NIST Measurement Services:

 Regular Spectral Transmittance 

NIST

Special 

Publication 

250-69 

David W. Allen, Edward A. Early, Benjamin K. Tsai, and Catherine C. Cooksey 

U.S. Department of Commerce 

Technology Administration 

National Institute of Standards and Technology 
NIST Special Publication 250-69 

NIST MEASUREMENT SERVICES: 

Regular Spectral Transmittance 

David W. Allen, Edward A. Early, Benjamin K. Tsai, and Catherine C. Cooksey 

Optical Technology Division 

Physical Measurement Laboratory 

National Institute of Standards and Technology 

Gaithersburg, MD 20899-0001 

March 2011 

U.S. DEPARTMENT OF COMMERCE 

Gary F. Locke, Secretary 

National Institute of Standards and Technology 

Patrick D. Gallagher, Director
National Institute of Standards and Technology Special Publication 250-69 

Nat. Inst. Stand. Technol. Spec. Publ. 250-69, 60 Pages, (March 2011) 

CODEN: NSPUE2 

NIST PRINTING AND DUPLICATING OFFICE 

GAITHERSBURG, MD: 2011
1

PREFACE 

The calibration and related measurement services of the National Institute of Standards and 

Technology are intended to assist the makers and users of precision measuring instruments in 

achieving the highest possible levels of accuracy, quality, and productivity. NIST offers over 

300 different calibrations, special tests, and measurement assurance services. These services 

allow customers to directly link their measurement systems to measurement systems and 

standards maintained by NIST. These services are offered to the public and private organizations 

alike. They are described in NIST Special Publication (SP) 250, NIST Calibration Services 

Users Guide. 

The Users Guide is supplemented by a number of Special Publications (designated as the 

"SP250 Series") that provide detailed descriptions of the important features of specific NIST 

calibration services. These documents provide a description of the: (1) specifications for the 

services; (2) design philosophy and theory; (3) NIST measurement system; (4) NIST operational 

procedures; (5) assessment of the measurement uncertainty including random and systematic 

errors and an error budget; and (6) internal quality control procedures used by NIST. These 

documents will present more detail than can be given in NIST calibration reports, or than is 

generally allowed in articles in scientific journals. In the past, NIST has published such 

information in a variety of ways. This series will make this type of information more readily 

available to the user. 

This document, SP250-69 (2011), NIST Measurement Services: Regular Spectral Transmittance 

is a new publication. It covers the special tests of spectral transmittance (test number 38061S in 

SP250, NIST Calibration Services Users Guide), the calibration of spectral transmittance filters 

(test numbers 38010C through 38040C), and survey scans for research and development. 

Inquiries concerning the technical content of this document or the specifications for these 

services should be directed to the author or to one of the technical contacts cited in SP250. 

NIST welcomes suggestions on how publications such as this might be made more useful. 

Suggestions are also welcome concerning the need for new calibrations services, special tests, 

and measurement assurance programs. 

James K. Olthoff Katharine B. Gebbie 

Deputy Director for Measurement Services Director 

Physical Measurement Laboratory Physical Measurement Laboratory 

 
2

ABSTRACT 

This document describes measurement services, instrumentation, and techniques for regular 

spectral transmittance over the spectral range from 250 nm to 2500 nm at the National Institute 

of Standards and Technology. Section 2 explains the basic theory in deriving the transmittance, 

while a more thorough derivation is reserved for the interested reader in Appendix A. Section 3 

describes the reference instrument hardware, software, validation, procedures, and uncertainties. 

Section 4 provides this same detailed information for the transfer instrument. Sample calibration 

reports and sample data are provided in Appendices B and C, respectively, and Appendix D 

details instructions for requesting Regular Spectral Transmittance Calibrations. The 

measurement services are described for the benefit of customers and potential customers, and the 

instruments, measurement procedures, and uncertainties are described in sufficient detail to 

allow comparisons with measurement methods at other laboratories. 

Key words: calibration, regular spectral transmittance, transmittance, uncertainty 
3

TABLE OF CONTENTS 

Abstract ............................................................................................................................................2 

1. Introduction ................................................................................................................................6 

2. Transmittance Measurement Equation ......................................................................................7 

3. Reference Instrument .................................................................................................................8 

 3.1 Hardware ..............................................................................................................................8 

 3.1.1 Illuminator...................................................................................................................9 

 3.1.2 Sample Translation ...................................................................................................10 

 3.1.3 Receiver ....................................................................................................................10 

 3.1.4 Geometrical Optics ...................................................................................................11 

 3.1.5 Spectral Characterization ..........................................................................................11 

 3.1.6 Electrical ...................................................................................................................19 

 3.2 Instrument Validation ........................................................................................................20 

 3.3 Measurement Procedure .....................................................................................................20 

 3.4 Data Acquisition ................................................................................................................21 

 3.5 Data Analysis .....................................................................................................................22 

 3.6 Uncertainties ......................................................................................................................23 

 3.7 Calibration Report ..............................................................................................................25 

4. Transfer Instrument ..................................................................................................................26 

 4.1 Instrument Description.......................................................................................................26 

 4.2 Instrument Calibration .......................................................................................................27 

 4.3 Measurement Procedure .....................................................................................................27 

