiation thermometry is primary thermometry which can lead to lower uncertainties than in ITS-90 based temperatures, but the uncertainty components need to be characterized and measured. 

In this work, we describe the uncertainty components in the detector-based radiation thermometry 

where the radiance responsivity of the radiation thermometer is measured using a tunable laser-irradiated, 

integrating sphere source. The uncertainty analysis 

is separated into those related to the calibrations of the 

radiance responsivity and the characterizations of the 

radiation thermometer. Both spatial and angular uniformity characterizations of the integrating sphere 

used in the realization are described. The interference fringes observed at the peak of the radiance responsivity is analyzed to determine the thickness of 

the layer causing the interference fringes. This listing of the uncertainty components will assist other 

laboratories attempting to develop similar primary 

thermometry capabilities. 

2. Detector-based Radiance Responsivity 

Calibrations 

The spectral radiance responsivity calibrations are 

performed in the NIST Spectral Irradiance and Radiance responsivity Calibrations using Uniform Sources 

(SIRCUS) facility [4]. In Tab. 1, the uncertainty 

Tab. 1 The total uncertainty of the radiance responsivity calibrations in the NIST SIRCUS facility broken down into the 

component uncertainties. Trap refers to the Si-diode trap detector used for the realization. 

 

SIRCUS Uncertainty Components 

(k = 1) Type [ % ] 

1 Trap responsivity A 0.025 

2 Aperture Area A 0.004 

3 Distance B 0.01 

4 

Sphere Spatial and 

Angular Uniformity B 0.025 

5 Amplifier gain A 0.005 

6 

Temperature coefficient of Trap B 0.002 

7 

Temporal Stability of 

Trap B 0.013 

 

Combined Standard 

Uncertainty (k = 1) 0.040 

 

Expanded Uncertainty (k = 2) 0.080 

components of the detector-based radiance responsivity calibrations are listed. Although these uncertainties are discussed in Ref. 4, additional measurements 

to support the uncertainties have been further performed since the initial publication about the SIRCUS 

facility. 

2.1 Si-trap detector responsivity 

At NIST, the detector-based radiation thermometry 

begins with the calibration of detectors using the Primary Optical Watt Radiometer (POWR) [5] which is a 

cryogenic electrical substitution radiometer. Cryogenic radiometers have been compared against each 

other using Si-trap detectors and have been found to 

be in agreement to within 0.012 % (k=1). In the 

wavelength region from 400 nm to 920 nm, the Sitrap detector is calibrated against the POWR in the 

NIST SIRCUS facility for spectral power responsivity 

at many different laser wavelengths as shown in Fig. 1. 

Since there is some scatter in the measurements, multiple measurements at various wavelengths are fitted 

using a modified Gaussian-Lorentzian fit and the residuals from this fit are shown in Fig. 1. Although 

the physical model of the quantum efficiencies is 

typically used to fit the spectral power responsivity of 

the trap detectors [6], such fitting is not needed if 

many laser wavelengths are used for the calibrations. 

The residuals of the measurements from the fitted 

functions are distributed evenly about the zero crossing. 

200 400 600 800 1000 1200 -1.5x10-3

-1.0x10-3

-5.0x10-4

0.0

5.0x10-4

1.0x10-3

1.5x10-3

Residuals from fit

Wavelength [ nm ]

Fig. 1 The residuals of the fitted spectral power responsivity 

of the trap detector from the individual measurements 
2.2 Aperture area uncertainties 

The uncertainties in row 2 of Tab. 1 are due to the 

aperture areas on both the trap detector and the integrating sphere sources (ISS), and the uncertainties in 

row 3 are due to the uncertainty in the separation distance between the precision aperture on the ISS and 

the trap detector. An international key comparison of 

aperture areas was recently completed to determine 

the whether the measurements at the different national 

measurement institutes (NMI) were within their stated 

uncertainties [7]. The comparison showed that the 

uncertainties of an individual laboratory for certain 

type of apertures could be at the value cited in Tab. 1 

but the differences between the NMIs could be larger 

than the uncertainties cited by the NMIs. 

 2.3 Distance measurement uncertainties 

The distance between the ISS and the trap detectors 

are determined through a modified 1/r2

 fit, 

( )2

o

o

rr

S

−

 (1) 

where both the amplitude, So, and the offset distance, 

r0, are fitted parameters using and the uncertainties are 

determined from the residuals of the fit. Furthermore, 

presence of scattered radiation from improper baffling 

can be determined from the residuals of the 1/r2

 fit. 

 2.4 Amplifier gain uncertainties 

The uncertainties in the amplifier gains are attributed 

to the uncertainties in the current-to-voltage conversion of the transimpedance amplifiers. The current 

measurements are performed with custom-designed 

preamplifiers with gains determined by high-precision, 

metal-film, feedback resistors in the operational amplifier circuit. The preamplifier gains are determined 

from electrical resistance calibrations of the feedback 

resistors. Care should be taken that the current-tovoltage conversion is linear since the parallel connections of the Si diodes in the trap detector results in a 

shunt resistance of the trap detector being lower than 

the shunt resistance of any single diode element. 

2.5 Si-trap detector temperature dependence and 

long-term stability 

 The next two rows in Table 1 are due to the temperature dependence of the trap detector responsivity 

and the long-term stability of the trap detector. Since 

the trap detector is constructed from three or more Si 

diodes which could have a temperature dependence, 

change in the spectral power responsivity could result 

from the temperature difference between the calibration against the cryogenic radiometer and the subsequent use of the trap detector. Such temperature dependence is expected to be greater near the band-gap 

energy of the Si diode. 

Since the trap detectors are only calibrated on an 

annual or biennial basis, the responsivity could 

change over time. The trap detectors are constructed 

using Si diodes without any windows, and any change 

in the reflectance of Si diodes due to oxide accumulation would be compensated by the increase in the 

photocurrent of the other Si diodes. Although, the 

trap detectors are stored in dust-free containers when 

not in use, any particulate contamination would lead 

to a change in the responsivity. Such contamination 

is evident in the change in the spatial uniformity of 

the trap detector or changes in the power responsivity 

when compared to the other sets of trap detectors. 

The results of the annual calibrations of the working 

standard trap detectors T-01 and T-02 are shown in 

Table 2. The power responsivities are determined by 

comparison against the cryogenic radiometer and the 

Tab. 2 The external quantum efficiencies of trap detectors T01 and T-02 with repeat calibrations in 2005, 2006 and 2007. 

Year 

Wavelength 

[ nm ] 

T-01 External Quantum 

Efficiency 

(EQE) 

T-02 External 

Quantum 

Efficiency 

(EQE) 

Ratio 

(T-1 

EQE/T02 EQE) 

2005 649.906 0.99573 0.99772 0.99801 

2005 649.9 0.99583 0.99778 0.99804 

2006 647.1600 0.99543 0.99766 0.99777 

2006 647.1400 0.99545 0.99766 0.99778 

2006 647.1200 0.99545 0.99768 0.99777 

2007 653.81 0.99566 0.99783 0.99783 

2007 653.84 0.99564 0.99785 0.99779 

external-quantum efficiencies (EQE) are determined. 
The slight differences in the wavelengths of the measurements and the resulting differences in the EQE are 

not significant, and if the trap detector has remained 

temporally stable, then the EQE’s are expected to repeat within the assigned uncertainties. One way to 

determine if the trap detectors have remained stable is 

to plot the ratios of the EQE’s of the trap detectors 

over time as shown in Fig. 2. The mean value of the 

ratios is indicated by the middle line and the expanded 

uncertainties assigned to the temporal stability of 

0.026 % is shown by the bracketing dotted lines. 

The data indicates that the temporal stabilities of the 

trap detectors are adequately accounted by the assigned uncertainties. 

2005 2006 2007

0.9972

0.9974

0.9976

0.9978

0.9980

0.9982

0.9984

Ratio ( T-01 EQE / T-02 EQE )

Year

Fig. 2 The ratios of the EQE’s of the trap detectors T-01 and 

T-02 over time shown with the mean and the assigned expanded uncertainties of 0.026 % indicated by dotted lines. 

3. Spatial Uniformity of the Integrating 

Sphere Source 

One of the most important characterization steps in 

the detector-based radiance responsivity is the measurements of the spatial and angular uniformity of the 

ISS. When the radiation thermometer is calibrated 

for radiance responsivity, the ISS acts as a monochromatic substitute for a blackbody, and the radiance 

output of the ISS, in turn, must be as uniform and 

lambertian as a Planckian source. It is difficult to 

have the ISS achieve the spatial and angular uniformity of a blackbody, since unlike a blackbody, the radiation enters from one or few ports and is reflected. 

The high emissivity of the blackbody is achieved by 

having every surface inside the blackbody emitting at 

a uniform temperature. 

 The spatial uniformity of the ISS can be measured with a radiometer which can be limited to a small 

field of view. The spatial uniformities of different 

diameter integrating sphere sources with 5 mm diameter openings measured with a radiometer limited to 

1 mm spot size at f/12 geometry are shown. Fig. 3 

shows the spatial uniformity of the 25 mm diameter 

sphere with the 5 mm diameter opening. All the ISS 

used in this study are internally coated with sintered 

polytetrafluoroethylene (PTFE) for the highest reflectance over a wide range of wavelengths. The laser is 

introduced into the ISS with a fiber input at 90 ° at the 

side of the sphere. Due to the small size of the 

sphere, the bright illumination of the initial bounce 

from the laser can be seen as a spatial non-uniformity 

of 0.1 % toward the upper right of the figure. -5-4-3-2-1

012345 -5

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

X axis [ mm ]

Y axis [ mm ]

1.0045-1.005

1.004-1.0045

1.0035-1.004

1.003-1.0035

1.0025-1.003

1.002-1.0025

1.0015-1.002

1.001-1.0015

1.0005-1.001

1-1.0005

0.9995-1

0.999-0.9995

0.9985-0.999

0.998-0.9985

0.9975-0.998

0.997-0.9975

0.9965-0.997

0.996-0.9965

Fig. 3 The spatial uniformity of the 25 mm diameter PTFE 

sphere with a 5 mm diameter opening. The insufficient mixing of the radiation can be observed from the non-uniformity of 

0.1 % toward the upper right side. 

Two other PTFE-lined ISS with 38 mm and 300 mm 

diameters have also been measured for spatial uniformity as shown in Figs. 4 and 5 with the same intensity scales as in Fig. 3. As expected, the spatial uniformity is found to increase with the diameter of the 

sphere. The throughput of the sphere decreases with 

increasing diameter so that the incident laser power 

must be increased to obtain the same irradiances or 

radiances as with the smaller diameter spheres. 
-5

-4-3-2-1

012345 -5

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

X axis [ mm ]

Y axis [ mm ]

1.0045-1.005

1.004-1.0045

1.0035-1.004

1.003-1.0035

1.0025-1.003

1.002-1.0025

1.0015-1.002

1.001-1.0015

1.0005-1.001

1-1.0005

0.9995-1

0.999-0.9995

0.9985-0.999

0.998-0.9985

0.9975-0.998

0.997-0.9975

0.9965-0.997

0.996-0.9965

Fig. 4 The spatial uniformity of the 38 mm diameter PTFE 

sphere with a 5 mm diameter opening. A center spot introduces a nonuniformity of 0.05 %. -5-4-3-2-1

012345 -5

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

X axis [ mm ]

Y axis [ mm ]

1.0045-1.005

1.004-1.0045

1.0035-1.004

1.003-1.0035

1.0025-1.003

1.002-1.0025

1.0015-1.002

1.001-1.0015

1.0005-1.001

1-1.0005

0.9995-1

0.999-0.9995

0.9985-0.999

0.998-0.9985

0.9975-0.998

0.997-0.9975

0.9965-0.997

0.996-0.9965

Fig. 5 The spatial uniformity of the 300 mm diameter PTFE 

sphere with a 5 mm diameter opening. The large sphere with 

a small opening results in uniformity of 0.025 %. 

4. Angular Uniformity of the Integrating Sphere 

Source 

The angular uniformity of the ISS can be measured 

with a trap detector with a characterized angular responsivity. If the internal diodes which form the trap 

configuration are not well aligned, then the angular 

responsivity of the trap detector will not be symmetric 

and be independent of the angular direction. Once 

the trap detector has been characterized, the ISS can 

be measured for angular output. The optical layout 

of the radiometric measurements is shown in Fig. 6. 

The integrating-sphere source is shown at left and the 

precision aperture of the trap detector is shown on the 

right. If the two apertures are translated in a perpendicular plane then the closest distance between the 

two apertures is indicated by the distance d, and the 

distance between the apertures when the trap detector 

is out of the plane is given by the distance r. For the 

optical configuration shown in Fig. 6, the relationship 

between r and d is given by d = r cos θ, where θ is the 

angle between the centers of the ISS and the trap detector. In addition to the change in the distance between the ISS and the trap detector, the projected areas of both the source and the detector apertures decrease by the cos θ, leading to a relationship between 

the irradiance at r as compared to the irradiance at 

position d, 

( ) ( ) θ 4 = dErE cos . (2) 

Thus, a plot of the normalized signal versus angle can 

A cosθ θ

d

θ

r

B cosθ

Fig. 6 The optical schematic for determining the angular uniformity of the irradiance at the plane of the trap detector. 

be fitted with Eq. 2 to determine any deviations from 

lambertian output of the ISS. The irradiance ratios 

are plotted in Fig. 7 and shown to be in agreement 

with Eq. 2 within ± 0.05 radian. 

-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.992

0.993

0.994

0.995

0.996

0.997

0.998

0.999

1.000

1.001

 cos4 δ

 Measured

50 mm diameter at 500 mm

Irradiance ratio [Eδ /Eo

]

Angle δ [ radian ]

Fig. 7 The irradiance ratios to the center measured by scanning the trap detector. Although the detector was scanned in 

the x and y planes, a one dimensional plot is shown to better 

demonstrate the fit to cos 4 θ dependence. 
5. Radiation thermometer uncertainties 

0.0

5.0x10-5

1.0x10-4

1.5x10-4

2.0x10-4

2.5x10-4

3.0x10-4

The uncertainties for the use of the radiation thermometer in measuring the temperature of fixed-point 

blackbodies are shown in Tab. 3. The uncertainty of 

the spectral radiance responsivity is transferred from 

Tab. 1, but additional uncertainties arise in the specific use of the radiation thermometer. One of the 

largest uncertainty components is due to the temporal 

stability of the responsivity arising from the change in 

the radiation thermometer throughput. The change in 

the throughput could be due to many factors such as 

the changes from the filter transmittance, the detector 

responsivity, contamination of the optics or structural 

changes of the radiation thermometer related to 

changes in the ambient temperature, among others. 

Although care is taken to design the radiation thermometer to minimize such unpredicted changes, it is 

difficult to eliminate all sources of temporal changes. 

645 650 655

Radiance Responsivity, A / W / cm2 nm sr

Wavelength [ nm ]

Fig. 8 The radiance responsivity of the NIST Absolute Pyobserved from the chang in the amplitude of the 

Tab. 3 Uncertainty components for a fixed-point blackbody 

temperature determination. 

Uncertainty Component [ % ]

1 Spectral Radiance Responsivity 0.040 

2 Temporal Stability of Responsivity 0.050 

3 Plateau Identification 0.005 

4 Emissivity 0.010 

5 Preamplifier Gain 0.025 

6 Dark current drift 0.015 

7 Size-of-source effect 0.010 

Total Uncertainty in Signal 0.072 

Expanded Uncertainty (k =2) 0.144 

Temperature Uncertainty [ K ] (k =2) 0.116 

The low uncertainty of the wavelength and dynamic 

range of the responsivity calibrations are made possible by the use of laser-based responsivity calibrations. 

However, due to the narrow linewidth of the lasers, 

interference fringes can be present in the responsivity 

calibrations. The radiance responsivity of the NIST 

Absolute Pyrometer 1 (AP1) is shown in Fig. 8. The 

interference fringes are observed at the peak of the 

responsivity, and the additional modulation can be 

rometer 1 (AP1) showing the interference fringes at the peak. 

es

interference fringes. The thickness of the material 

responsible for the interference fringes can be determined from 

λ = cosnd2m φ (3) 

where m is an integer, λ is the wavelength of the radiation, n is the refractive index, d is the thickness of 

the material, and φ is the incident angle of the radiation. For determining the cause of the interference 

fringes, an expanded plot of the peak responsivity is 

shown in Fig. 9. In Fig. 9, the interference fringes 

are found to be temporally stable with repeated calibrations from 2003 to 2006. Since the wavelength 

interval between the fringes can be measured from Fig. 

9, the thickness of the material can be found using 

Δχ = n2

1 d , (4) 

where 

1

11

+

−=Δ

λλ mm

χ . (5) 

If the refractive index is assumed to be 1.55 then the 

thickness of the material which results in the interference fringes seen in Fig. 9 is estimated to be 0.67 mm. 

Although the interferences could arise from several 

different sources, the fringes in the AP1 are determined to be from an element in the interference filter 

centered at 649.5 nm. At first, the protective window 
on the thermo-electrically cooled diode was postulated to cause the interference fringes. Both roughening the window surface and increasing the thickness 

of the window by gluing an additional glass window 

did not affect the fringes. However, when the Lyot 

stop diameter was increased, the amplitudes of the 

fringes were reduced, and the amplitudes increased 

with a decrease in the Lyot stop diameter. Since the 

Lyot stop is placed directly in front of the interference 

filter, one explanation for this behavior is that a layer 

within the filter is the cause of the fringes. The total 

thickness of the interference filter is about 11 mm so 

that the front and back surfaces of the filter are not the 

source of the fringes as estimated from Eq. 4. If this 

layer inside the filter has interfaces which are not parallel over the entire area of the filter, then the radiation is expected to have a greater degree of destructive 

interference when the radiation is transmitted over a 

larger surface of the filter. 

647 648 649 650 651 652

2.60x10-4

2.70x10-4

Radiance Responsivity, A / W / cm2 nm sr

Wavelength, nm

 March 2005

 June 2003

 November 2006

 June 2005

Fig. 9 An expanded plot of radiance responsivity showing the 

he presence of the fringes are not problematic if 

the r

uncertainties. 

y uncertainties 

uncertainty due to the 

lateau identification is low due to the long time duras of the radiation 

ermometer 

plifier gain during the calibration of 

e radiance responsivity and the use of radiation 

 the detector-based radiation therometry have been discussed and the experimental 

changes with each calibration and the persistence of the interference fringes.

T

adiance responsivity calibrations can adequately 

measure the peaks and valleys of the fringes, but the 

number of calibrations at the different wavelengths 

could be extremely time consuming. Furthermore, if 

the amplitude of the fringes were much larger than the 

< 2 % observed, then the sharp radiance responsivity 

changes with wavelength would require lower wavelength uncertainties. Any wavelength fluctuations of 

the source would be magnified by the amplitude 

changes of the responsivity function resulting in large 

6. Blackbod

For fixed-point blackbodies the 

p

tion of the freeze. Since the cavity is also surrounded 

by a constant temperature material undergoing the 

phase transition, the emissivity of the cavity is high 

and can be determined with low uncertainties. The 

uncertainties related to the use of fixed point blackbodies are well understood [8]. 

7. Systematic uncertaintie

th

Since the pream

th

thermometer can be different, uncertainties arise when 

the RT is used to measure blackbody temperatures 

which can vary widely in radiance. The size-ofsource effect can be controlled to low levels by using 

clean, low-scatter optics and a Lyot stop [9]. The 

additional sources of uncertainties are discussed in a 

prior publication [10]. The total uncertainties at the 

bottom of Tab. 3 are then converted to temperature 

uncertainties using the derivative of the Wien approximation as discussed in Ref. 10. 

8. Conclusions 

The uncertainties in

m

results for determining those uncertainties have been 

shown. The critical characterizations related to the 

fitting of the quantum efficiencies of the trap detectors 

and their long-term stabilities are shown. The spatial 

and angular uniformity of the integrating sphere 

sources are shown and found to be dependent on the 

ratio of the opening of the sphere to its internal surface area. The interference fringes observed in the 

radiance responsivities are described and minimized 

by increasing the radiated area on the spectrally selective filter. These characterizations are needed if the 

direct realizations of thermodynamic temperatures are 

to achieve lower uncertainties than the ITS-90 based 

temperatures. 
8 ACTA METROLOGICA SINICA 2008, October 

REFERENCES 

1. I. M. Mills, P. J. Mohr, T. J. Quinn, B. N. Taylor, and E. R. 

Williams. Metrologia. 2006, 43 (3): 227-246. 

2. B. Fellmuth, Ch. Gaiser, and J. Fischer. Meas. Sci. Technol. 

2006. 17 (10): R145-R159. 

3. Supplementary Information for the International Temperature Scale of 1990, H. Preston-Thomas, P. Bloembergen, T. J. 

Quinn, Sèvres, Bureau International des Poids et Mesures, 

1990. 

4. S. W. Brown, G. P. Eppeldauer, K. R. Lykke. Applied Optics. 2006, 45(32): 8218-8237. 

5. J. M. Houston, J. P. Rice. Metrologia. 2006. 43(2): S31-

S35. 

6. T. R. Gentile, J. M. Houston, and C. L. Cromer. Applied 

Optics. 1996, 35(22): 4392-4403. 

7. M. Litorja et al. Metrologia. 2007, 44: 02002. 

8. P. Saunders et al. International Journal of Thermophysics. 

2008, 29:1066–1083. 

9. H. W. Yoon, D. W. Allen, and R. D. Saunders. Metrologia. 

2005, 42(2): 89-96. 

10. H. W. Yoon, D. W. Allen, C. E. Gibson, M. Litorja, R. D. 

Saunders, S. W. Brown, G. P. Eppeldauer, K. R. Lykke, Applied 

Optics. 2007, 46(15): 2870-2880.
SSE- and noise-optimized InGaAs radiation thermometer 

H W Yoon , C E Gibson , V Khromchenko, G P Eppeldauer 

Optical Technology Division 

National Institute of Standards and Technology, Gaithersburg, USA 

Abstract 

For the measurements of radiance temperatures in the range from 150 °C to 1000 °C, low 

uncertainties in the temperature measurements can be achieved by using near-infrared InGaAs 

radiation thermometers. We describe the design and construction of the NIST near-infrared 

radiation thermometer (NIRT) which is optimized for low size-of-source effect and noiseequivalent temperatures. The NIRT utilizes a 50 mm diameter achromatic objective lens with 

low scatter which images a 4.5 mm diameter spot at a distance of 50 cm away from the objective 

in an on-axis design. A Lyot stop is implemented in the design with the aperture stop placed after 

the field stop resulting in a collection f/# = 12. A 3 mm diameter InGaAs detector is cooled to –

85 °C using a 4-stage thermoelectric cooler to obtain high-shunt resistance for linear, low-noise 

operation at high trans-impedance amplifier gains. For thermal and structural stability, the optical 

components are placed on four 15 mm diameter graphite-epoxy rods making the optical 

throughput stable. Optical ray tracing using a commercial program was used to determine the 

Strehl ratio and other imaging parameters. We discuss a possible approach for detector-based 

temperature scale in this range which could result in 10 mK (k = 2) thermodynamic temperature 

uncertainties at the In-point. 

KEY WORDS: radiance temperature, ITS-90, thermodynamic temperature, size-of-source 

effect, near-infrared radiation thermometer, noise-equivalent temperature difference 
1. INTRODUCTION 

Accurate determinations of radiance temperatures from 150 °C to 1000 °C are important for 

calibration of radiation thermometers which are used in turn for process control or used to 

transfer the calibration to other radiation thermometers. In this temperature range, one can 

establish a scale on radiation thermometers from the International Temperature Scale of 1990 

(ITS-90) using the ITS-90 fixed-point blackbodies (FPBBs) from the In-point to the Ag-point and 

applying an interpolation functional fit or by the use of a variable-temperature blackbody (VTBB) 

whose temperatures are determined using contact platinum resistance thermometers (PRT) [1]. 

In both approaches, the FPBB or the VTBB emissivity has to be measured or modeled so that th

lowest uncertainties in the transfer to the radiation thermometer can be achieved. International 

comparisons of scales in this temperature range has revealed that the lowest uncertainties in 

radiance temperatures can be achieved using the fixed-point interpolation technique instead of 

using a variable-temperature blackbody [

e 

2]. The lower uncertainties by utilizing the fixed-points 

are possible since the temperature is well known with high spatial uniformity of the cavity. 

Variable-temperature blackbodies are expected to have greater issues with achieving uniform 

temperature distributions within the cavity. 

Although the method of calibrations using fixed-points is well established, commercial radiation 

thermometers which are temporally stable and able to view the small cavity openings of the 

FPBBs are not readily available. Furthermore, custom InGaAs radiation thermometers 

constructed by the national measurement institutes have conflicting designs [3,4]. Although 

reduction of size-of-source effect is a critical design feature due to the comparison of small-area 
fixed point blackbody cavities to large variable-temperature blackbody openings, implementation 

of the Lyot stop has been lacking. 

In this paper, we describe a generalized design for an InGaAs-based radiation thermometer (RT) 

capable of measurements from the In-point to the Ag-point. The radiation thermometer also 

incorporates a Lyot stop while utilizing a low-scatter objective lens. The construction utilizes 

carbon-epoxy rods for structural stability with temporal stability of the responsivity increased by 

the use of room temperature-stabilized filter and cooled detector. The detector is contained in a 

hermetically sealed package to decrease the detector temperature in order to increase the shunt 

resistance for low-noise operations. It is hoped that instrumental designs discussed in this paper 

can be adopted in future radiation thermometer designs to improve the performance of transfer 

standard radiation thermometers. 

2. RADIATION THERMOMETER CHARACTERIZATION 

2.1 Physical Design 

The schematic of the radiation thermometer is shown in Fig. 1. The internal elements are 

mounted on four 15 mm diameter graphite-epoxy rods for structural stability. The graphiteepoxy rods have a coefficient of thermal expansion (CTE) of -0.5 x10-6 mm/mm which is smaller 

than that of fused silica [5]. The rods are attached to the front plate holding the objective lens 

and the various separation between the optical elements can be smoothly adjusted by sliding 

through rods. The angled field stop is constructed from polished stainless steel with a beveled 

3 mm diameter hole. The field stop angled to reduce the back reflection of the image onto the 

objective lens thus reducing the SSE. The specular reflection from the field stop is directed to a 

flat mirror for viewing through the telescope objective. The radiation through the field stop is 

the 
collimated by the 70 mm focal length achromat and the plane of the objective lens is focussed 

onto the Lyot stop. The presence of the Lyot stop is critical in reducing the SSE. 

333

Ø3.0 [Ø0.118]

130.0 [5.118]

100.0 [3.937]

50.0 [1.969]

FIELD MAIN LENS SHUTTER

STOP

LENS LYOT 

STOP FILTER DETECTOR 

LENS AMPLIFIER DIODE LASER and SPLITTER

Eyepiece

Figure 1. The schematic of the InGaAs-based radiation thermometer. The outer diameter of the main 

body is 20.3 cm with a total length of 75 cm excluding the front baffle. 

The room-temperature stabilized interference filter is constructed using hard, ion-assisted 

deposited layers at a center wavelength of 1550 nm. The full-width at half-maximum bandpass 

of the filter is 100 nm. Due to the 4-stage thermoelectric cooler which limits the maximum size 

of the regular InGaAs detector, a 3 mm diameter detector is used. The detector lens focusses the 

3 mm diameter object at the field stop onto a 1.5 mm diameter region on the detector, leading to 

an underfilled detector. 

The outer case of the radiation thermometer is floating from the optical elements which are 

attached to the graphite rods and is only fixed at the middle supporting plate. The case is 

constructed using 1.83 mm thick anodized aluminum tubing. The use of the al tube facilitates 

rapid thermal equilibrium between the laboratory temperature and the internal temperatures. The 
heat-sink plate for the InGaAs detector is additional thermally connected to the external tubing 

with copper-braided contacts which work to dissipate the heat generated from the TE cooler. We 

are able to achieve -85 °C with only passive cooling without the use of fans. Additional 

information on the construction of the radiation thermometer is given in Table 1. 

Table 1. The design parameters of the InGaAs radiation thermometer (RT). 

Object Distance 50 cm 

Image Distance 33.3 cm 

Objective Focal Length 20 cm 

Field Stop Diameter 3.0 mm 

Target Diameter 4.5 mm 

f/# 12 

Lyot Stop Diameter 8 mm 

Detector Type InGaAs 

Detector Diameter 3 mm 

Detector Temperature -85 °C 

Filter Center Wavelength 1550 nm 

Filter FWHM bandpass 100 nm 

Filter Temperature 22 °C 

Collimator Lens Focal Length 70 mm 

Detector Lens Focal Length 35 mm 

Image Diameter on Detector 1.5 mm 

RT Diameter 20.3 cm 

RT Length 76.2 cm 

2.2 Detector optimization 

The most important aspect of radiation thermometer design is the selection of the detector to be 

used in the radiation thermometer. Due to the linearity and the wavelength region of the spectral 

power responsivity, regular InGaAs diode was chosen. Since the small target diameter and the 

f/# limits the throughput of the RT, the preamplifier should have a dynamic range from 1010 V/A 

to 105

 V/A for measurements of blackbodies from the In-point to the Ag-point. In a transimpedance amplifier circuit, the shunt resistance of the input diode should have a value greater or 
equal to the feedback resistance for linear, low noise amplification of the current. The 

measurement of the shunt resistances of both 1 mm diameter and 3 mm diameter InGaAs diodes 

in Fig. 2 shows that the shunt resistances have a semi-logarithmic relationship to temperature. 

-40 -20 0 20 40

106

107

108

109

1010

1011

 IGA3mm

 IGA1mm

 IGA3mm2

Shunt Resistance, 

Ω

Temperature, oC 

Fig. 2. The temperature-dependent shunt resistances of 1 mm and 3 mm diameter 

InGaAs diodes. The shunt resistance of the diode should be comparable to the feedback 

resistance of the preamplifier circuit for low noise, linear operation. 

The shunt resistances also increase as linear function of the detector area as expected for a defects 

with a uniform surface density. The Fig. 2 shows that for 1 mm diameter diodes, shunt 

resistances of > 1010 Ω are achieved at detector temperatures of - 20 °C which is possible with 2-

stage TE cooling. For 3 mm diameter diodes, detector temperatures of at least - 40 °C are needed 

to achieve > 1010 Ω shunt resistance. Unless the diode material quality is improved, larger diode 

are expected to require greater cooling to obtain the same shunt resistances. 
2.3 Temperature-dependent detector performance 

The importance of the ability to cool the detector to below ambient temperature is shown by 

Fig. 3. The equivalent dark current (calculated from the output offset voltage in dark) and its 

standard deviation at a preamplifier gain of 1010 V/A are shown. The standard deviations are 

measured using 10 measurements at number of power-line cycles (NPLC) of 10 or 0.13 Hz. The 

equivalent dark current is only weakly dependent on the detector temperature with a decrease 

from 3 pA to about 1 pA as the detector is cooled from room temperature to -70 °C. The change 

in the dark current with decreasing temperature indicates that the stabilizing the detector 

temperature is important in avoiding dark-current drift, especially at the In point where the net 

photocurrent is only about 23 pA. With cooling of the detector, the standard deviation of the 

equivalent dark current changes much more, from about 100 fA to 2.4 fA. 

1

10

100

-80 -60 -40 -20 0 20 40

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

 St. Dev., fA

Dark Current, pA 

Detector Temperature, o C 

Fig. 3. Equivalent dark current and its standard deviation versus temperature. 
Although the detector was cooled to lower temperatures than -70 °C, the heat generated from the 

TE coolers could not be readily dissipated which lead to self heating of the detector. We 

observed a slow drift of the equivalent dark current when the temperature of the detector was set 

to lower temperatures which precluded stable measurements of standard deviations of the 

equivalent dark current. These measurements indicate that close to Si-type performance of few 

fA noise-equivalent current [6] is possible with 4-stage TE cooling. This low-noise performance 

is especially important at the In-point where any decrease in the noise-equivalent power directly 

leads to a decrease in the noise-equivalent temperatures. 

2.4 Size-of-source effect 

Since the radiation thermometer is designed for transfer of the ITS-90 temperatures to other 

blackbodies, the suppression of the SSE in comparing small fixed-point cavities to larger area 

variable temperature blackbody cavities is critical. In the design of a radiation thermometer to 

have small SSE, it is important to use a low-scatter objective lens in addition to the incorporation 

of a Lyot stop [7]. Although SSE can be changed by removing the objective lens, such drastic 

steps will result in decrease of the entrance pupil leading to extremely low throughput and 

inability to measure at low temperatures due to the high noise. Furthermore, the introduction of 

any element which can lead to further scatter into the field stop should be discouraged such as 

protective windows or viewing beamsplitters which are directly in the optical path of the 

radiation. The SSE measured using a 10 mm diameter central obscuration is shown in Fig. 4. 

The measurements are performed using a high-power 1 W LED source as described 

previously [8]. The LED source has sufficient output in the near infrared wavelength region for 

these measurements. The low SSE measured at 50 mm source diameter indicates that our design 

is effective at suppressing internal scatter. The comparison of the SSE in terms of temperature 
corrections are shown in Table 2 with SSE of 7x10-5 and 1x10-3 converted to their temperature 

corrections at the respective fixed points. If the SSE can be reduced to 7x10-5 then the 

corrections can be included as terms in the total uncertainty budget, while larger SSE require 

systematic correction terms as shown in Table 2. 

0 5 10 15 20 25 30 35 40 45 50 55

0.0

2.0x10-5

4.0x10-5

6.0x10-5

8.0x10-5

SSE 

Diameter, δ , mm 

Fig. 4. The SSE measured using a central obscuration of 10 mm diameter with the outer diameter 

opened up to 50 mm. The use of low scatter objective with a tilted field stop along with a Lyot 

stop results in low SSE. 
Table 2. The SSE = 7x10-5 and 1x10-3 converted to temperature corrections. The smaller SSE 

corrections can be folded into the uncertainty budget while the larger SSE requires a correction 

factor. 

Fixed Point Temperature [ °C ] 

SSE = 7x10-5 

[ K ] 

SSE = 1x10-3 

[ K ] 

In 156.5985 0.001 0.020 

Sn 231.928 0.002 0.027 

Zn 419.527 0.004 0.052 

Al 660.323 0.007 0.094 

Ag 961.78 0.011 0.164 

2.5 Optical Performance 

The InGaAs radiation thermometer utilizes a commercial 50 mm diameter achromat with a focal 

length of 200 mm with nearly 1:1 finite-conjugate imaging. Since commercial achromatic lenses 

are designed for infinite-conjugate imaging, the imaging performance suffers as shown by the 

Strehl ratio in Table 3. The Strehl ratio for a perfect point source imaging will be 1.0, and the 

ratio will approach this value as the imaging performance improves. The Strehl ratio increases as 

the wavelength increases which indicates that imaging performance is better at 1550 nm than at 

500 nm. Furthermore, achromatic lenses will generally have two wavelengths were the images 

distances will be equal for a set object distance with the chromatic focal shift depending on the 

lens material and thickness. Since the radiation thermometer is designed to transfer a temperature 

scale from one blackbody to another without any desired spatial structure within the cavity, the 

need for imaging performance is much reduced. Although a single achromat will have much 

worse imaging performance than that of multi-element photographic-type lenses, the single, 

cemented achromat will have reduced scatter and consequently much lower SSE than that of 

multi-element lenses. All these optical performance metrics can be modeled using a commercial 
modeling program. Table 3 shows that although the alignment of the radiation thermometer can 

be performed in the visible wavelength, the object distances to have the same image distance at 

1550 nm and at 500 nm differ by 25 mm. Since the internal focus is difficult to adjust, the object 

distance can be offset by this difference due to chromatic aberrations. 

Table 3. The optical parameters of the 200 mm focal length achromatic objective lens. 

Moving the object distance for 1550 nm results comparable image distance to the 

500 nm wavelength. The Strehl ratio also improves at 1550 nm as compared to 500 nm 

indicating better imaging performance. 

Wavelength [ nm ] 

Object Distance 

[ mm ] 

Image Distance 

 [ mm ] 

Strehl 

Ratio 

500 500 323.91 0.0738 

1550 500 334.49 0.213 

1550 525 324 0.238 

2.6 Preamplifier Gain Corrections 

Since the InGaAs radiation thermometer should have a linear signal versus radiance of the 

blackbody, the preamplifier gain settings need to be normalized against each other. In this 

radiation thermometer, precision, metal-film-on-ceramic resistors are used in the trans-impedance 

amplifier. The resistors are chosen to have low temperature variation of resistance. The 

preamplifier was attached to a Si detector with high shunt resistance and placed in front of a 

broad-band white LED source. The 1 W, high-power LED source was chosen for its temporally 

stable output so that the gain ratios can be determined with low uncertainty. The optical power of 

the LED source incident on the detector was varied by using a combination of diffusers, variable 
source apertures or by changing the distance between the source and the detector. The LED 

source, for the most stable operations, was left on for about 24 hours to reach a thermal 

equilibrium. The ratios of gain factors shown in Table 4 indicate that at the lower gain settings, 

the ratios between two gains different by 10 are at this value within the uncertainties of the 

measurements and the resistances. The greatest deviation is present at gain factors of 1010 V/A 

and 109 V/A where the resistors used in the preamplifer deviate more from their assigned values. 

Table 4. The gain ratios of the preamplifier measured using a 

1 W white LED source with a Si detector. 

Gains 

Compared Gain Ratios 

Measurement 

Uncertainty 

(k = 2) 

106/105 9.998 0.002 

107/106 10.001 0.002 

108/107 10.000 0.002 

108/109 10.000 0.002 

109/1010 9.957 0.002 

 

3. BLACKBODY MEASUREMENTS 

The InGaAs radiation thermometer was placed in front of a variable-temperature blackbody 

(VTBB) which was set at the respective ITS-90 fixed-point temperatures. The measurements on 

actual fixed-points could not be performed in time for this submission. These measurements are 

used to determine the gain settings of the preamplifier, the throughput of the radiation 

thermometer and to measure the noise-equivalent temperature difference at the fixed-point 

temperatures. Work is planned to measure the freezing-points directly using the InGaAs 

radiation thermometer. The measured NETD could be affected by the temporal stability of the 
VTBB, and our measurements shown in Table 5 give the upper value of this parameter. The 

photocurrent at the In-point is comparable to InGaAs radiation thermometers developed at other 

national measurement institutes indicating that the throughputs are comparable. The lower 

NETD exhibited by the NIST design is due to the optimization of the preamplifier and detector, 

especially by 4-stage cooling of the detector and the resultant decrease in the noise-equivalent 

photocurrent seen in Fig. 5. Once the NIST InGaAs radiation thermometer is calibrated using the 

ITS-90 fixed points, a modified 3-parameter Planck equation will be used for the interpolation. 