 4.4 Data Analysis .....................................................................................................................28 

 4.5 Uncertainties ......................................................................................................................28 

Acknowledgments..........................................................................................................................28 

References ......................................................................................................................................29 

Appendix A: Transmittance Theory and Measurement Equation .................................................30 

Appendix B: Sample Report ..........................................................................................................43 

Appendix C: Sample Data .............................................................................................................55 

Appendix D: How to Request Calibration Services ......................................................................57 
4

LIST OF FIGURES 

Figure 1. Schematic of the RTS .......................................................................................................9 

Figure 2. Slit-scattering function measured with emission line lamps for the indicated grating and 

slit width.........................................................................................................................................12 

Figure 3. Normalized signal from Ar+

 laser used to measure the stray-light rejection of the 

monochromator ..............................................................................................................................13 

Figure 4. Signal as a function of wavelength with the D2 arc lamp source and the PMT 

photomultiplier detector (a) with and (b) without the polarizer in the influx beam and 2 mm wide 

slits on the monochromator ............................................................................................................15 

Figure 5. Signal as a function of wavelength with the QTH incandescent lamp source and the Si 

photodiode without integrating sphere and 1 mm wide slits on the monochromator ....................16 

Figure 6. Signal as a function of wavelength with the QTH incandescent lamp source and the Si 

photodiode without integrating sphere and 2 mm wide slits on the monochromator ....................17 

Figure 7. Signal as a function of wavelength with the QTH incandescent lamp source and the Si 

photodiode with integrating sphere and 2 mm wide slits on the monochromator .........................18 

Figure 8. Signal as a function of wavelength with the QTH incandescent lamp source and the 

extended-range InGaAs photodiode with integrating sphere and 2 mm wide slits on the 

monochromator ..............................................................................................................................19 

Figure A1. Interactions of incident radiation with a surface boundary .........................................31 

Figure A2. Interactions of incident radiation within a layer ..........................................................35 

Figure A3. Transmittance as a function of incident angle for the indicated polarizations of the 

incident radiant flux of a sample with an index of refraction of 1.5, thickness of 2 mm, and 

attenuation coefficient of 0.005 mm−1 ...........................................................................................36 

Figure B1. Regular spectral transmittance as a function of wavelength  of neutral density 

filters ..............................................................................................................................................46 

Figure C1. Transmittance as a function of wavelength of the color filters ....................................55 

Figure C2. Transmittance, on a logarithmic scale, as a function of wavelength of the MAP 

(Measurement Assurance Program) filters ....................................................................................55 

Figure C4. Measured spectral transmittance of the holmium oxide glass filter for a spectral 

bandwidth of 1 nm .........................................................................................................................56 
5

LIST OF TABLES 

Table 1. Optical detector choices based on wavelength ................................................................11 

Table 2. Geometrical specifications of the RTS ............................................................................11 

Table 3. Spectral bandwidth used to measure the slit-scattering function .....................................13 

Table 4. Spectral specifications of the RTS ...................................................................................14 

Table 5. Gain ratios, for the indicated photodiode and gains, with uncertainties ..........................20 

Table 6. Sources of uncertainty and classifications for transmittance measurements ...................23 

Table 7. Sources of uncertainty and typical uncertainty contributions for transmittance .............25 

Table 8. Sources of uncertainties for various detector systems .....................................................25 

Table 9. Certified and measured wavelengths of minimum transmittance of a holmium oxide 

glass filter, for a spectral bandwidth of 1 nm .................................................................................27 

Table B1. Regular spectral transmittance as a function of wavelength  of a neutral density 

filter, serial number F1-001 ...........................................................................................................47 

Table B2. Regular spectral transmittance  as a function of wavelength  of a neutral density 

filter, serial number F1-002 ...........................................................................................................48 

Table B3. Regular spectral transmittance  as a function of wavelength  of a neutral density 

filter, serial number F1-003 ...........................................................................................................49 

Table B4. Regular spectral transmittance  as a function of wavelength  of a neutral density 

filter, serial number F2-001 ...........................................................................................................50 

Table B5. Regular spectral transmittance  as a function of wavelength  of a neutral density 

filter, serial number F2-002 ...........................................................................................................51 

Table B6. Regular spectral transmittance  as a function of wavelength  of a neutral density 

filter, serial number F2-003 ...........................................................................................................52 

Table B7. Uncertainty contributions and expanded uncertainty (k = 2) of the regular 

transmittance of a neutral density glass filter, serial number F1-001 ............................................53 

Table B8. Uncertainty contributions and expanded uncertainty (k = 2) of the regular 

transmittance of a neutral density glass filter, serial number F1-002 ............................................53 

Table B9. Uncertainty contributions and expanded uncertainty (k = 2) of the regular 

transmittance of a neutral density glass filter, serial number F1-003 ............................................53 

Table B10. Uncertainty contributions and expanded uncertainty (k = 2) of the regular 

transmittance of a neutral density glass filter, serial number F2-001 ............................................54 

Table B11. Uncertainty contributions and expanded uncertainty (k = 2) of the regular 

transmittance of a neutral density glass filter, serial number F2-002 ............................................54 

Table B12. Uncertainty contributions and expanded uncertainty (k = 2) of the regular 

transmittance of a neutral density glass filter, serial number F2-003 ............................................54 

Table C3. Nominal transmittance values at 548.5 nm and materials for the MAP filters ............56 
6

1. Introduction

NIST maintains and operates the reference instrument that establishes the national scale 

for regular spectral transmittance. It is within the NIST mission to maintain this national scale 

and disseminate it for the benefit of industry, government agencies, and others who need the 

highest accuracy measurements. Calibration services performed by the NIST Regular 

Transmittance Laboratory are intended to provide traceability to the national scale and are not 

intended to be used for meeting generic measurement needs. 

The calibration services for regular spectral transmittance are an integral part of the NIST 

spectrophotometry program, which includes calibration services for regular spectral 

transmittance, diffuse transmittance, bidirectional reflectance, and directional-hemispherical 

reflectance. For further information on these and other calibration services, see the existing 

SP250 documents [1-3] listed inside the back cover of this document. 

This laboratory only provides calibrations of regular spectral transmittance for solid 

samples, such as optical filters. It does not provide services for liquids in glass or fused silica 

cells. Optical filters can be classified as either neutral density filters or spectrally selective 

filters. The neutral density filters transmit light approximately equally across a given broad 

spectral range, while spectrally selective filters transmit light with marked spectral dependence. 

Such filters include colored glass, band-pass, and interference filters. 

The calibration services provided by this laboratory are not intended to be the only means 

of traceability to the national scale for spectral transmittance. Customers are encouraged to 

explore the use of secondary laboratories that provide similar services. Often those laboratories 

may be a more economical solution and provide acceptable measurement uncertainties. 

NIST does not state an expiration date for the calibration. The frequency of calibration 

for an item is determined by the customer. It should be based on the quality of the sample and 

how the sample is handled and maintained. High quality glass filters can be stable for many 

years. If the sample is cared for properly, a calibration interval of several years or greater may 

be reasonable. 

NIST is regularly updating services in the spectrophotometry program. For the latest 

information visit the spectrophotometry program website at 

http://www.nist.gov/pml/div685/grp03/spectrophotometry.html. 

Services Provided 

Measurement services are available for dissemination of the scales of transmittance 

maintained by the reference instrument. The primary purpose of the calibration services is to 

provide traceability to the scale, not for research on particular test items. Survey scans are 

available at a reduced cost to customers who do not need traceability to NIST. NIST provides 

the following calibration services: 

Special Tests of Spectral Transmittance (38061S) 

Measurements of spectral transmittance can be made at wavelengths from 250 nm to 

2500 nm for non-fluorescent submitted test items. In general, measurements are performed at 

room temperature with the incident beam normal to the front surface of the test item. Items with 

dimensions from 1 cm to 5.1 cm across perpendicular to the incident beam are routinely 

accommodated. Other sizes and measurement conditions are possible in consultation with NIST 
7

staff. In general, for calibration service 38061S the customer supplies the test item, which is 

measured under the spectral conditions specified by the customer. Uncertainty estimates will be 

given and will depend on the optical characteristics of the submitted test item and the instrument 

used to perform the measurement. Arrangements for these measurements on submitted test items 

must be made before shipment. The decision to perform the measurements and selection of the 

instruments to be used will rest with NIST. Test items not accepted for measurement will be 

returned. 

Spectral Transmittance Filters (38010C to 38040C) 

NIST calibrates standards of spectral transmittance for verifying the photometric scale of 

spectrophotometers. Limited quantities are available for purchase with the calibration service. 

These standards are either 30 mm diameter polished glass disks or 51 mm polished glass squares, 

2 mm to 3 mm thick, designated as cobalt blue (38010C), copper green (38020C), carbon yellow 

(38030C), and selenium orange (38040C). The relative expanded uncertainty ranges from 

approximately 0.2 % to 0.3 % of the transmittance value. Information provided to the user 

includes values of transmittance at 25 ° C at 10 nm intervals from 380 nm to 770 nm, the 

estimated uncertainty of each value, and wavelength-dependent temperature coefficients to 

estimate the variation of the transmittance with change in temperature. 

Wavelength Standards (38050C-38051C) 

NIST no longer provides a calibration service for holmium oxide glass standards. After 

decades of observations, NIST determined that holmium oxide glass standards are inherently 

stable. Users of holmium oxide glass wavelength standards, either provided by NIST or 

elsewhere, can compare the spectra obtained from transmission measurement and verify that the 

sample is holmium oxide. If the sample matches the spectra shown in Appendix C, Fig. C4, the 

user can self declare traceability for wavelength accuracy. Further details can be found in Ref. 

[4]. 

The holmium oxide filters are suitable only as wavelength standards and not as 

transmittance standards. Therefore, NIST does not provide transmittance measurements for 

these filters. 