0 100 200 300 400 500 600 700 800 900 1000 1100

0.001

0.002

0.003

0.004

0.005

1E-11

1E-10

1E-9

1E-8

1E-7

1E-6

1E-5

1E-4

Temperature, oC 

Photocurrent , A 

NETD, K 

Fig. 5. The measured photocurrents of the InGaAs radiation thermometer at the various fixed 

point temperatures. For convenience, the measurements were performed using a variabletemperature blackbody set to the ITS-90 temperatures. The NETD was determined from the 

standard deviation of the measurements. 
Table 5. The gains and the photocurrents at the fixed-point temperatures measured 

using a variable-temperature blackbody set at the respective temperatures. 

Fixed Point Temperature [ °C ] Gain [ V/A ] Signal [ A ] NETD [ °C ]

In 156.5985 1010 2.26251E-11 0.0050 

Sn 231.928 109 5.36748E-10 0.0011 

Zn 419.527 107 7.45110E-08 0.0015 

Al 660.323 106 2.23358E-06 0.0009 

Ag 961.78 105 2.63766E-05 0.0013 

We have also tried to use alternating-current (AC) mode measurements using a 10.1 Hz tuningfork chopper placed directly in front of the field stop with a lock-in detection system. With the 

AC mode, lower blackbody temperatures, to 80 °C, could be measured, although with the added 

complexities of using the lock-in amplifier. Further work is pursued to make low uncertainty AC 

mode measurements.

4. DISCUSSION AND FUTURE WORK 

Thus far, radiation thermometers with InGaAs detectors have only been used to transfer the 

source-based ITS-90 scale to other sources or blackbodies. Due to the developments of laserbased calibration facilities and low-noise and high linearities of InGaAs detectors, the possibility 

of detector-based thermodynamic temperature determinations are being explored. The detectorbased calibration of the InGaAs radiation thermometer would proceed in a similar way as with Sidiode based radiation thermometer [9]. A transfer radiometer would need to be calibrated for 

spectral power responsivity by comparison to the cryogenic electrical–substitution radiometer 

using infrared lasers, and thus the optical power scale would be derived from the electrical power. 

The transfer radiometer would need a precision aperture and known spatial uniformity of 

responsivity so that the power responsivity can be converted to spectral irradiance responsivity. 
The conversion to irradiance responsivity can be performed with detectors in a trap configuration 

or with detectors which are attached to integrating sphere inputs. With a laser-irradiated sphere 

along with the calibrated transfer radiometer, the InGaAs radiation thermometer can be calibrated 

for absolute detector-based radiance responsivity. Since Spectralon and other sintered or packed 

polytetrafluoroethylene (PTFE) materials have a high reflectance at 1.55 μm, integrating spheres 

have high throughput and spatial uniformity. It is anticipated that such a detector-based radiation 

thermometer could be calibrated to 0.05 % (k = 2) [10]. The resulting thermodynamic 

temperature uncertainties are shown in Table 6. Although these uncertainties are much larger 

than those obtained using gas thermometry, the uncertainties are lower than those achieved by 

noise-thermometry. 

Table 6. The thermodynamic temperature uncertainties for total uncertainty 

of 0.05 % (k = 2) at the respective fixed-point temperatures. 

Total Uncertainty = 0.05% 

Fixed Point Temperature [ °C ] (k = 2) [ K ] 

In 156.5985 0.0099 

Sn 231.928 0.0137 

Zn 419.527 0.0258 

Al 660.323 0.0469 

Ag 961.78 0.0821 

5. CONCLUSIONS 

We described a noise-optimized InGaAs radiation thermometer operating at 1550 nm which is 

capable of < 5 mK NETD at 157 °C. The SSE has also been reduced to < 7 x 10-5 at 50 mm 

which leads to low uncertainties when comparing fixed-point blackbodies to other larger-area 
 16 

variable-temperature blackbodies. These results are due to the implementation of 4-stage cooling 

of the diode resulting in high shunt resistances along with a Lyot stop which acts as an aperture 

stop. A stable chassis design is shown using graphite-epoxy rods for long-term stability of 

radiance responsivity. The preamplifier gain ratios are measured for use over the 5-decade 

dynamic range required of the radiation thermometer as the blackbody temperatures range from 

150 °C to 1000 °C. In addition to the use of this radiation thermometer as an ITS-90 transfer 

radiation thermometer, we outline a possible approach to directly measuring thermodynamic 

temperature using an absolute detector-based radiance responsivity calibration. 

REFERENCES 

1

 T. Ricolfi, M. Battuello, F. Girard, G. Machin, H. McEvoy, S. Ugur, A. Diril, Meas. Sci. Technol. 13, 

2090 (2002) 

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and Thermal Measurements in Industry and Science, ed. by D. Zvizdi ́c (FSB/LPM, Zagreb, Croatia, 

2005), pp. 827–832 

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and Thermal Measurements in Industry and Science, ed. by J.F. Dubbeldam, M.J. de Groot (Edauw 

Johannissen bv, Delft, 1999), pp. 593–598 

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International Symposium on Temperature and Thermal Measurements in Industry and Science, ed. 

by D. Zvizdi ́c (FSB/LPM, Zagreb, Croatia, 2005), pp. 605–610 

5 G. Romeo, G. Frulla, J. Compos. Mater. 29, 751 (1995) 

6 G.P. Eppeldauer, J. Res. Natl. Bur. Stand. (U.S.) 105, 29 (2000) 

7 H.W. Yoon, D.W. Allen, R.D. Saunders, Metrologia 42, 89 (2005) 

8 D.W. Allen, G. Dezsi, H.W. Yoon, in Proceedings TEMPMEKO 2004, 9th International Symposium 

on Temperature and Thermal Measurements in Industry and Science, ed. by D. Zvizdi ́c (FSB/LPM, 

Zagreb, Croatia, 2005), pp. 817–822 

9

 H.W. Yoon, D.W. Allen, C.E. Gibson, M. Litorja, R.D. Saunders, S.W. Brown, G.P. Eppeldauer, K.R. 

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10 S.W. Brown, G.P. Eppeldauer, K.R. Lykke, Appl. Optics 45, 8218 (2006)
INSTITUTE OF PHYSICS PUBLISHING METROLOGIA

Metrologia 40 (2003) S154–S158 PII: S0026-1394(03)56889-X

Linearity of InGaAs photodiodes

H W Yoon, J J Butler, T C Larason and G P Eppeldauer

Optical Technology Division, NIST, Gaithersburg, MD 20899-8441, USA

Published 7 February 2003

Online at stacks.iop.org/Met/40/S154

Abstract

In radiometry or pyrometry, radiometers are often used to assign the spectral

radiance or radiance temperatures of sources using ratios of signals which

can differ by several decades. For performing ratios between such sources

with low uncertainties, the linearity of the detectors used in the transfer

radiometers needs to be characterized. The linearity of InGaAs photodiodes

has been studied using the flux-addition method using a broadband infrared

source with a visible-blocking filter. Using this technique, 18 InGaAs

photodiodes from four different vendors were studied without spectral

filtering in a broad wavelength region from 900 nm to 1700 nm with the

diodes underfilled by the incident flux. The linearity of InGaAs photodiodes

was determined within the range of photocurrents from 10−8 A to 10−4 A.

All the InGaAs photodiodes demonstrated linearity from 10−7 A to 10−4 A

within the expanded uncertainties of 0.08% (k = 2). The uncertainty in the

linearity measurement below 10−8 A is increased due to the increased noise

in the photocurrent arising from the feedback resistance of the

transimpedance amplifier being greater than the shunt resistance of the

photodiode.

1. Introduction

InGaAs photodiodes are critical components in optical networks, and as the manufacturing process for InGaAs improves,

they are being increasingly used as detectors in thermal imaging, pyrometry [1] and spectroradiometry [2]. Previously, the

electronic characteristics of InGaAs and Ge photodiodes using

current preamplifiers were compared, and the InGaAs photodiodes were found to have much a smaller temperature dependence and lower noise floor than Ge photodiodes [3]. Although InGaAs photodiodes are widely used as receivers in

optical networks, they have not been extensively evaluated for

use in spectroradiometry. Since the detector could be used to

assign the spectral radiances of vastly different sources using

radiance ratios or signal ratios from one source to another, the

linearity of the detectors must be quantified for use in spectroradiometry. In addition, these particular photodiodes have

been used as working standards in the key comparison K2.a of

the Consultative Committee on Photometry and Radiometry

for the intercomparison of spectral power responsivity from

900 nm to 1600 nm [4]. Since each laboratory participating

in the intercomparison could use different optical power levels to assign the spectral responsivity, the determination of

the linearity of these InGaAs photodiodes is critical. To our

knowledge, there has not been a study of InGaAs photodiode linearity although the linearity of these detectors is an

important issue in many applications. The different InGaAs

diodes studied and their electrical characterizations are listed in

table 1.

The linearity of detectors can be measured with several

different techniques. A common technique is to insert a filter

into the optical path at different optical power levels. The nonlinearity is measured as a change in the filter-in to the filter-out

signal ratios. Another well-known method is the beam-flux

addition using double apertures. In this study, we use the

combination of these two methods with the Beamconjoiner III

apparatus developed at the National Institute of Standards and

Technology [5].

Although the linearity of photodiodes can also be

dependent on the wavelength of the measurements, such

wavelength dependences were not investigated during this

study. The InGaAs photodiode was illuminated using a

broadband source, an FEL lamp, and only a single visible

blocking filter was placed in front of the photodiode. All the

photodiodes studied had active areas of 5 mm diameter, and

the incident flux was made to underfill the diode. Wavelengthdependent non-linearities are possible, especially near the

band-gap wavelength of the InGaAs around 1.7μm.

The linearity of InGaAs photodiodes was determined to

an expanded uncertainty of 0.08% (k = 2) within the range

of photocurrents from 10−8 A to 10−4 A. Below 10−8 A, the

uncertainty in the linearity measurement is larger due to the

increased noise in the photocurrent arising from the feedback

resistance of the transimpedance amplifier being greater than

0026-1394/03/SS0154+05$30.00 © 2003 BIPM and IOP Publishing Ltd Printed in the UK S154
Linearity of InGaAs photodiodes

Table 1. The shunt resistances and the shunt capacitances of all the tested photodiodes are shown. The shunt capacitance of the NIST 14

photodiode could not be measured.

Shunt Shunt

Serial resistance/ capacitance/

Detector Manufacturer and model number M nF

NIST 01 Fermionics 123 17.50 1.41

NIST 02 Fermionics 124 12.80 1.43

NIST 03 Fermionics 125 15.40 1.42

NIST 04 GPD GAP5000, D/C 9812 1 1.78 1.33

NIST 05 GPD GAP5000, D/C 9812 2 2 1.1

NIST 06 GPD GAP5000, D/C 9812 3 1.9 1.14

NIST 07 GPD GAP5000, D/C 9812 4 1.8 1.2

NIST 08 EG&G Optoelec. C30723G 6 3.75 0.826

NIST 09 EG&G Optoelec. C30723G 9 5.00 1.50

NIST 10 EG&G Optoelec. C30723G 11 5.71 1.58

NIST 11 EG&G Optoelec. C30723G 13 4.44 1.67

NIST 12 TDC P/N: 35PD5M-TO 2 5 1.8

NIST 13 TDC P/N: 35PD5M-TO 3 2.5 1.87

NIST 14 TDC P/N: 35PD5M-TO 4 0.00125 —

NIST 15 TDC P/N: 35PD5M-TO 5 5 1.85

NIST 16 GPD GAP5000, D/C 9849 11 1.80 1.27

NIST 17 GPD GAP5000, D/C 9849 12 0.58 1.37

NIST 18 GPD GAP5000, D/C 9841 13 1.40 1.44

the shunt resistance of the photodiode. The shunt resistances

and the junction capacitances of the photodiodes have also

been measured, and the increased noise at the low power

levels is correlated with the differences in the respective shunt

resistances.

2. Experimental method

The linearity of the InGaAs photodiodes was determined

using the Beamconjoiner III apparatus. Our method utilizes

a visible-blocking filter (Hoya R72)1 and reflective neutral

density filters to provide 40 different flux values, resulting

in 120 different combinations to attenuate the light source, a

current-stabilized FEL lamp. The incident light on the InGaAs

diodes is broadband infrared with the visible range filtered.

The neutral density filters were constructed using metallized

quartz substrates for transmission from 0.2μm to 2.5μm. The

optical diagram of the Beamconjoiner III is shown in figure 1.

The incident flux is introduced into the opening of the lighttight box and is split into two directions by the beamsplitter 1.

Each of the filter wheels 1 and 2 has four different reflective

neutral density filters with circular openings of 4 cm diameter,

and the filter wheel 3 has five filters. Combined with the

blocked value for each of the filter wheels, a total of (5×5×6)

150 different combinations can be formed. The filter wheel

3 acts to reduce the total level of the combined flux, and

the dynamic range in the optical flux of the highest level to

the lowest level is about 500 : 1. The rotation of the filter

wheels is controlled using three separate stepper motors, and

the rotational positions of the filter wheels are verified with a

check of the home position optical switch each time the stepper

motor is rotated. The change in the optical flux is performed

in the collimated beam before the imaging of the flux onto the

detector by the spherical mirror.

1 Certain commercial equipment, instruments or materials are identified

in this paper to foster understanding. Such identification does not imply

recommendation or endorsement by the National Institute of Standards and

Technology, nor does it imply that the material or equipment are necessarily

the best available for the purpose.

filter 

wheel 1

beam 

splitter 2

mirror 1

filter 

wheel 3

beam 

splitter 1

filter 

wheel 2

source

mirror 2

light-tight 

box

visible 

blocking 

filter

imaging 

mirror

detector

Figure 1. Optical diagram of the Beamconjoiner III apparatus. The

source is split into two directions using the beamsplitter 1 and

recombined at the detector using beamsplitter 2. The combination

of the three filter wheels can produce 120 different signal levels

using 40 different flux levels. The optical flux is changed in the

collimated beam before imaging onto the detector.

In the measurement protocol, each of the filter wheel

positions is assigned a distinct value i, k, j corresponding to

the positions of the filter wheel 1, 2, 3, respectively. Each of

the 120 different filter combinations is in turn also assigned

a distinct number, and the sequence of filter wheel positions

for each run is determined using a random number generator

prior to each run. Every group of four measurements is

followed by a dark measurement, resulting in 30 separate dark

measurements for each run. Since each dark signal has a time

stamp, any change in the dark signal can be monitored. None

of the InGaAs photodiodes discussed in this study showed any

evidence of dark signal drift.

Since each run could take up to 1.5 h or longer depending

upon the signal averaging needed for optimal signal-to-noise

ratios, the source flux has to be temporally stable. The

lamp was stabilized by measuring the voltage drop across a

calibrated resistor to determine the current, and a closed-loop

Metrologia, 40 (2003) S154–S158 S155
H W Yoon et al

current stabilization was used, which adjusted the current every

5 s to the desired value.

Although the power responsivity of the InGaAs

photodiodes is temperature sensitive, the photodiodes used

in the CCPR K2.a were not operated with temperature

stabilization. The temperature was monitored using a

thermistor held in contact with the back of the photodiode,

and each photodiode was allowed sufficient time to come

to temperature equilibrium with the ambient laboratory

environment. Temperature changes of the photodiode of few

degrees resulted in noisy signal/flux values since the doublebeam flux method requires both the source and the detector to

be stable during the 120 different measurements.

3. Linearity analysis

Although 150 different signals are possible, only 120 signals

are measurements of fluxes from the source. Each signal can

be written as a response to the incident flux, or conversely, each

flux results in signal as a function of the flux,

φ(i, j, k) = φ(i, j ) + φ(j, k)

= r0 + s(i, j, k) + r2s2

(i, j, k) + ··· + rnsn(i, j, k) (1)

where φ(i, j, k) denote the flux, s(i, j, k) is the measured

signal at the detector, and r0, r2,...,rn are the coefficients

which relate the signal to the flux. The total flux at the detector

is a sum of the individual fluxes, φ(i, j ) and φ(j, k), and

flux addition is inherently linear. Since each flux can be an

independent flux or sums of independent fluxes, and although

120 signals are measured along with 30 dark signals, only 40

different fluxes exist with 20 fluxes from each of the two paths.

Thus equation (1) becomes an over-determined equation with

40 unknown fluxes and one or many unknown coefficients, r0,

r2,...,rn, but with 120 equations. The unknown fluxes are

found by setting up a system of linear equations and performing

a least-squares fit of the signals for the 40 unknown fluxes and

the coefficients.

Due to the complexity of the matrix inversion and the

possibility of errors in the convergence, the analysis program

was tested using artificial data sets which simulated the

experimental results from the Beamconjoiner. Different

constant values were used in the simulations, and second-order

correction factors were also simulated. The analysis program

was able to correctly converge on all of the coefficients in the

artificial data sets.

The determination of linearity is measured using the

residuals of the fluxes found using the fit to the measured signal

corrected by the appropriate coefficients. Initially, only the

constant correction, r0, is applied and the residuals of the fit,

φ(i, j, k) − [r0 + s(i, j, k)] (2)

are plotted against the signals and examined for indications

of the need for higher order corrections. The linearity of the

signals is determined from a plot of the ratio of the measured

signal to the calculated flux,

s(i, j, k)

φ(i, j, k) (3)

and the ratios are fitted using a linear function to determine the

uncertainty component of the total signal due to non-linearity.

Since flux is inherently linear, and the signals could be nonlinear, any non-linearity of the signal will be evident from the

curvature of the ratios.

4. Discussion

A plot of the ratios of the measured signals to the fluxes

versus the signals for the NIST 01 photodiode is shown

in figure 2. The plot shows signal/flux ratios from three

separate runs, each consisting of 120 signal measurements.

The measurements were performed using an additional neutral

density filter between the filter wheel 3 and the detector to

reduce the overall signal such that the wide dynamic range

could be spanned from 10−9 A to 10−4 A. The symmetry of

the residuals above and below the y = 0 axis in figure 2

indicates the goodness of fit, since any non-linearity would

be manifest in deviations from a symmetric distribution. From

the plot, the detector is determined to be linear from 1×10−8 A

to 1 × 10−4 A in photocurrent with an uncertainty of 0.08%

(k = 2). The uncertainty is determined from the goodness of

a linear fit to the values in the same range.

All the InGaAs photodiodes examined showed linear behaviour with an uncertainty of 0.08% between 5×10−8 A and

1 × 10−4 A. Some of the photodiodes also exhibited increased

noise below 5 × 10−8 A with decreasing photocurrent. A plot

of the signal/flux is shown for the detector NIST 18 in figure 3

and shows that the signal to flux ratios below 5 × 10−8 A become noisy as compared to the same measurements of NIST

01. The reasons for the increase in the signal noise will be explored in the noise analysis section of this paper. For example,

the Beamconjoiner was used to measure the linearity of silicon

photodiodes from 10−11 A to 10−3 A to within 0.054% (k = 2),

since Si diodes have typical shunt resistances of 1 G [5].

In conjunction with the linearity testing, all the InGaAs

photodiodes were also measured for shunt resistance and shunt

capacitance. Table 1 shows the measured shunt resistances and

the shunt capacitances of the individual InGaAs photodiodes.

With the exception of two diodes, NIST 08 and NIST 14, all

1E-10 1E-9 1E-8 1E-7 1E-6 1E-5 1E-4 1E-3

0.990

0.995

1.000

1.005

1.010

NIST 01

Signal * Flux-1

Photocurrent / A 

Figure 2. The ratios of the signal divided by the calculated flux

plotted versus the signal for the NIST 01 photodiode (17.5 M

shunt resistance). A total of three runs are plotted with each run

consisting of 120 different signal levels. The ratios can be measured

with <0.1% uncertainty for photocurrents below 1 × 10−8 A.

S156 Metrologia, 40 (2003) S154–S158
Linearity of InGaAs photodiodes

1E-10 1E-9 1E-8 1E-7 1E-6 1E-5 1E-4 1E-3

0.990

0.995

1.000

1.005

1.010

NIST 18

Signal * Flux-1

Photocurrent / A 

Figure 3. The ratios of the signal divided by the calculated flux

plotted versus the signal for the NIST 18 photodiode (1.40 M

shunt resistance). The ratios can be measured within the <0.1%

uncertainty for photocurrents below 5 × 10−8 A, and the noise

increases rapidly at lower photocurrents.

the diodes had similar shunt capacitances ranging from 1.10 nF

to 1.87 nF. The shunt resistances varied from 0.583 M

(NIST 17) to 17.5 M (NIST 01).

5. Noise analysis

According to our previous measurements [3], there are

two major noise components at the output of an InGaAs

photodiode current meter—1/f voltage noise and the resistor

noise. The 1/f voltage noise arises from the operational

amplifier in the current-to-voltage converter. The other major

noise component is the resistor noise that is determined by

the parallel connection of the detector shunt resistance and

the feedback resistance.

Figure 4 shows the two major noise components at the

output of the InGaAs photocurrent meter plotted as a function

of the shunt resistance. The resistor noise was calculated

with two different electrical bandwidths and the output 1/f

noise was calculated with two different feedback resistors.

In the first example; the resistor noise was calculated with

0.3 Hz bandwidth (lowest, dotted curve) and a feedback resistor

of Rf = 100 M. The output 1/f noise, shown with

the shorter dashed curve, is independent of the bandwidth

selection [6]. The 0.3 Hz bandwidth originates from the

1.7 s integration time (duration of 100 power line cycles) of

the DVM connected to the output of the photocurrent meter

(current-to-voltage converter). We used 0.35μV 1/f noise in

the present calculations. This is a typical value from our earlier

measurements on OPA128 and OPA111 operational amplifiers

[6]. In the second example, the 1/f output noise was calculated

with a feedback resistor of 1 G (longer dashed curve on the

top). This noise was an order of magnitude larger than that with

100 M. The resistor noise in this case was calculated with a

bandwidth of 1 Hz (solid line). The shunt effect of the 1 G

feedback resistor for the maximum 200 M shunt resistance

was neglected.

Since the resistor noise increases and the voltage

amplification decreases with increasing shunt resistance, the

10-7

10-6

10-5

10-4

101 102

Output RMS Noise / V

Shunt Resistance/MΩ

resistor noise, 

f = 1 Hz, Rf

=1 GΩ

resistor noise, 

f = 0.3 Hz, Rf

=100 MΩ

1/f noise, Rf=102 MΩ

1/f noise, Rf= 1 GΩ

Figure 4. Output root-mean-squared (RMS) noise components of

the InGaAs photocurrent meter for the 108 V A−1 and 109 V A−1

gains versus photodiode shunt resistance.

output noise could be optimized. In both examples, the

two output noise components could be equalized at a shunt

resistance of 200 M. The shunt resistance increases when

the photodiode is cooled. Our earlier experiments showed

that a 2 M shunt resistance at 25  ̊C could be increased to

55 Mat a controlled temperature of−30  ̊C [3]. Accordingly,

an InGaAs photodiode with 7.3 M shunt resistance at 25  ̊C

could produce 200 M shunt resistance at −30  ̊C. A 300 M

shunt resistance will equalize the two major output noise

components fora1G feedback resistor and a bandwidth of

0.3 Hz. To perform the optimization in this third example, an

InGaAs photodiode with a shunt resistance of about 11 M

at 25  ̊C should be selected. The achievable (equivalent)

photocurrent noise at −30  ̊C will be about 1 fA (1 μV/1 G).

In our present linearity measurements, the feedback

resistors could be changed from 104  to 109 . At the

100 M and 1 G gain selections, the resistor noise was

dominated by the photodiode shunt resistance. The shunt

resistance at room temperature was smaller than 20 M for

all measured photodiodes. At the low gain selections, where

the feedback resistor was smaller than the shunt resistance, the

resultant resistance was dominated by the feedback resistor.

At these gain selections, the voltage amplification for the 1/f

input voltage noise was close to unity. Accordingly, resistor

noise and output 1/f noise were similar for the shunt resistance

interval (about one decade) shown in table 1. For detectors

with small shunt resistance, the voltage amplification at high

feedback resistor selections can be very large, resulting in a

dominating 1/f noise component in the output signal. This is

why the noise floor of the NIST 18 photodiode was an order

of magnitude higher than that of the NIST 01.

6. Conclusion

The linearity and signal dynamic range of 18 InGaAs

photodiodes have been studied. The major noise components

of the InGaAs photocurrent meters were analysed versus shunt

resistance, signal gain and bandwidth. A limit sensitivity of

1 fA can be achieved at 109 V A−1 gain if the amplified 1/f

noise and the resistor noise are equalized at the output of the

current meter. For the tested room temperature photodiodes,

Metrologia, 40 (2003) S154–S158 S157
H W Yoon et al

linearity could be measured from 10−8 A to 10−4 A with an

expanded uncertainty of 0.08% (k = 2). When the shunt

resistance was increased by cooling one of the photodiodes,

the linearity measurement range could be extended a decade

due to the increase of the shunt resistance.

References

[1] Gutschwager B and Fischer J 1999 An InGaAs radiation

thermometer with an accurate reference function as transfer

standard Proc. TEMPMEKO ’99 (Delft, Netherlands)

ed J F Dubbledam and M J deGroot

[2] Yoon H W, Proctor J E and Gibson C E 2003 FASCAL 2:

A new NIST facility for the calibration of the spectral

irradiance of sources Metrologia 40 S30–4

[3] Eppeldauer G 1997 Electronic characteristics of Ge and InGaAs

radiometers Proc. SPIE 3061 833–8

[4] Larason T C, Brown S W and Lykke K R 2002 InGaAs

photodiodes used in a CCPR near-infrared key comparison

Proc. NEWRAD02 (Gaithersburg, MD)

[5] Thompson A and Chen H M 1994 Beamcon III, a linearity

measurement instrument for optical detectors J. Res. Natl.

Inst. Stand. Technol. 99 751–5

[6] Eppeldauer G and Hardis J E 1991 Fourteen-decade

photocurrent measurements with large-area silicon

photodiodes at room temperature Appl. Opt. 30 3091–9

S158 Metrologia, 40 (2003) S154–S158
Short-wave infrared radiometers design and characterizations 

George P. Eppeldauer and Howard W. Yoon 

National Institute of Standards and Technology 

Gaithersburg, MD USA 20899 

ABSTRACT 

Short-wave infrared (SW-IR) radiometers have been developed to extend the National Institute of Standards 

and Technology (NIST) reference responsivity scales from the silicon wavelength range to 2500 nm. In 

addition to spectral power responsivity measurements, where 5 mm diameter extended-InGaAs (EIGA) 

detectors are underfilled by the incident radiation, irradiance responsivity calibrations are needed. Irradiance 

measuring radiometers are used as reference detectors to calibrate field radiometers in both irradiance and 

radiance measurement modes. In irradiance mode, smaller detectors with high shunt resistance, such as 1 mm 

diameter short-wave HgCdTe and EIGA detectors are used. Mechanical, optical, thermal, and electronic design 

considerations of SW-IR radiometers are discussed. Noise equivalent currents (NEC) were measured to 

evaluate noise equivalent power (NEP) and D*. 

Keywords: detectivity, extended-InGaAs, infrared, infrared detectors, noise equivalent power, short-wave infrared, 

shunt resistance, spectral responsivity, thermoelectric cooling 

1. INTRODUCTION 

While Si, Ge, and InGaAs detector applications, characterizations, and calibrations have been described in detail [1, 2], 

understanding of radiometer design issues, characterizations and calibrations for short-wave infrared (SW-IR) detectors 

is still lacking. Photovoltaic extended-InGaAs (EIGA) and short-wave HgCdTe (PV-MCT) detectors are commercially 

available with high detector shunt resistance [3]. These detectors do not have large ambient-background-produced 

signals because their upper wavelength cut-off is low. Consequently, higher radiometer responsivity and lower 

radiometer output noise can be achieved, which is an important requirement for the SW-IR range where the radiant flux 

from ambient temperature targets is lower than at longer wavelengths [3]. Using small-area detectors the shunt 

resistance can be further increased, which is important to make radiometers with decreased output noise, linear 

operation, and low photocurrent-to-voltage conversion uncertainty [1]. The main goal in designing SW-IR radiometers 

is to increase the detectivity (D*) close to the background-noise-produced theoretical limit. These improved D* SW-IR 

radiometers can be used for ambient temperature measurements [4]. It is anticipated that NIST, in the near future, will 

begin to issue detector calibration services in the SW-IR wavelength region to 2.5 μm utilizing these standards. 

The design of high-D* SW-IR radiometers needs special considerations. Cryogenic cooling is not needed for these 

detectors, but 4-stage thermoelectric (TE) coolers must be used to operate the detectors at temperatures close to -80 o

C 

in order to obtain high shunt resistance. Delivering the dissipated heat away from the TE coolers is an additional 

problem compared to traditional temperature control of Si, Ge, and InGaAs detectors. 

Applying SW-IR detectors in a new radiometer design, the NIST spectral power responsivity scale can be extended to 

2.5 μm. Also, in addition to spectral radiant power responsivity, spectral irradiance and radiance responsivities can be 

measured by changing the input optics of these radiometers. Characterization of SW-IR radiometers for measuring the 

different radiometric quantities is necessary to keep the measurement uncertainty low. SW-IR transfer standard 

radiometers have also been developed within this project to convert power responsivity into irradiance responsivity. 

These irradiance mode radiometers will be used as reference standards to calibrate both irradiance and radiance 

Infrared Technology and Applications XXXIII, edited by Bjørn F. Andresen, Gabor F. Fulop, Paul R. Norton,

Proc. of SPIE Vol. 6542, 65420O, (2007) · 0277-786X/07/$18 · doi: 10.1117/12.720548

Proc. of SPIE Vol. 6542 65420O-1
measuring SW-IR radiometers. The calibrated SW-IR radiometers are used as working standards to disseminate the 

pyroelectric radiometer realized NIST infrared responsivity scales in the 1 μm to 2.5 μm wavelength range [5, 6]. 

2. SW-IR DETECTORS 

Photovoltaic EIGA detectors are available with 1.9 μm, 2.2 μm, 2.4 μm, and 2.6 μm (50 %) wavelength cut-offs. The 

wavelength cut-off of PV-MCT detectors can be tuned by changing the material composition [3]. The PV-MCT 

detectors, tested in this work, have a 2.8 μm wavelength cut-off. While the diameter of the EIGA detectors can be as 

large as 5 mm, PV-MCT detectors are usually not larger than 2 mm. 

The custom-made detector can for a 5 mm diameter EIGA detector is shown in Fig. 1. The sapphire window that has a 

4o

 wedge angle is positioned above the detector-chip tilted by 4o (both are shown within circle C). The non-parallel 

surfaces serve to eliminate interference effects in the detector response. In case of traditional detector cans (such as 

Model 3CN), the side walls can absorb heat from the thermal energy rejected by the TE cooler. To avoid this problem, a 

cold field-of-view limiter (e.g. with 30o

 acceptance angle) can be applied to 3CN cans to keep the background signal 

low. The main advantage of the shown custom-made detector can is that the front and side surfaces around the detector 

will not warm up because of the heat conducted from the hot side of the 4-stage TE cooler and there will be no excess 

background radiation for the detector. 

Fig. 1. SW-IR detector can with a wedged window and a tilted 5 mm diameter detector. 

Shunt resistance is one of the most important detector characteristics [1, 3]. High shunt resistance is required to obtain 

low noise at a radiometer output, high signal-gain in the photocurrent meter, and high stability and repeatability in 

signal measurements. In order to achieve a high shunt resistance, the detectors have to be operated at a low and stable 

temperature. Figure 2 shows that the shunt resistance changes exponentially with the detector temperature (the Y scales 

are logarithmic and the X scale is linear). While the shunt resistance of a 1 mm diameter regular InGaAs (IGA) detector, 

that has a 1.7 μm wavelength cut-off, can reach 10 GΩ at a temperature close to -20 o

C, 1 mm diameter SW-IR 

detectors (EIGA and PV-MCT) need cooling to about -80 o

C to obtain a shunt resistance close to 10 MΩ. The IGA 

detector needs only two-stage thermoelectric (TE) cooling to obtain that high shunt resistance. For SW-IR detectors 

four-stage TE coolers must be used to achieve about -80 o

C detector temperature. While 3 mm diameter EIGA detectors 

can have shunt resistances between 1 MΩ and 3 MΩ at -70 o

C, shunt resistances only between 70 kΩ and 90 kΩ were 

measured on 5 mm diameter EIGA detectors at this same temperature. Material quality problems were the reasons of 

these lower-than-expected shunt resistances. 

Proc. of SPIE Vol. 6542 65420O-2
vol ww jo [wqo] eoue;s!sei ;unqs 

104

105

106

107

108

107

108

109

1010

1011

-80 -60 -40 -20 0 20

PV MCT 1mm

EIGA 1 mm

IGA 1mm

Temperature [oC]

Fig. 2. Shunt resistance versus temperature of regular IGA and SW-IR (EIGA and PV-MCT) photodiodes. 

3. SW-IR RADIOMETER DESIGN 

The radiometer measuring-head design for SW-IR detectors needs several important considerations. The measuring 

head includes input optics, a heat removing attachment for the TE cooler, temperature control for the detector (using the 

TE cooler and the temperature sensor), and a photocurrent-to-voltage converter. 

3.1. Measuring head 

The cross section of an irradiance mode measuring head is shown in Fig. 3 to illustrate the input optics and the side fan 

for cooling. An aperture is usually located at the front. There is an IR diffuser between the aperture and the 3 mm 

diameter EIGA detector to maintain the angular responsivity close to the theoretical cosine function of irradiance 

measurements [7]. While the aperture is underfilled by the incident radiation (beam) in power mode measurements, it is 

overfilled in irradiance measurement mode. In this measuring head design, the 4-stage TE cooled detector is inside of a 

traditional (Model 3CN) can which is mounted on a thick copper plate. The plate conducts the heat from the hot side of 

the TE cooler to the heat sink, which is part of the cylindrical Aluminum housing. The fan attached to the side of the 

housing produces forced air cooling for the heat sink. The thermistor pins and the pins of the 4-stage TE cooler are 

connected from the bottom of the detector can to a multiple-pin connector on the side of the housing. An external 

temperature controller that regulates the detector temperature to a low (about -85 o

C) and constant value is attached to 

this connector. The detector leads are connected to the inputs of a photocurrent-to-voltage converter through a 4-pin 

connector located at the right side of the shown housing. The converter is inside of another cylindrical housing (not 

shown here) which can be attached to the bottom (on the right) of the shown housing and has the same outside diameter. 

Another measuring head design is shown in Fig. 4 using the detector-can of Fig. 1. In this head design, the heat removal 

is performed with water cooling. The water coolant that delivers the heat away from the 4-stage TE cooler of the 5 mm 

diameter detector is circulated with a heat exchanger (radiator). A selectable-speed fan is built into the heat exchanger 

that removes the heat from the water coolant. The temperature stabilization is done by an external temperature 

controller. The side view of the measuring head is shown on the left side and the cross section is shown on the right side 

of the figure. The different heat dumping solutions shown on Figs. 3 and 4 can work equally well. As a result of the 

efficient heat removal, the external temperature controller can regulate the detector temperature to < 0.01 o

C. 

Proc. of SPIE Vol. 6542 65420O-3
AIR FLOW

OUT

EXT InGoAs DETECTOR

IR DIFFUSER\

APERTURE

AIR FLOW

INTAKE

Fig. 3. Radiometer head for a 3 mm EIGA detector using fan produced air flow for heat removal. 

Fig. 4. Side view and cross-section of a radiometer head built for a 5 mm EIGA detector. The detector can 

shown in Fig. 1 is used and water-coolant is circulated for heat removal. 

3.2. Electronic design considerations 

The photocurrent meter characteristics are matched to the electrical characteristics of the SW-IR detector. The shunt 

resistance of SW-IR detectors (as discussed above) is significantly lower than that of Si and cooled regular InGaAs 

photodiodes. In case of high shunt resistance (such as with Si and cooled regular InGaAs detectors) and high signal gain 

(feedback resistor of the current-to-voltage converter) selections, the output noise of a radiometer (measuring head) is 

dominated by the resistor noise [1]. The equivalent source-resistance of a photodiode photocurrent meter can be 

calculated as a parallel connected shunt resistance and feedback resistance. For instance, when the shunt resistance is 

Proc. of SPIE Vol. 6542 65420O-4
3 MΩ and the feedback resistance is higher, the 3 MΩ shunt resistance will shunt the feedback resistance and will 

dominate the resultant source-resistance. This means that the resistor noise will remain small and constant for feedback 

resistors higher than the 3 MΩ shunt resistance. In this case, the resistor noise will not be the dominating noise 

component of this radiometer. The dominating output noise, in contrast to other IR (such as InSb) detector applications, 

will be the amplified input voltage noise of the operational amplifier of the current-to-voltage converter. This input 

noise has both white noise and 1/f noise components. In contrast to Si photodiode current meters, where low inputcurrent operational amplifiers are used (for the 2 GΩ to 5 GΩ optimum shunt resistances), low input voltage noise 

operational amplifiers are to be selected for SW-IR detectors. The amplification for the input voltage noise is shunt 

resistance dependent [1]. The higher the shunt resistance the lower the voltage amplification (for feedback resistors 

higher than the shunt resistance). Accordingly, increasing shunt resistance will decrease the dominant output voltage 

noise component for the radiometer output. At the same time (using the same feedback resistor), the background current 

noise will not change at the output. The goal is to decrease the output voltage noise, by increasing the shunt resistance, 

until the background current noise will be the dominating noise component. In this case, there will be a reasonable limit 

for increasing the detector shunt resistance. AC mode Si radiometer noise-performance will not be achieved with SWIR radiometers even if the shunt resistances were increased to GΩ values and a cold field-of-view limiter was applied 

for the EIGA detector. In case of an optimized SW-IR radiometer design, the noise performance will be limited by the 

background noise, which is small in the SW-IR wavelength range but never as small as the noise-equivalent-power 

(NEP) of noise-optimized AC mode Si radiometers [1]. Test measurements can determine the reasonable limit for the 

shunt resistance increase. 