2. Transmittance Measurement Equation 

The transmittance  of a sample illuminated by unpolarized incident radiant flux is given 

by 

2

( ,0 ) ( ,90 ) ( )        

  , (1) 

where λ is the wavelength, 0o refers to 0o polarization, and 90o refers to 90o polarization. The 

average of the two orthogonal polarization states is assumed to be equivalent to the transmittance 

using unpolarized light. Equation (1) states that the measured sample transmittance is 

determined by calculating the average of the two polarizations of the transmitted radiant flux at 

0o and 90o. At each polarization, , the transmittance is determined by the ratio, 
8

( , )

( , )

( , )

( , )

( , )

( , ) ( , )

t i

i i

i i

t i

i i

t i

i  

 

 

 

 

 

  

G

G

S

S

I

I    , (2) 

where I is the intensity, S is the measured signal, G is the transimpedance amplifier gain, and the 

subscripts i and t denote incident and transmitted, respectively. It is implicitly assumed that 

there is no change in the polarization state of the radiant flux that is transmitted by the sample 

and that the detector is insensitive to the polarization of the radiant flux. For a more detailed 

discussion, see Appendix A. 

3. Reference Instrument 

The Reference Transmittance Spectrophotometer (RTS) is the national reference 

instrument for regular spectral transmittance measurements of non-fluorescent samples at room 

temperature (23 °C ± 2 °C). The RTS performs absolute measurements of the regular 

transmittance on samples with widths from 1 cm to 5.1 cm. The measurements are usually 

performed with a collimated incident beam at normal incidence, meaning that the illumination 

axis is parallel to the normal of the sample. The spectral range for the measurements is 250 nm 

to 2500 nm. For neutral samples, the smallest measurable transmittance is 10−6

. For narrowband samples, such as interference filters, the smallest measurable transmittance is 10−4

. 

Unless requested by the customer, the measurements will be performed with the sample 

centered on the influx beam. The diameter of the influx beam is variable from 4 mm to 20 mm, 

with 20 mm as the typical diameter. 

Filter uniformity is not routinely measured. Arrangements can be made to measure the 

sample at several spatial positions at one wavelength for an additional cost. NIST may also be 

helpful in suggesting other means for obtaining uniformity information. 

3.1 Hardware 

The RTS is located in Building 220, Room A324 on the NIST Gaithersburg campus. The 

RTS is a custom-built instrument which consists of an illuminator, sample mount, and receiver 

on a vibration-isolation table. The instrument is enclosed by a black light-tight box with side 

panels and forced filtered-air ventilation. Electronics are located on top of the box, and an 

adjacent computer provides automated instrument control, data acquisition, and analysis. All 

critical electronics are maintained on a 14 kVA uninterruptible power system to eliminate data 

errors and down time from line-voltage fluctuations. A schematic diagram of the RTS is shown 

in Fig. 1, indicating the major systems and components. 
9

Figure 1. Schematic of the RTS with the systems and components labeled. The light path 

from source to detector is shaded. The Illuminator system consists of QTH – 

quartz-tungsten-halogen lamp, D2 – deuterium lamp, AL – alignment laser, FM1 

– flat mirror, SRS – source rotation stage, SM1 – spherical mirror, LC – light 

chopper, PR – prism monochromator, GM – grating monochromator, FM2 – flat 

mirror, PM – parabolic mirror, P – polarizer, and I – iris. The Sample system 

consists of S – sample holder, XTS – x-translation stage, and YTS – y-translation 

stage. The Receiver system consists of ST – shutter, FM3 – flat mirror, DRS – 

detector rotation stage, SM2 – spherical mirror, IS – integrating sphere, and D – 

detector. 

3.1.1 Illuminator 

The illuminator provides a monochromatic, polarized influx beam centered on the 

sample, with a triangular spectral bandwidth determined by the monochromator slit function. It 

consists of a radiation source, mirrors, light chopper, prism-grating monochromator, polarizer, 

and iris. The source and the monochromator’s grating and slit settings are selectable. 

The two possible sources are a quartz-tungsten-halogen (QTH) incandescent lamp and a 

deuterium arc lamp. In general, the deuterium lamp is used for wavelengths less than 350 nm 

and the QTH lamp is used for longer wavelengths. A water circulator cools the housing 

surrounding the QTH lamp to prevent overheating. 

The appropriate source is selected using a rotating flat mirror. The radiant flux is 

directed towards a spherical mirror with a 15 cm diameter and 28 cm focal length, which focuses 
10

the flux from the source onto the entrance slit of the monochromator at a distance of 570 mm 

from the source. A light chopper can be placed in front of the entrance mask as needed for use 

with the extended indium-gallium-arsenide (InGaAs) detector. 

The f/8.7 monochromator is a 1-m prism-grating system with a two-grating turret and 

remote selection of the entrance port, entrance and exit slit width, and grating. For wavelengths 

shorter than 1100 nm, a grating with 600 lines/mm blazed at 200 nm is used. For longer 

wavelengths, a grating with 600 lines/mm blazed at 1250 nm is used. Individual motors move 

the prism and gratings, so their wavelengths can be set independently. An encoder is attached to 

the grating shaft to determine the wavelength, while the wavelength of the prism is determined 

by the number of motor steps from the home position. The gratings are mounted on a vertical 

translation stage. The approximate bandwidth,  determined by the slit width and grating, is 

given by 

    SW

GD 



 



   600 lines/mm  1.5 nm/mm , (3) 

where GD is the groove density in [lines/mm] and SW is the slit width in [mm]. For a 1 mm slit 

width and a 600 lines/mm grating, the spectral bandwidth is 1.5 nm. 