In case of SW-IR detectors, the background current is orders of magnitude smaller than with InSb detectors. However, it 

still can be comparable to the photocurrent of the optical signal to be measured. High sensitivity can be achieved if the 

useful signal (to be measured) is chopped and is measured by a lock-in amplifier. In this case, the DC background signal 

and its changes will not be measured because it will not have any frequency components that the chopping frequency 

synchronized lock-in amplifier could measure. Because of the low DC background current, the feedback resistor can be 

two orders of magnitude higher than with background optimized InSb detectors. Accordingly, the responsivity of SWIR radiometers can be much higher than InSb radiometers. The highest value for the feedback resistor in the current-tovoltage converter is limited by the required upper roll-off frequency of the radiometer. The upper roll-off is determined 

by the time constant of the feedback impedance (the product of the feedback resistance and the feedback capacitance). It 

is important to keep the parallel stray (feedback) capacitance low if high roll-off frequencies are needed at high signalgains. In an optimum design, the chopping frequency is about one order of magnitude lower than the upper roll-off 

frequency, to obtain an operating point on the flat (constant) signal-gain versus frequency function of the photodiode 

current-meter. Accordingly, the chopping frequency should be high enough to be near the elbow of the 1/f noise 

spectrum of the current-to-voltage converter and small enough to avoid problems when optimizing the feedback 

capacitance during frequency compensations. Partial frequency compensations are needed in AC measurement modes 

to optimize the three fundamental gains of photodiode current meters. These gains are the signal-gain (discussed above), 

the closed-loop voltage gain (that gives the amplification for the input voltage noise), and the loop gain (product of the 

operational amplifier open-loop gain and the feedback attenuation produced by the feedback resistor and the detector 

shunt resistance) that determines the uncertainty of the current-to-voltage conversion [1]. 

4. CHARACTERIZATIONS 

In order to verify the above design considerations, test radiometers have been made and their performance 

characteristics were measured. First, tests were made to evaluate the minimum signal (photocurrent) that can be 

measured in DC mode with a reasonably low uncertainty. This information is needed for high signal (such as laserbased source) measurements which is typical in responsivity scale transfers. However, the main goal of the performed 

tests was to determine the noise equivalent current (NEC), the noise-equivalent power (NEP), and the D* values of the 

newly developed SW-IR radiometers. 

The DC tests were made at detector temperatures of -85 o

C. The background current measured on a 3 mm EIGA 

detector was 17 nA. The background current of a 1 mm EIGA detector, equipped with a cold 30o

 field-of-view limiter, 

was only 0.6 nA. These small DC currents can be easily compensated in the current-to-voltage converter. The DC mode 

NEC will depend on the fluctuations of the background current if the temperature of the detector is kept constant. The 

Proc. of SPIE Vol. 6542 65420O-5
Output voltage noise 

3 mm detector, which has a shunt resistance of 3 MΩ, was measured at a signal-gain of 107 V/A. A 40 μV standard 

deviation was obtained from 20 measurements. Each measurement was taken using an integrating digital voltmeter with 

a measurement integration time of 100 power line cycles. At this 0.3 Hz bandwidth [1], a DC mode NEC= 4 pA can be 

calculated from the ratio of the measured 40 μV output noise to the 107

 V/A signal-gain. The minimum signal will be 4 

nA to receive a signal-to-noise ratio of 1000 for performing a 0.1 % measurement uncertainty. The DC mode NEC of 

the 1 mm EIGA detector has not been tested but it is estimated to be significantly lower because of the higher shunt 

resistance (15.3 MΩ) and the 30 times lower background current. 

In AC measurement mode, the output total noise voltage of the EIGA radiometers was measured at different signalgains. The output noise voltage was measured with a lock-in amplifier attached to the output of the current-to-voltage 

converter. The chopping frequency was 7.5 Hz and the integrating time constant of the lock-in amplifier was 1 s. The 

measured voltage noise changed from 0.1 μV at gain 106

 V/A to 20 μV at gain 109 V/A. Figure 5 shows the measured 

output voltage noise on the left-Y axis. The right-Y axis shows the NEC which was calculated as the ratio of the output 

voltage noise to the selected feedback resistor. A constant NEC=20 fA was obtained for the high signal gains from 

107 V/A to 109

 V/A. The NEC of the 1 mm EIGA detector was tested at a signal-gain of 108 V/A, a chopping frequency 

of 9 Hz, and an electrical bandwidth of 0.16 Hz. This detector has five times larger (15.3 MΩ) shunt resistance and 

about 30 times lower background current. The obtained NEC was 7 fA. 

0.1

1

10

10

100

106 107 108 109

Voltage noise 

NEC 

Feedback resistor [Ω]

Fig. 5. The output voltage noise and the noise equivalent current (NEC) of a 

3 mm EIGA radiometer with a shunt resistance of 3 MΩ. 

The NEP of a SW-IR radiometer can be calculated from its NEC: 

R

NEC NEP = (1) 

where R is the peak responsivity of the detector in A/W. Using a typical 1.3 A/W peak responsivity (manufacturer’s 

data), an NEP=15.4 fW can be calculated for the above discussed 3 mm EIGA radiometer. An NEP=5.4 fW was 

calculated for the radiometer using the 1 mm EIGA detector with the cold FOV limiter. This result is very close to the 

3 fW DC-mode NEP of well-designed silicon radiometers [8]. 

The detectivity D* of a SW-IR radiometer (with detector area A) can be calculated as: 

NEP

A D* = (2) 

Proc. of SPIE Vol. 6542 65420O-6
The wavelength dependence of the D* of several high quality AC measurement-mode radiometers, such as photovoltaic 

Si and InGaAs, EIGA, PV-MCT and InSb are shown in Fig. 6. The background-limited power (BLIP) curve, that gives 

the theoretical limit for the D* was calculated with an f/2 detector field-of-view (FOV) for a 295 K background 

radiation. The noise due to the ambient background at temperature, T, is given by the mean square deviation in the total 

rate of photon arrival per unit area and per unit interval given by 

( ) 2 2

2

2

1

c

2

⎟

⎠

⎞ ⎜

⎝

⎛ −

∆ =

kT

h

kT

h

e

e N ν

ν

πν , (3) 

where c is the speed of light, ν is the frequency, h is the Planck constant and k is the Boltzmann constant. The BLIP is 

then given by 

( ) ( )

2

1

2

2

0 2

1

*

BLIP

1 2

c D ,

−

∞

⎥

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎢

⎣

⎡

⎟

⎠

⎞ ⎜

⎝

⎛ −

= ∫ ν

ν

η ν

π ν

η λ ν

ν

d

e

e

h

T

kT

h

kT

h

, (4) 

where η is the quantum efficiency of the detector [9]. The graph shows that the D* of a room temperature (RT) E-IGA 

radiometer was increased by almost three orders of magnitude when the detector was cooled to –85 oC. As a result of 

the above discussed design considerations, the obtained D* value of 3 x 1013 cm Hz1/2/W is very close to the given 

background noise theoretical limit. The PV-MCT radiometer, that has a 2.8 μm cut-off, is also very close to the BLIP 

curve. The D* of an InSb radiometer (with optimized background rejection) is about two orders of magnitude lower. 

The AC mode Si and InGaAs radiometers have very high D* values but they are not suited for detection of IR radiation 

since there is insufficient signal at these wavelengths (the BLIP is > 1018 cm Hz1/2/W). We note that the detectivities of 

the TE-cooled SW-IR detectors greatly exceed that of the liquid nitrogen-cooled InSb detectors. 

0 2 4 6 8 10

1010

1011

1012

1013

1014

1015

1016

-85 oC

RT

Wavelength , μm

 -85 oC IGA

 -85 oC PV-MCT

 -85 oC EIGA

 77 K InSb

 22 oC EIGA

 22 oC Si

 295 K BLIP

Detectivity D*

λC , cm Hz1/2/W

Fig. 6. D* of AC mode Si, InGaAs, EIGA, PV-MCT and InSb radiometers with the background-limited 

power curve at 295 K calculated with an f/2 detector FOV and electrical bandwidth of 0.16 Hz. 

Proc. of SPIE Vol. 6542 65420O-7
5. CALIBRATION TRANSFER 

The spectral responsivity calibration of the above discussed SW-IR radiometers will be derived from the NIST 

electrical-substitution cryogenic radiometer (ESR). The ESR measures the total radiant power in the incident laser beam 

with a relative expanded uncertainty of 0.02 % (k=2). In order to propagate the radiant power responsivity scale with a 

minimal increase in the uncertainty, transfer standard SW-IR radiometers have been developed. These radiometers are 

expected to measure the total beam power with uncertainties of about 0.1 % (k=2). The spatial non-uniformity of 

response of EIGA detectors (as measured by the manufacturer) is between 0.5 % and 1 %. This non-uniformity is too 

high to propagate the responsivity scale with the expected measurement uncertainty. In order to improve the spatial nonuniformity of response, two of the EIGA radiometers (with 3 mm diameter detectors) were modified. Spectralon#

 coated 

integrating spheres of 38 mm diameter with 5 mm diameter input apertures were attached to the front of the 

radiometers. This attachment makes it possible to convert an EIGA radiometer from power measurement mode into 

irradiance measurement mode. The irradiance responsivity is equal to the product of the power responsivity and the 

aperture area. The picture of a modified EIGA radiometer head is shown in Fig. 7. The picture shows not only the 

entrance aperture in the sphere, but also the side connector for the temperature controller and the tube-connector on the 

heat sink for circulating the water-coolant. The uniformity was tested by scanning a 1 mm diameter beam over the 8 mm 

diameter sphere entrance port (with the 5 mm aperture removed). The precision aperture was removed during this test. 

The measurement results are shown in Fig. 8. The input sphere improved the spatial non-uniformity of the EIGA 

radiometer by about a factor of five. This improvement is needed to perform 0.1 % (k=2) responsivity uncertainty in 

power measurement mode even if different beam positions and different beam diameters are used. Using these 

optimized transfer standard radiometers, a factor of three uncertainty decrease can be expected compared to the present 

near-IR detector spectral responsivity calibrations [2]. Also, these radiometers make it possible to extend the NIST 

spectral responsivity calibrations to 2.5 μm with close to 0.1 % (k=2) responsivity uncertainties in both radiant power 

and irradiance measurement modes. 

Fig. 7. Transfer standard EIGA radiometer head with an aperture equipped integrating sphere. 

Proc. of SPIE Vol. 6542 65420O-8
Fig. 8. Spatial non-uniformity of response of a sphere-input radiometer at 1250 nm. 

6. CONCLUSIONS 

Radiant power and irradiance measuring transfer- and working-standard SW-IR radiometers have been developed to 

extend the NIST spectral responsivity scale to 2.5 μm with close to 0.1 % (k=2) responsivity uncertainty. Instead of 

cryogenic cooling, 4-stage thermoelectric coolers were used to stabilize the temperature of the applied 5 mm, 3 mm, and 

1 mm diameter detectors at -85 o

C. The dissipated heat from the TE coolers was removed using heat sinks constructed 

with either air flow or circulated water cooling. As a result of an additional analog control loop, the temperature of the 

applied SW-IR detectors could be stabilized at temperatures as low as -85 o

C. The radiometers were characterized in 

both DC and AC measurement modes. In DC mode, at a bandwidth of 0.3 Hz, an NEC of 4 pA was measured with a 

3 mm diameter EIGA detector. In AC mode, an NEC=7 fA was measured with a 1 mm diameter EIGA detector (using a 

cold FOV limiter) at a bandwidth of 0.16 Hz. This corresponds to an AC-mode NEP = 5.4 fW which is close to the 

3 fW DC-mode NEP of silicon photodiodes. 

7. ACKNOWLEDGEMENTS 

This project was funded by the U.S. Air Force Primary Standards Laboratory in the Calibration Coordination Group. 

The authors thank C. R. Lustenberger of Gamma Scientific, Inc. for participating in the design of the radiometers and T. 

C. Larason of NIST for measuring the spatial uniformity of response of the sphere radiometers. 

# Certain commercial equipment, instruments, or materials are identified in this paper to foster understanding. Such 

identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, 

nor does it imply that the material or equipment are necessarily the best available for the purpose.

REFERENCES 

1. G. P. Eppeldauer, NIST Technical Note 1438, Optical Radiation Measurement with Selected Detectors and Matched 

Electronic Circuits Between 200 nm and 20 μm, U.S. Government Printing Office, Washington, DC, 20402, 2001. 

2. T. C. Larason, S. S. Bruce, and A. C. Parr, Spectroradiometric Detector Measurements: Part II – Visible to NearInfrared Detectors, Special Publication 250-41, U.S. Department of Commerce, February, 1998. 

1.000

1.002

-3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5

-3.5

-2.5

-1.5

-0.5

0.5

1.5

2.5

3.5

x [mm]

y [mm]

Proc. of SPIE Vol. 6542 65420O-9
3. H. W. Yoon, M. C. Dopkiss, and G. P. Eppeldauer, Performance comparisons of InGaAs, extended InGaAs and 

short-wave HgCdTe detectors between 1 μm and 2.5 μm. SPIE, Vol. 6297, p. 629703-1 to 629703-10, 2006. 

4. G. P. Eppeldauer and H. W. Yoon, AC-Mode SW-IR Radiation Thermometers for Measurement of Ambient 

Temperatures, Tempmeko 2007, to be published. 

5. G. P. Eppeldauer, J. Zeng, and L. M. Hanssen, Development and calibration of pyroelectric radiometer standards at 

NIST, SPIE Proc. Vol. 6201, pp. 620119-1 to 620119-12, 2006. 

6. G. P. Eppeldauer, M. Racz, and L.M. Hanssen, Spectral responsivity determination of a transfer-standard 

pyroelectric radiometer, SPIE Infrared Spaceborne Remote Sensing X., Symposium Proc. Volume 4818, p. 118-126, 

Seattle, Washington, July 10-11, 2002. 

7. G. Eppeldauer, M. Racz, and T. Larason, Optical Characterization of Diffuser-input Standard Irradiance Meters, 

Optika’98, 5th Congress on Modern Optics, 14-17 September, Budapest, Hungary. SPIE Proc. Vol. 3573, p. 220-224, 

1998. 

8. G. Eppeldauer, Noise-optimized silicon radiometers, J. Res. Natl. Inst. Stand. Technol. Vol. 105, No. 209, p. 209-

219, 2000. 

9. P. R. Norton, in “Photodetectors,” Handbook of Optics, ed. By M. Bass, 1995 (McGraw-Hill, New York) P. 15.11 

to 15.13. 

Proc. of SPIE Vol. 6542 65420O-10
 

Measurement of thermal radiation using regular 

glass optics and short-wave infrared detectors 

H. W. Yoon1*, G. P. Eppeldauer1 

1

Optical Technology Division 

National Institute of Standards and Technology 

100 Bureau Drive 

Gaithersburg, MD 20899, USA 

*Corresponding author: hyoon@nist.gov

Abstract: The measurement of thermal radiation from ambienttemperature objects using short-wave infrared detectors and regular glass 

optics is described. The detectors are chosen to operate in the 2.0 μm to 

2.5 μm atmospheric window. Selection of detectors with high shunt 

resistance along with the 4-stage thermo-electric cooling of the detectors to 

-85 o

C results in detectivity, D*, of 4 x 1013 cm Hz1/2/W which is near the 

back-ground limited performance at 295 K. Furthermore, the use of the 

regular-glass commercial optics to collect the thermal radiation results in 

diffraction-limited imaging. The use of a radiation thermometer 

constructed with these elements for the measurement of a blackbody from 

20 o

C to 50 oC results in noise-equivalent temperature difference (NETD) of 

< 3 mK at 50 °C. The operation at shorter wavelengths than traditional 

thermal imagers also leads to lower sensitivity to the emissivity of the 

object in determining the temperature of the object. These elements are 

used to construct a calibrator for an infrared collimator, and such a system 

demonstrates noise-equivalent irradiances of < 5 fW/cm2

. These results 

indicate that thermal imagers using short-wave infrared sensors could be 

constructed utilizing commercial glass optics with possible better imaging 

performance and lower NETD than existing, cryogenically-cooled thermal 

imagers. 

© 2007 Optical Society of America 

OCIS codes: (040.3060) Infrared Detectors; (120.4640) Optical Instrumentation 

____________________________________________________________________ 

References and links 

1. A. Rogalski and K. Chrzanowski, Infrared devices and technique, Opto-Electronics Review 10(2): 111(2002). 

2. D.G. Crowe, P.R. Norton, T. Limperis and J. Mudar, “Detectors,” in Electro-Optical Components, W. D. 

Rogatto ed., Infrared Information Analysis Center, Michigan, 1993. 

3. Schott glass designations. 

4. H.W. Yoon, D.W. Allen, and R.D. Saunders, “Methods to reduce the size-of-source effect in 

radiometers,” Metrologia 42, 89-96 (2005). 

#

 Certain commercial equipment, instruments, or materials are identified in this paper to foster understanding. 

Such identification does not imply recommendation or endorsement by the National Institute of Standards and 

Technology, nor does it imply that the material or equipment are necessarily the best available for the purpose. 

____________________________________________________________________________________
 

1. Introduction 

The needs for measurement of thermal radiation from ambient-temperature and highertemperature objects are vast and wide ranging [1]. These needs arise from requirements of 

surveillance and non-destructive testing to early and accurate detection of hot objects at far 

distances for defense and other applications. At present, these needs are met by the use of 

cryogenically-cooled quantum detector materials such as InSb or HgCdTe or by the use of 

thermal detectors such as thermopiles, pyroelectrics or bolometers [2]. Although the quantum 

detectors have sufficient sensitivities to be able to measure thermal radiation with low noiseequivalent temperature difference (NETD), the need for cryogens or cryo-coolers and the 

accompanying vacuum jacket for low-noise operations limit their versatility in many 

applications. Furthermore, the thermal cycling and eventual ice build-up inside the cryostat 

lead to poor long-term stability of the responsivity and require routine maintenance of the 

system. Instruments utilizing thermal detectors suffer from low signal-to-noise ratios 

resulting from the low-power responsivities of the thermal detectors which lead to high NETD. 

Also, the use of thermal detectors can result in drift of the measured signal from any change 

in the surrounding ambient temperatures. For collection optics, these traditional detectors 

also require the use of either reflective mirrors or refractive lenses which transmit in the midinfrared and long-infrared wavelength such as those constructed using Si, Ge or ZnSe. 

In the past, the use of short-wave infrared (SWIR) wavelength region for thermal imaging 

has been limited due to the poor signal-to-noise performances of the existing detectors. The 

most commonly utilized detector in this wavelength region is the photoconductive PbS which 

requires operation with dry ice at 193 K for optimum operation. However, photoconductive 

PbS was found to be limited by its high noise-equivalent power, poor long-term stability of 

response and possible signal nonlinearity. Other SWIR detectors such as photoconductive 

HgCdTe (MCT), PbSe and InAs detectors have also been used but with limited success. 

Due to the rapid improvements in InGaAs material fabrication driven by the optical fiber 

communications, the InGaAs photodiodes are the preferred detectors in the 900 nm to 

1700 nm range. With modification of the fabrication process, InGaAs can be made to be 

sensitive to infrared radiation from 900 nm to 2500 nm, with the long-wavelength bandgap 

occurring at around 2500 nm. However, the extension of the responsivity to longer 

wavelengths results in the ex-InGaAs diodes having lower shunt resistances than the regular 

InGaAs photodiodes. The shunt resistances of the ex-InGaAs diodes can be increased by 

cooling the diode with 1-stage to 4-stage thermo-electric (TE) coolers. Similarly, 

photovoltaic (pv) MCT photodiodes can also be used. The MCT photodiodes can be 

fabricated for sensitivity from 2.0 μm to 2.5 μm with long-wavelength cutoffs near 2.5 μm, 

distinct from the usual 10 μm to 12 μm operation of these devices. The shunt resistances of 

the SWIR MCT detectors can also be increased by TE cooling, and such detectors can be 

substituted for ex-InGaAs. 

In this work, the use of TE cooled, extended InGaAs and short-wave, pv MCT diodes for 

the measurement of thermal radiation from ambient-temperature objects is described. The 

work is motivated by the examination of the thermal emission and the radiance ratios between 

the object and the background radiation. The SWIR radiometers can be designed to operate in 

a clear, atmospheric window between 2.0 μm and 2.5 μm. In this wavelength region, in 

contrast to other IR bands, off-the shelf, glass optics can be utilized for the collection of the 

emitted radiation. Optical modeling using glass lenses indicates that diffraction-limited 

performance is achieved. As examples, we demonstrate, using a TE-cooled ex-InGaAs 

radiation thermometer and a radiometer for measuring collimated sources, that such 

radiometers can achieve significantly better irradiance and radiance sensitivity than 

radiometers utilizing cryogenically-cooled InSb. 
 

2. Planck Radiance Analysis 

The choice of the optimum wavelengths for the detection of Planck radiation depends upon 

many factors. Although the obvious choice of the wavelength would be at the peak of the 

Planck radiance of the emitting body, other considerations can mitigate the signal advantages 

from measuring at the peak of the spectral distribution. Often, object of interest will be in the 

presence of ambient background radiation which is also detected by the sensors leading to a 

large contaminating, background signal. The background radiation could come from objects 

in the field-of-view of the radiometer or from the thermal emission from body of the 

radiometer. Much of the unwanted background signal can be eliminated by the use of lock-in 

detection and the placement of the modulator. However, outside of the laboratory 

environment, the optimum modulation, which is directly at the source, is not feasible. 

In many applications, the detection of thermal radiation from an object which is hotter 

than the ambient background is desired. In such cases, the advantages of using the shortest 

wavelength while having sufficient signals from the target area can be seen from Fig. 1. The 

0 1000 2000 3000 4000 5000

10-3

10-2

10-1

100

101

102

103

104

105

 Spectral Radiance [ W/ cm2/cm sr ]

Wavelength [ nm ]

 22 oC

 300 oC

 500 oC

 1000 oC

Figure 1. The spectral radiances from the use of the Planck radiance law for blackbodies at the respective 

temperatures. In the spectral region from 2.0 μm to 2.5 μm, a blackbody at 22 °C and a blackbody at 300 °C will 

differ by a factor > 19,000 while at a center wavelength of 4.0 μm, such ratio is ~ 370. 

Planck radiances for the temperatures of interest are plotted, and for comparisons, the 

radiance differences between the ambient background at 22 °C and the target at 300 °C at 

2.4 μm and at 4.0 μm can be compared. At 4.0 μm, the spectral radiance ratio from the roomtemperature 22 °C background and a blackbody at 300 °C is 

( )

( ) 370

22

300

0.4

0.4 ≅

CL

CL

o

m

o

m

μ

μ . (1) 

However, at a center wavelength of 2.4 μm, the Planck radiance ratio is much larger at 
 

( )

( )

4

4.2

4.2 10x9.1

22

300

≅

CL

CL

o

m

o

m

μ

μ . (2) 

The radiance from the 22 °C ambient at 2.4 μm is lower than at 4.0 μm by a factor of 260 

which will result in lower interfering radiances from the background at the shorter 

wavelengths. This simple analysis indicates that if sufficiently sensitive detectors with low 

noise and high responsivity can be developed, then such detectors will be less influenced by 

the background radiation while still being able to detect the radiation source. It is critical that 

the band-gap of the detectors cut-off is at or near 2.5 μm so that the sensor is less sensitive to 

the ambient background radiation. The Planck radiances also indicate that the dynamic range 

of the signals (the useful-signal and background-signal ratios) for a source at 300 °C and at 

1000 °C will be greater at 2.25 μm than at 4.0 μm, thus leading to greater contrast ratios 

between the objects. 

3. SWIR Detectivity or D* 

The relative performances of detectors can be compared independently from the detector 

element sizes using the criterion of D* or detectivity (sometimes called Jones) with units of 

cm Hz1/2 / W. The D* of the detector can be increased by decreasing the noise-equivalent 

power (NEP). A decrease in the NEP can be achieved by increasing the shunt resistance, RS, 

of the detector which will decrease the noise at the output of the photodiode trans-impedance 

amplifier. The RS can be increased by several techniques. Since the shunt resistance is 

typically due to the areal density of the electrical imperfections of the detector, it depends on 

the surface area of the detector. A detector with a smaller surface area will have higher shunt 

resistance resulting in a lower NEP and a higher D*. 

The shunt resistances of semiconductor photodiodes also depend on the temperature of 

the diode. The shunt resistances of 3 mm and 1 mm diameter ex-InGaAs and short-wave 

MCT (2.8 μm bandgap) detectors were measured as a function of diode temperature. The 

temperatures were varied using the built-in 4-stage thermoelectric coolers with thermistor 

feedback controls. The shunt resistances shown in Fig. 2 were determined from the inverse 
-80 -60 -40 -20 0 20 40

103

104

105

106

107

108

3 mm exInGaAs

1 mm exInGaAs

1 mm swMCT

Shunt Resistance [ 

Ω ]

Temperature [ oC ]

 3 mm exInGaAs

 1 mm swMCT

 1mm exInGaAs

 1 mm swMCT w/cap

 1 mm exInGaAs w/cap

Figure 2. The temperature dependence of shunt resistance for 1 mm and 3 mm diameter InGaAs, extended InGaAs 

and 1 mm diameter swMCT detectors. Shunt resistance increase of 1000 over the room temperature values are easily 

achieved using TE cooling. The notation “w/cap” refers to the addition of a TE-cooled 30° field-of-view limiting 

baffle incorporated onto the front of the diode in the detector housing. 

slope of the current-voltage (I-V) curves. All the detectors are found to have a semilogarithmic dependence on diode temperature. These results indicate that the shunt 

impedances for the ex-InGaAs detector and the sw-MCT can be increased by a factor > 1000, 

resulting in 3x106 Ω with the 3 mm diameter detector cooled to -85 °C (188 K). The 3 mm 

diameter diode has a lower shunt resistance than the 1 mm diameter diode which is inversely 

proportional to the area of the diode. This indicates that the defects which limit the shunt 

resistance are uniformly distributed across the diode area. 

The D* or the detectivity of various detectors at the peak wavelength of their spectral 

responsivities are shown in Fig. 3 along with the back-ground-limited performance (BLIP) at 
0 2 4 6 8 10

1010

1011

1012

1013

1014

1015

1016

-85 oC

RT

Wavelength [μ m]

 -85 oC InGaAs

 -85 oC swMCT

 -85 oC exInGaAs

 77 K InSb

 22 oC ex InGaAs

 22 oC Si

 295 K BLIP

Detectivity, D*

λ C [ cm Hz1/2/W ]

Figure 3. The background-limited power (BLIP) restricted to F/2 field-of-view for 295 K background with the 

detectivity of NIR, SWIR and MIR sensors plotted versus their bandgap wavelengths. The detectivities plotted are 

for electrical bandwidth of 0.16 Hz. The detectivities of the uncooled exInGaAs at room temperature (RT) does not 

meet the BLIP curve while the 4-staged TE cooled detectors lie near the BLIP curve. 

295 K. The BLIP limits the performances of detectors operating in typical laboratory 

environments since the fluctuations in the arrival rate of photons from the ambient 

background will limit the noise floor. One can observe that much higher detectivities, without 

being limited by the BLIP, are possible as the detection wavelengths are made shorter than the 

peak of the 295 K Planck radiances at 10 μm. With cooling of the ex-InGaAs diode, the 

measured D* is > 3 x 1013 cm Hz1/2 / W, which is almost a factor of 100 greater than that of 

liquid-nitrogen cooled InSb detector at ~ 5 x 1011 cm Hz1/2 / W. These detectivities at long 

wavelengths would be unusable in ambient environments because of the limitations of the 

BLIP, but at the shorter wavelengths, the reduction in the BLIP allows even higher D*. 

4. Spectral Responsivity and Atmospheric Transmission 

The advantages of higher detectivities for these detectors cannot be utilized if the spectral 

responsivities of the detectors are in regions of atmospheric absorption bands. The spectral 

irradiance responsivity of a 2-stage cooled ex-InGaAs photodiode is shown in Fig. 4. The 
 

1000 1500 2000 2500

0.00

0.02

0.04

0.06

0.08

Spectral Irradiance Responsivity [ A / W / cm2 ]

Wavelength [ nm ]

Figure 4. The NIST-measured spectral irradiance responsivity of an ex-InGaAs detector demonstrating the peak of 

the responsivity lies in the 2.0 μm to 2.5 μm region. 

peak of the responsivity can be tuned by selecting the material composition such that the 

band-gap energy of InGaAs or HgCdTe diodes can be made to occur at a range of 

wavelengths from 1.7 μm to 2.6 μm. Since these are direct band-gap materials, the quantum 

efficiency of the photon-to-electron conversion is also high. 

In Fig. 5, the atmospheric transmission as a function of wavelength is plotted showing 

1.0 1.5 2.0 2.5 3.0

0.0

0.2

0.4

0.6

0.8

1.0

Transmittance

Wavelength [ μm ]

Figure 5. The transmittance at sea level for a 1 m path length of atmosphere showing the window between 2.0 μm to 

2.5 μm. 

that such spectrally selected radiometers can operate in an atmospherically clear transmission 

region. To avoid fluctuations due to atmospheric changes in the transmission or absorption, 

ex-InGaAs radiometers can be constructed with cut-on filters to further restrict the spectral 

region from 2.0 μm to 2.5 μm. 
 

5. Detector Signals from Ambient Objects 

The results of initial feasibilities studies of using SWIR detectors for measurements of 

ambient temperature objects are shown in Table 1. A 3 mm diameter ex-InGaAs detector was 

Table 1. The signals from various objects at the estimated temperatures filling the field-of-view with the 3 mm 

diameter, 4-stage TE cooled (-85 °C) ex-InGaAs photodiode with a preamplifier gain of 107

 V/A. These signals 

clearly demonstrate that there is sufficient signal for thermal imaging. The differences in the spectral emissivity of 

the room temperature objects account for the different signals. 

Material Signal [ V ] St. Dev. [ V ] 

LN2 dewar ( 77 K) 0.026 2.5 x 10-5

Al foil ( 295 K ) 0.0912 2.5 x 10-6

Anodized Al ( 295 K ) 0.115 2.5 x 10-6

Black polymer ( 295 K ) 0.137 2.5 x 10-6

Human hand ( 307 K ) 0.226 2.5 x 10-6

TE cooled to -85 °C and the photocurrents were converted to voltages using a current-tovoltage amplifier at a gain of 107

 V/A. Various objects with differing temperatures and 

emissivities were placed to fill the field-of-view of the detector. Although the detector was 

placed over the mouth of a liquid-nitrogen (LN2) dewar to reduce the ambient background 

signal, the field-of-view could not be completely filled with a 77 K environment. The signals 

from the various objects are listed in col. 2 of Table 1. The lower temperature background of 

the LN2 dewar results in lower signals, and the low emissivity of the aluminum foil also leads 

to low signals. The difference in the signals with the changing temperature and the emissivity 

of the objects at room temperature and human body temperatures can be observed. These 

results clearly indicate that SWIR detectors have the sensitivity to measure objects at ambient 

temperatures. 

6. Use of Traditional Glass Refractive Optics 

One of the greatest advantages of operating in this atmospheric window is that unlike the 

traditional mid- or thermal-infrared regions where the choices of refractive lens materials are 

limited, many optical glasses transmit to 2.5 μm. The transmittances of 10 mm thick BK7 

and SF5 glasses [3], which are used in typical achromat lens combinations, are shown in Fig. 

6. These off-the- 
1.4 1.6 1.8 2.0 2.2 2.4 2.6

0.5

0.6

0.7

0.8

0.9

1.0

Transmittance 

Wavelength [ μm ]

 BK7 10 mm

 SF5 10 mm 

Figure 6. The transmittances of 10 mm thick BK7 (crown) glass and SF5 (flint) glass elements which are commonly 

used to form achromat lenses. Other optical glasses have generally similar transmittances. 

shelf achromats are used to collect the SWIR radiation. Since these glasses also transmit in 

the visible radiation, the optical alignment can be performed using visible radiation and then 

refocused to optimize the thermal infrared signal. Such lenses could be easily optimized for 

diffraction-limited optical performance as shown later by optical modeling using commercial 

software. In addition, if the detectors are designed so that the back substrate is thinned, then 

the spectral responsivities can be made to range from the visible to 2.5 μm. For such a 

detector, these optical glass lenses can be refocused to use a single lens system for visible to 

thermal imaging. 

7. Imaging Performance of Traditional Glass Optics in the SWIR 

Optical performances of lenses used in the visible wavelength region can be assessed for the 

SWIR by using an optical modeling software. In Table 2, typical achromat specifications are 

Table 2. The specifications of the 200 mm focal length achromatic lens used for the optical modeling. 

Radius of Curvature 

[ mm ] Thickness [ mm ] 

Radius of 

Entrance Aperture 

[mm ] 

Material 

121.342 8.0 25.4 BK7 

-91.445 4.0 25.4 SF5 

-271.562 -- 25.4 -- 

shown with the surface curvatures and thicknesses along with the glass types. The achromat 

specifications are for an off-the-shelf achromat which has been optimized for infinite 

conjugate in the visible wavelength region. Typically, if the optics has been optimized at a 

shorter wavelengths, the performance at longer wavelengths will be better than at the 

optimized wavelengths. The specifications in Table 2 for a 200 mm focal length lens are used 

to model the optical performance shown in Table 3 at 2.45 μm. Table 2 shows the root-mean- 
 

Table 3. The optical performance of the achromatic lens at infinite conjugate at a wavelength of 2.45 μm. The 

performance is diffraction limited as indicated by a smaller geometric, root-mean-squared (RMS) radius than the 

diffraction limit radius. 

Beam Entrance 

Radius [ mm ] 

Geometric RMS 

Radius [ mm ] 

Diffraction Limit 

Radius [ mm ] Strehl Ratio 

24.0 0.002123 0.013145 0.9883 

squared radius as compared to the diffraction-limited radius indicating that the lens is 

diffraction limited with close to optimum Strehl ratio of 1.0 for an infinite conjugate operation 

at 2.45 μm. Although the optical performance will suffer if infinite conjugate optimized 

lenses are used in finite conjugate (1:1) imaging, custom lenses with computer-optimized 

curvatures and thicknesses can be fabricated if better performance is desired. 

8. SWIR detector performance in radiation thermometers 

To compare the performances of SWIR detectors against traditional cryogenically cooled 

detectors, the SWIR detectors were constructed into experimental radiation thermometers. 

Since optical glasses transmit at these wavelengths, regular achromats were used as objective 

lenses in the prototype shown in Fig. 7. A variable-temperature blackbody set to room 

Blackbody

Field 

Stop

Objective 

Lens

Chopper 

Wheel

Lyot 

stop

Photodiode

Aperture

Figure 7. The SWIR detector was constructed into a radiation thermometer configuration to determine the noiseequivalent temperature difference as a function of the blackbody temperature. The distance between the objective 

lens and the blackbody aperture was 500 mm with a 50 mm diameter objective resulting in roughly a f/10 collection 

geometry. A 6 mm diameter target was focused at the blackbody opening. 

temperatures and higher was used as the source of radiation. A 6 mm diameter target was 

imaged by the radiation thermometer at a distance of 50 cm between the source aperture and 

front of the objective lens. The radiation was imaged onto a field stop with a chopper wheel 

placed close to the field stop. The radiation was collimated and focused onto the 3 mm 

diameter detector with achromats. The ex-InGaAs detector was cooled to –85 °C with 

thermoelectric cooling. The Lyot stop [4] serves as the aperture stop behind the field stop. 

Due to the low scatter objective, the Lyot stop and the internal field-of-view limiter, this 

radiation thermometer design has out-of-field rejection which enables internal chopping. A 

novel chopper using a mirrored surface was used to have the TE-cooled diode view itself 

using the self-staring or “Narcissus” effect. The reference for the chopped radiation then 

becomes the radiation from the temperature-stabilized detector leading to long-term stability 

of the chopped signal. 
 

The results of the measurements with the blackbody at 50 °C can be seen in Fig. 8. A 

11:19 11:20 11:21 11:22 11:23 11:24

49.98

49.99

50.00

50.01

50.02

Temperature [ 

o C ]

Time [hh:mm]

Figure 8. The stability of the chopped radiation thermometer measuring the radiance temperature of the 50 oC 

blackbody. The blackbody was constructed with a spherical geometry and a control loop was used to stabilize the 

blackbody temperature. 

noise-equivalent temperature difference (NETD) of < 3 mK can be observed from the 

standard deviation of the temperature measurements taken with an electrical bandwidth of 

0.16 Hz. A longer time sequence of temperatures showed changes due to the fluctuations 

from the heater controller of the blackbody which are not shown in the short time sequence in 

Fig. 8. 

The NETD plotted as a function of the blackbody temperature is shown in Fig. 9. The 

20 25 30 35 40 45 50

0

20

40

60

80

100

NETD [ mK ]

Blackbody Temperature [ oC ]

Figure 9. The noise-equivalent temperature difference (NETD), at an electrical bandwidth of 0.16 Hz, obtained from 

the standard deviation of the radiation thermometer measurements at the respective blackbody temperatures. The 
 

increase in the NETD from the low signals as the blackbody temperature approaches the laboratory ambient 

temperatures is observed. The NETD at human body temperature of 36 °C is below 10 mK. 

NETD increases rapidly as the target temperature becomes comparable to the chopper-wheel 

temperature, but at the human body temperature of 36 o

C, the NETD remains < 10 mK. 

These results demonstrate that the NETD is comparable to that of InSb detectors for 

blackbody temperatures > 25 °C without the need for cryogenic cooling. 

9. Noise-equivalent Irradiance 

To test the limits of detection for irradiance, a blackbody at 300 °C was placed at the entrance 

to the 1.24 m focal length collimator as shown in Fig. 10. An aperture wheel was placed in 

Chopper 1

1.24 m fl Collimator

200 mm fl SWIR Radiometer

Blackbody

Chopper 2

Figure 10. The schematic of the SWIR radiometer used to measure the collimated output from an infrared collimator. 

The use of the two chopper positions allows comparison of “upstream” chopping at the source to “down-stream” 

chopping inside the radiometer. 

front of the blackbody, and the chopper wheel (Chopper 1) was placed between the blackbody 

and the aperture wheel. From the geometry of the collimator, the calculated irradiance at the 

40 mm diameter entrance pupil of the radiometer can be determined. Another alternatively 

used chopper wheel (Chopper 2) was placed inside the radiometer for “down-stream” 

chopping at the radiometer. The measurements of the noise-equivalent irradiance (NEI) with 

the setup in Fig. 11 are shown in Table 4. 

Table 4. The noise-equivalent irradiances found using the SWIR radiometers from the measurements of the 

collimator shown in Fig. 10 with the blackbody source with the respective source diameters at 300 °C. 