 After the exit slit of the monochromator, the optical path expands a distance of 177 mm to 

a parabolic mirror (f = 177 mm), which collimates the beam before arriving at the polarizer. The 

polarizer is a 2 cm square, uncoated Glan-Taylor prism made of calcite, which has an extinction 

ratio of greater than 1:100000 and transmits light from 250 nm to 2300 nm. For cases where the 

polarizer is not suitable (such as when measuring at wavelengths outside practical spectral 

ranges), the sample is rotated 90° for repeat measurements. 

3.1.2 Sample Translation 

The sample location is determined by the positions of two translation stages, one for 

horizontal (x-axis) movement and the other for vertical (y-axis) movement. A platform on the 

arm attached to the y-axis stage accommodates a variety of sample holders, chosen based upon 

the size and shape of the sample. 

3.1.3 Receiver 

The receiver measures both the influx and efflux. The receiver consists of a shutter, 

mirrors, an integrating sphere, and a detector. The optical axis of the receiver is aligned to the 

optical axis of the illuminator. The shutter, used to collect the dark current, has a diameter of 

65 mm and is coated black to limit scattered light reaching the detector. The integrating sphere, 

used with the silicon (Si) and the extended-range InGaAs detectors, is lined with 

polytetrafluoroethylene (PTFE) and has an entrance port of 1 cm and an inside diameter of 5 cm. 

A baffle is placed in front of the integrating sphere to further reduce the effect of scattered light 

on the measurements. The entrance port of the integrating sphere is located approximately at the 

focus of the spherical mirror, so that an image of the exit slit of the monochromator is formed at 

the port. 

Several optical detectors are used, and the choice depends on the wavelength range, as 

detailed in Table 1. The photomultiplier-tube (PMT) is a module attached to its own integrating 

sphere, which is also lined with PTFE and has an entrance port of 3 cm and an inside diameter of 

10 cm. The high-voltage of the PMT is controlled by a potentiometer, and the output voltage is 
11

the current multiplied by 106

 V/A. The Si detector is temperature-controlled at 26° C with a 

transimpedance amplifier having gains that are selected manually or remotely. The extendedrange InGaAs detector, temperature-controlled at –40° C, contains a transimpedance amplifier 

with gains that are selected manually or remotely. The output current of the extended-range 

InGaAs detector passes through a lock-in amplifier. 

Table 1. Optical detector choices based on wavelength 

Detector Wavelength Range [nm] 

PMT 200 to 400 

Si 250 to 1100 

Extended-range InGaAs 900 to 2500 

3.1.4 Geometrical Optics 

The optical system of the monochromator in Fig. 1 is designed to provide adequate and 

appropriate illumination for the transmittance samples. The degree of collimation determines the 

illumination or beam quality. Table 2 shows a summary of the geometrical specifications of the 

RTS, including the degree of collimation or maximum angular deviation of the incoming ray 

from the receiver axis for both the illuminator and the receiver. 

Table 2. Geometrical specifications of the RTS 

 

Property Illuminator Receiver 

Type of geometry Directional Directional 

Direction of axis 0o (typical) 180o (typical) 

Region 31 mm maximum 35 mm by 50 mm 

Sampling Aperture Influx aperture 

Cone half-angle as measured 

from PM in Fig. 1 

7o (typical 

maximum) 

1.9o by 2.7o 

Maximum deviation from 

collimation at sample 

0.16o to 0.81o 

(depending on slit) 

Same as for illuminator 

3.1.5 Spectral Characterization 

Slit Scattering Function 

The slit-scattering functions measured with emission lamps for the various gratings and 

slit widths are shown in Fig. 2, and the spectral bandwidth (FWHM) for each measurement of the 

slit-scattering function is given in Table 3. For both slit widths, the slit-scattering function is 

triangular. For a 1 mm slit width the spectral bandwidth is approximately 1.5 nm, while for the 

2 mm slit width it is approximately 3.0 nm. The gratings listed in Fig. 2 and Table 3 are located 

in the automated turret. Grating A covers the visible range, while Grating B is used for the 

infrared region. 
12

543 544 545 546 547 548 549

0.00

0.02

0.04

0.06

0.08

(a) Grating A, 1 mm slits

Signal [nA]

Wavelength [nm]

540 541 542 543 544 545 546 547 548 549 550 551 552

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

(b) Grating A, 2 mm slits

Signal [nA]

Wavelength [nm]

1524 1525 1526 1527 1528 1529 1530

0.00

0.05

0.10

0.15

0.20

0.25

0.30

(c) Grating B, 1 mm slits

Signal [nA]

Wavelength [nm]

1524 1525 1526 1527 1528 1529 1530

0.00

0.02

0.04

0.06

0.08

(d) Grating B, 2 mm slits

Signal [nA]

Wavelength [nm]

2025 2026 2027 2028 2029 2030 2031

0.000

0.002

0.004

0.006

0.008

0.010

(e) Grating B, 1 mm slits

Signal [nA]

Wavelength [nm]

2024 2025 2026 2027 2028 2029 2030 2031 2032

0.00

0.02

0.04

0.06

0.08

0.10

(f) Grating B, 2 mm slits

Signal [nA]

Wavelength [nm]

Figure 2. Slit-scattering function measured with emission line lamps for the indicated 

grating and slit width. 
13

Table 3. Spectral bandwidth for each slit width, emission line, and grating used to measure the 

slit-scattering function 

Slit Width 

[mm] 

Lamp Line 

[nm] 

Grating Order FWHM 

[nm] 

1 Hg 546.1 A 1 1.6 

1 Ar 763.5 B 2 1.4 

1 Hg 1014 B 2 1.3 

 

2 Hg 546.1 A 1 3.3 

2 Ar 763.5 B 2 3.1 

2 Hg 1014 B 2 2.8 

Stray Light Rejection 

The stray-light rejection was measured by operating an Ar+

 laser on six lines 

simultaneously, as shown in Fig. 3. The stray light was estimated by readings at a wavelength 

offset from the laser line wavelengths, normalized against the sum of readings at the six laser 

line wavelengths. An integrating sphere was placed at the entrance of a 2 mm entrance slit. The 

beam from an Ar+

 laser was projected into the entrance port of the sphere. No polarizer was used 

in the beam path. The stray-light rejection, approximated as the ratio of the out-of-band signal to 

the in-band signal, is estimated to be about 106. 

350 400 450 500 550 600

1E-7

1E-6

1E-5

1E-4

1E-3

0.01

0.1

1

Normalized Signal

Wavelength [nm]

Figure 3. Normalized signal from Ar+ laser used to measure the stray-light rejection of the 

monochromator. 
14

Wavelength Calibration 

The wavelength was calibrated using Hg, Ne, and Ar emission lamps for both gratings 

and slit widths of 1 mm and 2 mm. The wavelength uncertainty (k = 1) is 0.05 nm for the 1 mm 

slit width and 0.10 nm for the 2 mm slit width for both gratings. For each line, this uncertainty 

was estimated from the maximum deviation between known atomic lines to the measured 

wavelength, or the difference between the calculated and the observed values. A summary of the 

spectral specifications of the illuminator is given in Table 4. 

Table 4. Spectral specifications of the RTS 

Property Value 

Wavelength Range 250 nm to 2500 nm 

Spectral Bandwidth 1.5 nm, triangular (1 mm slits) 

3.0 nm, triangular (2 mm slits) 

Stray-light Rejection 106

Wavelength Uncertainty 0.05 nm (1 mm slits) 

0.10 nm (2 mm slits) 

Polarization 0o (horizontal) to 90o (vertical) 

Signal as a Function of Wavelength 

The signal as a function of wavelength for all combinations of sources and detectors is 

given in Figs. 4 through 8. The spiky structure observed at 0 polarization for several of the 

signal distributions is due to Wood’s anomalies [5]. 
15

200 250 300 350 400

0

50

100

150

200

250

300 D2

 source, PMT detector (a)

Signal [nA]

Wavelength [nm]

 = 0

 = 90

200 250 300 350 400

0

200

400

600

800

1000

1200

1400

1600

1800

2000

D2 source, PMT detector (b)

Signal [nA]

Wavelength [nm]

200 250 300 350 400

0.01

0.1

1

10

100 D2

 source, PMT detector (c)

Signal Noise [%]

Wavelength [nm]

 = 0

 = 90

200 250 300 350 400

0.01

0.1

1

D2 source, PMT detector (d)

Signal Noise [%]

Wavelength [nm]

Figure 4. Signal as a function of wavelength with the D2 arc lamp source and the PMT 

photomultiplier detector (a) with and (b) without the polarizer in the influx beam 

and 2 mm wide slits on the monochromator. The signal noise as % of signal for 

these two conditions is shown in (c) and (d). 
16

200 400 600 800 1000 1200

0

2

4

6

8

10 QTH source, Bare Si detector, 1 mm slits (a)

Signal [nA]

Wavelength [nm]

 = 0

 = 90

200 400 600 800 1000 1200

0.1

1

10

QTH source, Bare Si detector, 1 mm slits (b)

Signal [nA]

Wavelength [nm]

 = 0

 = 90

200 400 600 800 1000 1200

1E-3

0.01

0.1

QTH source, Bare Si detector, 1 mm slits (c)

Signal Noise [%]

Wavelength [nm]

 = 0

 = 90

Figure 5. Signal as a function of wavelength with the QTH incandescent lamp source and 

the Si photodiode without integrating sphere and 1 mm wide slits on the 

monochromator on an (a) linear and (b) logarithmic scale. The signal noise as % 

of signal is shown in (c). 
17

200 400 600 800 1000 1200

0

20

40

60

80

100

120

140

160

180

200

QTH source, Bare Si detector, 2 mm slits (a)

Signal [nA]

Wavelength [nm]

 = 0

 = 90

200 400 600 800 1000 1200

0.1

1

10

100

QTH source, Bare Si detector, 2 mm slits (b)

Signal [nA]

Wavelength [nm]

 = 0

 = 90

200 400 600 800 1000 1200

1E-3

0.01

0.1

QTH source, Bare Si detector, 2 mm slits (c)

Signal Noise [%]

Wavelength [nm]