Diameter 

[ um ] 

Measured 

Signal [ V ] 

Standard 

Deviation 

[ V ] 

Standard 

Deviation/Signal 

Noise equivalent 

irradiance [ W / cm2 ] 

250.0 9.54 x10-3 1.50 x10-6 1.57 x10-4 1.00 x10-14

150.0 3.62 x10-3 6.40 x10-7 1.77 x10-4 4.06 x10-15

50.0 3.78 x10-4 7.30 x10-7 1.93 x10-3 4.94 x10-15
 

10. Applications of SWIR Radiometers 

One of the advantages of using the SWIR radiometers is the transparency of glass in buildings, 

automobiles and other equipment at these wavelengths. If SWIR thermal imagers with low 

NETD could be developed at these wavelengths, then it would be possible to perform thermal 

imaging for human detection through the automotive glass and building windows. 

Firefighters and emergency personnel could determine the presence human beings without 

having to break the window and risk acceleration of smoldering fires. Such thermal imaging 

is not possible for the currently used long-wavelength infrared detectors. In addition, thermal 

imagers are used for diagnostics of electrical power switches where the operator must be 

protected from potentially lethal voltages with a protective cover. Often, these covers require 

special infrared transmitting glasses for thermal imaging in order to determine which switches 

are overheating and about to fail. Regular window glass covers could be used in these 

applications. There are also a large number of military applications, especially in target 

discrimination at long distances where the traditional InSb and MCT detectors are not 

sensitive enough for accurate sensing. 

11. Conclusions 

We demonstrate that SWIR detectors with a 2.5 μm wavelength cut-off can be used as new 

generation of sensors for IR radiometers and radiation thermometers. Although the cut-on at 

2.0 μm can be accomplished with a filter, the cut-off at around 2.5 μm must be intrinsic to the 

detector material from the fabrication process to avoid large background currents. These 

detectors can be used in a spectral wavelength region where the atmosphere has a clear 

window from 2.0 μm to 2.5 μm, leading to the use of refractive-glass optics without central 

obscurations. Furthermore, equivalent or better infrared detection capability than the 

traditionally used detectors can be achieved in a compact, low-maintenance design with the 

capabilities of measuring human body temperatures. 
 

#

 Certain commercial equipment, instruments, or materials are identified in this paper to foster understanding. Such 

identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, 

nor does it imply that the material or equipment are necessarily the best available for the purpose. 

References 

1. A. Rogalski and K. Chrzanowski, Infrared devices and technique, Opto-Electronics Review 10(2): 111(2002). 

2. D.G. Crowe, P.R. Norton, T. Limperis and J. Mudar, “Detectors,” in Electro-Optical Components, W. D. Rogatto 

ed., The Infrared and Electro-Optical Systems Handbook, Infrared Information Analysis Center, Michigan, 

1993. 

3. Schott glass designations. 

4. H.W. Yoon, D.W. Allen, and R.D. Saunders, “Methods to reduce the size-of-source effect in radiometers,” 

Metrologia 42, 89-96 (2005).
AC-Mode Short-Wavelength IR Radiation Thermometers for 

Measurement of Ambient Temperatures 

G. P. Eppeldauer and H. W. Yoon 

Optical Technology Division, National Institute of Standards and Technology, 

Gaithersburg, Maryland 20899, USA 

ABSTRACT 

Recent improvements in the fabrication of short-wave infrared (SW-IR) quantum 

detectors have opened a new era in radiation thermometry. Ambient and higher 

temperatures can be measured with low uncertainties using thermoelectrically (TE) 

cooled extended-InGaAs (E-IGA) and short-wave photovoltaic-HgCdTe (SW-MCT) 

detectors. Since these detectors have low cut-off wavelengths (2.5 μm and 2.8 μm, 

respectively), they do not respond past cut-off and are less sensitive to the background 

infrared radiation, resulting in orders of magnitude lower background noise than 

traditionally used broad-band infrared detectors such as cryogenically cooled quantum 

detectors or thermal detectors. At the same time, the cut-off is far enough in the infrared 

to obtain a large enough signal from the source of interest. Because of the low detector 

cut-off wavelength, traditional glass-based optics can be used in the radiation 

thermometers. A chopper produced alternating-current (AC) signal was used to measure 

low temperatures by separating the AC signal from the background-radiation-produced 

direct-current (DC) signal and its fluctuations. Design considerations and characteristics 

of a newly developed SW-IR radiation thermometer are discussed. A noise-equivalent 

temperature difference (NETD) of < 3 mK for a 50 °C blackbody was measured. At the 

human body temperature of 36 °C, the obtained NETD of ~ 10 mK indicates that these 

detectors can be used in non-contact temperature measurements to replace thermopile- or 

pyroelectric-based radiation thermometers. 

KEY WORDS: ambient temperatures; infrared; input optics; NETD; NEP; noise; optical 

radiation; radiance; radiation thermometer; responsivity; non-contact body temperature 

1. INTRODUCTION 

Traditional infrared detectors, such as cryogenically cooled quantum detectors and 

thermal detectors, operate in background-limited mode because of their long cut-off 

wavelengths. In this mode, the background radiation is orders of magnitude larger than 

the target radiation. In addition, the high background-radiation-produced DC signal is not 

stable and has a large noise component. The signal to be measured is usually AC to 

separate it from the DC background signal. However, the large noise component of the 

DC background signal will dominate the output noise of the radiometer unless the 

background signal is significantly reduced. 
Furthermore, ambient-temperature thermal detectors (e.g. thermopiles or 

pyroelectric detectors) have low responsivities and, thus, high noise-equivalent powers 

(NEP). They need large signals (sufficient thermal radiation within the detector system 

bandpass) to obtain reasonable signal-to-noise ratios at the output of the radiometers. In 

many applications, large thermal radiation to be measured is not available, and the signal 

(photocurrent) gain in the radiometers cannot be increased to improve the poor signal-tonoise ratios. Both of the above limitations are apparent in current designs of radiation 

thermometers for measuring human body temperatures. They are prone to drift from 

changes in the immediate thermal environment around the detector and also are not 

capable of transferring a temperature scale to within ± 0.2 °C from 32 °C to 45 °C [1]. 

We describe the development of a short-wave infrared (SW-IR) radiation 

thermometer that can be used as a transfer standard to measure low-temperature 

radiometric sources with low uncertainty and high stability. The design issues and the 

characteristics of this thermometer are discussed here, and we show that cryogenic, 

quantum detector-based radiation thermometer performance can be achieved with 

thermo-electrically cooled SW-IR radiation thermometers. 

2. NETD AND NEP OF RADIATION THERMOMETERS 

The noise-equivalent temperature difference (NETD) and the NEP of a radiation 

thermometer are noise figures-of-merit that are closely related. The NETD shows the 

sensitivity (temperature resolution) of a thermometer while the NEP is used to optimize 

the detectivity of a radiation thermometer. 

The NETD is determined when the thermometer measures the radiation from a 

stable source. In this case, the standard deviation (STD) of the measured photocurrent 

values is divided by the mean of the values to obtain the NETD. The noise equivalent 

signal fluctuation Δ SS can come from both the emitted radiation and the noise in the 

output signal of the thermometer. Using the derivative of the Wien approximation, 

2

2

T

c T

L

L

S

S Δ = Δ = Δ

λ (1) 

where L is the source radiance, = 1.4387752 x 10-2 m·K , T is the temperature of the 

source, and λ is the wavelength where the detector is responsive to the broad-band source 

radiation (such as a blackbody), the NETD can be equated with the calculated ΔT . 

c2

In contrast to the above suggested NETD measurements, the NEP is measured at 

zero (dark or blocked) signal, or close to zero signal. The NEP is the ratio of the output 

noise N to the responsivity R of the radiation thermometer, usually at an electrical 

bandwidth of 1 Hz, 

( )

R

outputN NEP = . (2) 

The output noise can be obtained as the standard deviation (STD) of the thermometer 

photocurrent (output voltage per photocurrent-to-voltage gain). The unit of NEP is W·Hz1/2. The detectivity D* of the thermometer (comprised of the radiation detector and the 

preamplifier) can be calculated from the NEP, 
 NEP

A D* = , (3) 

where A is the active area of the detector. The unit of detectivity is cm·Hz1/2·W-1. 

In traditional broad-band detector applications, where the background-produced 

photocurrent is high, the photocurrent-to-voltage gain (a component of R) cannot be 

increased to high values without saturating the photocurrent-to-voltage converter, but the 

low R will result in a high NEP. The lower background signal of SW-IR detectors makes 

it possible to increase the photocurrent-to-voltage gain in the preamplifier of the 

radiometer. 

The NETD of ambient thermal detectors is higher than 0.1 K, which makes them 

difficult to use for low-uncertainty measurements in many applications, such as for ear 

thermometers [1]. The responsivity of such detectors, i.e. thermopiles and pyroelectric 

detectors, is low. For example, the power responsivity of a pyroelectric detector is 6 

orders of magnitude lower than that of InGaAs (including extended-InGaAs) detectors, 

resulting in 6 orders of magnitude higher NEP. 

Detectors with high responsivity for the SW-IR and low responsivity (high 

rejection) for the long-wave infrared (LW-IR) should be used to achieve low NEP and 

NETD in radiation thermometers. In order to obtain maximum responsivity, the feedback 

resistance of the photocurrent-to-voltage converter should be equal to the shunt resistance 

of the detector. Also, the output noise, N, should be minimized. 

3. DECREASE OF THERMOMETER OUTPUT NOISE 

The output noise of a thermometer can be decreased in a few ways. The dominating noise 

components are the amplified 1/f noise of the current measuring preamplifier, the resistor 

(Johnson) noise (which is obtained from the parallel combination of the detector shunt 

resistance and the feedback resistance of the current meter), and the remaining 

background noise [2]. These three noise components must be minimized to achieve low 

values of NEP. This is in contrast to the dominantly background-noise-limited 

operational mode of traditional mid-IR and long-IR thermometers. 

The 1/f noise can be significantly decreased using AC signal techniques. In this 

case, the signal frequency is much higher than in DC mode measurements. The signal 

frequency should be selected near the elbow of the 1/f noise spectrum of the current-tovoltage converter (preamplifier). A high photodiode shunt resistance can keep the closedloop voltage gain of the photocurrent-to-voltage converter low [3], resulting in low noise 

at the output of the radiometer. The noise of the remaining background signal can be 

further decreased using a metal detector case with a built-in thermoelectric (TE) cooler 

and a cold field-of-view (FOV) limiter for the detector. The side of the metal can, 

viewed by the detector, should remain at room temperature to avoid radiating excess heat 

onto the detector. The achievable signal-to-noise ratio is determined by the performance 

of the first-stage amplifier (preamplifier), which includes the detector and the current-tovoltage converter. As the noise is electrical bandwidth dependent, it can be further 

reduced if the AC signal of the radiometer (thermometer) output is measured with a lockin amplifier that has a large time-constant low-pass filter. 
4. PHOTOCURRENT MEASUREMENT 

In order to describe the effects of detector and feedback impedances and noise sources in 

a photodiode current meter, the equivalent circuit must be discussed. As shown in Fig. 1, 

a photodiode P can be substituted by an ideal current source (double circle) and parallelconnected shunt resistance RS and junction capacitance CJ. The photocurrent IP from 

photodiode P is converted into a voltage V at the output of the operational amplifier 

(OA). R is the feedback resistance and C is the feedback capacitance of the OA. IIN is the 

input current noise and VVN the input voltage noise of the OA. The resistor noise that 

originates from the parallel connection of R and RS is not illustrated here to keep the 

equivalent circuit simple. The resistor noise will be superimposed on V without any 

amplification. 

Fig. 1. Equivalent circuit of a photodiode current meter. 

The photodiode P is denoted by the dotted line. 

The signal gain (current-to-voltage conversion) is the following: 

⎟

⎠

⎞ ⎜

⎝

⎛

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ = −1

P 1

1

1

1

RCj G

R

I

V

ω (4)

where RC is the time constant produced by the feedback components. It determines the 

upper frequency roll-off of the signal. G is the loop gain and it must be large at the signal 

(i.e. the chopping) frequency to keep the uncertainty of the current-to-voltage gain low. 

The loop gain (the product of the OA open-loop gain A and the feedback attenuation β) is 

 G = Aβ (5) 

where β = RS/(RS+R) at low frequency, i.e. as with DC measurements. High loop gain can 

be obtained if β is close to unity (its maximum value). To achieve this condition, the 

shunt impedance, ZS ( S +≡ ω CRjR SS 1 ), must be high at the signal frequency. CS is the 

shunt capacitance of the photodiode. 

The closed-loop voltage gain that determines the amplification of the input noise, 

offset, and drift for the output of the current-to-voltage converter is the reciprocal of β :

CJ

RS

IP

P

C

R

V

O

A

VV

N

I

IN
S

S

V R

RR A + = (6) 

Again, AV can be kept small (close to unity) if the shunt resistance is high relative to the 

feedback resistance. As with the signal-gain above, both G and AV are frequency 

dependent [4]. 

When the shunt resistance is high, the feedback resistor of the current-to-voltage 

amplifier (that determines the signal gain) can be high as well. 

The input impedance of the above photocurrent meter can be calculated as the 

parallel connection of the down-transformed feedback resistor and the up-transformed 

feedback capacitor of the OA: 

( ) 1 1

1

I

1 − −

−

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ ⎟ + ⎠

⎞ ⎜

⎝

⎛ = ACjA

R Z

ω

 (7) 

Linear signal-gain (response) can be achieved if the short-circuit photocurrent of the 

photodiode is measured. In this case, the photodiode shunt impedance must be much 

larger than the input impedance of the current meter: 

ZI << ZP (8)

The preamplifier should not produce any distortion in the wave-shape of the chopped 

optical signal. This requirement can be achieved if the upper roll-off frequency of the 

pre-amplifier is selected high enough: 

RC

f

2π

1 = (9) 

where RC is the time constant from Eq. 4. In practice, the time constant is tuned by 

changing C. In addition to affecting the frequency dependence of the signal gain, 

changing C will modify the frequency dependence of G and AV as well. Therefore, these 

three gains are to be optimized together for the signal (chopping) frequency at all signalgain selections [3]. 

5. SECOND-STAGE LOCK-IN AMPLIFIER 

A large signal-to-noise ratio, as the result of the above discussed first-stage (detectorcurrent meter) optimization, can be further increased using a second-stage lock-in 

amplifier. The lock-in amplifier makes a phase-sensitive rectification of its AC input 

signal and filters out those signal components at frequencies other than the chopping 

frequency (of the optical signal to be measured). The filter of the lock-in amplifier limits 

the electrical bandwidth around the signal (chopping) frequency. Using a sine-wave 

measuring lock-in amplifier, only the fundamental frequency component of the AC input 

signal will be measured. The theoretical reading (conversion factor) of a sine-wave 

measuring lock-in amplifier is: 

H H S 9003.0 4

2 1 == π

 (10) 

where H is half of the peak-to-peak amplitude of the square wave signal (which is equal 

to zero when the chopper blocks the radiation). This conversion factor is not always 
accurate. It can be calibrated against a digital voltmeter (DVM) in DC mode if the input 

signal has a large signal-to-noise ratio. If the chopper is stopped, the DVM reading will 

be S2=2H. The real correction factor will be the ratio of the lock-in amplifier reading to 

the DVM reading. 

In many cases, the frequency-dependent responsivity of a detector-preamplifier 

standard is measured during its calibration and the DC responsivity is reported. When this 

detector-preamplifier standard is used in an application where the chopper and the lock-in 

amplifiers are different, the frequency-dependent responsivity is measured again with 

these different instruments and the DC responsivity is extended to the signal frequency of 

this application using the measured curve. Using the theoretical conversion factor S1, the 

DC responsivity is 2/0.9003 = 2.22 times higher than the value measured by the lock-in 

amplifier. 

6. DESIGN OF SENSITIVE RADIATION THERMOMETERS 

The wavelength interval for a sensitive radiation thermometer should be properly selected 

to obtain high ratios of signal from the target to that of the background. Figure 2 shows 

different blackbody radiance curves for target temperatures ranging from -63 °C to 

850 °C. The graph shows that at long wavelengths the target-signal to background-signal 

(contrast) ratios are much smaller than in the atmospheric window between 2 μm and 

2.5 μm where the SWIR detectors operate. The vertical lines show orders of magnitude 

increase in the contrast ratio when the thermometer measures at 2.25 μm instead of 4 μm. 

01234567

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

104

Spectral Radiance, W/ cm2/ cm sr 

Wavelength, μm 

 22 oC

 300 oC

 350 oC

 600 oC

 850 oC

 -63 oC

Fig. 2. Planck radiance curves between -63 °C and 850 °C. The target-signal to 

background-signal ratios are shown with vertical lines at 2.25 μm and 4 μm. 

Figure 2 also shows that the target signal at 2.25 μm is about an order of 

magnitude smaller than at 4 μm or longer. Therefore, detectors with high D* should be 

selected for the atmospheric window between 2 μm and 2.5 μm. Figure 3 shows the 
spectral power responsivity of an extended-InGaAs (E-IGA) detector. It can be seen that 

the responsivity is high in the 2 μm to 2.5 μm wavelength range. 

0

0.2

0.4

0.6

0.8

1

1.2

1000 1400 1800 2200 2600

Wavelength, nm

Fig. 3. Spectral power responsivity of an extended-InGaAs detector. 

Figure 4 shows the wavelength dependence of D* of several high radiometric 

quality detector-preamplifier units (radiometers), such as Si and InGaAs (near-IR) 

radiometers and different infrared radiometers, including SW-IR such as E-IGA and SWHgCdTe (SW-MCT), and mid-wave infrared (mid-IR) InSb. 

0 2 4 6 8 10

1010

1011

1012

1013

1014

1015

1016

-85 oC

RT

Wavelength , μm

 -85 oC InGaAs

 -85 oC swMCT

 -85 oC exInGaAs

 77 K InSb

 22 oC ex InGaAs

 22 oC Si

 295 K BLIP

Detectivity D*

λC , cm Hz1/2/W

Fig. 4. D* of silicon, near-IR, SW-IR, and mid-IR radiometers with the backgroundlimited power curve at 295 K calculated with an f/2 detector FOV and an electrical 

bandwidth of 0.16 Hz. 
The background-limited power (BLIP) curve, which gives the theoretical limit for 

the D* [5], was calculated with an f/2 detector field-of-view (FOV) for a 295 K 

background radiation. The graph shows that the D* of a room-temperature E-IGA 

radiometer was increased by almost three orders of magnitude when the detector was 

cooled down to –85 °C. As a result of equalizing the three dominant noise components, 

the obtained D* value of 3 x 1013 cm·Hz1/2·W-1 is very close to the background noise 

theoretical limit. The SW-MCT radiometer, with a 2.8 μm cut-off, is also very close to 

the BLIP curve. The D* of an InSb radiometer (with optimized background rejection) is 

about two orders of magnitude lower. The Si and InGaAs radiometers have very high D* 

values but they are not suited for detection of objects at ambient temperatures since there 

is insufficient signal at these wavelengths (the BLIP is > 1018 cm·Hz1/2·W-1). 

Thermometers with high D* (high responsivity and low noise) can be developed 

if detectors with high shunt resistance are used. The shunt resistance of a 1 mm diameter 

SW-IR detector can be increased to about 10 MΩ from 10 kΩ (at room temperature) 

when it is cooled to about -70 °C or lower [6]. Instead of cryogenic cooling, which is 

traditionally used for InSb detectors, four-stage thermo-electric (TE) coolers can be used. 

7. SW-IR RADIATION THERMOMETER CONSTRUCTION 

Using the above design considerations, an experimental radiation thermometer was 

constructed to determine the NETD as a function of blackbody temperature. Since optical 

glasses transmit at these wavelengths, regular achromats were used as objective lenses in 

the prototype shown in Fig. 5. A variable-temperature blackbody set to room 

Field 

Objective Stop

baffle

Objective Lens

Chopper 

Wheel

Lyot 

stop

Photodiode

Collimating 

lens

Blackbody

Aperture

Fig. 5. SW-IR radiation thermometer construction. 

temperatures and higher was used as the source of radiation. A 6 mm diameter target was 

imaged by the radiation thermometer at a distance of 50 cm between the source aperture 

and the front of the objective lens. The radiation was imaged onto a field stop with a 

chopper wheel placed close to the field stop. The radiation was collimated and focused 

onto a 1 mm diameter detector with achromats. The detector was underfilled by the 

image. The extended-InGaAs detector was cooled to –85 °C with TE cooling. The 

detector was attached to a short-circuit photocurrent meter built with a low-noise 

operational amplifier. The Lyot stop [7] serves as the aperture stop behind the field stop. 
Due to the low-scatter objective and the Lyot stop, the thermometer has excellent out-offield rejection that enables internal chopping.

8. NEP AND NETD MEASUREMENT RESULTS 

The output total noise voltage was measured versus signal-gain selections for a 3 mm 

(3 MΩ shunt resistance) extended-InGaAs photodiode current-meter. The temperature of 

the detector was controlled to -85 °C using a 4-stage TE cooler. The noise equivalent 

current (NEC) is equal to the measured total noise voltage divided by the current-tovoltage gain (the value of the feedback resistor). The total noise voltage was measured by 

a lock-in amplifier attached to the output of the photocurrent meter. The chopping 

frequency was 7.5 Hz and the integrating time constant of the lock-in amplifier was 1 s. 

The signal source was a 314 °C blackbody located about 50 cm from the radiometer. The 

NEP was calculated as the ratio of the NEC to the detector (peak) power responsivity of 

1.2 A/W (at 2 μm). The NEC and NEP results are shown on the two Y-axes of Fig. 6. 

10

100

8

9

10

20

30

40

50

60

70

106 107 108 109

Feedback resistor, Ω

Fig. 6. NEP (right-Y) and NEC (left-Y) of a 3 MΩ shunt resistance E-IGA photodiode 

current meter at a lock-in amplifier integrating time constant of 1 s. 

The measured data points are connected with straight lines for better illustration. The 

graph shows that a NEP=15 fW was obtained with the 1 s integration time constant. The 

NEP of this SWIR detector is more than six orders of magnitude lower than the 50-100 

nW·Hz-1/2 NEP of pyroelectric detectors. The 15 fW (obtained with 1 s time constant) 

NEP (and the related output signal-to-noise ratio) could not be improved at the 108

 V·A-1

and 109 V·A-1 signal-gains relative to the 107

 V·A-1 selection where the shunt resistance is 

roughly equal to the feedback resistance. At gain selections of 107 V·A-1 and higher, the 

constant 3 MΩ shunt resistance dominates the resistor noise. The 108

 V·A-1 and higher 

signal gains should be utilized only with higher than 3 MΩ shunt resistance detectors 
because the loop gain decreases and there is no further signal-to-noise advantage. Higher 

shunt resistances of 10 MΩ - 15 MΩ were measured for 1 mm diameter E-IGA and SWMCT detectors. In these cases, the NEP can be further decreased. 

At a blackbody temperature of 50 °C, a NETD of < 3 mK was obtained from the 

standard deviation of the temperature measurements taken with an electrical bandwidth 

of 0.16 Hz. 

The NETD plotted as a function of the blackbody temperature is shown in Fig. 7. 

The NETD increases rapidly as the target temperature becomes comparable to the 

chopper-wheel temperature, but at the human body temperature of 36 °C, the NETD is ~ 

10 mK. These results demonstrate that the NETD is comparable to that of InSb detectors 

for blackbody temperatures > 25 °C without the need for cryogenic cooling. 

20 25 30 35 40 45 50

0

20

40

60

80

100

NETD, mK 

Blackbody Temperature, o C 

Fig. 7. NETD of the experimental radiation thermometer versus target temperature.

9. CONCLUSIONS 

Thermoelectrically-cooled SW-IR detectors attached to noise-optimized photocurrent 

meters can be incorporated into radiation thermometers utilizing traditional achromats to 

measure objects at human-body temperatures. The SW-IR thermometers operate in the 

2 μm to 2.5 μm atmospheric window where the target signal is lower than in the mid-IR. 

However, the target-signal to background-signal ratio is orders of magnitude higher than 

in the mid-IR or long-IR ranges. The NEP of the SW-IR thermometers is more than six 

orders of magnitude lower than that of pyroelectric thermometers. An optically- and 

electronically-optimized SW-IR radiation thermometer was designed, built, and tested. 

Regular glass input optics are used and the incident radiation is chopped. The achieved 

NEP was 15 fW (with 1 s integrating time constant) and the NETD increased from 3 mK 

at 50 °C to 10 mK at 36 °C. While standards-quality radiation thermometers with high 

sensitivity are not presently available, the described SW-IR thermometer can measure 

ambient temperature sources, such as water-bath or tin-point blackbodies, with very low 
uncertainties. With this suggested radiation thermometer standard, the temperature of the 

human body can be measured with a NETD of 10 mK, which is about an order of 

magnitude improvement over existing ear-thermometers. These results indicate that 

transfer standard radiation thermometers for measurements of human-body temperatures 

can be constructed without utilizing cryogenic or thermal detectors. 

REFERENCES

1. I. Pusnik, E.van der Ham, J. Drovsek, Physiol. Meas. 25, 699 (2004) 

2. G.P. Eppeldauer, A.L. Migdall, L.M. Hanssen, Metrologia 35, 485 (1998) 

3. G.P. Eppeldauer, Optical radiation measurement with selected detectors and 

matched electronic circuits between 200 nm and 20 μm. NIST Technical Note, 

2001, 1438 (U.S. Government Printing Office). 

4. G.P. Eppeldauer, J. Res. NIST, 103, 153 (1998) 

5. A. Rogalski, K. Chrzanowski, Opto-Electronics Review 10, 111 (2002) 

6. H.W. Yoon, M.C. Dopkiss, G.P. Eppeldauer, Performance comparisons of 

InGaAs, extended InGaAs and short-wave HgCdTe detectors between 1 and 2.5 

micrometers. SPIE Proceedings, 2006. 6297: p. 629703-1 to 629703-10. 

7. H.W. Yoon, D.W. Allen, R.D. Saunders, Metrologia 42, 89 (2005) 
. .  , 2003, . 24, . 2, 339–356

System-level calibration of a transfer radiometer used to validate EOS

radiance scales

B. C. JOHNSON*, S. W. BROWN, G. P. EPPELDAUER and

K. R. LYKKE

National Institute of Standards and Technology, Optical Technology Division,

Gaithersburg, MD 20899, USA

Abstract. A number of transfer radiometers have been developed by the National

Institute of Standards and Technology (NIST) with the support and funding of

the National Aeronautics and Space Administration’s (NASA’s) satellite sensor

calibration programmes. The transfer radiometers travel to NASA satellite builder

and calibration facilities and validate the radiance scale of calibration sources at

those facilities. One of these instruments, the Earth Observing Systems (EOS)

Visible Transfer Radiometer (VXR), was calibrated for spectral responsivity in

different facilities at NIST using two types of integrating sphere sources (ISSs):

an incandescent lamp-illuminated ISS and a laser-illuminated ISS. The laserilluminated ISS results in reduced uncertainties and a greater dynamic range in

radiance responsivity. We will discuss the calibration procedures using the two

types of source, compare results of calibrations of two of the VXR filter channels

in the two NIST facilities, and suggest additional irradiance and radiance responsivity calibrations that are now possible using the new laser-illuminated facility.

1. Introduction

The National Institute of Standards and Technology (NIST) has undertaken a

role to support the Earth Observing System (EOS) calibration programme of the

National Aeronautics and Space Administration (NASA). The EOS programme is

a major component of NASA’s Earth Sciences Enterprise, which is, in turn, a

significant component of the US Global Change Research Program. The EOS

programme utilizes space-based and ground-based measurement systems to provide

the scientific basis for understanding global change. The unprecedented accuracies

and long-term stability of the measurements required place new and stringent

demands upon the metrology systems that underpin the effort. One of the requirements of the EOS calibration programme is to document the relationship between

radiometric quantities as realized by NIST with those realized by EOS participants,

who often use NIST-traceable radiometric standards (Butler and Barnes 1998).

To accomplish this task, NIST has developed a number of portable artefacts for

establishing the shortest possible measurement chains to the EOS community. These

include transfer radiometers for the visible (Johnson et al. 1998), the short-wave

*e-mail: cjohnson@nist. gov.

Paper presented at the Conference on Characterization and Radiometric Calibration for

Remote Sensing held at Utah State University, Logan, 9–11 November 1999.

International Journal of Remote Sensing

ISSN 0143-1161 print/ISSN 1366-5901 online © 2003 Taylor & Francis Ltd

http://www.tandf.co.uk/journals

DOI: 10.1080/01431160110113205

Downloaded By: [Ingenta Content Distribution TandF titles] At: 01:37 25 December 2008
340 B. C. Johnson et al.

infrared (SWIR; Brown, et al. 1998), and the thermal infrared (Rice and Johnson

1998, Rice et al. 2002) wavelength regions as well as a portable radiance source

(Brown and Johnson 1999, 2002). The transfer artefacts travel to NASA instrument

builder and calibration facilities to verify the radiance of sources used to calibrate

the responsivity of air-and space-borne sensors. They therefore serve as a direct

link from the instrument builder and NASA calibration facilities to the national

radiometric scales maintained at NIST.

This strategy has been successfully implemented at a number of facilities and

locations (Sakuma et al. 1996, Johnson et al. 1997, Butler et al. 1999). The comparisons in Japan in 1995 for the support of the Ocean Color and Temperature Scanner

(OCTS) and the visible radiometer for the Advanced Spaceborne Thermal Emission

and Reflection Radiometer (ASTER) are of particular interest because they related

radiometric scales from two national metrological institutes. For these comparisons,

the agreement between the results with the transfer radiometers and the values

determined by the manufacturer (NEC Corporation) was within±4% (Sakuma et al.

1996, Johnson et al. 1997).

A more involved approach was used with the Sea-viewing Wide Field-of-view

Sensor (SeaWiFS) in 1997 (Johnson et al. 1999). In addition to the radiometric

calibration performed by the instrument manufacturer, a pre-flight radiometric calibration was done at the spacecraft integrator’s facility using an integrating sphere

source that was calibrated at NIST (Early and Johnson 1997). The radiance of this

source at the time of the SeaWiFS pre-flight calibration was determined by using

the SeaWiFS transfer radiometer (SXR) (Johnson et al. 1998) to relate the spectral

radiance of the source from the NIST calibration (in April 1995) to the time of the

SeaWiFS measurements (in spring 1997). Including sphere degradation effects, radiance non-uniformity and other sources of additional uncertainty, the SeaWiFS

radiance responsivity was determined with standard uncertainties of 1.2–3.3%,

depending on the instrument channel (Johnson et al. 1999).

On-orbit solar and ocean colour measurements confirmed the SeaWiFS prelaunch calibration strategy. Solar-based transfer-to-orbit experiments agreed on-orbit

with predicted ground-based values to within 2.5% (Barnes and McClain 1999).

Similarly, vicarious calibrations of SeaWiFS using an ocean buoy near Hawaii under

the auspices of the Marine Optical Buoy (MOBY) programme (Clark et al. 1997,

Herring 1997) to measure the spectral radiance of the ocean has provided corrections

of 3.2% or less to the laboratory-derived calibration coefficients (Barnes and McClain

2000). The good agreement between the pre-launch calibration and on-orbit measurements is a consequence of the thorough calibration approach used by the SeaWiFS

and the MOBY programmes, in particular the direct traceability to NIST established

by the transfer radiometers for the satellite sensor calibration and during field

calibrations of radiometers used at the MOBY site (Cromer and Johnson 1996).

Owing to the increasing constraints in the uncertainties of on-orbit radiometric

measurements by satellite sensors, it is desirable to calibrate the transfer radiometers

with the lowest possible uncertainty. For example, the Moderate Resolution Imaging

Spectroradiometer (MODIS) requires on-orbit radiometric uncertainties* of 5% or

less in radiance and 2% or less in reflectance over the spectral range 412–2130nm

*The coverage probability is not stated explicity but corresponds to an estimated standard

deviation.

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Characterization and radiometric calibration 341

(Guenther et al. 1996). For an on-orbit satellite sensor standard uncertainty in

radiance responsivity of 5%, we would like to validate the calibration source radiance

in the laboratory with standard uncertainties of 1–2%. Current uncertainties in the

spectral responsivity of transfer radiometers in the visible and near-infrared (VNIR)

approach those target levels (Butler et al. 2000), while they are between 2% and 4%

in the SWIR (Yoon et al. 1998), so reduction in the uncertainties of the SWIR

radiometers is important to achieve the laboratory calibration goals.

To understand better the origin of our calibration uncertainties, and in an attempt

to reduce those uncertainties, we calibrated the EOS Visible Transfer Radiometer

(VXR) using two approaches relying on very different types of integrating sphere

sources (ISS): a typical incandescent lamp-illuminated ISS and a laser-illuminated

ISS. The lamp-illuminated source was calibrated for spectral radiance on the NIST

Facility for Automated Spectral Radiance Calibrations (FASCAL) (Walker et al.

1987); the radiance scale in this facility is derived from a variable temperature black

body that is traceable to a gold-point black body. This method was the only one

available at NIST until recently.

The new laser-illuminated ISS takes advantage of the recent technological

advances in the development of laser sources. Sources are now available to cover

the spectral range from the ultraviolet (below 0.2mm) to the infrared (20mm). We

have taken advantage of these laser sources in a new facility termed the Spectral

Irradiance and Radiance response Calibrations with a Uniform Source (SIRCUS)

(Lykke et al. 1998, Brown et al. 2000, Eppeldauer et al. 2000). In this facility, the

output from a variety of lasers is directed into an integrating sphere. The integrating

sphere serves as a uniform, monochromatic, Lambertian source for both irradiance

and radiance response calibrations. Calibrations in the SIRCUS facility are based

on the direct substitution method using detectors whose responsivity is traceable to

the NIST High Accuracy Cryogenic Radiometer (HACR) (Gentile et al. 1996a, b).

A schematic diagram of the VXR is shown in figure 1. An objective lens forms

an intermediate image at the field stop. Wedged mirrors reflect the field stop onto

the six different filter channels. Each VXR channel consists of a narrow-band

interference filter and a silicon photodiode; channel band-moment wavelengths and

Figure 1. Schematic diagram of the VXR, with the critical components labelled. The side

view of the optical system is shown using marginal and chief rays for a single channel.

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full-width-square (FWS) bandwidths are given in table 1. (The band-moment wavelengths are a weighted average using the relative spectral responsivity of the channel

for the weight.) The interference filters, photodiodes, and the precision aperture that

functions as the field stop are all mounted on a temperature-controlled plate. During

operation, they are maintained at 26° C. A relay lens images the field stop onto an

eyepiece used to align the VXR to its target.

We will describe the calibration strategies using two ISSs and compare calibrations of two VXR filter channels using the different approaches. We will then

discuss future applications of the laser-illuminated ISS.

2. Calibration using a lamp-illuminated ISS

The measurement of a broadband source for one channel of the VXR is described

by a simplified measurement equation: S=AVG ∆

t(l)R

f

(l)L

l

(l)dl (1)

whereS is the output signal (V), the productAV is the throughput (m2sr),G is the

(fixed) gain of the transimpedance pre-amplifier (V A−1),t(l) is the spectral transmittance of the optical system (dimensionless), Rf(l) is the spectral flux (subscript f

for flux) responsivity of the silicon photodiode (A W−1),L

l

(l) is the spectral radiance

of the ISS (Wm−2sr−1 nm−1), andl is the wavelength (nm). The variablesAV,G,

t(l), andR

f

(l) depend on the VXR channel under consideration. The outputS is

then the integrated response for the channel.

Let the functionf(l)=t(l)R

f

(l) represent the spectral portion of the VXR

response. Also define the relative spectral responsivityr(l,l

j

)=f(l)/f(l

j

), where the

reference wavelengthl

j is arbitrary but usually near the value that results in the

maximum value off(l). The equation (1) can be written as S=(AVGf(lj)∆r(l, lj

)dl)

∆r(l,l

j

)L

l

(l)dl

∆r(l,l

j

)dl (2)

The factor inside the parentheses on the right-hand side of equation (2) is the

radiance responsivity (or calibration coefficient) for one channel in the VXR, and it

is independent of the choice of the normalization wavelengthl

j

. The ratio of the

integrals is also independent ofl

j

. Equation (2) and measurements of an ISS with

known spectral radianceL

l

(l) are used to determine the calibration coefficientD

b (V mW−cm2srnm). The subscript b stands for broadband. Db= S (∆r(l)L l(l)dl)/(∆r(l)dl)−1 (3)

Table 1. Channel, band-moment wavelength and full-width square bandpass of the VXR

filter channels.

Wavelength Bandpass

Channel (nm) (nm) 1 411.77 10.76 2 441.01 10.50 3 548.40 10.21 4 661.40 9.47 5 775.47 11.11 6 869.93 13.35

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Characterization and radiometric calibration 343

Because the explicit dependence on the normalization wavelength is not necessary, r(l, lj

) is written asr(l). Equation (3) also applies when the VXR is used to assess

the accuracy of sources calibrated independently by the EOS participants. The

comparison is between the actual signals obtained with the VXR to those predicted

using equation (3) and the independent determination of the spectral radiance.

From equation (3), it is clear that three types of measurements are required to

characterize and calibrate the VXR using the lamp-illuminated ISS: (1) determination

of the spectral radianceL

l

(l) of the ISS; (2) determination of the relative spectral

responsivityr(l) of the VXR channels; and (3) determination of the net VXR signal

S corresponding to measurements of the ISS when it is operated to produce the

same radiance as during its calibration. These three steps are illustrated in figure 2.

In general, the ISS need only be calibrated at a single radiance level, but implementation of the basic scheme at multiple, independent levels provides a measure of the

reproducibility of the procedure.

2.1. ISS calibration on FASCAL

The VXR has been calibrated using a number of lamp-illuminated ISSs, most

recently the NIST Portable Radiance Source (NPR) source (Brown and Johnson

1999, 2001). The VXR measured the source a total of 10 times at NIST from January

1999 through September 1999. Monitor photodiodes mounted in the sphere were

used to verify the stability of the ISS radiance over this time period (Brown and

Johnson 2002).

Figure 2. Calibration and characterization of the VXR using the Vis/SCF, FASCAL and the

NPR ISS. The propagation of the radiant flux is indicated by the direction of the lines

with single arrows; lines with double arrows indicate linear translation for the purpose

of source or detector substitution.

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344 B. C. Johnson et al.

The NPR was calibrated for spectral radiance over the wavelength range

300–900nm on FASCAL in May 1999. The primary radiometric standard in

FASCAL is a fixed-point black body at the freezing temperature of gold. The

spectroradiometrically determined temperature (1337.3±0.1)K (k=1), is in agreement with the value defined on the International Temperature Scale of 1990 (Mielenz

et al. 1990). The temperature of the gold-point black body is too low to produce

any measurable flux below about 500nm, so a higher temperature black body is

used to calibrate the ISS. A number of steps are required to calibrate the higher

temperature black body. First, a spectroradiometer, consisting of a prism-grating

monochromator and a photomultiplier, is used to match the spectral radiance of the

gold-point black body to that from a vacuum tungsten-strip lamp at 654.6nm. Next,

the tungsten-strip lamp is used to calibrate a higher temperature, commercial, vacuum

tungsten-strip lamp so that its radiance corresponds to a black body at a temperature

of about 1530K. This lamp holds the scale, and is used to determine the temperature

of a high emittance, variable temperature black body source, again at 654.6nm.

Once the temperature of the black body is known, its spectral radiance at any

wavelength can be calculated using Planck’s equation.

The spectroradiometer is used to transfer the radiance scale from the variable

temperature black body to the ISS. The typical measurement interval for an ISS to

be used with a VNIR instrument such as the VXR is 350–900nm with a step size

of 10nm in the ultraviolet, 50nm in the visible and 100nm in the SWIR. The NPR

spectral radiance and the FASCAL uncertainty of the spectral radiance calibration

are shown in figure 3.

2.2. Relative spectral responsivity measurements

The relative spectral responsivity for the VXR was determined by adaptations of

the NIST Visible/Spectral Flux Comparator (Vis/SCF) (Larason et al. 1998) for

Figure 3. The spectral radiance of the NPR ISS with four lamps in operation. The values

and their relative standard uncertainties, which are identified in the legend, were

determined using FASCAL.

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Characterization and radiometric calibration 345

operation in a relative mode. The Vis/SCF consists of a prism-grating monochromator illuminated by a lamp, a monitor detector, a shutter and a set of working

standard detectors (silicon and germanium photodiodes). These detectors are calibrated using transfer standards (silicon photodiode trap detectors) that are calibrated

against the HACR.

The relative spectral responsivity of the VXR was determined using the same

procedures as described for the SXR (Johnson et al. 1998). As with the SXR, the

low flux levels meant that the instrumental bandwidth could not be smaller than

about 1nm, which is finite compared to the 10nm bandwidth of the VXR channels.

Because the output of the Vis/SCF did not fill the entrance pupil of the VXR, several

steps were required. First, the VXR was aligned on the optical axis of the exit beam

of the Vis/SCF and focused to image the intermediate image of the exit slit of the

monochromator. Because the output of the monochromator is f/8 by f/16, this

underfilled the VXR’s field of view. A translation stage could be positioned between

the VXR and the monochromator such that the intermediate image of the exit slit

coincided with the working standard detector. A bandwidth of 1nm and a step size

of 0.5nm was used near the centre of each channel, and a bandwidth of 4nm and a

step size of 3–5nm was used in the wings. The monitor detector was used to reduce

the variability from source fluctuations.

A second scan across the central portion of each channel was performed under

conditions that filled the VXR field of view, but with poor measurement resolution

due to the reduced flux. A diffuse reflectance standard was placed perpendicular to

the optical axis at a distance that gave a spot size large enough to fill the VXR

entrance window. The VXR was aligned to measure the radiance reflected from the

diffuser. The field of view was then filled, resulting in a small wavelength shift

compared to the on-axis measurements. The data acquired with the diffuser were

used to correct the on-axis data for this small shift. The largest identifiable uncertainty

components in the determination of the relative spectral responsivity result from the

responsivity of the working standard and the effect of the 0.1nm uncertainty in the

Vis/SCF wavelength calibration. The magnitude of these effects depends on the

wavelength (VXR channel). A likely, but difficult to quantify, additional component

of uncertainty is that associated with the procedure itself, including the finite bandwidth of the source, corrections for the field of view effects, and matching the

in- and out-of-band scans.

2.3. VXR calibration

Given the FASCAL values forL

l

(l) of the ISS at one set of discrete wavelengths,

and the functionr(l) from the Vis/SCF data, the integrals in equation (1) were

determined numerically using the alternative extended Simpson’s rule. The wavelength step corresponded to the r(l) data. A commercial cubic spline routine was

used to determine the values ofL

l

(l) at these wavelengths, with the input values

just encompassing ther(l) dataset. For example,r(l) for channel 1 of the VXR was

measured from 380–600nm and theL

l

(l) values for one calibration of the ISS on

FASCAL at 360, 380, 400, 450, 500, 550 and 600nm were input to the cubic

spline routine.

The relative combined standard uncertainty of the individual determinations of

D

b using the NPR and the relative responsivity measurements on the Vis

/SCF are

given in table 2 for VXR channels 1 and 5. The 0.1nm uncertainty in the wavelength

calibration of the monochromators for ther(l) andL

l

(l) measurements affects the

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346 B. C. Johnson et al.

Table 2. Relative combined standard uncertainty of the individual determinations ofD

b using

the NPR and relative responsivity measurements on the Vis/SCF.

Channel 1 Channel 1 Channel 5 Channel 5

type A type B type A type B

Uncertainty origin (%) (%) (%) (%) EVects that are always present

VXR alignment 0.10 0.10

VXR linearity 0.10 0.10

Vis/SCF, spectral flux scale* 0.11 0.09

Vis/SCF, measurement uncertainty<0.002<0.0002

Vis/SCF, overall technique 0.21 0.10

Vis/SCF and FASCALl calibration 0.32 0.02

EVects that depend on the ISS

Lamp current 0.40 0.21

Radiance uniformity in exit aperture 0.15 0.15

Short-term drift 0.10 0.03

FASCAL calibration 0.40 0.33

Numerical analysis 0.10 0.10

EVects that depend on each measurement

VXR measurement uncertainty<0.1<0.06

DVM accuracy<0.01<0.01

VXR amplifier gain 0.02 0.02

Relative combined standard uncertainty 0.76 0.48

*Larason et al. (1998).

determination of the band-weighted radiance by an amount that is proportional to

the relative change in the spectral radiance with wavelength (Early and Thompson

1996). The effect of the current resolution of the lamp power supply is proportional

to inverse wavelength. At 654.6nm, we used the scaling law [L

l

(l)+DL

l

(l)]/L

l

(l)=

[(I+DI)/I ]6.24 (Walker and Thompson 1994) to estimate this uncertainty component. The FASCAL calibration of the NPR also results in an uncertainty that is

wavelength-dependent. Not given in table 2 is the long-term drift of the NPR over

the nine-month measurement interval. This component cannot be estimated from

the FASCAL data because only one calibration has been performed to date.

However, the output of the NPR internal monitor photodiodes was stable from

April 1999 to September 1999 (Brown and Johnson 2002). Also, the standard

deviation of the VXR measurements over this interval is less than 0.2%. Because

this is less than the uncertainty of the FASCAL spectral radiance calibration, it

is satisfactory to model the sphere as a constant source of radiance during the

measurement interval.

3. Calibration using a laser-illuminated ISS

We use a number of tunable and discrete laser sources to calibrate the VXR on

SIRCUS over the spectral range 400–1000nm. Continuous wave dye lasers and a

Ti5sapphire laser provide tunable coverage from 550–1000nm, while frequency

doubling these lasers gives a tunable source over the spectral range 275–500nm.

The spectral range 500–550nm is currently covered using discrete emission lines

from various lasers, which affects the calibration of VXR channel 3. We expect to

have continuous coverage over this spectral range using a dye laser pumped by an

argon ion laser in the near future. The output from the various lasers is sent through

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Characterization and radiometric calibration 347

an intensity stabilizer prior to entering the ISS. The intensity stabilizer reduces the

relative standard deviation of the power in the laser beam to less than 0.05%, and

enables variable control over the power in the beam sent into the integrating sphere.

We used a 20cm diameter Spectralon@ (a product of Labsphere, Inc.*) integrating

sphere with a 5.1cm diameter exit port to calibrate the VXR. The source is of

sufficiently extended area that it overfills the VXR entrance pupil. Typical power

levels of radiation introduced into the ISS range from a few milliwatts to a few

hundred milliwatts, depending on the laser used, giving a source radiance varying

from 2×10−5Wmm−2sr−1 to 1×10−7Wmm−2sr−1.

3.1. Radiance responsivity calibrations on SIRCUS

The measurement of an extremely narrow-band source for one channel of the

VXR is also given by equation (1). The laser-illuminated source is so narrow, with

a bandwidth of about 2.5×10−5 nm, that the source spectral radiance is adequately

described by a delta function and equation (1) becomes

S(l)=AVGt(l)R

f

(l)L (l) (4)

whereL(l) is the radiance (Wm−2sr−1) of the laser-illuminated ISS at wavelengthl.

At eachl, the radiance responsivityR(l) is determined:

S(l)

L (l)

=AVGt(l)R

f

(l)¬R(l) (5)

The responsivity for each VXR channel is found from integration over all wavelengths

where the radiance responsivity is non-negligible: Dd

= ∆ R(l)dl (6)

HereD

d is the laser-illuminated calibration coe

fficient. For the EOS intercomparisons, an equation of the form of equation (3) is used, with Db replaced by Dd and r(l) replaced by R(l).

From equation (5), it is clear that two types of measurements are required to

characterize and calibrate the VXR using the laser-illuminated ISS: (1) determination

of the radianceL(l) of the ISS; and (2) determination of the net VXR signalS

corresponding to measurements of the laser-illuminated ISS at the same timeL(l)

is determined. In comparison to the lamp-illuminated determination of the VXR

calibration coefficients, the SIRCUS method is more direct, with a shortened

measurement chain to the HACR.

The calibration strategy is shown in figure 4. Test sensors and a reference detector

are located on a translation stage at a fixed (and measured) distance from the sphere

exit port. The test sensors are calibrated against the reference detector using the

substitution method. A monitor photodiode mounted in a small port on the side

wall of the ISS corrects for small source intensity fluctuations during a calibration.

A computer controls and monitors the laser power and wavelength over much of

the spectral range, controls the positions of the detectors and sources, and records

test and reference detector signals.

*Certain commercial equipment, instruments or materials are identified in this technical

memorandum to foster understanding. Such identification does not imply recommendation

or endorsement by NIST, nor does it imply that the materials or equipment used are necessarily

the best available for the purpose.

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348 B. C. Johnson et al.

Figure 4. Experimental system for the determination of the radiance responsivity of the VXR

using SIRCUS. The propagation of the radiant flux is indicated by the direction of

the lines with single arrows; lines with double arrows indicate linear translation for

the purpose of detector substitution. The vibrating mirror reduces the non-uniformities

of the radiance in the exit port of the sphere that arise from speckle.

We use a silicon trap detector equipped with a precision aperture as our reference

detector for calibrations over the wavelength range 406–920nm. An aperture of

known area is located at the sphere exit port for radiance calibrations using the trap

detector as an irradiance standard. Before the trap detector measures the sphere

radiance, its responsivity must be determined. The optical power responsivity of the

trap detector is derived from measurements on HACR. HACR is an electrical

substitution radiometer, relating optical power (flux) to the electrical watt. It serves

as the primary US national standard for optical power measurements. The irradiance

responsivity of the trap detector is the product of its power responsivity and the

aperture area. The source radiance is calculated from the irradiance on the trap

detector using the distance between the trap detector aperture and the source aperture

and the area of the source aperture.

During a calibration, a laser is tuned to the wavelength of interest. The trap

detector is then placed in front of the sphere exit port, typically at a distance of

approximately 1m, and measures the irradiance of the sphere. It is moved out of

the way, and replaced by the radiance detector under test. The test detector measures

the radiance within the exit port and the radiance responsivity R(l) is calculated by

dividing the test detector output signal by the sphere radiance (see equation (5)).

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Characterization and radiometric calibration 349

Any changes in the sphere radiance between the reference detector measurements

and the test detector measurements are accounted for by referencing both signals to

the output of the monitor photodiode. For a full spectral calibration, the wavelength

is changed, and the calibration sequence repeated.

3.2. Uncertainty budget for VXR radiance response calibration

Each component in the calibration contributes to the overall uncertainty in

radiance responsivity calibrations. Additional uncertainties arise from the repeatability and reproducibility of the measurements, and include thermal effects as well as

any small detector ageing effects. Table 3 lists all known contributions to the uncertainty in radiance responsivity calibrations on SIRCUS. While the uncertainty in

the transfer to test detector will vary slightly from detector to detector, the current

combined standard uncertainty in radiance responsivity for a typical test detector

is 0.25%.

4. Calibration of the VXR

In figure 5, the spectral responsivity determinations from the two techniques—

using the Vis/SCF and SIRCUS—are shown for two channels of the VXR. The

channel at 412nm was selected because this value ofD

b is the most uncertain due

to the wavelength-dependent components of uncertainty described previously

(table 2). Also, experience with two other ISSs at NIST had revealed temporal drifts

of the sphere radiance that resulted in larger than desired combined uncertainties.

Hence SIRCUS could be expected to make the largest impact on the calibration of

the VXR at 412nm. The channel at 775nm was selected because the ISS-based

uncertainties are lower and because application of VXR measurements for EOS

programmes is often of interest for a broad wavelength interval.

For comparison purposes, the data were normalized using the maximum values

in each dataset (figure 5). The Vis/SCF data were acquired in November and

December 1996 and the SIRCUS measurements were performed in June 1999. At

412nm (shown in figure 5(a)), there is a wavelength shift of about 0.33nm, with the

Table 3. Relative combined standard uncertainty of radiance responsivity calibrations on

SIRCUS.

Type A Type B

Uncertainty origin (%) (%)

Source radiance

Trap detector spectral power responsivity 0.15

Trap detector aperture area* 0.01

Source-to-trap detector distance (squared) 0.05

Trap detector repeatability 0.04

Source aperture area 0.05

Amplifier gain 0.04

T ransfer to test detector

Source spatial radiance non-uniformity 0.1

Test detector repeatability 0.05

Test detector size-of-source effect 0.15

Amplifier gain 0.04

Relative combined standard uncertainty 0.25

*Fowler et al. (1998).

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Figure 5. Comparison of the spectral shapes of the relative responsivity determined on the

Vis/SCF in 1996 and the normalized radiance responsivity determined using SIRCUS

in 1999 for the (a) 412 nm and (b) 775 nm channel.

SIRCUS results at the shorter wavelength. There are also small differences in the

shape of the responsivity functions in the region 408–415nm. The SIRCUS measurements were made only over the central portion of the response, but the normalized

data can be compared from unity to about 10−4 of the maximum value. The effect

of the missing out-of-band response in the SIRCUS results can be estimated from

the Vis/SCF data, where the integrated response from 450–600nm is 0.05% of the

total integrated response. We estimate the effect for measurements of a broadband

source to be 0.1% or less.

At 775nm, there is a wavelength shift of about 0.35nm, again with the SIRCUS

results at the shorter wavelength. The Vis/SCF results are larger than those of

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Characterization and radiometric calibration 351

SIRCUS from 790–850nm by about 50% on average, but the effect on the integrated

response is only 0.05%. It is clear from the SIRCUS measurements beyond 850nm

that this laser-illuminated determination is able to achieve accurate values at 10−6

of the peak. There was evidence in the Vis/SCF data for the SXR at 775nm of a

decrease in responsivity beyond 850nm (Johnson et al. 1998), but with signal-tonoise ratios of less than unity, interpretation was difficult. Therefore SIRCUS is able

to explore the lower limits of the instrument responsivity with much improved

accuracy.

The two methods of determining the calibration coefficient for the 412nm and

the 775nm channels of the VXR are compared in figure 6. The values ofD

b for all

measurements of the NPR source from 13 January to 31 August 1999 are plotted

for the two radiance levels of the NPR source that were determined on FASCAL.

These levels correspond to all four lamps in operation, or only one lamp (designated

lamp number 1) in operation. The FASCAL calibration for these settings was

performed on 19–21 May 1999. As explained in §2, the band-averaged radiance was

determined using the 1996 Vis/SCF relative responsivity data,r(l).

The calibration coefficients derived from the SIRCUS data are also shown

in figure 6. At 412nm, the averageD

b from the NPR measurements is

0.041948Vcm2srnmmW−1, and the SIRCUS result is 0.041869Vcm2srnmmW−1,

for a difference of 0.19%. At 775nm, the averageD

b is 0.026303Vcm

2srnmmW−1,

the SIRCUS result is 0.026267Vcm2srnmmW−1, and the difference is 0.14%. This

agreement is better than expected given the magnitude of the relative standard

uncertainties inD

b and may be fortuitous. Most uncertainty components in

D

b are

systematic, and cannot be reduced by repeat measurements.

The SIRCUS values for the absolute spectral radiance responsivity can be used

in equation (3) to determineD

b

. This provides a more robust and reasonable

comparison of the two methods because the VXR filters could have changed between

the Vis/SCF measurements in 1996 and the SIRCUS measurements in 1999.

Recalculation ofD

b at 412nm gives 0.042161Vcm

2srnmmW−1, which agrees with

SIRCUS to within 0.7%. At 775nm,D

b changes by less than 0.1% because the

spectral radiance of the NPR changes slowly with wavelength compared to its

behaviour at 412nm, so the calibration coefficient at 775nm is less sensitive to the

wavelength shift ofR(l) with respect tor(l).

5. Future applications using SIRCUS

Higher radiance levels, lower wavelength uncertainty, negligible bandpass, and

no out-of-band radiation all contribute to reducing the uncertainty in radiance and

irradiance responsivity calibrations on SIRCUS. Our current uncertainties in irradiance and radiance responsivity calibrations are 0.1% and 0.25%, respectively, over

the spectral range 406nm–920nm. With minor improvements in the facility, we

expect to be able to reduce our uncertainties for both irradiance and radiance

responsivity calibrations to 0.05% or less (Anderson et al. 1992). SIRCUS could

easily be adapted for optical flux linearity studies, and offers an alternative to the

NIST beamconjoiner. In addition, the uniformity of the exit aperture of the laserilluminated ISS has been exploited in the study of two-dimensional array detectors.

Reduction of our uncertainties on SIRCUS will impact calibrations of the VXR

while extension of the wavelength coverage using secondary working standards will

enable calibration of other ultraviolet, visible and infrared transfer radiometers.

SIRCUS may be used, for example, to calibrate the SWIR transfer radiometers

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352 B. C. Johnson et al.

1 January 1 March 1 May 1 July 1 September

1999 1999 1999 1999 1999

Date

Cal. Coeff. (V cm2 sr nm μW_1)

Date

Cal. Coeff. (V cm2 sr nm μW_1)

1 January 1 March 1 May 1 July 1 September

1999 1999 1999 1999 1999

Figure 6. Comparison of the calibration coefficients determined using the NPR ISS and

SIRCUS for the (a) 412 nm and (b) 775 nm channel of the VXR. Two levels were used

with the NPR and they are identified in the legend. The vertical lines illustrate

representative relative standard uncertainties.

developed by NIST, the University of Arizona and other institutions. The current

variation in sphere radiance measurements in the SWIR is about 4%, which is

comparable to the uncertainties in the calibration of the transfer radiometers. With

SIRCUS, we expect to be able to calibrate radiometers out to 2.5mm with relative

standard uncertainties of 0.5% or less. Therefore, calibrating the SWIR transfer

radiometers on SIRCUS should reduce the variance in radiance measurements

with these instruments and provide a better estimate of the accuracy of the scale

assignments made by the EOS participants.

Further in the infrared, we anticipate calibrating the Thermal-infrared Transfer

Radiometer (TXR) (Rice and Johnson 1998, Rice et al. 2002). The TXR is a vacuumcompatible, liquid nitrogen cooled filter radiometer with two 1 mm-wide filter

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Characterization and radiometric calibration 353

channels centred at 5mm and 10mm, respectively. The TXR is important to the

remote sensing community in that it offers a relatively simple and economical method

of verifying the radiometric scales that are used for ground calibration of thermalinfrared channels of the many remote sensing instruments in use. As with the VXR,

SIRCUS provides an accurate and direct method of calibrating the TXR spectrally

against the NIST detector-based radiometric scale. The SIRCUS data will enable a

comparison to the relative spectral responsivity determined using the ambient

infrared spectral comparator (Migdall et al. 1994, Rice and Johnson 1998).

Integration of the SIRCUS data over the TXR channel will provide a calibration

coefficient that can be compared to the one derived using an ambient black body

source (Rice and Johnson 1998, Rice et al. 2002). The SIRCUS facility will reduce

the uncertainties associated with calibration of the TXR at NIST by enabling direct

measurements of a number of effects that previously could only be estimated.

In a separate application, SIRCUS is well suited to calibrate instruments used

in a number of environmental monitoring and remote sensing applications. For

example, a global network of sun photometers, the Aerosol Robotic Network

(AERONET) has been established under the auspices of NASA’s EOS programme

to provide globally distributed near-real-time observations of aerosol optical depths,

aerosol size distributions and precipitable water in diverse aerosol regimes (Holben

et al. 1998). The sun photometers are filter radiometers with a number of channels

with band centre wavelengths ranging from the visible to the near-infrared; the Cimel

CE318-2 sun photometer has filters at 440, 670, 870, 936 and 1020nm, for example.

Reduction in uncertainties in the calibration of the sun photometers will aid the

validity of data products that result from AERONET.

Finally, SIRCUS is being used to improve the accuracy of NIST’s spectroradiometric, photometric and radiance temperature calibration services. The primary

impact to the EOS community will be in the reduction of uncertainty in the spectral

irradiance values assigned to 1000W standard lamps. These standard lamps are

currently calibrated from 250–2400nm on FASCAL and used by the EOS community

as irradiance standards for both irradiance and radiance calibrations (in combination

with diffuse reflectance standards). To date, filter radiometers have been calibrated

using the Vis/SCF and used to determine the radiance temperature of a hightemperature black body with an uncertainty of 0.5K near 2900K (Yoon and Gibson

1999). The high-temperature black body will be used to directly determine the

spectral irradiance of the standard irradiance lamps. The new method will result in

a reduction of the uncertainty in the NIST irradiance scale by a factor of up to five,

depending on wavelength. Because the principal source of uncertainty in the calibration of the filter radiometers is the spectral irradiance responsivity, the calibrations

using SIRCUS results will reduce the uncertainties even further.

6. Summary

The VXR, a portable filter radiometer for radiance measurements with six narrowband channels, has been calibrated using two different methods, both involving

measurements of integrating sphere sources. Measurements with the broadband,

lamp-illuminated ISS require ancillary measurements on the spectral responsivity,

while the laser-illuminated calibration results in a direct determination of the spectral

radiance responsivity. We present results for one lamp-illuminated ISS and one laserilluminated ISS for two channels of the VXR; the agreement is within the combined

uncertainties. The laser-illuminated ISS method is more accurate.

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354 B. C. Johnson et al.

The improved accuracy from SIRCUS is the result of many factors. First, systemlevel calibrations are more accurate than combinations of component level measurements, and the high flux levels and appropriate geometric properties of the source

make the system-level determinations possible. Secondly, the advancements in tunable lasers allow for thorough studies in the spectral regions of interest. Thirdly, the

availability of suitable transfer detectors ensures a short measurement chain to the

fundamental measurements on HACR.

The improvement in the calibration accuracy, especially for the spectral region

below 500nm and above 800nm, will have a significant impact on the utility of the

radiometric intercomparisons performed by NASA’s Goddard Space Flight Facility

and NIST for EOS. First, SIRCUS will be used to characterize and calibrate the

EOS/NIST transfer radiometers in the SWIR and thermal infrared; work with the

VXR will also continue. Secondly, SIRCUS may be used with other important EOS

radiometers. Thirdly, SIRCUS will be used to improve the accuracy of the NIST

spectroradiometric quantities, which will reduce the uncertainties in critical standards

such as the 1000W quartz-halogen irradiance lamps.

Acknowledgments

We would like to thank NIST colleagues M. V. Annageri, S. S. Bruce,

C. E. Gibson, T. C. Larason and R. D. Saunders for assistance, and acknowledge

support by NASA’s EOS Project Science Office under contract number S-41365-F

and the US Air Force Metrology under contract numbers 97-421 and 98-439.

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Spectral Irradiance and Radiance responsivity Calibrations using 

Uniform Sources (SIRCUS) facility at NIST 

Steven W. Brown, George P. Eppeldauer, Joseph P. Rice, Jun Zhang, Keith R. Lykke 

National Institute of Standards and Technology 

Gaithersburg, MD 20899-8442 

ABSTRACT 

Detectors have historically been calibrated for spectral power responsivity at the National Institute of Standards and 

Technology (NIST) using a lamp-monochromator system to tune the wavelength of the excitation source. Silicon 

detectors can be calibrated in the visible spectral region with uncertainties at the 0.1 % level. However, uncertainties 

increase dramatically when measuring an instrument’s spectral irradiance or radiance responsivity. In addition, the 

uncertainties are even larger in the UV and IR ranges. We will discuss a new laser-based facility for Spectral 

Irradiance and Radiance responsivity Calibrations using Uniform Sources (SIRCUS) that was developed to calibrate 

instruments directly in irradiance or radiance mode with uncertainties approaching those available for spectral power 

responsivity calibrations. In this facility, high-power, tunable lasers are introduced into an integrating sphere using 

optical fibers, producing uniform, quasi-Lambertian, high radiant flux sources. Reference standard irradiance detectors, 

calibrated directly against national primary standards for spectral power responsivity, are used to determine the 

irradiance at a reference plane. Knowing the measurement geometry, the source radiance can be readily determined as 

well. The radiometric properties of the SIRCUS source coupled with state-of-the-art transfer standard radiometers 

whose responsivities are directly traceable to primary national radiometric scales, result in typical combined standard 

uncertainties in irradiance and radiance responsivity calibrations less than 0.1 % in the visible (larger in the UV and IR). 

Details of the facility are presented and examples of unique calibrations possible in the facility are given, including 

system-level responsivity calibrations in support of the National Aeronautics and Space Administration’s (NASA’s) 

remote sensing activities. 

Keywords: calibration, detectors, lasers, ocean color, remote sensing 

1. INTRODUCTION 

NASA's Earth Observing System (EOS) is an international, multi-instrument, multi-platform satellite remote sensing 

program designed to produce long time series data on global climate change. EOS constitutes the major component of 

NASA's Mission to Planet Earth and data products from the EOS program will be used as a guide for the 

implementation of international environmental policies [1]. The utility of these remotely sensed data products in 

helping to establish and understand driving mechanisms behind global environmental changes occurring on decadal 

time scales will depend on the accuracy of the calibration of the full ensemble of EOS instruments on the multiple 

platforms flown over the duration of the EOS mission. State-of-the-art sensor uncertainties are necessary to obtain the 

required uncertainty in relevant data products. Consequently, detailed sensor characterization and accurate radiometric 

calibration (both pre-launch and on-orbit) as well as long-term sensor degradation measurements are integral to the 

success of the EOS program. The EOS program office established a Calibration Validation (Cal/Val) program to 

validate radiometric uncertainties in instrument builder sources used to calibrate satellite sensors and to validate prelaunch and on-orbit sensor radiometric uncertainties [2]. 

Primary national radiometric scales are maintained and disseminated by NIST. Artifacts, both sources and detectors, 

calibrated at NIST directly against primary and secondary standards will have the lowest possible uncertainties. To 

ensure traceability to primary national (and international) radiometric standards and to ensure radiometric measurements 

with the lowest achievable uncertainties, the EOS Cal/Val program office has enlisted NIST’s assistance in calibration 

validation activities to support EOS sensors. In this paper, we discuss a new laser-based calibration facility at NIST that 

helps support the EOS calibration validation program. Unprecedented accuracies in both radiance and irradiance 

responsivity calibrations are achievable in this facility for Spectral Irradiance and Radiance responsivity Calibrations 

Earth Observing Systems IX, edited by William L. Barnes, James J. Butler, Proc. of SPIE

Vol. 5542 (SPIE, Bellingham, WA, 2004) · 0277-786X/04/$15 · doi: 10.1117/12.559577

363
using Uniform Sources, dubbed SIRCUS. While the facility has been in operation for only a few years [3], it has

supported a number of EOS programs. We first describe the facility and then go into detail on a few of the systems

calibrated using SIRCUS that are related to EOS.

2. SIRCUS FACILITY

The SIRCUS facility has been described in detail recently [4], so we briefly discuss the facility here. SIRCUS is shown 

schematically in Figure 1. In the SIRCUS facility, high-power, tunable lasers are introduced into an integrating sphere

producing uniform, quasi-Lambertian, high radiant flux sources. The laser is first directed through an intensity

stabilizer that controls the relative optical power in the beam to within 0.01 % of the set point. A portion of the laser 

beam is sent into a wavemeter that measures the wavelength of the radiation to within 0.001 nm. A beamsplitter sends

another portion of the laser beam into a Fabry-Perot interferometer to measure the bandwidth and mode stability of the

laser. Finally, the laser radiation is introduced into an integrating sphere, often using an optical fiber [5]. Occasionally,

a collimator coupled to the sphere is used as a calibration source. Speckle in the image from the source, originating

from the coherent nature of the laser radiation, is effectively removed by either rastering the beam inside the sphere with

a galvanometer-driven mirror or by placing a short length of optical fiber in an ultrasonic bath.

Reference standard irradiance detectors, calibrated directly against national primary standards for spectral power 

responsivity [6] and equipped with a precision aperture measured on the NIST Aperture Area facility [7], are used to

determine the irradiance at a reference plane. The source radiance can be readily determined from the measurement

geometry as well. A monitor photodiode is located on the sphere to correct for any radiant flux changes in the sphere

output between measurements with the reference instrument and the device under test. The sources are located inside a

light-tight box. Two baffles are typically installed between the source and the detectors to minimize effects of stray

radiation on the measurement. Instruments are calibrated

Tunable Laser Stabilizer

Ultrasonic bath

Wavemeter

Digital Voltmeter

Computer

Integrating sphere

Monitor Detector

Baffles

Standard

detector

Exit port

Optical fiber

Lens

Tunable Laser Stabilizer

Ultrasonic bath

Wavemeter

Digital Voltmeter

Computer

Integrating sphere

Monitor Detector

Baffles

Device

under test Standard

detector

Exit port

Optical fiber

Lens

Linear

Encoder

Figure 1: Schematic of SIRCUS facility. 364 Proc. of SPIE Vol. 5542
directly in irradiance or radiance mode with expanded uncertainties (k=2) of 0.15 %, approaching or exceeding those

achievable for spectral power responsivity calibrations. 

There are two separate SIRCUS facilities; the UV/Vis/NIR SIRCUS and the IR SIRCUS. The UV/Vis/NIR SIRCUS

covers the range from 200 nm to 1.6 um while the IR SIRCUS facility covers the spectral region from 780 nm to 5 um.

There is some overlap between the two facilities for scale intercomparisons. The two facilities are very similar; the main

distinction is in the laser source used to illuminate the integrating spheres and the reference transfer standards used to

determine the irradiance at a reference plane.

2.1 Sources

A number of different lasers are used to cover the spectral range from about 210 nm to 5000 nm. Continuous tunability

in the UV/visible/NIR is provided by dye lasers and Ti:Sapphire lasers that are pumped by either an Argon ion laser

(25 W all lines visible, 7 W all lines UV) or a frequency-doubled Nd:Vanadate laser (10 W at 532 nm). A number of

discrete wavelengths are provided by the pump lasers themselves.

Figure 2: Output powers versus wavelengths for SIRCUS sources.

Continuous tunability in the NIR/IR is provided by optical parametric oscillators (OPO’s) pumped by solid state lasers 

(typically, Nd:YAG, Nd:Vanadate, frequency-doubled Nd:Vanadate). These systems are briefly discussed below and

illustrated in Figure 2 [8].

Dye lasers at SIRCUS cover the spectral region from 415 nm to 700 nm (E in the figure); dyes used include Stilbene 3

(415 nm-475 nm), Coumarin 480 (470 nm-520 nm), Coumarin 521 (505 nm-565 nm, [9]), Rhodamine 6G (550 nm620 nm), and DCM (610 nm-700 nm). A separate laser is used for each dye so that the full tuning range can be rapidly

covered and no dye change or optical reconfiguration is required. Ti:Sapphire lasers cover the spectral range from

680 nm to 1050 nm (F in Figure 2) [10]. Frequency doubling of Ti:Sapphire lasers enables tuning from 350 nm to 500

nm (D in figure). Two different types of frequency doubling are available: The first approach uses an external power Proc. of SPIE Vol. 5542 365
build-up cavity that requires a frequency-stabilized, single-mode laser to pump it. The second is a NIST-built 

intracavity-doubled Ti:sapphire laser that requires no frequency stabilization. Over 300 mW of optical power is 

available from the dye lasers and the Ti:Sapphire laser (with optical powers of 1 W or greater over much of the spectral 

range). The power available from the cw, frequency-doubled radiation is typically in the range from 100 mW to 200 

mW. Computer-controlled actuators rotate the angle of the birefringent tuner in the dye and Ti:sapphire lasers for 

automated wavelength tuning.

The IR systems developed at NIST include a cw periodically poled Lithium Niobate (PPLN) OPO pumped by a 

Nd:YAG laser, a mode-locked (220 MHz, 7 ps) PPLN OPO pumped by a Nd:Vanadate laser, and a mode-locked LBO 

OPO pumped by the 2nd harmonic of the Nd:Vanadate laser. The first two systems tune from approximately1.4 Pm to 

5 Pm (H and J), while the LBO OPO tunes from approximately 700 nm to 2000 nm (not shown in the figure). The 

power level is in the 100 mW to 1 W range. 

 Mode-locked systems have been shown in the past to work for radiometric situations [11]. A commercial mode-locked 

system that should allow continuous tunability from about 200 nm to 3 Pm (part of the range is shown as G and F) was 

recently installed in the facility. One useful feature we hope to exploit is that the bandwidth of these mode-locked 

systems is considerable broader than the cw systems discussed above. This may help to alleviate some of the problems 

associated with interference fringes (see below). These mode-locked systems are easy to frequency triple (B in figure) 

and quadruple (A in figure). 

Different integrating spheres are used, depending on the radiometric calibration and the wavelength of calibration. 

Small diameter integrating spheres – typically diameters of 2 cm to 5 cm – equipped with precision apertures with 

diameters ranging from 3 mm to 8 mm are typically used for irradiance responsivity calibrations. Larger diameter 

spheres – 30 cm diameter – with 5 cm to 10 cm diameter exit ports are used for radiance measurements. The spheres 

are made of either sintered polytetrafluoroethylene-based coating (SpectralonTM,Labsphere, Inc.) that has high diffuse 

reflectance from about 250 nm to 2.5 Pm or infragold for calibrations from 1 Pm to 20 Pm. Typical irradiance levels at 

1 m using 2.54 cm diameter integrating sphere with a 5 mm diameter aperture range from approximately 1 PW/cm2

 to 

10 PW/cm2. The irradiance levels can be continuously decreased using the laser intensity stabilizer to check for 

linearity. The irradiance can be increased by moving closer to the sphere (falls off as 1/r2

) or by collimating the output 

of the sphere using either an off-axis parabolic mirror or a lens. Figure 2 shows typical irradiances for different 

wavelengths. Radiance levels between 1 mW/cm

/sr and 5 mW/cm/sr are standard for a 30 cm diameter sphere with a 

7.5 cm diameter output port. Note that the exit apertures are normally calibrated at the NIST facility for aperture area 

measurement [7]. A monitor detector is mounted on the sphere wall to monitor and correct for fluctuations in the source 

radiant flux during a calibration. 

2.2 Detectors

The uncertainty in the spectral irradiance responsivity of reference standard detectors is the largest component in the 

calibration uncertainty budget on SIRCUS. Ultimately, the quality and characteristics of the reference standard 

detectors determine the uncertainty achievable on SIRCUS. Silicon tunnel-trap detectors, configured to operate in both 

radiant power and irradiance measurement modes, are the highest-level transfer standards used in the UV/Vis/NIR 

SIRCUS facility. They cover the spectral range from 350 nm to 1050 nm. Nitrided Si reflection traps have been 

developed to cover the 200 nm to 400 nm spectral range. These detectors are calibrated against a cryogenic radiometer 

[12]. InGaAs detectors, calibrated against an electrical substitution Si bolometer (ESB) [13], cover the range from 1 Pm

to 2.5 Pm while InSb detectors cover the 2 Pm to 5 Pm range. HgCdTe detectors are being developed to cover the 

spectral range from 3 Pm to 20 Pm.

2.3 Calibration method

The entire data collection sequence is automated. Initially, an electronic shutter that blocks the laser radiation before it 

enters the optical fiber is closed and a background signal is acquired for both the reference standard trap detector and 

the sphere monitor. Then the shutter opens and the signals from the trap and the monitor on the sphere are recorded. 366 Proc. of SPIE Vol. 5542
The signals are initially amplified using a current to voltage amplifier and then fed into a digital voltmeter set to average 

over some number of power line cycles (the signal is averaged for a few seconds at most). Typically 3 'shutter closed' 

signals and 9 'shutter open' signals are averaged. The mean reference-to-monitor ratio and the standard deviation of the 

ratio are recorded. After this, the stage moves to the Device Under Test (DUT) position, and the data acquisition 

sequence is repeated. This gives the DUT mean signal-to-monitor ratio and the standard deviation of the ratio. The 

standard deviations of the ratios are monitored; trap detector measurement standard deviations larger than 0.01 % are an 

indication of laser power instabilities. 

Under routine calibration conditions, the intensity-stabilized laser wavelength is read by the wavemeter and transferred 

to the computer during each measurement. Along with mean ratios, the mean and standard deviation of the wavelength 

are recorded. This enables ready identification of laser wavelength instabilities during a scan. Occasionally, for faster 

data acquisition, the wavelength is only recorded at the beginning of the acquisition sequence. Following the data 

acquisition sequence, the wavelength is changed and the sequence is repeated.

3. EXAMPLES OF SYSTEM-LEVEL CALIBRATIONS

In the following, we present a few examples of SIRCUS calibrations that relate to the EOS or space-based radiometers. 

One of the unique features of SIRCUS is that the calibration can be done at system level. The three examples we 

discuss are the Marine Optical BuoY (MOBY), the SCRIPPS-NIST Advanced Radiometer (NISTAR), and Sun 

Photometers. 