 = 0

 = 90

Figure 6. Signal as a function of wavelength with the QTH incandescent lamp source and 

the Si photodiode without integrating sphere and 2 mm wide slits on the 

monochromator on an (a) linear and (b) logarithmic scale. The signal noise as % 

of signal is shown in (c). 
18

200 400 600 800 1000 1200

0

2

4

6

8

10

QTH source, Si detector with sphere, 2 mm slits (a)

Signal [nA]

Wavelength [nm]

 = 0

 = 90

200 400 600 800 1000 1200

0.01

0.1

1

10

QTH source, Si detector with sphere, 2 mm slits (b)

Signal [nA]

Wavelength [nm]

 = 0

 = 90

200 400 600 800 1000 1200

1E-3

0.01

0.1

QTH source, Si detector with sphere, 2 mm slits (c)

Signal Noise [%]

Wavelength [nm]

 = 0

 = 90

Figure 7. Signal as a function of wavelength with the QTH incandescent lamp source and 

the Si photodiode with integrating sphere and 2 mm wide slits on the 

monochromator on an (a) linear and (b) logarithmic scale. The signal noise as % 

of signal is shown in (c). 
19

800 1000 1200 1400 1600 1800 2000 2200 2400 2600

0

5

10

15

20

25

QTH source, InGaAs(ext) detector, 2 mm slits (a)

Signal [nA]

Wavelength [nm]

 = 0

 = 90

800 1000 1200 1400 1600 1800 2000 2200 2400 2600

0.01

0.1

1

10

100

QTH source, InGaAs(ext) detector, 2 mm slits (b)

Signal [nA]

Wavelength [nm]

 = 0

 = 90

800 1000 1200 1400 1600 1800 2000 2200 2400 2600

1E-4

1E-3

0.01

0.1

1

QTH source, InGaAs(ext) detector, 2 mm slits (c)

Signal Noise [%]

Wavelength [nm]

 = 0

 = 90

Figure 8. Signal as a function of wavelength with the QTH incandescent lamp source and 

the extended-range InGaAs photodiode with integrating sphere and 2 mm wide 

slits on the monochromator on an (a) linear and (b) logarithmic scale. The signal 

noise is shown in (c). 

3.1.6 Electrical 

For all detectors, the output current is converted to voltage using a transimpedance 

amplifier before being measured by the digital voltmeter or lock-in amplifier. The Si and 

extended InGaAs detectors have a selectable gain on the transimpedance amplifier. Both the 

voltmeter and lock-in amplifier have ranges, determined by the signal. Since the transmittance 

involves ratios of signals, it is necessary to determine if the signal is proportional to the current 

from the detector. This involves measuring the linearity of the signal within a range and gain 

setting, the range ratio between range settings, and the gain ratio between gain settings, where 

appropriate. The first assures that the signal is proportional to the current for signals within the 

range; the second assures that the signal measured in one range is the same as that measured in 

another range; and the third assures that the signal measured at one gain is the same as that 

measured at another gain. Ideally, the signal will be linear within a range, the range ratio will be 

one, and the gain ratio will be 0.1. 

The linearity is defined as the ratio of an equivalent signal at two different gain levels, 
20

and is determined by the double-aperture method [6]. All that is required is that the detection 

system is linear over the full range of light possible through the monochromator with maximum 

slit width and without the sample. All settings used within this range must be tested. 

Nonlinearity, NL, is defined by 

 

   

 























 

 

0

0

0

0

1

1

% 100

G

R I

G

R I

G

R I

NL , (4) 

where R(I0) [V/A] and G0 are the responsivity and gain at some reference detector current level 

and R(I1) is the responsivity [V/A] at some other gain and current level. 

The PMT was linear to within 0.2 %; the Si photodiode was linear to within 0.05 %; and 

the extended range InGaAs photodiode was linear to within 0.075 %. For the digital voltmeter 

the range ratios were one to within 0.02 %. The range ratios for the lock-in amplifier were one 

to within 0.02 % with the Si photodiode. The gain ratios and the relative uncertainties for the 

photodiodes are given in Table 5. 

Table 5. Gain ratios for the indicated photodiode and gains, with relative uncertainties 

Photodiode Gains Gain Ratio Uncertainty [%] k = 1

Si 7 8 0.1 0.01 

8 9 0.1 0.10 

Extended 

InGaAs 

7 8 0.1 0.07 

8 9 0.1 0.07 

3.2 Instrument Validation 

The RTS facility uses three means of measurement assurance: instrument 

characterization, measurement of check standards, and comparison with other laboratories. 

Characterization includes assessing the wavelength accuracy and validating the photometric 

scale. 

A full instrument characterization is performed on an annual basis. Check standards are 

used over the course of a year between measurements to assure the instrument is properly 

operating. For assessing wavelength accuracy, emission lamps are used. Intercomparisons and 

reproducibility studies employing neutral-density and colored filters are used for validating the 

photometric scale. 

Control charts track changes in instrument performance over days and years. Data 

plotted in the control chart include transmittance of check standards at specific wavelengths. 

3.3 Measurement Procedure 

A measurement is performed by aligning the sample, configuring the instrument for the 

desired measurement, entering the parameters in the data acquisition program, and running the 
21

program to acquire and analyze the data. For each polarization and wavelength, a signal is 

measured, which is proportional to the efflux. To cancel the effect of source drift to first order, 

an average of the clear readings bracketing the transmitted reading is used for the incident flux. 