3.1 MOBY

Ocean color satellites such as the Sea-Viewing Wide Field-of-View Sensor (SeaWiFS) and the Moderate Resolution 

Imaging Spectrometer (MODIS) require vicarious calibration for accurate and continuous measurements of the waterleaving radiance. The primary reference instrument for most ocean color satellites is the MOBY, a radiometric buoy 

stationed in the waters off Lanai, Hawaii [14, 15]. 

Detector array-based spectral imaging systems, such as spectrographs, enable the simultaneous acquisition of an entire 

spectrum over some finite spectral region of interest; they can acquire a spectral image in a matter of seconds. The 

ability to rapidly acquire a full spectrum has led to the use of array-based systems in a variety of ocean color 

applications where the source may not be stable over minutes. Spectrographs commonly consist of an entrance port, a 

dispersing element (such as a grating) to spatially resolve the spectral components of the incident radiation, and mirrors 

to image the entrance port (often a slit) onto a detector reference plane. Because of the dispersing element, the spatial 

image of the entrance port falls on different regions of the detector array, depending on its wavelength; broadband 

sources form an image across the entire array. The spectral coverage of a spectrograph is determined by the size of its 

detector array, the dispersion properties of its grating, and its optical layout. 

Two CCD-spectrographs, one for the blue spectral region (360 nm to 640 nm), referred to as the BSG, and another for 

the red (560 nm to 940 nm), the RSG, form the basis of the Marine Optical System (MOS), the sensor used in MOBY 

[14]. The same dual-spectrograph design is used for the MOS Profiler, a ship-board-deployable version of the MOBY 

sensor used in the development of bio-optical algorithms. The response of the two MOS spectrographs to 

monochromatic laser excitation is shown in Fig. 3. The spectra are similar for both spectrographs. There are four 

components to the image: a strong sharp peak corresponding to the image of the spectrograph entrance slit on the CCD; 

a broad, peaked structure around the slit image; a non-zero constant component; and an additional peak. The first three 

components are similar to specular, haze, and diffuse components of reflectance, respectively. They remain 

approximately invariant as the excitation wavelength is changed and the image moves across the CCD array. From 

physical examination of the spectrographs, the fourth component (the additional peak) arises from a spurious reflection 

off a mirror coupled with higher-order diffraction from the grating. As the image moves across the array, the reflection 

peak changes size, shape and position with respect to the primary peak. The specular component corresponds to the 

Proc. of SPIE Vol. 5542 367
Figure 3: MOS response to monochromatic excitation at (a) 550 nm (for the blue spectrograph) and (b) 700 nm (for 

the red spectrograph).

properly imaged radiation; the other components arise from light scattered in the spectrograph, principally from the

grating. The ‘specular’ component in the spectrograph image is analogous to the ‘in-band’ component of a filter

radiometer’s responsivity, while the sum of the other three components is analogous to the ‘out-of-band’

component.This unwanted background radiation, while small, is fairly typical for single grating spectrographs and can

give rise to unforeseen errors, often much larger than anticipated, when the spectral distribution of a source being

measured differs significantly from that of the calibration source. Such a situation is routinely encountered in ocean

color measurements, where instruments are calibrated against incandescent sources having peak radiances in the near 

infrared and subsequently measure the optical properties of the ocean, where the up-welled radiance peaks in the blue to

green spectral region. Consequently, to fully understand the radiometric performance of a spectrograph used for ocean

color measurements, it is important to characterize the stray light in the system.

Knowing the relationship between the excitation wavelength and the position of the image on the array enables us to 

determine the fraction of incident light at some wavelength that is scattered onto a particular element. For example, for 

the wavelength Oex in Fig. 3(top), 0.01 % of the light imaged on element 190 (BSG) is scattered onto element 300.

Assuming each element in the detector array has the same average spectral responsivity, the signal from element 300 to

radiation at wavelength Oex is 0.01 % of the signal from element 190.

A single data set, shown in Fig. 3, does not give us the spectral resolution required to determine a pixel’s in-band 

relative spectral response. For this information, it is necessary to tune the monochromatic excitation source in fine

steps, a situation SIRCUS is well equipped to address. Figure 4 shows the relative spectral response of adjacent pixels

of the MOS RSG detector array as the laser excitation wavelength on SIRCUS is tuned over the range from 587 nm to

593 nm in 0.1 nm steps. At each excitation wavelength, the responsivity of each pixel is separately determined. By

tuning the excitation wavelength over a broad spectral range, a single pixel’s absolute spectral responsivity (and slit

scatter function [16]) can be determined.

368 Proc. of SPIE Vol. 5542
Figure 4: Spectral responsivity of pixels 428 to 432 (from left to right).

As discussed in detail by Brown et al. [17], MOBY’s system response has been corrected for stray light. MOBY is used

for the vicarious calibration of a number of ocean color satellites and any changes in MOBY-derived water-leaving 

radiances are directly reflected in satellite sensor calibration coefficients for the relevant channels. Consider the impact

on MODIS as a representative example of the impact of the stray light correction of MOBY. MODIS bands 8 through

12 (412 nm to 551 nm) are vicariously calibrated against MOBY [18]. The stray-light-correction factors for MOBY

(the correction factors are simply the ratio of the stray-light-corrected to the uncorrected measurements) in terms of

 at the MODIS band-averaged wavelengths over 5 years of deployments are given in Fig. 5. Each left-to-right

grouping in the figure is a separate buoy deployment. Note that two different MOS spectrograph systems are used:

LWN   O

Figure 5: MOBY LWN stray light correction factors for MODIS bands. Proc. of SPIE Vol. 5542 369
one for even numbered buoy deployments and another one for odd numbered buoy deployments. The correction factors 

range from + 8 % for Band 8 to –2.5 % for Bands 11 and 12. There are slight differences in the stray light corrections 

for the two different MOS systems. There was an increase in the magnitude of the stray light correction factor for Band 

8 for 3 Buoy deployments around 1999. During these deployments, a different optical fiber was used. With the 

exception of these buoys, the correction factors have been stable over the entire deployment sequence, implying that the 

MOBY imaging and the MOS slit-scatter functions, along with the ocean color, have remained stable over this time 

frame. The observed radiometric stability of the MOBY systems [14, 17, 18] enables us to correct previous 

deployments for stray light with confidence.

3.2 NISTAR

Scripps-NISTAR is a space-qualified radiometer package composed of three electrical substitution cavity radiometers 

and one photodiode radiometer [19]. It was designed and built to orbit the Earth’s Lagrange-1 (L1) point as part of 

NASA’s proposed Deep Space Climate Observatory (DISCOVR) mission and measure the energy emitted and reflected 

by the Earth with an accuracy of 0.1%. The Scripps-NISTAR package contains 1) a total (<0.2 Pm to >100 Pm) 

channel (Band A) to measure total radiant power in the UV, visible, and infrared wavelengths; 2) a solar (0.2 to 4 Pm) 

channel (Band B) to measure reflected solar radiance in the UV, visible and near infrared wavelengths; 3) a near 

infrared (0.7 to 4 m) channel (Band C) to measure reflected IR solar radiance; and 4) a photodiode (0.3 to 1 Pm) 

channel to be used as an on-board calibration reference for the Scripps-NISTAR instrument. 

SIRCUS was used to make absolute irradiance responsivity measurements of the three cavity radiometers and the Si 

photodiode. During pre-flight calibration of NISTAR at the SIRCUS facility, the instrument was in a thermal-vacuum 

chamber to simulate the space environment. Through windows in the chamber, it viewed the output of a laserilluminated integrating sphere, simulating the geometry of the view of Earth from L1. Shown in Figure 6 is the 

normalized irradiance responsivity using 532 nm radiation emitted from a 2.54 cm diameter integrating sphere located 

approximately 2 m from the cavities. The sphere was illuminated by ~10 W of fiber optically coupled light from a 

frequency-doubled, diode-pumbed Nd: Vanadate laser. 

Shown in Figure 7 is the transmittance of three different Band C filters obtained with collimated light from a 

Ti:Sapphire laser. For these measurements, the monochromatic, uniform output from a 2.54 cm diameter integrating 

sphere was collimated with an off-axis parabolic mirror. Also shown in the figure, for comparison, is the measurement 

of the transmittance of the filters with a monochromator. The SIRCUS results are a little different (probably because of 

inter-reflections) from the “piece parts” approach and will help to put them on an absolute scale. 

SIRCUS has also helped to calibrate another instrument on the DSCOVR mission, the Earth Polychromatic Imaging 

Camera (EPIC) [20].

3.3 Sun photometers

Sun photometers and sky radiometers are used for atmospheric characterization. Sun photometers determine the 

atmospheric optical depth while radiance determined from sky radiometers constrains the aerosol models input into 

radiative transfer codes that calculate the atmospheric contribution to the at-sensor signal. There are several networks 

of sun photometers distributed globally to measure aerosol concentrations and distributions, e.g. the Aerosol Robotic 

Network (AERONET) [21]. The Sensor Intercomparison and Merger for Biological and Interdisciplinary Oceanic 

Studies (SIMBIOS) Project Office at NASA’s Goddard Space Flight Center (GSFC) uses in situ atmospheric data to 

validate MODIS and other ocean color satellite aerosol optical products, to evaluate aerosol models used for 

atmospheric correction, and to develop vicarious sensor calibration methodologies [22]. 

370 Proc. of SPIE Vol. 5542
Figure 6: Normalized irradiance responsivity of three receiver cavities calibrated on SIRCUS. For each cavity, the

measurements were performed two times in order to assess repeatability within a two week period.

Figure 7: Absolute transmittance for 3 Band C filters measured using either monochromatic measurements forming a 

piece parts approach (lines) or using the system-level approach enabled by SIRCUS (symbols).

0.9900

0.9950

1.000

1.005

1.010

112233

Irradiance Responsivity, RN

Receiver Cavity Number

0.86

0.88

0.90

0.92

0.94

700 750 800 850 900 950 1000

F1System Level

F5 System Level

F8 System Level

F1 Piece Parts

F5 Piece Parts

F8 Piece Parts

Transmittance

Wavelength (nm)

Instruments are calibrated for irradiance responsivity against reference sun photometers using the cross-calibration

technique at NASA’s GSFC [23]. Reference sun photometers that are part of the AERONET project are calibrated 

using the Langley-Bouger technique at the Mauna Loa Observatory on regular intervals. The cross-calibration technique

consists of near simultaneous solar observations at GSFC with the uncalibrated instrument and a calibrated reference

sun photometer. The method assumes that the ratio of the output voltages for the same channel (e.g., same spectral 

Proc. of SPIE Vol. 5542 371
responsivity) for the reference and uncalibrated radiometers and a particular air mass is proportional to the ratio of the

output voltage at zero air mass. If the spectral responsivities differ, a correction is made for spectral differences related

to Rayleigh, ozone, and aerosol attenuation. The uncertainty in the calibration at GSFC is approximately 2 %.

Instruments are calibrated for radiance responsivity at NASA’s GSFC using a NIST-traceable lamp -illuminated

integrating sphere source known as the ‘Hardy’ source. A reference spectroradiometer equipped with an integrating

sphere irradiance collector, the OL746/ISIC, is calibrated for irradiance responsivity against a NIST standard irradiance

lamp. The irradiance calibration is then transferred to the Hardy sphere using the OL746/ISIC. Knowing the irradiance

responsivity of the OL746/ISIC, the distance between the sphere exit port and the entrance aperture to the 746/ISIC, and 

the sphere exit port area, it is straightforward to calculate the spectral radiance of the “Hardy” sphere. The uncertainty in

the radiance responsivity calibration is estimated to be approximately 5 % (k = 2).

As a first assessment of the uncertainties assigned to the radiance and irradiance responsivity calibrations of sun

photometers, two multi-channel filter radiometers used in the SIMBIOS program were calibrated for irradiance and 

radiance responsivity on SIRCUS and the results compared with standard calibrations [24]. The Satellite Validation for

Marine Biology and Aerosol Determination (SimbadA) radiometers are eleven-channel filter radiometers with

bandpasses of approximately 10 nm and center wavelengths at 350 nm, 380 nm, 410 nm, 443 nm, 490 nm, 510 nm, 565

nm, 620 nm, 670 nm, 750 nm and 870 nm, respectively. For comparison to the GSFC sun photometer cross-calibration

results, the SIRCUS-derived irradiance responsivities s(O) were used to predict a top-of-the-atmosphere (TOA) signal

Vo(SIRCUS):

Vo    SIRCUS 3s O E O dO , (1)

where s(O) is the spectral responsivity of one of the radiometer channels and E(O) is an exo -atmospheric solar

irradiance spectrum. Souaidia et al. [24] used the exo -atmospheric solar irradiance spectra developed by others. To

perform the integration, the s(O) and the E(O) were interpolated to a uniform wavelength interval of 0.25 nm and 

integrated.

The dominant source of uncertainty in the SIRCUS-based predicted TOA signal was the solar irradiance spectrum used.

Changes of 1 % or so were observed, depending on the exo-atmospheric solar irradiance spectrum chosen. Given a 

cross-calibration uncertainty of ~ 2 %, we are able to validate the cross-calibration with a combined expanded 

uncertainty (k = 2) of ~ 4 %. Predicted results for the 750 nm channel and the 490 nm channel agreed with the crosscalibration to within 2 %; the agreement for the 440 nm channel was approximately 5 %. The agreement for the 490 nm

and 750 nm channels is within the combined uncertainties, but the 440 nm results are not and warrant further 

investigation [24].

In order to compare the two sets of radiance measurements, radiance responsivities, s(O), were interpolated to a uniform

wavelength interval, as were the sphere spectral radiance values, L(O), for the lamp-illuminated integrating sphere

source. The measured signal was then compared to the predicted signal using equation 1, but replacing E(O) with L(O)

and using the instrument’s radiance responsivity instead of it’s irradiance responsivity. We obtained differences in the

calibrations between 2 % and 4 %, depending on wavelength. The radiance responsivity results were consistent with

results of an intercomparison performed at NASA’s Goddard Space Flight Center in 2001 [25, 26].

4. SUMMARY 

SIRCUS is a laser-based facility recently developed at NIST to provide system-level characterization and calibration of 

a vast assortment of radiometers, including EOS instruments, with state-of-the-art uncertainties. We continue to

improve the radiometric calibration capabilities of SIRCUS by decreasing the uncertainties and increasing the spectral

coverage. In many situations, such as with MOBY, it is impossible to bring the instrument to NIST for calibration.

Recognizing the need and taking advantage of the miniaturization of lasers, a “traveling SIRCUS” has been developed

to perform in-situ calibrations of EOS and related sensors. Currently, the spectral coverage available with this traveling 372 Proc. of SPIE Vol. 5542
SIRCUS is from 360 nm to 1050 nm; the spectral coverage is being expanded to include the short-wave infrared out to 

2.5 Pm. 

ACKNOWLEDGMENTS 

We wish to thank John Grangaard for his support of this facility and acknowledge the continued support of the Air 

Force component of the Calibration Coordination Group of the armed services. We also thank Steven Lorentz, Carol 

Johnson and Edward Early from NIST for significant contributions to this work. 

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374 Proc. of SPIE Vol. 5542
ABSOLUTE RADIOMETRIC CALIBRATION OF DIGITAL IMAGING SYSTEMS

Steven W. Brown, Thomas C. Larason, Catherine Habauzit, George P. Eppeldauer, 

Yoshihiro Ohno, and Keith R. Lykke 

National Institute of Standards and Technology, Gaithersburg, MD 20899 

ABSTRACT 

We have developed a tunable laser-based facility for the absolute radiometric calibration of digital imaging systems such as 

CCD cameras, spectrographs, and microscopes. Several types of silicon-based digital imaging systems have been calibrated 

in this new facility, including a commercially available camera equipped with a removable photopic filter, a custom-designed 

digital microscope, and a CCD spectrograph. We present results of the CCD camera calibration in detail and discuss relevant 

aspects of the microscope and spectrograph calibrations. During the radiometric calibration, the pixel-to-pixel uniformity, 

linearity, and absolute spectral responsivity of each system were determined over the visible spectral range (400 nm to 

800 nm). Each of these aspects of the CCD camera calibration will be presented, along with a discussion of the measurement 

uncertainties. 

Keywords: calibration, CCD, digital camera, radiometry 

1. INTRODUCTION 

Improvements in the operation and performance of Digital Imaging Systems (DIS’s) have led to an explosion in the use of 

these systems in a variety of scientific, medical, and industrial imaging applications. In many of these new applications, it is 

important that the spectral characteristics of the imaging system as well as its spatial (geometric) properties be well 

characterized and its photometric, radiometric, or colorimetric performance known. This has resulted in increased demand 

for characterization and calibration methodologies traceable to common standards. 

By knowing the spectral responsivity of a DIS, one can accurately predict its performance under differing operating 

conditions. Currently, these systems can be calibrated with relative combined standard uncertainties of approximately 5 % to 

10 %. In many cases, DIS’s are calibrated against broad-band incandescent sources — such as Illuminant A — and 

subsequently measure sources with very different spectral power distributions. In this case, the measurement uncertainties 

are not well known in general, and can be much larger than expected. 

2. DESCRIPTION OF THE SIRCUS FACILITY 

We have developed a facility at the National Institute of Standards and Technology (NIST) for Spectral Irradiance and 

Radiance Responsivity Calibrations using Uniform Sources (SIRCUS) to calibrate DIS’s. In this facility — shown in 

Fig. 1 — lasers are directed into an integrating sphere to produce a monochromatic, Lambertian source for irradiance and 

radiance responsivity calibrations. This integrating sphere source (ISS) has been used to calibrate the spectral radiance and 

irradiance responsivity of a variety of detectors and imaging systems [1]. The two critical cornerstones of the facility are 

broadly tunable continuous-wave (cw) laser sources and reference standard detectors that are well-characterized and 

calibrated with low uncertainties to determine the radiance of the ISS with low uncertainty. 

A variety of lasers are used to provide continuous coverage over the spectral range from 370 nm to 1000 nm. A Ti:sapphire 

laser provides tunable coverage from 690 nm to 1000 nm, frequency-doubling enables tunability from 370 nm to 450 nm. 

Discrete lasers were used for the spectral range from 450 nm to 550 nm and dye lasers are used to cover the spectral region 

from 550 nm to 700 nm. Currently, dye lasers are used to cover the spectral range from 415 nm to 700 nm. 

Reference standard detectors with spectral power responsivities directly traceable to the NIST primary standard equipped 

with precision apertures were used to determine the sphere radiance [2]. These trap detectors are calibrated for spectral 

power responsivity directly against a cryogenic radiometer over the spectral range from 405 nm to 920 nm [3]. From the 

power responsivity and the aperture area, the irradiance responsivity of the trap detector is determined. By measuring the 

distance between the sphere exit port and the trap detector entrance aperture and the area of the ISS exit port, the radiance of 

Sensors and Camera Systems for Scientific, Industrial, and Digital Photography Applications II,

Morley M. Blouke, John Canosa, Nitin Sampat, Editors, Proceedings of SPIE Vol. 4306 (2001)

© 2001 SPIE · 0277-786X/01/$15.00

13
the ISS was determined with a relative combined 

standard uncertainty of 0.1 % [4, 5]. A silicon 

monitor detector mounted on the wall of the ISS was 

used to correct for small power fluctuations in the 

laser between measurements with the reference 

standard detector and the DIS. 

3. CALIBRATION RESULTS 

In general, the absolute spectral responsivity (ASR) of 

an instrument, R(λ), relates the signal measured by a 

detector, S, to the spectral radiance of the source 

being measured, L(λ): 

 

S = ∫ R(λ)L(λ)dλ . (1) 

The integration is over the full spectral bandwidth of 

the source. A DIS can be considered to be comprised 

of i by j independent detectors, with an individual 

measurement equation for each detector, or pixel, in 

the array. Each pixel in the array will also image a 

different area of the ISS, and in general: 

 

Si, j = Ri, j (λ)Li, j ∫ (λ)dλ , (2) 

with i defining the column position and j equal to the corresponding row in the array. Li,j(λ) refers to the radiance of the 

spatial region of the sphere exit port imaged onto pixel i, j. Note that for uniform sources, we can eliminate the spatial 

dependence on radiance: Li,j (λ)~L(λ). 

Because we are using narrow-band laser sources (with a bandwidth of approximately 10 MHz, or 0.00001 nm), L(λ) can be 

approximated by a delta function, L(λ)=L(λο)δ(λ − λο), and Eq. 2 can be rewritten as, 

 

Si, j = Ri, j (λo )L(λo ) . (3) 

Knowing the source radiance L(λο) and measuring the CCD signal S(λo), we obtain a direct measurement of the desired 

quantity Ri,j(λo):

 

Ri, j(λo ) = Si, j L(λo) . (4) 

By tuning the wavelength of the calibration source, we directly obtain the absolute spectral responsivity of each element in 

the DIS. 

To complete the radiometric calibration of an instrument, other factors need to be considered as well, including the linearity 

of the response and the exposure time correction. 

3.1. Camera Calibration 

We calibrated an 8-bit silicon-based CCD camera with 640 x 480 pixels equipped with a 35 mm focal length lens and a 

removable photopic filter. The instrument field-of-view under normal operating conditions is 13.5o

. It comes equipped with 

8 user-selectable shutter speeds, enabling measurements of luminance levels as low as 0.34 cd/m2

. It has a short-term 

repeatability of 0.4 %, and is calibrated by the manufacturer against Illuminant A with a stated relative combined standard 

uncertainty (k=1) of 4 %. The camera pixel-to-pixel response uniformity, linearity, and absolute responsivity — both with 

and without the photopic V(λ) filter on the front of the camera — were determined. 

We used a 20 cm diameter Spectralon-coated integrating sphere with a 5.34 cm diameter exit port to calibrate the CCD 

camera. Typical power levels of radiation introduced into the ISS range from a few mW to a few hundred mW, depending on 

the laser used, giving a source radiance in the range from 1 x 10-7 W/mm2

/sr to 1 x 10-4 W/mm2/sr. Prior to determining the 

responsivity of the CCD camera, the monitor detector was calibrated against the reference standard detector over the 

wavelength range of interest. The calibration related the monitor detector signal to the ISS radiance. The CCD camera was 

Laser Intensity stabilizer

Iris

lens

vibrating mirror

mirror

Integrating sphere

Monitor detector

Wavemeter

Device Under Test

Transfer Standard 

Detector

baffle

aperture

baffles

Voltmeter

shutter

Computer

Fig. 1. Schematic diagram of the SIRCUS facility. 

14 Proc. SPIE Vol. 4306
then aligned in front of the ISS and its radiance 

responsivity determined. During the camera 

calibration, the sphere radiance was determined at a 

particular wavelength by measuring the monitor 

detector signal. 

We measured the uniformity of the ISS at 488 nm, 

532 nm, and 633 nm using a temperature-stabilized Si 

radiometer with a narrow field of view mounted on a 

computer controlled two-axis (XY) translation stage. 

The stage was stepped in 2 mm increments over a 6 cm 

by 6 cm square area (an area larger than the area of the 

sphere exit port). The radiometer signal, normalized by 

the sphere monitor photodiode signal, was recorded at 

each position. Results are shown in Fig. 2 for the 

relative radiance over the ISS exit port at 532 nm; 

results for 633 nm and 488 nm were similar. As shown 

in the figure, the radiance from upper right quadrant of 

the sphere is slightly larger than the radiance from the 

rest of the sphere. We therefore allow Li, j(λ) ≈ L( )λ , 

with an added relative standard uncertainty of 0.25 %. 

We then positioned the camera in front of the ISS exit port. Using a target grid centered on the ISS exit port, we positioned 

the camera to image the central 4 cm by 3 cm region of the sphere exit port. Prior to determining the absolute responsivity of

the CCD, it is necessary to measure and correct for any non-linearity in the response of the camera. We therefore measured 

the response of the CCD array, averaged over the central 50 by 50 pixels, as the sphere radiance was changed. The 

measurements involved changing the intensity of the laser light entering the ISS (by adjusting the throughput of a laser power 

controller) and comparing the radiance of the sphere measured by the CCD with the known ISS radiance determined by the 

calibrated monitor photodiode. The 8-bit camera has a maximum digital number (DN) of 255, corresponding to a 90 % of 

the CCD full-well capacity; data were taken with the 

same CCD exposure time (2 ms) over a radiance 

range giving count levels varying from approximately 

10 DN to 240 DN. The resultant data are plotted in 

Fig. 3 as the ratio of the CCD signal to the sphere 

radiance versus the CCD signal (DN). If the CCD 

response were linear, the ratio of the CCD signal to 

the ISS radiance would remain constant as a function 

of CCD count level. However, the ratio increased 

sharply as the CCD camera signal increased from 

10 DN to 100 DN. Above 100 DN, the ratio 

continued to rise slightly, increasing from a value of 

approximately 60 at 100 DN to a value of 

approximately 63 at 230 DN. In determining the 

absolute radiance responsivity of the CCD, we 

normalized individual data sets to the high-count 

level, with the individual scaling factors determined 

by the results shown in Fig. 3. 

Note that we only calibrated the linearity of the CCD 

using a shutter setting corresponding to an exposure 

time of 2 ms. It is difficult to distinguish between a 

non-linearity in the CCD response, and a variability in 

the camera readout offset value. For example, we 

performed a correction to the response of the CCD by 

Fig. 2. ISS exit port radiance uniformity with 532 nm excitation. 

40

45

50

55

60

65

0.9

1

1.1

1.2

1.3

1.4

1.5

0 50 100 150 200 250

Ratio [Signal/Monitor]

Scaling Factor

Signal [DN]

Fig. 3. Non-linear response of the CCD camera and the resultant 

scaling factors used in the absolute responsivity calibration. 

Proc. SPIE Vol. 4306 15
changing the offset level by 7 DN. Applying this simple correction to the data in Fig. 3, the response of the CCD camera was 

linear to within 1 % over the range from 25 DN to 230 DN. 

The CCD camera was then positioned in front of the ISS, and its spectral responsivity, in DN per second per unit radiance, 

was determined. During the calibration on SIRCUS, the laser was tuned to the wavelength of interest. The CCD camera 

measured the radiance from the ISS exit port and the radiance responsivity (DN/s/(W/cm2

/sr)) was calculated by dividing the 

CCD output signal, corrected for the exposure time, by the sphere radiance. During the calibration, images were acquired 

with several different exposure times. The CCD responsivity was measured for different exposure times at several 

wavelengths during the calibration. The CCD responsivity agreed to within 1 % for the different exposure times. 

In Fig. 4, the pixel-to-pixel responsivity of the camera is shown for 580 nm excitation. Without the photopic filter in place,

the total response variation over the central 90 % of the array was approximately 5 %, as shown in Fig. 4(a). With the 

photopic filter installed, the non-uniformity in the CCD responsivity increased to approximately 10 %, as shown in Fig. 4(b). 

All measurements were performed under the same conditions. The data were not corrected for the non-uniformity of the ISS 

radiance because it was negligible compared with the non-uniformity of the pixel-to-pixel responsivity of the CCD. 

To determine the ASR, we averaged the response of the central 50 by 50 pixels over the wavelength range from 400 nm to 

800 nm. At the time of the calibration, we did not have continuously tunable lasers for the spectral range from 450 nm to 

550 nm. To fill in this spectral region, we calculated the relative responsivity using the output from a lamp-monochromator 

source (4 nm bandwidth) [6], and determined the absolute responsivity by comparison with results obtained on SIRCUS. For 

this part of the calibration, relay optics were used to create a parallel 2.5 cm diameter beam. The radiation, under-filling the 

CCD field-of-view, was imaged onto a small region in the center of the CCD array. During the calibration, the radiant power 

in the beam was measured at each wavelength using reference detectors and an image subsequently acquired by the CCD. A 

35 by 35 pixel area on the CCD was selected to give an averaged response. The data were subsequently corrected for the 

nonlinear response of the CCD and normalized to the radiant power in the beam, giving a relative responsivity of the CCD. 

To determine the absolute responsivity of the camera, the data were normalized to the SIRCUS results near 580 nm. Results 

are shown in Fig. 5 for the camera (a) with and (b) without the photopic filter attached. 

 (a) (b) 

Fig. 4. Pixel-to-pixel uniformity (a) without and (b) with the photopic filter installed for 580 nm 

excitation. The total variation is 5 % in (a) and 10 % in (b). 

16 Proc. SPIE Vol. 4306
3.2. Uncertainty of camera radiance responsivity 

Each component in the calibration chain contributes to the overall uncertainty in the radiance responsivity calibration. We 

estimated the contributions of all known components to the combined standard uncertainty in the CCD radiance responsivity 

calibration on SIRCUS. These contributions are listed in Table 1. We estimate the relative combined standard uncertainty in 

the sphere radiance to be 0.1 %; the uncertainty in the non-linear correction to the responsivity to be 1 %; the uncertainty in

the exposure time correction to be 0.5 %; and the reproducibility, including short-term repeatability, alignment and focus, to 

be approximately 2 %. After taking the root-sum-square of the individual components, the relative combined standard 

uncertainty in the CCD radiance responsivity calibration is 2.3 % (coverage factor k=1). For imaging applications, there will 

be an additional uncertainty of approximately 1 % from the non-uniformity of the CCD. 

Table 1. Relative combined standard uncertainty of the CCD radiance responsivity 

calibration on SIRCUS. 

Component Uncertainty [%] 

Sphere Radiance 

(Monitor detector calibration) 

0.1 

Sphere Radiance Non-uniformity 0.25 

CCD Non-linearity 1 

Exposure time correction 0.5 

Reproducibility 2 

Relative Combined Std. Uncertainty 2.3 

The radiant power distribution in the beam from the monochromator was highly non-uniform, leading to increased 

uncertainty in the calibration of the CCD, both because of the increased uncertainty in the reproducibility of the 

measurements, and also because of the increased uncertainty in the non-linearity correction of the averaged response. There 

was an additional uncertainty in the normalization of the response to the measurements on SIRCUS. Consequently, 

measurements using the lamp-monochromator had a relative combined standard uncertainty of approximately 4 %. 

For measurements of photometric quantities, a source spectral radiance distribution is weighted by the V(λ) function [7]. The 

photometric uncertainty is different than the above discussed radiometric responsivity measurement uncertainty and depends 

on how closely the response of the camera with the photopic filter approximates the V(λ) function. For poor matches, the 

photometric uncertainty can be large and will depend on the source spectral distribution. There will be an additional 

uncertainty for imaging applications from the larger non-uniformity in the pixel-to-pixel response. 

-2.0 108

0.0

2.0 108

4.0 108

6.0 108

8.0 108

1.0 109

1.2 109

1.4 109

300 400 500 600 700 800 900 1000

Responsivity [DN/s/(W/mm2/sr)]

Wavelength [nm]

(a)

(b)

Fig. 5. CCD camera ASR (a) without and (b) with the 

photopic filter installed. 

Proc. SPIE Vol. 4306 17
3.3 Microscope Calibration 

The microscope consists of an objective lens and a 1024 by 1024 pixel cooled CCD array. It is used to determine x-ray 

phosphor efficiencies from scintillator crystals [8]. Imaging a scintillation region on a crystal is extremely advantageous 

because the radiation from scintillators is Lambertian and viewing the source distribution enables the determination of 

radiometric quantities with lower uncertainties. We measured the linearity, exposure time correction, pixel to pixel 

uniformity and the absolute spectral radiance responsivity of the microscope on SIRCUS. For these measurements, we used 

a 5 cm diameter ISS with a 2 mm aperture. The microscope, equipped with a 10X objective, was positioned in front of the 

ISS. Each pixel imaged the same region of the ISS exit port, resulting in minimal additional uncertainty in the calibration 

from any potential non-uniformity in the sphere exitance. 

The CCD array had a 12-bit A/D converter, with 4095 DN corresponding to 90 % of the CCD full-well capacity. We first 

determined the exposure time and the non-linearity corrections in the response of the microscope; results are shown in Figs. 6 

and 7, respectively. The exposure time correction was negligible for exposure times greater that 500 ms. For shorter 

exposure times, a correction — as large as 100 % for 10 ms exposure times — had to be applied. In many of these systems, 

there is a delay in opening and closing the shutter, leading to an exposure time that is slightly different than the nominal 

value. For this instrument, adding 10 ms to the nominal exposure time reduced the correction to the 5 % level for the shortest

exposure times. The system response was linear for count rates larger than 100 DN. Offset variations and uncertainty in the 

determination of the background signal could contribute to the non-linear behavior at the smaller count rates. During the 

absolute radiometric calibration, the count rates were kept larger than 1000 DN and the exposure time was kept constant at 

100 ms. This is easy to accomplish using a laser-based ISS; we merely adjust the power into the ISS at a given wavelength to 

achieve these goals. 

The microscope response was uniform to with 0.2 % over the central 90 % of the CCD array; the ASR, averaged over the 

central 25 by 25 pixels, is shown in Fig. 8. Because of the smaller non-linear correction, the better pixel to pixel uniformity 

and the 12 bit digitization, we estimate the relative combined standard uncertainty in the microscope ASR measurement to be 

approximately 1 %. 

3.4 Spectrograph Calibration 

Spectrographs are typically calibrated for spectral radiance responsivity against broad-band sources such as lamp-illuminated 

integrating sphere sources (ISSs) and plaques. Stray light, wavelength errors, and lack of knowledge of the single pixel 

relative responsivity all give rise to increased uncertainties in the calibration and subsequent operation of these instruments. 

Many of these sources of calibration error can be greatly reduced or eliminated using tunable, monochromatic laser sources in 

place of conventional broad-band sources. 

0.80

1.0

1.2

1.4

1.6

1.8

2.0

2.2

0.94

0.96

0.98

1

1.02

1.04

0 1000 2000 3000 4000 5000 6000

Ratio [DN/Exp. Time]

Ratio [DN+10/Exp. Time]

Exposure Time [ms]

Fig. 6. Digital microscope exposure time correction. 

0.0

5.0 102

1.0 103

1.5 103

2.0 103

2.5 103

3.0 103

3.5 103

4.0 103

0.9

1

1.1

1.2

1.3

1.4

0.0 0.2 0.4 0.6 0.8 1.0

Camera Signal [DN]

Correction Factor

Sphere Radiance [a.u.]

Fig. 7. Microscope response linearity. 

18 Proc. SPIE Vol. 4306
A dual-spectrograph radiometer was calibrated on SIRCUS for radiance responsivity over the spectral range from 400 nm to 

850 nm. Details of the calibration are described elsewhere [4, 5]. In this instrument, radiation enters the spectrograph 

through an entrance slit, is dispersed using a grating, and imaged onto the CCD array using a mirror, as shown in Fig. 9. For 

excitation using monochromatic radiation, the image 

formed is a line reflecting the image of the entrance slit 

on the CCD (Fig. 10). Note that the image is spread out 

over several pixels in the horizontal (dispersion) 

direction, is not centered vertically on the CCD array, and 

shows a pronounced curvature (Fig. 11). By tuning the 

excitation wavelength, the image moves across the array 

and each pixel’s ASR can be determined. In this work, 

we measured the responsivity of the averaged central 100 

pixels in each column. Eq. 4 was modified to: 

 

Ri(λo ) = Si L(λo ) , (5) 

where i now refers to the particular column in the array. 

In Fig. 12, we show the absolute spectral responsivity, 

Ri(λ), for columns 243 – 247 over the wavelength range 

from 735 nm to 750 nm. We measured a 0.8 nm 

separation between the maximum responsivity of adjacent pixels and nominal single pixel bandwidth of 2 nm. The curvature 

in the spectrograph image, Fig. 11 gave rise to the pronounced shoulder observed at shorter wavelengths in the ASR. This 

shoulder in the single pixel ASR was attributed to the CCD not being located at the spectrograph image plane. We estimate 

the relative combined standard uncertainty in the calibration to be approximately 3 %. Note that the determination of each 

pixel’s ASR is difficult to obtain using any technique other than the tunable-laser-based ISS approach developed on SIRCUS. 

4. SUMMARY 

We have developed a flexible, detector-based calibration facility using tunable laser sources and high accuracy reference 

standard detectors for the irradiance and radiance responsivity calibration of digital imaging systems. We have calibrated a 

number of instruments on this facility, and presented results for a digital camera, a digital microscope and a digital 

spectrograph. This approach has several advantages over conventional calibration techniques using broad-band sources, 

including uniform, monochromatic irradiance and radiance sources; lower wavelength uncertainty; no stray light contribution 

0.0

2.0 108

4.0 108

6.0 108

8.0 108

1.0 109

300 400 500 600 700 800

Responsivity [DN/s/(W/cm2/sr)]

Wavelength [nm]

Fig. 8. ASR of digital microscope. 

CCD 

camera

M1

M2

Entrance Slit

Grating

Fig. 9. Spectrograph optical layout. 

Proc. SPIE Vol. 4306 19
 

550 600 650 700 750 800 850 900 950 

0 

2 

4 

6 

8 

10 

12 

14 

[ADU s-1] 

0 10000 20000 30000 40000

0 100 200 300 400 500 

column 

Slit height [mm] 

Wavelength [nm] 

Fig. 10. Spectrograph image of ISS with 745 nm excitation. 

244 246 248 250

50

100

150

200

250

300

350

400

450

500

column

0 10000 20000 30000 40000

Fig. 11. Expanded view of spectrograph 

image of ISS with 745 nm excitation. 

0

5 108

1 109

1.5 109

735 740 745 750

Responsivity 

[(ADU s-1 pixel-1 W-1 cm2 sr]

Wavelength [nm]

C243

C244

C245

C246

C247

Fig. 12. Absolute spectral responsivity of columns 243 to 247. 

20 Proc. SPIE Vol. 4306
 

to the signal; and the ability to determine each pixel’s responsivity. By using this approach, uncertainties in the radiometric 

calibration of DIS’s can be reduced by a factor of 2 or greater over conventional calibration techniques. 

5. ACKNOWLEDGMENTS 

We would like to thank Carol Johnson for useful discussions and acknowledge support for this work by the U. S. Air Force 

Metrology under contracts 97-421 and 98-439. 

6. REFERENCES 

1 S. W. Brown, G. P. Eppeldauer, and K. R. Lykke, “NIST facility for spectral irradiance and radiance responsivity 

calibrations with uniform sources,” Metrologia 37, 579-582 (2000). 

2 G. P. Eppeldauer and D.C. Lynch, "Opto-mechanical and electronic design of a tunnel-trap Si-radiometer," J. Res. Natl. 

Inst. Stand. Technol. (in press). 

3 T. R. Gentile, J. M. Houston, J. E. Hardis, C. L. Cromer, and A. C. Parr, “National Institute of Standards and Technology 

high accuracy cryogenic radiometer,” Appl. Opt, 35, 1056-1068 (1996). 

4 C. Habauzit, et al., “Radiometric characterization and absolute calibration of the Marine Optical System (MOS) bench 

unit,” J. Atmos. and Ocean. Technol., to be submitted. 

5 S. W. Brown, C. Habauzit, B. C. Johnson, and K. R. Lykke, “Tunable-laser-based calibration of a digital spectrograph,” 

Appl. Opt., to be submitted. 

6 T. C. Larason, S. S. Bruce, and A. C. Parr, Spectroradiometric Detector Measurements, Natl. Inst. Stand. Technol. Spec. 

Publ. 250-41, U. S. Government Printing Office, Washington, DC, 1998. 

7 Yoshihiro Ohno, Photometric Calibrations, Natl. Inst. Stand. Technol. Spec. Publ. 250-37, U. S. Government Printing 

Office, Washington, DC, 1997. 

8 Steven Grantham, NIST, personal communication. 

Proc. SPIE Vol. 4306 21
Uniform calibration of night vision goggles and test sets 

George P. Eppeldauer 

Optical Technology Division 

National Institute of Standards and Technology 

Gaithersburg, Maryland 20899-8441 

ABSTRACT 

There are orders of magnitude differences between the ~0.1 % (k=2) uncertainty of NIST reference detector calibrations 

and the uncertainty of night vision (NV) goggle measurements. NIST developed a night vision radiometer calibration 

facility and NV radiometer transfer standards. The transfer standards, that propagate the radiance responsivity scale to 

the military primary standards laboratories, are calibrated against a NIST reference radiometer. The reference 

radiometer has been calibrated on the NIST Spectral Comparator Facility (SCF) for spectral power and irradiance 

responsivities. Spectral considerations are discussed to lower the uncertainties of the radiance responsivity scale transfer 

to the test sets and then to the goggles. Since direct determination of the final uncertainties in goggle calibrations and 

measurements is difficult, models have been made to estimate the most important uncertainty components based on 

individual spectral measurements of the source distributions and radiometer spectral responsivities. It is also shown, that 

because of source spectral mismatch problems, the goggle measurement uncertainty at applications can be much higher 

than at calibration. A suggestion is being made to mimic the no-moon (stars only) night sky radiation distribution using 

several LEDs in the test-sets to decrease the large spectral mismatch errors. A broad-band correction factor has been 

developed to further decrease calibration uncertainty when the goggles to be used have different spectral responsivities 

than the standard. Geometrical considerations to optimize the radiance measurement angle and the out-of-target 

blocking are also discussed to decrease the uncertainty in the radiance responsivity transfer. 

Keywords: calibration, night vision goggle, radiance, radiometer, scale transfer, spectral responsivity, test-set 

1. INTRODUCTION 

The night vision (NV) goggles are the key sensors for human beings for night operations. The goggles have several 

technical parameters that can be used to characterize them. The most important parameters are spatial resolution, fieldof-view, image distortion, transfer-gain (output luminance / input radiance), and spectral responsivity. The spectral 

responsivity is one of the most critical parameter for flying safety. The MIL-STD-3009 [1], written in 2001, shows the 

assumed night vision imaging system (NVIS) spectral response characteristics that shall be used to define NVIS 

compatibility criteria with aircraft lighting. The standard extends the NVIS radiance requirements from the previous 

defining document [2]. Though a full framework would be necessary for NVIS radiance measurement requirements, the 

new (2001) document does not address calibration aspects of the new NVIS technology. 

Because of the lack of standardized goggle calibrations, individually applied maintenance actions are performed, such 

as pass/fail tests to determine whether the goggle will perform as expected when it is used (or as it has performed in the 

past). At present, there are no standard criteria that state the goggle gain must be higher than some specified value. The 

users are tasked to locally establish a value based on past performance of the goggles that will satisfy their needs. There 

are some initial recommendations for each goggle type, but it is still the responsibility of the users to establish their own 

test methods. Also, in the past two decades, different source distributions have been applied in different test-sets. The 

earlier used tungsten lamps were replaced with LEDs. Some manufacturers use an 815 nm (peak) light emitting diode 

(LED) irradiating source in the test-sets when determining the transfer gain of the goggles. The transfer gain is the 

luminance at the eye-piece of the goggle divided by the radiance viewed by the goggle. The luminance is a photometric 

quantity that can be measured easily. However, the radiance viewed by the goggle has a spectral distribution and it is 

measured by the goggle which has a spectral responsivity different from the human visual system (the CIE standard 

photometric observer). Accordingly, the radiance viewed by the goggle needs a (broad-band) radiometric measurement Electro-Optical and Infrared Systems: Technology and Applications IV, edited by David A. Huckridge, Reinhard R. Ebert,

Proc. of SPIE Vol. 6737, 67370M, (2007) · 0277-786X/07/$18 · doi: 10.1117/12.737814

Proc. of SPIE Vol. 6737 67370M-1
where photometric units cannot be used. The spectral distribution of the viewed radiance (in the test-sets) has not been 

standardized. The manufacturers claim that the calibration of the goggles using either a tungsten (close to Planckian) 

distribution or a narrow-band source distribution is satisfactory because the responsivity of the goggles is constant 

versus wavelength. They do not examine the errors when the broad-band night sky radiation is measured (at application) 

as compared to the narrow-band distribution of the LED (at calibration). According to the relative spectral responsivity 

characteristics of Classes A, B, and C in the MIL-STD-3009, the responsivity curves look flat (constant versus 

wavelength) because of the logarithmic responsivity scale used for illustration. However, as shown in Fig. 1, the 

spectral responsivity of different generation Gen-3 goggles can change significantly [3]. As an example, the Class-A 

standard and realized filter transmittance (cut-on) curves are also shown that will limit the goggle responsivities at the 

short wavelength side. A model is shown below to show the errors that the 815 nm LED source application and the 

constant goggle responsivity assumption can produce in night sky radiation measurements. The night sky irradiance 

distributions for full moon and no moon (only stars) [4] and the normalized spectral power distribution of a test set LED 

are shown in Fig. 2a on a logarithmic scale and in Fig. 2b on a linear scale (the full moon distribution is not shown here) 

to illustrate the difference in the wavelength coverage for the spectral range where the goggles are sensitive. 

0

40

80

120

160

200

240

280

320

0

0.2

0.4

0.6

0.8

1

400 500 600 700 800 900

Gen-3 early 1990

Gen-3 mid 1990

Gen-3 present

Class-A transmittance

Class-A 625 nm transm ITT

Wavelength [nm]

Fig. 1. Spectral responsivity curves of different generation Gen-3 goggles and the 

transmittance curves of the standardized Class-A and realized ITT [5] minus-blue filter. 

A recently published work examined the impact of goggle spectral responsivity changes on NVIS compatibility to 

aircraft interior lighting [6]. The goggle responsivity changes are caused by the changes introduced in image tube 

parameters and objective lens coatings. In the referenced publication, the authors believed it is necessary to develop and 

offer a more complete framework for NVIS related radiometric calculations. They started to explore the cockpit lighting 

compatibility issues associated with differing night-vision goggle spectral responsivity distributions. In addition to the 

relative spectral responsivity curves of the Class A and B goggles standardized in the MIL-STD-3009, they calculated 

the Class C relative spectral responsivity curve, using the transmission of the (“leaky green”) objective lens (from MILSTD-3009), and the spectral responsitivity of an ITT image intensifier (“hot”) tube responsive from 450 nm to 950 nm. 

In spectrally broad-band measurements, such as goggle calibrations, the detector spectral responsivities are to be 

standardized to perform uniform integrated responsivity (INR) measurements. Similarly to the standardized V(λ) 

function in photometry, the Class A, B, and C spectral responsivity curves can be used as reference goggle spectral 

Proc. of SPIE Vol. 6737 67370M-2
Night sky irradiance LW/cm 

distributions. The goggle signals can be calculated as the product of the goggle spectral responsivity and the source 

spectral distribution seen by the goggle. If the realized (manufactured) detector spectral responsivity is different than the 

10-9

10-8

10-7

10-6

0.1

1

500 600 700 800 900

No moon irradiance

Full moon irradiance

normalized LED distribution

Wavelength [nm]

0

2 10-9

4 10-9

6 10-9

8 10-9

1 10-8

0.2

0.4

0.6

0.8

1

500 600 700 800 900

Wavelength [nm]

 Fig. 2a. Spectral distribution curves of night sky Fig. 2b. Spectral distribution curves of night sky (no 

irradiance and a test-set LED on logarithmic scales. moon) irradiance and a test-set LED on linear scales. 

standardized responsivity, large systematic measurement errors can be obtained if the source distribution to be measured 

is very different than the distribution of the source used at calibration. 

To avoid these large errors, in addition to the standardization of the detector spectral responsivity, the spectral power 

distribution of the source at calibration can be standardized (similarly to the CIE Illuminant A, D65, and other 

distribution functions) as well. In NV goggle calibrations, frequently an LED light source is used in the test-set. Since, 

the LED spectral power distribution is very different from the night sky distributions (during goggle applications), large 

goggle measurement errors can be obtained. The measurement uncertainties can be decreased if the source spectral 

distribution in the test-sets is standardized (at calibration) and the standardized spectral distribution is similar to the 

night sky radiation (at application). This standard source distribution function does not have to be equal to the different 

night sky radiation curves. It can be similar to those to obtain low calibration uncertainties. Similar considerations have 

been made in detector-based photometric and colorimetric calibrations [7]. This idea can be realized using several LEDs 

[8, 9] in a test-set instead of using one LED (that usually peaks around 815 nm). Also, a broad-band correction factor 

(similar to the color correction factor in photometry [7]) that can be easily applied for goggle spectral responsivities that 

are different than the standard curve, can be developed to decrease goggle calibration uncertainty. 

Applying the above discussed INR measurement considerations, the goggle transfer-gain calibrations can be made in a 

uniform way with low uncertainties. The suggested goggle calibration system is based on the standardized goggle 

responsivity functions in the MIL-STD-3009 and it is traceable to the SI units through the NIST detector responsivity 

scales. The suggested uniform calibration system could significantly improve the goggle measurement uncertainties. 

2. THE NIST REFERENCE DETECTORS AND RESPONSIVITY SCALES 

Participation of NIST in the night vision goggle calibration program started in the late 1980s after NIST developed the 

high sensitivity silicon radiometers [10]. The noise equivalent photocurrent of these radiometers was 10-16 A, similar to 

Proc. of SPIE Vol. 6737 67370M-3
FO V limiter

Aperture

Diffrsé

Thermoelectric

cooler

Silicon

photodiode

the photomultiplier tubes the Army used for goggle calibrations before acquiring the NIST radiometer standards. A few 

years later NIST developed a night vision detector (radiometer) calibration facility (NVRCF) funded by the Navy. The 

NIST responsivity scale is derived from electrical-substitution cryogenic radiometers. Silicon trap-detector transfer 

standards are calibrated against these primary standards in radiant power measurement mode. The trap detectors are 

equipped with precision apertures to convert the power responsivity into irradiance responsivity. The trap detectors have 

relative combined expanded uncertainties of less than 0.1 % (k=2) [11]. The trap detectors propagate the reference 

responsivity scale to two other NIST responsivity calibration facilities. The first one, the Spectral Irradiance and 

Radiance Responsivity Calibration using Uniform Sources (SIRCUS) facility [11] is an extended version of the NVRCF 

and it can be used for general purpose detector irradiance and radiance responsivity calibrations. The other facility is the 

Spectral Comparator Facility (SCF) [12] which was used to calibrate the NIST night vision reference radiometer for 

both power and irradiance responsivity [13]. Several NV radiometer transfer standards were also developed at NIST for 

the Army, Navy, and the Air Force, to propagate the NIST radiance responsivity scale to the military primary standards 

laboratories. The radiance responsivity of these radiometers is typically determined at the NVRCF. The NIST 

luminance scale is transferred separately to the three services [14]. 

2.1 The NIST Reference Radiometer 

The NIST reference radiometer operates in irradiance measurement mode. The cross-section of the radiometer front is 

shown in Fig. 3. In front of the radiant power measuring silicon photodiode, there is a diffuser and a thin aperture 

attached to the front of the diffuser. The aperture determines the reference plane of irradiance measurements. The 

diffuser dominates the directional responsivity of the radiometer. The input geometry was optimized experimentally to 

obtain an angular responsivity close to the theoretical cosine function [13]. The field-of-view (FOV) limiter rejects 

optical radiation outside the radiometer FOV. The detector is temperature stabilized with a thermoelectric (TE) cooler at 

Fig. 3. The cross-section of the NIST night vision reference radiometer 

25 o

C. The angular responsivity was measured using a small incandescent lamp at a separation of about 3 m and the 

radiometer was rotated around the center of the aperture. The measurement results are shown on Fig. 4. The solid line is 

the cosine function and the open circles are the measured data points. The results show, that the irradiance meter has an 

angular responsivity very close to the cosine function in a FOV of 11.6o

 (full angle). 

Proc. of SPIE Vol. 6737 67370M-4
relative irradiance response 

0.994

0.995

0.996

0.997

0.998

0.999

1.000

-5.8 -4.35 -2.9 -1.45 0 1.45 2.9 4.35 5.8

cosine

meter

angle [degree]

Fig. 4. Relative angular responsivity of the irradiance measuring NIST radiometer standard 

2.2 The NV radiometer transfer standard 

The NV radiometer transfer standards, that propagate the NIST responsivity scale to the military primary standard 

laboratories, were developed at NIST to perform uniform spectral responsivity transfer and high sensitivity. The cross 

section of the radiometers are shown in Figs. 5 and 6. The first generation radiometer is shown in Fig. 5. Figure 6 shows 

the cross section of the second generation radiometer with a 90o

 rotation relative to the view for the photodiode holding 

block in Fig. 5. In both radiometers, the silicon photodiode is mounted in a temperature stabilized copper holder. The 

copper holder has a threaded hole where the photodiode can be mounted at a given position relative to the input optics 

using retainer rings and washers. Three nylon screws pull the copper holder against a copper heat sink with a TE 

cooler/heater in between. The heat sink is attached to the Aluminum housing. The photocurrent meter is mounted in a 

separate housing (not shown in these figures) which is attached to the bottom of the front part of the measuring head 

using a four-pin connector. The leads of the TE cooler and a thermistor (not shown) are soldered to the side connector. 

The input optics attached to the front of the radiometer is different in the two figures. The widely used PVS-7 input 

optics is shown in Fig. 6 and a simplified input optics (with a radiance measurement angle of α) is shown in Fig. 5. The 

design considerations and the angular radiance responsivity measurements are discussed below in Section 3.2. The 

silicon photodiode has high power responsivity in the spectral response range of the NV goggles. The high photodiode 

shunt resistance produces low amplification for the amplifier noise in the photocurrent meter, resulting in high 

sensitivity for the NV radiometer. 

The picture of the first generation radiometer transfer standard with the PVS-7 input optics is shown in Fig. 7. 

2.3 The NV radiometer calibration facility (NVRCF) 

The NV radiometer transfer standards are calibrated for radiance responsivity at the NVRCF. The scheme and the 

picture of the inside arrangement of the NVRCF are shown in Figs. 8 and 9. The standard for the calibration is the NIST 

reference radiometer. The uniform source for the calibration transfer is a 20 cm diameter integrating sphere illuminated 

by a light source. The light source can be either a diode laser (as shown in Fig. 8) or a light emitting diode (LED) 

attached to the entrance port of the sphere. For a diode laser, both the temperature and the current are controlled, for an 

LED, only the current is regulated. A silicon monitor detector compensates for intensity changes of the sources. 

Proc. of SPIE Vol. 6737 67370M-5
Retainer Connector for

Detector

output connector

—Nylon screws

— Aluminum

housing

temperature control /

Silicon I Copper holder

photodiode on top of TE

cooler/heater

Fig. 5. Cross section of the front head of the NV Fig. 6. Cross section of the front head of the new 

radiometer transfer standard using a biconvex lens generation radiometer transfer standard with the 

input optics. PVS-7 input optics. 

Fig. 7. Picture of the NV radiometer transfer standard with the PVS-7 input optics and the attached amplifier unit. 

 

The radiance, L, of the integrating sphere source is determined from a measurement made with the NIST reference 

radiometer. The flux transfer calculation is based on the geometry of the flux transfer unit. The reference radiometer is 

calibrated for spectral radiant power responsivity ss(λ) [A/W] traceable to the NIST spectral responsivity scale [12]. 

The radiant power responsivity for a given light source is calculated from ss(λ) and the spectral distribution of the 

source. The radiant power responsivity of the reference radiometer for the LED is: 

∫

∫ =

λ

λ

λ λ

λ λ λ

( )d

( ) s( )d

s,LED

S

S s

s (1) 

where S(λ) is the relative spectral power distribution of the LED. 

aperture 

stop

α

biconvex lens

Si photodiode 

 (field stop)

focal plane

TE cooler

 heat 

sink

Proc. of SPIE Vol. 6737 67370M-6
Heat

sink

£J Transfer

- - standard

radiometer

F,

Fig. 8. Scheme of the NV transfer standard radiometer calibration at the NVRCF. 

Fig. 9. Picture of the NIST Night Vision Radiometer Calibration Facility. 

 

The cosine-corrected reference radiometer has a sufficiently large acceptance angle for the flux transfer. The irradiance 

responsivity of the reference radiometer is obtained from spatial responsivity integrals determined by a raster scanning 

procedure. The effective area of the radiometer aperture is given by the ratio of its total irradiance responsivity to the 

radiant power responsivity in the center of the aperture. 

The radiance L of the sphere exit port is determined from the radiant power P from the source incident on the detector, 

and the geometric extent G: 

Proc. of SPIE Vol. 6737 67370M-7
 G

P L = (2) 

where 

G = 2

2

π ( )( ) ⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎭

⎬

⎫

⎩

⎨

⎧ + + − + + −

1/ 2

2 2 2 2 2 2 2 2 2 4 S D S D S D d r r d r r r r (3) 

The rS is the radius of the source (sphere) exit port aperture (≈ 27 mm), rD is the radius determined from the effective 

area of the radiometer aperture (≈ 4 mm), and d is the distance between the source aperture and the radiometer aperture 

(≈ 22.6 cm). In our case, the units are W for P, W cm-2 sr-1 for L, and cm2

 sr for G. 

As the second step, the NV radiometer transfer standard, with the attached PVS-7 input optics, is calibrated for the exit 

port radiance. The transfer standard radiometer (as shown in Fig. 8) is placed and aimed at the center of the sphere exit 

port. The separation between the sphere aperture and the front of the PVS-7 optics is only 50 mm because of the poor 

out-of-target rejection of the PVS-7 equipped radiometer (see below in Fig. 13). At this separation, the sphere radiation 

overfills the radiance measurement angle of the transfer standard and the surrounding angular region where the device 

has undue sensitivity. The radiance responsivity of the transfer standard is determined as the ratio of its output current 

to the radiance of the sphere exit port calibrated against the reference radiometer. 

The improvement of the out-of-target rejection using a simplified (biconvex) input optics (discussed in Section 3.2) 

decreased the 2.4 % (k=2) uncertainty component of the distance dependent radiance responsivity of the PVS-7 

equipped radiometer to less than 1 % (k=2). The combined relative expanded uncertainty of the radiance responsivity 

calibrations using the PVS-7 input optics is 3.0 % (k=2). 

3. SCALE TRANSFER 

The military calibration laboratories further transfer the radiance responsivity from the NV radiometer transfer standard 

to their field NV radiometers. The field radiometers are similar to the construction of the above discussed NV 

radiometer transfer standard. The radiance responsivity transfer for the field radiometers is made using integrating 

sphere sources illuminated possibly with the same LED type used in the test sets. The field NV radiometers are used to 

calibrate the radiance of the test-sets. The goggles are calibrated against the test-set radiance. The spectral distribution 

of the test-set radiance is dominated by the LED spectral power distribution which is much narrower than both the night 

sky radiation and the goggle spectral responsivity range. 

In order to decrease calibration and measurement uncertainties it is necessary to analyze the spectral and geometrical 

issues during the radiance scale transfer from the NIST NVRCF to the military primary standard laboratories. The 

results and conclusions of the analysis below can be applied to the scale transfer from the military primary standard 

laboratories to the field test-sets. When the radiance scale transfer to the test-sets is performed according to the 

considerations discussed below smaller than 10 % (k=2) test-set radiance calibration uncertainties can be achieved. 

Otherwise, the uncertainties can be significantly higher. The additional uncertainties of the radiance scale propagation to 

goggle calibrations and goggle field measurements are also discussed below. 

3.1 Spectral considerations 

Spectral problems during the scale propagation from the NIST reference detector to test-sets, and then from the test-sets 

to the night vision goggles, can significantly increase the calibration uncertainties. However, when the spectral 

characteristics are different at the goggle calibration compared to the follow-on goggle applications, the goggle 

performance can be very different. To avoid these differences, the spectral issues during the radiance responsivity scale 

transfer and the following goggle calibrations and applications are to be analyzed. 

Proc. of SPIE Vol. 6737 67370M-8
['] ApA!suodsej jopejep !S 

3.1.1 Scale transfer from NIST to field test sets 

During the scale transfer, broad-band detectors (radiometers) measure broad-band sources. Photometric measurements, 

where the spectral responsivity of the photometer is standardized [7], are a good example to make uniform broad-band 

measurements. In the above discussed radiometric scale transfer, a similar standardization can be performed if the same 

silicon detector type is used in all night vision transfer standard radiometers. 

The responsivity transfer errors were modeled between LED measurements and laser calibrations using two different 

types of silicon photodiodes in the transfer standard radiometer. Two (available) LED source distributions were selected 

with similar peak wavelengths (692 nm and 697 nm) and different spectral coverage. Two lasers were used as the third 

type of source distribution and tuned to the two LED peak wavelengths. Figure 10 shows the Si photodiode spectral 

responsivities and the two LED spectral power distributions and one laser tuned to the peak of the 697 nm LED. 

Equation 1 can be used to calculate the INR of a detector for an LED source. For the laser lines, instead of the INR, the 

laser responsivity of the detector at the laser wavelength is used. 

Four INRs were calculated first (using Eq. 1) for two Hamamatsu (1227 and 1337) silicon photodiodes and the two 

LEDs. Then, each INR was compared to the laser responsivity by calculating the percent error between the INR and the 

laser (reference) responsivity. These examples are shown in Table 1 to illustrate the responsivity error propagations 

caused by using a different source (LED) at application (or scale derivation) than at calibration (laser). The results show 

that the errors are smaller with the 1337 detector than with the 1227. The responsivity of the 1337 detector is linear 

versus wavelength and it is similar to the unity quantum efficiency line. The 1227 detector has a lowered responsivity in 

the red and it is very different from a straight line. Also, the responsivity propagation errors are smaller when a narrow 

band LED (like the 692 nm peak LED) is measured compared to the errors with the 697 nm (peak) LED which has a 

much wider spectral distribution. Utilizing the above considerations, the responsivity errors can be kept small in the 

responsivity scale propagation even if a laser is used at calibration and an LED is applied at scale derivations or field 

applications. This conclusion will not apply if more LEDs with different spectral distributions are used in the test-sets. 

0

0.2

0.4

0.6

0.8

1

0

0.1

0.2

0.3

0.4

0.5

0.6

600 650 700 750 800 850 900

697 nm peak LED

692 nm peak LED

1227

1337

Wavelength [nm]

Fig. 10. Spectral responsivity of two different Si detectors, and spectral power distributions of 

two LEDs with similar peak wavelengths. A laser line is also shown tuned to the 697 nm (peak) LED. 

Proc. of SPIE Vol. 6737 67370M-9
Table 1. 

Percent errors between LED integrated responsivity and laser responsivity measurements 

for two different LEDs and two different silicon photodiodes. 

INR (697 nm LED & 1227) 

--------------------------------- 

697 nm laser resp. of 1227 

INR (692 nm LED & 1227)

---------------------------------

692 nm laser resp. of 1227

INR (697 nm LED & 1337)

---------------------------------

697 nm laser resp. of 1337

INR(692 nm LED & 1337)

---------------------------------

692 nm laser resp. of 1337

4.6 % 0.6 % 2.8 % 1 % 

3.1.2 Scale transfer from test-sets to goggles 

It is not enough to determine the radiance responsivity scale propagation uncertainties from the NIST NVRCF to the 

test-sets. When the radiance scale is propagated from the test-sets to the goggles, the spectral bandwidth of the test-set 

source distribution and the deviation of that from the source distributions at the goggle applications will have a major 

influence to the uncertainties of goggle calibrations and applications. The transfer-gain is one of the most important 

goggle characteristics that should be determined. It is the ratio of the output luminance (at the eye piece) to the input 

radiance viewed by the goggle. The luminance is usually transferred from the NIST photometric scale [14]. The 

luminance at the output depends on the goggle signal which depends not only on the test-set radiance but also on the 

radiance spectral distribution. In order to obtain the same (or similar) goggle transfer gains at both calibration and 

application(s), the test-set source distribution should be similar to the source distributions at night vision applications. 

Third generation (Gen-3) goggles are being used for military applications because of the high resolution and gain 

produced by improved image intensifier tubes and the Gallium Arsenide coated photocathode that enhanced the 

sensitivity (responsivity). These goggles can measure very low-level radiation from the visible to about 900 nm. Filters 

with a cut-on edge of about 600 nm and 630 nm are deposited on the input optics of Class-A and B goggles. The ClassC goggles have a cut-on edge of about 660 nm, that allows the use of red cockpit lights without causing large goggle 

signals or saturation, and also a decreased narrow-band transmittance at about 550 nm (called leaky green) that allows 

the goggle user to see a green display (monitor) through the goggle. 

The radiance scale is transferred to the goggles from test-sets. A frequently used test-set light-source that irradiates the 

reticle-plane, is an LED that peaks around 815 nm. There are other test sets using a different LED type that peaks at 

about 690 nm. In both cases, the spectral power distribution of the LED covers only part of the wavelength range where 

the goggle is responsive. Also, in applications, where the goggles measure reflections under night sky irradiance, the 

spectral power distribution is much broader than that of a test-set LED. According to the present calibration 

considerations, if one LED distribution is used (as a reference distribution) for all Gen-3 goggle calibrations, then the 

calibration results (the transfer gain of the goggle) will be uniform. The assumption here is that the individual goggle 

responsivities will not change significantly within the wavelength interval of the LED (of the test-set). Another problem 

is that the spectral distribution of the source to be measured by the goggle at applications is ignored. As an example, the 

night sky radiation is very different from the spectral power distribution of an LED. The night sky radiation has a very 

broad distribution that will cover the overall responsivity range of the goggle resulting in a much larger signal than the 

goggle signal for a given LED distribution (for normalized distributions). The larger goggle signal at application does 

not mean that the produced systematic error is in the good direction (that the transfer gain of the goggle will be much 

higher in field applications than at calibration) because in a correct goggle calibration, the source distribution should be 

similar to the distribution at applications. The goggle transfer-gain at calibration should be very similar to that at 

applications. A modeling is described below to estimate the errors for an LED source at calibration and the broad-band 

night sky radiation at application. 

The model shows the errors what an 815 nm LED source application (during calibration in the test sets) and the 

“constant goggle responsivity versus wavelength” assumption can produce in night sky irradiated measurements 

(applications). In the calculations, the night sky irradiance distributions for full-moon and no-moon (only stars) are used 

as source distributions during goggle applications. The normalized spectral power distribution of an 815 nm (peak) LED 

Proc. of SPIE Vol. 6737 67370M-10
with the two different night sky distributions (already shown in Figs. 2a and 2b) are used. In this model, the wavelength 

coverage for the calibration-source and application-source distributions is very different in the shown spectral range 

where the goggles are responsive. The different spectral resposivities of Gen-3 night vision goggles from the early 1990, 

the mid 1990, and present, have also been shown in Fig. 1. Figure 1 also shows that the Class-A (standard and realized) 

filter transmittance (cut-on) curves that limit the goggle responsivities at the short wavelength end. All three goggles in 

Fig. 1 used in the modeling are used as Class-A goggles. Their responsivities are calculated as the product of the cut-on 

filter transmittance (the ITT filter curve) and the real spectral responsivity of the three Gen-3 goggles as shown in 

Fig. 1. The goggle responsivities are normalized at their peaks. Also, the spectral distributions of the night sky radiation 

in Figs. 2a and 2b are normalized at their peaks to make the spectral products. First, the signal, which is the product of 

the goggle spectral responsivity and the source spectral distribution, was calculated for the (same) “Gen-3 present” 

responsivity and the three source distributions (the 815 nm LED, the full-moon irradiance, and the no-moon (stars only) 

irradiance). Then, the three different signals were compared by making two signal ratios to the reference signal (using 

the LED). The ratios in Table 2 show how large the goggle signal errors can be between calibration and (two) 

applications (using the “Gen-3 present” goggle). Following that, the “Gen-3 mid 1990” and then the “Gen-3 early 

1990” goggle responsivities were substituted for the spectral products in the numerators (for both the full-moon and nomoon source distributions) and the denominator of the ratios was the spectral product of the “Gen-3 present” goggle and 

the 815 nm LED (used at calibration in the model). 

Table 2. 

Calculated ratios (systematic measurement errors) of the “Gen-3 present” goggle signals (when measuring 

two different night sky radiation distributions) to its reference signal (when measuring the 815 nm LED).

INR (Gen-3 present & full-moon) 

------------------------------------------ 

INR (Gen-3 present & 815 nm LED) 

INR (Gen-3 present & no-moon) 

------------------------------------------ 

INR (Gen-3 present & 815 nm LED) 

6.00 1.41 

The calculation results show that a factor of six (equal to 500 %) error can be obtained with the “Gen-3 present” goggle 

when it is calibrated using an 815 nm LED and then applied to measure full-moon night sky radiation. When it 

measures no-moon (stars only) radiation distribution, the error (ratio) decreases to 1.41 which means a 41 % 

measurement error. This error is much smaller because of the very different distribution of the two night sky radiation 

curves as shown in Fig. 2a. The linear Y scale of Fig. 2b better illustrates that the no-moon radiation is much lower at 

the short wavelength range of the goggle than the full-moon radiation. 

In the second part of this model, the spectral responsivities of the two other Gen-3 goggles were substituted for the 

“Gen-3 present” goggle to model the errors caused by different goggle spectral responsivities. The INRs were calculated 

for both full moon and no-moon source distributions and were referenced again to the INR of “Gen-3 present” and the 

815 nm LED (as in Table 2). The ratios, that show the measurement errors using these other two goggles instead of the 

“Gen-3 present” goggle (with the assumption that only the “Gen-3 present” goggle was calibrated using the 815 nm 

LED source), are shown in Tables 3 and 4. 

Table 3. 

Calculated ratios (systematic measurement errors) of the “Gen-3 mid 1990” goggle signals (when measuring two 

different night sky source distributions) to the reference signal (the “Gen-3 present” measures the 815 nm LED). 

INR (Gen-3 mid 1990 & full-moon) 

------------------------------------------ 

INR (Gen-3 present & 815 nm LED) 

INR (Gen-3 mid 1990 & no-moon) 

------------------------------------------ 

INR (Gen-3 present & 815 nm LED) 

5.88 1.26 

Proc. of SPIE Vol. 6737 67370M-11
Table 4. 

Calculated ratios (systematic measurement errors) of the “Gen-3 early 1990” goggle signals (when measuring two 

different night sky source distributions) to the reference signal (the “Gen-3 present” measures the 815 nm LED). 

INR (Gen-3 early 1990 & full-moon) 

------------------------------------------ 

INR (Gen-3 present & 815 nm LED) 

INR (Gen-3 early 1990 & no-moon) 

----------------------------------------- 

INR (Gen-3 present & 815 nm LED) 

6.54 1.21 

The ratios, in Tables 3 and 4, show that substituting the “Gen-3 present” goggle (used for calibration) with two other 

Gen-3 goggles (of different spectral responsivities), the goggle measurement errors can change up to 20 % for no-moon 

and 54 % for full-moon distributions (related to the 6.00 and 1.41 ratios in Table 2 where the errors are caused by the 

different source distributions). 

All the errors calculated in Tables 2 to 4 are caused by spectral mismatch errors. In Table 2, the spectral mismatch of 

the applied night sky source distributions is large relative to the spectral distribution of the 815 nm LED (used at 

calibration). In Tables 3 and 4, the spectral mismatch is between the “Gen-3 early 1990” and “Gen-3 mid 1990” goggles 

relative to the “Gen-3 present” goggle (that represents the standard goggle spectral responsivity in this model). 

The above measurement errors can be lowered if the spectral mismatch is less. For Table 2, the errors can be drastically 

decreased if several LEDs are used in the test sets instead of the 815 nm LED. Since the full-moon and no-moon night 

sky distributions are very different, and any distribution can happen between these two extreme distributions, the best 

results can be obtained if the LED distributions in the test sets (using several LEDs) will mimic (roughly) the no-moon 

distribution. The no-moon distribution is the best choice for reference source distribution because it has the lowest 

irradiance where large measurement uncertainties are not allowed (to perform safe goggle operations). The goggle 

measurement uncertainties can be higher at full moon (or between no-moon and full-moon) radiation where the signals 

are much higher and the measurement uncertainty is less of a problem. 

For Tables 3 and 4, the measurement errors can be decreased if goggles are used with spectral responsivities similar to 

the standards Class A, B, or C. In field applications, the individual measurements of goggle relative spectral 

responsivities cannot be expected. If possible, goggles should be used with known typical relative spectral responsivities 

that are similar to each other (e.g. from the same fabrication batch). In this case, a broad-band correction factor can be 

used to further decrease the errors. This correction factor can be determined as shown below. 

The goggle (NVIS) radiance is: 

λ λ λ

λ

R G N d s( ) ( ) ∫ = (4) 

where (λ) Gs is the normalized standard spectral radiance responsivity of the goggle, N(λ) is the spectral radiance of 

the source measured, and λ is the wavelength. The signal of the goggle is: 

∫ = λ

S G(λ)N(λ)dλ (5) 

where G(λ) is the (realized/fabricated) absolute spectral radiance responsivity of the goggle that measures 

the N(λ)spectral radiance. The absolute radiance responsivity can be written as 

Proc. of SPIE Vol. 6737 67370M-12
(λ) ( ) (λ) G G peak Gn = ⋅ (6) 

where G( peak) is the absolute radiance responsivity of the goggle at the peak and (λ) Gn is the normalized relative 

responsivity of the realized/fabricated goggle. The goggle broadband responsivity is the ratio of Eq. 5 to Eq. 4: 

∫

∫ = =

λ

λ

λ λ λ

λ λ λ

G N d

G peak G N d

R

S

s

s

n

( ) ( )

( ) ( ) ( )

 (7) 

The goggle calibration factor is the reciprocal of s and the broad-band (spectral mismatch) correction factor is: 

∫

∫ = =

λ

λ

λ λ λ

λ λ λ

G N d

G N d

s

G peak C

n

s

( ) ( )

( ) ( ) ( ) (8) 

In practice, a broad-band correction factor can be calculated from the typical normalized spectral responsivity curve of 

the goggle relative to the normalized spectral responsivity curve of the standard (such as Class-A). The source can be 

the no-moon (stars only) night sky distribution. If the realized/fabricated goggle spectral responsivity is equal to the 

standardized spectral responsivity of a goggle type (from Class A, B, or C), the correction factor is unity. In case, the 

relative spectral responsivity of the goggle is known (e.g. measured), the correction factor will compensate for the 

spectral mismatch errors. The correction factor also can be used when goggles that belong to two different classes (such 

as Class A or B) are used to measure similar source distributions and uniform measurement results are needed. 

While the errors calculated above have not been measured directly, the individual characteristics and functions, such as 

source distributions and spectral responsivities used in the calculations, were measured. The described modeling was the 

best approach to estimate the main goggle calibration and measurement uncertainties. 

3.2 Geometrical considerations 

In order to lower uncertainty in both the radiance responsivity calibration of the transfer standard radiometers (described 

in Section 2.3) and in the following radiance responsivity scale propagations, the traditionally used PVS-7 input optics 

was tested. This input optics which is a multi-element objective lens, was originally used for goggles where spatial 

distortions (aberrations) could lower the image quality. The PVS-7 input optics is also used at the front of the transfer 

standard radiometer where a good out-of-target rejection (radiation attenuation outside of the radiance measurement 

angle) would be more important than high image quality. An analysis has been made to improve the out-of-target 

blocking of the PVS-7 equipped radiometer using a simplified input optics of improved angular responsivity. The PVS7 input optics is still needed for the goggles. 

The radiance measurement angle depends on the front geometry of the radiometer. Figure 11 shows the radiance 

measurement scheme of the biconvex lens equipped radiometer. The solid angle Ωo of the S source as viewed 

(subtended) by the radiance measuring radiometer is usually not measured. Instead, the radiometer should have a well 

defined radiance measurement angle α. A radiance meter is usually a modified irradiance meter. At the output of the 

input optics, either the Si photodiode itself or an aperture can be used as a field stop (L). In the shown example, there is 

an aperture of diameter D1 at the front of the Si photodiode. The diameter of the objective lens is D2 and f is the focal 

length of the biconvex lens. There is an aperture stop A with a diameter of D3 in front of the lens to limit the viewing 

field. This way, the input optics has a constant f#, equal to f/D3. The objective (biconvex) lens can be moved along the 

optical axis, relative to L to form an image of the (D4 diameter) measured area of source S in the plane of L. S must be 

larger than D4 to overfill L. According to the scheme on Fig. 11, the radiance measurement half-angle is: 

Proc. of SPIE Vol. 6737 67370M-13
2 tan ( 2 ) 1

1 D i − α = (9) 

where i is the image distance. If the object distance o between S and the center of the objective lens is much larger than 

i, then i = f = constant, otherwise i is different than f. In the radiometer shown in Fig. 5, no aperture was applied, and the 

photodiode was in the focal plane of the biconvex lens, that is the i = f condition has been achieved and α is constant. 

The angular responsivities of the same transfer standard radiometer head, when equipped with the two different input 

optics, are shown in Fig. 12 and 13. Using the biconvex lens, instead of the PVS-7 input optics, the out-of-target 

rejection could be improved by at least an order of magnitude at +/- 12 o

 and larger angles. The improvements are better 

illustrated on the logarithmic scale of Fig. 13. The linear scale on Fig. 12 shows that the field-of-view from the FWHM 

values is 15o for the PVS-7 and about 10 o for the biconvex-lens input optics. 

Using the simplified input optics with the more efficient out-of-target blocking, the distance dependence of the radiance 

responsivity (between the exit port of the integrating sphere and the input optics of the transfer standard radiometer) 

could be decreased from a 3.2 % change to less than 1 % during the (radiance responsivity) scale transfer. 

Fig. 11. Radiance measurement scheme of the transfer standard radiometer when using a biconvex objective lens. 

For the night vision goggles, D1 is equal to the diameter of the photocathode (since no aperture is used in front of the 

goggle) which is significantly larger than the diameter of a silicon photodiode used (also without any aperture) in the 

transfer standard radiometer. Since α depends on D1, different size target spots can be obtained for the goggles and the 

transfer standard radiometers if the same PVS-7 input optics is used. The uncertainty of the scale transfer (from the 

transfer radiometer to the goggles) can be smaller if the input optics of the transfer standard radiometer (such as the 

biconvex lens) is designed such that the target spots of both the radiometer and the goggles are of similar sizes. This 

requirement can be important if the test-set radiance is spatially non-uniform. 

Since both the goggles and the transfer standard radiometers have large radiance measurement angles, the radiance 

source applied in the radiance responsivity transfer should overfill the acceptance angle of both the radiometers and the 

goggles. Integrating sphere sources can be used as transfer sources, however, the standard remains the transfer standard 

radiometer. Application of collimators should be avoided. Also, careful mechanical and optical alignments are 

necessary in each step of the calibration transfer to keep the calibration uncertainties low. 

α

D1

D2

F

Si

A L

F

f

o i

S

D3

D4

Ωo

Proc. of SPIE Vol. 6737 67370M-14
0

2 10-1

4 10-1

6 10-1

8 10-1

1 100

1.2 100

-20 -15 -10 -5 0 5 10 15 20

 Biconvex

 PVS-7

Angle [degree]

10-3

10-2

10-1

100

-20 -15 -10 -5 0 5 10 15 20

 Biconvex

 PVS-7

Angle [degree]

Fig. 12. Normalized angular responsivity of the NV Fig. 13. Normalized angular responsivity of the NV 

radiometer in a linear scale when equipped either radiometer in a logarithmic scale when equipped either 

with the biconvex lens or the PVS-7 input optics. with the PVS-7 input optics or a biconvex lens. 

4. CONCLUSIONS 

The NIST NVRCF has been developed and used on a regular basis to transfer the NIST reference radiance responsivity 

scale to the military primary standard laboratories. Spectral considerations have been discussed to obtain low 

uncertainties in the responsivity scale transfer to the test-sets and then to the goggles. A model showed that lasers can be 

used at radiance responsivity calibrations and scale transfers if the right detector spectral responsivity and test-set source 

distribution are used. However, use of only one LED type in the test-sets produces a significant spectral mismatch 

between calibration and applications. At applications, the goggles measure reflections of night sky radiation which has a 

much broader spectral distribution than that of the test-set LED. As a result of this spectral mismatch, a goggle will have 

different transfer-gains at calibration and applications. The goggle views a narrow-band LED distribution at calibration 

and measures a very different broad distribution at applications (night sky radiation). These errors have been modeled. 

The calculation results showed that 500 % error can be obtained with a Gen-3 goggle when it is calibrated using an 

815 nm LED and then applied to measure full-moon night sky radiation. When the same goggle measures no-moon 

(stars only) radiation distribution, the measurement error decreases to 41 %. In the second part of this model, the 

spectral responsivities of two Gen-3 goggles were substituted for a third Gen-3 goggle (the reference goggle in this 

model) to calculate the errors caused by the different goggle spectral responsivities. The calculations showed that the 

goggle measurement errors can change up to 20 % for no-moon and 54 % for full-moon night sky distributions when 

different goggles of the same type (uncalibrated in the model) are substituted for the reference goggle. The reason for 

these errors is the spectral mismatch between the two “test” goggles and the reference goggle. 

Suggestions are made to decrease the spectral mismatch between calibration and applications for both the source 

distributions and the goggle spectral responsivities. In order to decrease goggle measurement errors, it is suggested to 

use several LEDs with different distributions in the test sets instead of the 815 nm LED. Since the full-moon and nomoon night sky distributions are very different, and all application distributions are between these two extreme 

distributions, the best results can be obtained if the LED distributions in the test sets will mimic (roughly) the no-moon 

distribution. This distribution has the lowest irradiance where large measurement uncertainties cannot be allowed to 

Proc. of SPIE Vol. 6737 67370M-15
perform safe goggle operations. The goggle measurement uncertainties can be allowed to be higher at other night sky 

radiations where the signals are much higher and increased measurement uncertainty is less of a problem. A broad-band 

correction factor was introduced for goggle calibrations (to further decrease measurement uncertainties) for applications 

where the spectral responsivity of the applied (test) goggle is different than that of the standard. 

Geometrical considerations have also been discussed to decrease uncertainties in the radiance responsivity transfer. The 

design of a simplified radiance measuring input optics was discussed with improved out-of-target rejection. The results 

of angular responsivity measurements illustrate the optimum radiance measurement angles and the improved radiance 

measuring characteristics of the NIST developed transfer standard radiometers. 

5. ACKNOWLEDGEMENTS 

The author thanks the U.S. Navy for funding the development of the NV Radiometer Calibration Facility, C. Randy 

Lustenberger for making the drawing of the NV radiometer front-head, Irena Fryc for participating in the model spreadsheet calculations, and Joe Velasquez for his fruitful discussions on goggle and test-set calibrations. 

REFERENCES 

1. MIL-STD-3009, Department of Defense Interface standard for Lighting, Aircraft, Night Vision Imaging 

System (NVIS) Compatible, 2 February, 2001.

2. MIL-L-85762A, Military specification for Lighting, Aircraft, Interior, Night Vision Imaging System (NVIS) 

Compatible, 26 August, 1988. 

3. Bender, E.J., Personal communication, U.S. Army Night Vision and Electronic Sensors Directorate, Imaging 

Technology Branch, Science and Technology Division, Fort Belvoir, VA 22060-5806, 2007. 

4. Littleton, R., Personal communication, Night Vision and Electronic Sensors Directorate, Fort Belvoir, VA 

22060-5806, 2007. 

5. Disclaimer, The mention of certain commercial products in this paper is for information purposes only and 

does not constitute an endorsement of the product by the author or his institution. 

6. Task, H.L. and Marasco, P.L., The impact of changing night-vision goggle spectral response on night-vision 

imaging system lighting compatibility. SPIE proceedings, 2004. 5442. 

7. Eppeldauer, G.P., et al., Improved accuracy photometric and tristimulus-color scales based on spectral 

irradiance responsivity. Proc. of 25th Session of the CIE, 2003. 1: p. D2-30 to D2-33. 

8. U.S.patent 20050194516, , Programmable LED spectral light source. 2007. 

9. Brown, S.W., Santana, C., and Eppeldauer, G.P., Development of a Tunable LED-based Colorimetric Source.

J. Res. NIST, 2002. 107(4): p. 363-371. 

10. Eppeldauer, G. and Hardis, J.E., Fourteen-decade photocurrent measurements with large-area silicon 

photodiodes at room temperature. Applied Optics, 1991. 30: p. 3091-3099. 

11. Brown, S.W., Eppeldauer, G.P., and Lykke, K.R., Facility for Spectral Irradiance and Radiance Responsivity 

Calibrations using Uniform Sources (SIRCUS), Applied Optics, 2006. 32: p. 8218-8237. 

12. Larason, T.C., Bruce, S.S., and Parr, A.C., Spectroradiometric detector measurements. NIST Special 

Publication, 1998. 250-41. 

13. Eppeldauer, G., Racz, M., and Larason, T., Optical Characterization of Diffuser-input Standard Irradiance 

Meters. SPIE proceedings, 1998. 3573: p. 220-224. 

14. Ohno, Y., NIST measurement services: Photometric calibrations. NIST Spec. Publ., 1997. 250-37. 

Proc. of SPIE Vol. 6737 67370M-16
Traceability of photocurrent measurements to electrical standards 

 

George P. Eppeldauer 

Optical Technology Division 

National Institute of Standards and Technology 

Gaithersburg, MD 20899 

Abstract 

In detector output-signal measurements, where the measurement uncertainty critically 

impacts the total uncertainty of a detector-based radiometric scale realization, traceability 

of the photocurrent measurement to SI traceable electrical standards is needed. A 

reference photocurrent-to-voltage conversion scale has been developed and described 

here. The new standard has internal reference resistors for all signal-gain selections to 

decrease noise pickup of traditionally used external reference resistors. The internal 

resistors were calibrated by the NIST Quantum Electrical Metrology Division against 

standard resistors. Using the substitution method, the reference photocurrent-to-voltage 

conversion scale was transferred from the converter standard to other converters up to a 

maximum signal-gain of 1010 V/A with an expanded uncertainty of 0.013 % (k=2). The 

DC conversion scale was extended to AC mode signal-gain calibrations where the 

photocurrent measurement uncertainty is 0.05 % (k=2). 

1. Introduction 

The 0.01 % (k=2) uncertainty of optical power measurements with cryogenic radiometers 

and the 0.06 % (k=2) uncertainty of irradiance responsivity measurements at the NIST 

Spectral Irradiance and Radiance Responsivity Calibration with Uniform Sources 

(SIRCIUS) facility [1] needed the development of a technique to measure photodiode 

output signals with an expanded uncertainty close to 0.01 % (k=2). Similar uncertainties 

are needed in those detector output signal measurements where the signal measurement 

uncertainty critically impacts the total uncertainty of a detector-based calibration. For 

photodiodes, that are the most accurate transfer and working standards, the output shortcircuit currents are to be measured to perform low signal-measurement uncertainty [2]. 

Standardized techniques are not available to calibrate photocurrent meters with the 

required 0.01 % (k=2) uncertainty especially at low (close to 1 pA) photocurrents. 

Traditionally, electrometers (picoammeters) or current-to-voltage converters are used to 

measure small photocurrents. Research papers report low current-measurement 

uncertainties. However, these publications usually discuss only electrical current 

measurements and the calibration of the current meters. Typically, they do not discuss 

photodiode related low-current measurements which is a special area of low-current 

measurements where the electrical characteristics of the photodiodes (such as the shunt 

resistance) can influence the measurement uncertainties. 

An intrinsically stable cryogenic current comparator (CCC) was reported recently for 

accurate measurement of small electrical currents [3]. Uncertainties of 0.002 % (k=1) 
were reported for 300 pA and 0.005 % (k=1) for 100 pA current measurements. A low 

DC current source, also based on the charging capacitor method using a linear voltage 

ramp, was reported for the calibration of picoammeters [4]. At 10 pA, an uncertainty of 

0.003 % (k=1) was reported. The uncertainty increased to 6 % (k=1) at 1 fA. A 

measurement setup to calibrate picoammeters between 100 pA and 100 nA has also been 

reported where the measurement uncertainty was 0.042 % (k=2) at 100 pA [5]. 

In photodiode output-signal measurements, the signal measuring circuit operates in a 

linear mode if the photocurrent of the photodiode is measured. The current is converted 

into a voltage for data recording and evaluation. For low photocurrent measurements, 

high load-resistors are needed to obtain a high enough voltage that can be measured with 

regular digital voltmeters. Since high load-resistors (comparable to the shunt resistance of 

the measured detector) can produce non-linearity in the signal conversion, operational 

amplifier based current meters (producing lower load-resistances) are used for low 

photocurrent measurements. The conversion is made with a large precision resistor in the 

feedback loop of the operational amplifier [2]. The low-uncertainty signal-conversion is 

needed up to a feedback resistance of 10 GΩ. 

A photocurrent-to-voltage converter calibration method was published [6] where the 

expanded uncertainties were 0.38 % (k=2) at 1 pA and 0.046 % (k=2) at 10 pA. A high 

constant-voltage was converted into small currents with high-resistance resistor standards 

and the test-converter measured the small currents. The calibration uncertainty was 

dominated by two dominant uncertainty components: the voltage-dependence and the 

stability of the 10 GΩ to 100 TΩ resistor standards and the 1/f noise from the converter. 

In our earlier work, precision resistors were used as reference resistors to calibrate an 

operational amplifier based current-to-voltage converter. In the first application, the 

reference resistors were serially connected to the converter input to transfer the converter 

from current mode into voltage measurement mode. In this case, the unknown feedback 

resistance of the operational amplifier is determined from the measured voltageamplification which depends on the serial reference-resistance and the feedback 

resistance. Here, both the input and the output voltages can be measured with low 

uncertainty. In the other application, the reference resistors are used to measure the 

current from a stable current source. With both methods, because of the use of external 

reference resistors, the converter output noise is large especially at high signal-gain 

selections. Usually, the signal dynamic range and the achievable uncertainty of the 

converter signal-gain calibrations are limited at high feedback resistances where the noise 

pickup can be significant and the noise-voltage amplification is high. 

In order to obtain improved signal conversion uncertainties, a reference current-tovoltage converter has been developed using internal (electrically shielded by the metal 

box of the converter) reference feedback resistors. With this design, the noise pickup can 

be decreased. Circuit design details (such as isolation resistance issues, printed circuit 

board design, shielding etc) are not discussed here. These questions have been discussed 

earlier [2]. This work focuses on a signal-conversion scale realization and its propagation 

to applications. The reference current-to-voltage converter can be used first for the 
current-to-voltage conversion-scale realization and then, in a second step, it can 

propagate the signal-conversion scale to a test current-to-voltage converter. The signalconversion scale is an electrical scale where the current-to-voltage gains and the 

corresponding conversion uncertainties are determined. The reference signal conversion 

scale (implemented by the converter standard) can be transferred to different radiometric 

and photometric calibrations where it works like a sub-scale. The uncertainty of the subscale must be low enough to avoid dominating the combined uncertainty of the related 

radiometric or photometric scale realizations. Propagation of the reference sub-scale to 

field applications with low current-to-voltage conversion uncertainty is also an important 

requirement. 

2. The current-to-voltage converter standard 

A current-to-voltage converter standard with internal reference resistors has been 

developed to improve noise performance and uncertainty at high signal-gain calibrations 

of test converters. 

Commercially available precision resistors with excellent electrical and thermal 

characteristics have been acquired and then calibrated against NIST resistor standards. 

The manufacturer reported resistances of the purchased resistors (Caddock, TF Series) 

have 0.01 % tolerances to their nominal decade values between 104 Ω and 5 x 107 Ω [4]. 

Two, 5 x 107 Ω resistors were connected serially to obtain a 108 Ω feedback 

resistance. The temperature coefficient of resistance for these resistors is 10 ppm/0

C or 

less. The characteristics of the highest feedback resistor, 109 Ω, used in the current-tovoltage converter standard (Ohmite, Mini-MOX) were worse than the lower feedback 

resistors. The tolerance for the decade nominal value was 0.5 % and the temperature 

coefficient of resistance was 100 ppm/o

C. 

The traditional circuit diagram used for the current-to-voltage converter standard is 

shown in Fig. 1. This converter has a BNC IN connector to measure the input current and 

a BNC OUT to measure the output voltage. One resistor from a set of feedback resistors 

can be selected with a rotary switch to switch signal-gain (current sensitivity). The 

selected resistor with its parallel capacitance is switched into the feedback loop of the 

operational amplifier OA. An electrometer-grade OA is to be used because it has very 

low bias current, low offset and drift, high open-loop gain and common-mode rejection. 

The feedback resistors (discussed above) are R1=104 Ω, R2=105 Ω, R3=106 Ω, R4=107

Ω, and R5=108 Ω. Instead of using the manufacturer reported resistance tolerances, the 

resistors were calibrated against resistor standards at the NIST Quantum Electrical 

Metrology Division. The highest feedback resistor was R6=109 Ω. This resistor does not 

have parallel connected external capacitance to obtain a 3 dB roll-off frequency of about 

100 Hz. The other parallel capacitors C1 to C5 were used for frequency compensations to 

optimize the fundamental gains and the minimum upper 3 dB roll-off frequency was 

again 100 Hz [2]. The parallel feedback capacitors are C1=C2=6.8 nF, C3=1500 pF, 

C4=150 pF, and C5=15 pF. The converter housing was electrically shielded. The 

common of the circuit is combined with the shielding wire (connected to the ground-pin 
of the 120 VAC power line connector) at the 0 V pin of the +/- 15 V power supply. The 

printed circuit board of the converter is illustrated with a dashed line on Fig. 1. 

In order to utilize the advantage of group policy, two sets of feedback resistors were 

calibrated for the 104 V/A to 108 V/A signal-gain selections. The obtained resistance 

corrections for the manufacturer reported nominal values and the expanded relative 

measurement uncertainties are shown in Table 1. The results show that the differences 

between the manufacturer reported nominal resistance values and the NIST Quantum 

Electrical Metrology Division measured resistances are always smaller than 0.012 % and 

the highest relative expanded uncertainty of the NIST resistance calibrations was also 

0.012 % (k=2). 

After the resistance calibrations, all feedback resistors were inserted into the current-tovoltage converter standard. Since the 1 GΩ feedback resistor has worse electrical 

characteristics than the others and we wanted to keep the measurement uncertainty low, it 

was not calibrated against any external resistor standard. Instead, this signal-gain was 

calibrated against the neighboring signal-gain as it will be discussed below. 

3. DC signal-gain calibrations using the current-to-voltage converter standard 

Improved conversion uncertainty can be achieved with test current-to-voltage converters 

if they are calibrated against the above discussed current-to-voltage converter standard. In 

this case, the noise pickup problem can be eliminated and the low uncertainty signal-gain 

calibration can be extended to the 1010 V/A gain of a test current-to-voltage converter. 

The 109 V/A signal-gain (using the 1 GΩ feedback resistor) was calibrated against the 

108

 V/A gain by measuring the output voltage ratio with the two gains when applying the 

same (5 nA) constant current to the input of the converter standard. 

Table 1. 

Evaluation of the NIST Quantum Electrical Metrology Division calibrations 

for two sets of feedback resistors 

Feedback resistor 

Serial Number 

Nominal Value 

[Ω] 

Correction 

[μΩ/Ω] 

Relative expanded 

uncertainty [%] 

R1 104 42.8 0.0001 

R2 105 14.7 0.0001 

R3 106 12.0 0.0002 

R4 107 116.5 0.0014 

R5 108 88 0.0116 

R1’ 104 2.3 0.0001 

R2’ 105 -2.8 0.0001 

R3’ 106 76.2 0.0002 

R4’ 107 124.1 0.0014 

R5’ 108 173 0.0116 
OA

SHIELD

+15V

4

1 6

7

5

-15V

0V

BNC OUT

3

2

P1

ZERO

CONNECTOR

8

C1

C2

C3

C4

C5

R6

R5

R4

R3

R2

R1

A B

E D

H

4

BNC IN 9

Fig. 1. Circuit diagram of the current-to-voltage converter standard 

The current from the variable output current source is measured with the current-tovoltage converter standard. Figure 2 shows the simplified scheme of the substitution type 

current-to-voltage converter calibration. 

I

R

A

B

C

D

V1

Current 

Source

 Digital 

Voltmeter

Fig. 2. Current determination with the current-to-voltage converter standard. 
The current I from the electronic current source is introduced into the current-to-voltage 

converter standard. The output voltage V1 of the converter standard can be measured with 

a digital voltmeter. The value of the input current can be calculated after two output 

voltage measurements: 

R

IVIV

I )0()( − 11 = = (1) 

where V1(I) is the converter output voltage for input current I, V1(I = 0) is the converter 

output voltage for I = 0, and R is the resistance of the feedback reference resistor in the 

converter. The voltage subtraction cancels the output offset voltage of the converter 

standard. 

After the determination of I, test current-to-voltage converters can be substituted for the 

converter standard at points A, B, C, and D. Points B and D are the “common” of the 

circuits that also give the electrical shielding for the connecting (input and output) cables. 

The output voltage of a test current-to-voltage converter is V2. The signal-gain of the test 

current-to-voltage converter is: 

 I

IVIV GS

)0()( 2 2 =− = (2) 

where V2(I) is the test converter output voltage for input current I, V2(I = 0) is the test 

converter output voltage for I = 0, and I is the current as determined by Eq. 1. The output 

offset voltage of the test converter is canceled out by the voltage subtraction in Eq. 2. In 

order to obtain high signal-to-noise ratios, GS = R is the best choice. However, when GS = 

1010 V/A in the test converter, the maximum built-in feedback resistance of R = 109 V/A 

(corresponds to the highest feedback resistor of 1 GΩ) is used in the converter standard. 

In this case, the test current from the current source must be lowered to 0.5 nA where the 

output resistance of the current source (Keithley Model 263) is 1 GΩ. This sourceresistance increase is needed to keep the output noise (and the signal-gain uncertainty of 

the test-converter) low. 

4. Loop-gain related DC signal-conversion uncertainty 

When a small load-resistor converts a large current into a voltage, the conversion is done 

according to Ohm’s law and the conversion uncertainty can be low. In case of small 

photocurrent measurements, when an operational amplifier is used with high feedback 

resistors, the conversion uncertainty can be high. This complication is the reason why 

national metrology institutes (NMIs) do not offer calibration services for low current 

measurements. 
The signal-gain of a photocurrent-to-voltage converter in DC (low-frequency 

measurement) mode is: 

1 1

1 − + =

L

S

G

RG . (3) 

In an ideal case, 

 I

V R = , (4) 

where V is the output voltage and I is the input current of the current-to-voltage 

converter, R is the feedback resistance of the operational amplifier and GL is the loop gain 

of the analog control loop of the converter. A realized current-to-voltage conversion can 

be close to the ideal case if the conversion uncertainties are kept low. Otherwise, the 

loop-gain can produce a significant component in the uncertainty of the current-tovoltage conversion. The DC loop gain can be written as

L = AG β 00 , (5) 

where β 0 is the DC feedback attenuation and is the DC open-loop gain of the 

operational amplifier used in the converter. When RS photodiode-shunt-resistance is 

connected to the input of the converter, the DC feedback attenuation will be 

A0

 RR

R

S

S

+

β 0 = . (6) 

For a Si-tunnel-trap detector, if the photodiodes are selected for equal shunt resistance, 

the typical resultant shunt resistance is between 30 MΩ and 50 MΩ [2]. With RS=50 MΩ

shunt resistance and R=1 GΩ maximum feedback resistance (R6 in Fig. 1), β =0.048 

that produces a loop gain of about GL=5 x 104

. This loop gain will result in a current-tovoltage conversion uncertainty of 0.002 %. The calculation also shows that the shunt 

resistance for a 0.01 % conversion-uncertainty cannot be smaller than 10 MΩ when using 

gain 109

 V/A. The output resistance of the current source in Fig. 1 at 5 nA test-current 

was 100 MΩ resulting in a conversion uncertainty of 0.001 % using gain 109

 V/A at 

calibration. 

5. Uncertainty of DC current measurement using the converter standard 

The uncertainty components of current measurement I using the current-to-voltage 

converter standard at gain 108

 V/A are shown in Table 2. The test-current from the 

current source was 5 nA and the output resistance of the current source was 100 MΩ. 

The gain-ratio (step-down) method was used to calibrate the 109

 V/A (highest) gain of the 

converter standard against the calibrated 108 V/A gain. The highest feedback resistor 

calibrated by the NIST Quantum Electrical Metrology Division was 108 Ω. 
Table 2. Uncertainty of input current measurement at gain 108

 V/A 

of the current-to-voltage converter standard 

Uncertainty components Type Relative uncertainty 

[%] 

Feedback resistance B 5.8 x 10-3

Short-term instability of input current I A 1 x 10-3

V1 voltage measurement B 2 x 10-4

Output noise and drift A 1 x 10-4

Loop gain A 2 x 10-4

Combined standard uncertainty (k=1) of I measurement 5.89 x 10-3

Expanded total uncertainty (k=2) of I measurement 0.012 

During the gain calibration transfer, two uncertainty components will change. Because of 

the increased closed-loop voltage gain [2], the output noise and drift produced 

uncertainty component will increase to 1 x 10-3 % (k=1). The increased feedback 

attenuation will increase the loop-gain produced uncertainty component to 1 x 10-3 % 

(k=1). The combined standard uncertainty of the current measurement at 109

 V/A will be 

6.06 x 10-3 % (k=1), and the rounded expanded total uncertainty will remain 0.012 % 

(k=2). The results show that the uncertainty of the current measurements at both the 

108 V/A and 109

 V/A gains is dominated by the uncertainty of the feedback resistance 

measurement (of the 108 Ω in Table 1). 

The final uncertainty determination of the current measurements with the current-tovoltage converter standard has been made experimentally, by measuring the neighboring 

gain ratios (using the step-down method). At each neighboring gain ratio of (n+1)/n, 

where n is the gain number (4 to 7 in this test), the input-current was kept at a constant 

value. The reference gain-resistance ratios in Table 1 were divided by the measured 

output-voltage ratios for all gains. The four gain ratios from 108

/107 to 105/104 were 

determined five times (from five different current determinations) and all the four 

average ratios were smaller than 1.00010. The conclusion after these gain ratio (reference 

to measured) comparisons is that the current measurement uncertainty of the converter 

standard is 0.012 % (k=2) for gains 108

 V/A and 109 V/A, and 0.01 % (k=2) for the lower 

gains. 

6. Uncertainty of a test converter DC signal-gain calibration 

In order to calibrate a test current-to-voltage converter with the 1010 V/A highest gain, the 

test-current from the current source must be lowered to 0.5 nA and the 109

 V/A gain of 

the converter standard must be used to determine the current. At the 0.5 nA input current, 

the output resistance of the current source is 1 GΩ, one order of magnitude higher than at 

the 5 nA selection (used above). This source-resistance increase decreases the output 

noise and drift and also the loop-gain produced uncertainty components of the current 

determination but the expanded total uncertainty will remain 0.012 % (k=2). However, 

the 1 GΩ source resistance makes it possible to keep the output noise and drift and also 
the loop-gain produced uncertainty components of the test-converter calibration low in 

spite of the 1010 V/A (maximum) gain selection of the test converter. The uncertainty 

budget of the signal-gain determination of a test current-to-voltage converter using 

0.5 nA input-current at the 1010 V/A signal-gain is shown in Table 3. 

Table 3. Uncertainty of the signal-gain determination of a test current-to-voltage 

converter at gain 1010 V/A using 1 GΩ current-source-resistance 

Uncertainty components Type Relative uncertainty 

[%] 

I measurement B 0.006 

Short-term instability of input current I A 2 x 10-3

V2 voltage measurement B 2 x 10-4

Output noise and drift A 1 x 10-3

Loop gain A 1 x 10-3

Combined standard uncertainty (k=1) of GS measurement 6.48 x 10-3

Expanded total uncertainty (k=2) of GS measurement 0.013 

Using the above introduced DC signal-gain calibration method and procedure, even at the 

highest signal-gain selection of a test converter (GS = 1010 V/A), an expanded total gainuncertainty of 0.013 % (k=2) can be achieved. During the calibration part of this method 

and procedure, photodiodes have not been used. 

If the above discussed calibration/measurement uncertainties are to be repeated in real 

photocurrent measurements (applications), where different photodiodes are connected to 

the input of a current-to-voltage converter (test or standard), the shunt resistance of the 

connected photodiode must be known. E.g., the shunt resistance must be 100 MΩ or 

higher when the 109

 V/A signal-gain of the converter-standard is used (as discussed in 

Section 7). Similarly, the shunt resistance must be higher than 1 GΩ when the 1010 V/A 

(maximum) signal-gain of a test converter is selected. Otherwise, the output noise and 

drift uncertainty component in Tables 2 and 3 will increase resulting in an increase in the 

combined uncertainties as well. 

The shunt resistance of the applied photodiode will determine the smallest photocurrent 

that can be measured with the above reported uncertainties (obtained using the electronic 

current source). E.g., when the noise equivalent current (NEC) is 1 x 10-15 A (k=2) [2], 

the minimum signal-current should be at least four orders of magnitude higher (10 pA) to 

obtain a maximum 0.01 % (k=2) uncertainty contribution (to the 0.012 % and 0.013 % 

expanded total uncertainties of Tables 2 and 3) from the output signal-to-noise ratio of 

the converter. This would result in a 10 pA photocurrent measurement expanded total 

uncertainty of 0.016 %. 

Using AC mode current-to-voltage conversion (discussed below), the NEC can be 

decreased to 8 x 10-17 A [2]. However, the inherent uncertainty of AC signal-gain 

calibrations is somewhat higher than that of the above discussed DC calibrations.
7. Extension of the DC current-to-voltage conversion to AC 

The signal-gain versus frequency characteristics of a current-to-voltage converter at 

different gain selections are different because the 3 dB upper roll-off points are usually at 

different frequencies. In practice, fine tuning of the feedback capacitances to obtain the 

same 3 dB roll-off frequencies is either a very difficult or an impossible task. 

In order to describe the signal-gain of a photocurrent-to-voltage converter in AC 

measurement mode, Eq. 3 (that describes the DC signal-gain only) must be extended with 

the frequency dependent components of the loop-gain and the current-to-voltage 

conversion [2]: 

[ ] 1 )(1

1

1

1 )( − + + = ω ω

ω

L

S RCj G

RG (7) 

 

In order to achieve low photocurrent-to-voltage conversion uncertainty in AC mode, both 

the current-to-voltage conversion and the loop-gain are to be optimized at the signal 

(chopping) frequency. 

When the above described DC photocurrent-to-voltage conversion scale is extended to 

AC, even if the signal frequency is kept constant, additional AC mode measurements are 

needed. The above determined DC signal-gains are the reference values of a DC and AC 

mode current-to-voltage converter for signal frequencies close to 0 Hz. In order to 

propagate the DC signal-gain scale to higher signal frequencies, the signal-gain versus 

frequency curves are to be known for all signal-gain selections of the converter. When 

these curves are known, the above discussed current-to-voltage converter standard can be 

used in AC mode as well. 

As an example, Fig. 3 shows the measured signal-gain versus frequency curve of the 

current-to-voltage converter standard (discussed above) for one signal-gain selection. The 

photocurrent from a Si tunnel-trap detector-standard was converted into voltage by the 

converter standard, using signal-gain 105

 V/A, and the voltage was measured by a lock-in 

amplifier. During the measurement, the detector-standard was illuminated by the chopped 

radiation of a tungsten halogen lamp. The frequency of the chopper was tuned from 4 Hz 

to 180 Hz and the lock-in amplifier was synchronized to the chopping (signal) frequency. 

Each data point is an average of 20 measurements. The data points are shown with an 

open circle on the left-Y logarithmic scale. This AC signal-gain curve is used as a relative 

curve and it will be converted into an absolute curve using a DC (0 Hz) absolute tie point 

(as discussed above). The standard deviation of the mean of the 20 measurements is 

shown with open squares on the linear right-Y axis of the graph. The frequency (X-axis) 

scale is also a logarithmic scale to obtain the popular Bode-plot for the signal-gain 

function. As shown in the graph, a one-time-constant RC roll-off curve-fit was applied to 

the measured (response) data points: 
0.27

0.28

0.29

0.3

0.31

0.32

0.33

0.34

0.35

0

5 10-5

1 10-4

1.5 10-4

10 100

Frequency [Hz]

y = m1/sqrt((1+(M0/m2)^ 2))

Value Error

m1 0.34417 4.1224e-5

m2 236.42 0.19455

Chisq 2.1499e-6 NA

R 0.99996 NA

Fig. 3. Frequency dependent response of the converter standard at signal-gain 105

 V/A. 

2

2

0

1

1 ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

=

m

M

m

y (8) 

where m1 is the DC response, M0 is the frequency, and the upper roll-off frequency is 

Hz. 236.4

2

1

2 == RC

m

π

 (9) 

The fit verifies that the upper roll-off of a Si-photodiode current meter is exclusively 

determined by the time constant of the feedback RC components [2]. 

The integrating time-constant at this 105

 V/A signal-gain (see Section 4) is R2C2=6.8 x 

10-4 s gives a 3 dB upper roll-off frequency of 234.2 Hz. The 3 dB roll-off frequency 

obtained from the curve fit is slightly higher because the actual C2 is different from the 

6.8 nF nominal value of the (externally connected) feedback capacitor. From the fit 

parameters and the standard deviation of the data points, an AC measurement uncertainty 

of 0.04 % (k=2) can be estimated. 

Similar signal-gain versus frequency measurements were made for the other signal-gain 

selections as well. The one-time-constant curve-fit worked well for all signal-gain 

selections. The results are summarized in Table 4. 
Table 4. 

Results of the 3 dB upper roll-off frequency measurements from one-time-constant 

curve fits at the different signal-gain selections of the converter standard. 

Signal gain 

[V/A] 

3 dB roll-off 

nominal frequency 

[Hz] 

3 dB roll-off 

measured frequency 

[Hz] 

Standard deviation 

of the signal mean 

[%] (k=1) 

104 2341.7 3131.5 0.014 

105 234.2 236.4 0.015 

106 106.2 102.7 0.02 

107 106.2 105.3 0.025 

108 93.7 91.5 0.025 

At signal-gain 108

 V/A, the nominal frequency was calculated with a 2 pF estimated stray 

capacitance parallel connected to the C5=15 pF feedback capacitor. The standard 

deviation of the measured data points are shown for all signal-gain selections in the last 

column. The above described 0.04 % (k=2) relative expanded uncertainty of the signalgain 105

 V/A also applies to the signal-gains of 104 V/A and 106 V/A. The uncertainty 

(shown by the standard deviations) is increased to 0.05 % (k=2) for the signal gains of 

107

 V/A and 108 V/A. 

The results indicate that the signal-gain versus frequency measurements may not be 

needed if the C feedback capacitors are measured (before mounting them into the circuit) 

and the parallel stray capacitances are known. In this case, the RC time constants and 

then the relative roll-off functions can be calculated. The uncertainty may increase at the 

higher gain selections where the value of the parallel stray capacitance is comparable to 

the value of the externally connected feedback capacitor. The parallel stray capacitance 

that can be performed with a regular printed-circuit-board (PCB) design is about 2 pF. 

This capacitance can be decreased by an order of magnitude if three layers are 

implemented on the PCB. In this case, the inverting-input and the output pin of the 

operational amplifier are to be soldered to two different layers (the top and bottom) that 

are separated with the shielded (third) copper layer to minimize the stray capacitance 

between the input and the output (where the feedback resistors are connected). 

Even if the relative roll-off functions can be calculated, measurement of the frequency 

dependent signal-gains may be necessary to avoid gain peaking. Optimization of the 

signal- and the loop-gains needs partial frequency compensations for the different gain 

selections [2]. Frequency compensation can be applied to eliminate gain peaking. 

For an AC measuring test current-to-voltage converter, the reference values (tie points) of 

the signal-gain versus frequency functions are the DC signal-gains. Usually, the signalgain at a given signal frequency is not transferred directly from the reference current-tovoltage converter to the test AC-mode converter. Only the DC signal-gains are 

transferred from the reference converter to the AC-mode test converter. In detector 

responsivity measurements, using the here discussed method, the DC responsivity of the 
detector standard can be extended to the AC measuring current-to-voltage converter 

attached to the detector. Usually, NIST reports the DC responsivity of the issued 

detector-standard without the signal-gain of the current-to-voltage converter standard 

used to calibrate this detector. In this case, the signal-gain versus frequency curves of the 

AC measuring test converter (used with the NIST issued detector standard) should be 

known to extend the detector DC responsivity with the AC signal-gain of the attached 

test-converter at the signal (chopping) frequency. This method can produce similar AC 

signal-gain uncertainties for both the reference and the test current-to-voltage converter. 

Since the DC and AC signal-gain calibration uncertainties are random and uncorrelated, 

the root-mean-square-sum of the DC and AC signal-gain uncertainties will produce the 

combined uncertainty of an AC-operated test current-to-voltage converter. 

8. Conclusions 

In order to satisfy the less than 0.02 % (k=2) expanded total uncertainty requirement of 

NIST reference radiometric calibrations, a new calibration method and procedure has 

been developed for calibrating the signal-gains of current-to-voltage converters that 

operate in a wide photocurrent range. A reference current-to-voltage converter has been 

developed where all the feedback resistors are inside of an electrically shielded housing 

to avoid noise pickup. The feedback resistors from 10 kΩ to 100 MΩ have been 

calibrated at the NIST Quantum Electrical Metrology Division against resistor standards. 

The 0.0116 % expanded uncertainty (k=2) of the 108 Ω feedback resistor of the converter 

standard made it possible to realize a photocurrent measurement scale with 0.012 % (k=2) 

uncertainty for the 108

 V/A and 109 V/A gains, and 0.01 % (k=2) uncertainties for the 

lower gains. These are about a factor of three improved uncertainties over the 

uncertainties of our traditional (external reference-resistor based) calibrations at the 

109 V/A signal-gain. During the scale realization, the stable output current of a DC 

current source of high output-resistance was measured with the current-to-voltage 

converter standard. The output offset voltage of the converter was compensated at both 

the scale realization and the following scale transfer. Secondary (and field) current-tovoltage converters up to 10 GΩ feedback resistors could be calibrated against the 

reference current-to-voltage converter using the (converter) substitution method. The 

uncertainty obtained at the 10 GΩ (maximum) feedback resistor of a test converter, was 

an order of magnitude lower than with the traditional method. Following the electronic 

signal-gain calibrations of the current-to-voltage converters, considerations have been 

made for the minimum shunt resistances of the photodiodes that can be connected to the 

input of the calibrated converters. As a result of high photodiode shunt-resistance 

selections, a 10 pA photocurrent can be measured with 0.016 % (k=2) uncertainty. By 

determining the gain versus frequency characteristics of the converter standard for all 

signal-gain selections, the method/procedure (based on the converter standard) was 

extended to AC mode calibrations where the signal-gain uncertainty was 0.05 % (k=2). 

It is planned to compare the current-to-voltage converter standard with reference lowcurrent sources at 10 pA and 100 pA. 
References 

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and Radiance Responsivity Calibrations using Uniform Sources, Applied Optics, Vol. 45, 

No. 32, p. 8218-8237, 2006. 

[2] G. P. Eppeldauer, NIST Technical Note 1438, Optical Radiation Measurement with 

Selected Detectors and Matched Electronic Circuits Between 200 nm and 20 μm, U.S. 

Government Printing Office, Washington, DC, 20402, 2001. 

[3] G. Rietveld, P. de la Court, and H. E. van den Brom, Intrinsically stable CCC for 

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Colorado. 

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[7] Certain commercial equipment, instruments, or materials are identified in this paper 

to foster understanding. Such identification does not imply recommendation or 

endorsement by the National Institute of Standards and Technology, nor does it imply 

that the material or equipment are necessarily the best available for the purpose.