Dark signals are also measured after each influx and efflux measurement. 

The sample is placed in an appropriate sample holder, based on the size and shape of the 

sample. The sample translation stages are adjusted until a 550 nm beam of light from the lamp, 

with a selected beam diameter, is centered on the sample. The source is then changed to the HeNe alignment laser at 632.8 nm, and the tilt and rotation of the sample are adjusted until the 

retro-reflected beam is collinear with the incident beam. 

Following alignment of the sample, the appropriate lamp source is selected, turned on, 

and allowed to equilibrate for a period of one hour to reach stable operation. The appropriate 

detector and related electronics are selected, and signal levels and stability are checked. The 

input parameters are selected in the program. They include the source, detector, sample position, 

wavelength range, and wavelength increment. The measurement is initiated using the scan 

routine of the software program described in Section 3.4, which can incorporate a list of arbitrary 

wavelengths. The resulting data files are transferred to appropriate directories. 

If the sample being measured is similar to previously measured samples or check 

standards, then the repeatability will be obtained from a previous measurement, and the sample 

being calibrated will only be measured once. Repeatability of the instrument is typically 

determined when the check standards are measured for instrument validation. 

Customer-supplied samples are inspected prior to measurement, and the condition is 

noted in the calibration report. The samples are kept in the original container provided by the 

customer until the measurements are made. Samples are typically handled by the edges using 

powder free gloves, and they are not cleaned except for the removal of loose dust using an air 

bulb blower. Customers are responsible for ensuring the cleanliness quality, surface quality, etc. 

before submission. Customers who are not satisfied with the condition of a sample should either 

clean or replace the sample prior to sending it to NIST for calibration. 

3.4 Data Acquisition 

A Visual Basic program is used for data acquisition and analysis. (Certain commercial 

equipment or materials are identified in this paper to foster understanding. Such identification 

does not imply recommendation or endorsement by NIST, nor does it imply that the equipment 

or materials are necessarily the best available for the purpose.) The computer is connected to the 

equipment through GPIB and RS-232 interfaces. For each sample measurement, four data files 

are generated: raw, format, final, and combined. The files are stored in hierarchy-specific 

directories. All files are saved in the comma-separated-variable (CSV) format. 

The raw file (*.raw) stores the multiple digital voltmeter readings of the signal for each 

sample stage position at a given wavelength and polarization. Each data entry consists of a 

reading made at one polarization, wavelength, and position with the associated gain and 

voltmeter electrical range for the detector. The positions correspond to efflux through the 

sample, influx, or no flux and are referred to as sample, clear, or dark, respectively. 

The format file (*.csv) groups the readings from each position for a given wavelength 

and calculates the signal, or average of all readings, for a given polarization and wavelength. 

This enables the transmittance to be calculated from the data in each set. The repeatability 

uncertainty component is the standard deviation of the readings without moving the sample. 

The final file (*.cal) presents the values of transmittance for each polarization and the 
22

average of both polarizations as a function of wavelength. The calculation procedure is detailed 

in Section 3.5 below. 

The combined file (*.cmb) calculates an average repeat transmittance value based on 

multiple scans and also calculates the uncertainties for repeatability, wavelength, and linearity. 

The repeatability uncertainty contribution is evaluated from the standard deviation of repeat 

measurements, determined in advance as a function of wavelength and absorbance. The 

wavelength uncertainty contribution is evaluated from the derivative of the transmittance with 

respect to wavelength. The linearity uncertainty contribution includes effects from both the 

detector and the signal electronics. See also Section 3.6 for the uncertainty analysis. In most 

cases the repeatability is determined previously from multiple scans of identical check standards. 

The combined files contain a compilation of the final values from multiple files when 

transmittance is measured, and are generated automatically after all the scans are complete. 

Details of the data analysis and uncertainties are given in Sections 3.5 and 3.6. The data from 

the combined file are used for the values in the calibration report. 

3.5 Data Analysis 

The transmittance values in the combine files are initially scanned for outlying data 

points, due, for instance, to a power line glitch. Any outliers are either substituted by 

interpolated values or values from other scans of the same sample when available. Interpolated 

values will be noted in the calibration report. If multiple detectors and/or sources are used, the 

values from both files are combined and overlap between spectral regions compared. 

The data are reduced automatically to transmittance  in the software files using the 

following procedures. For each set of n readings at polarization , wavelength , and position, 

the average signal S(, ) is given by 





n

i

S i

n

S

1

( , , ) 1 (, )   . (7) 

For each polarization and wavelength, the transmittance (, ) is given by 

s

c

c c d

s s d

G

G

S S

S S    ( , ) ( , )( , ) ( , ) ( , )

,

,

   

   

   , (8) 

where Gc and Gs are the gains for the clear and sample signal measurements, respectively. The 

order of measurement is Sc (clear signal), Sc,d (dark clear signal), Ss (sample signal), Ss,d (dark 

sample signal), and Sc. The net signal is the signal with the clear beam path minus the signal 

with the shutter blocking the beam path. If the lock-in amplifier is used as the electrical detector, 

no signal is measured with the shutter blocking the beam path, in which case this signal is set to 

zero. For an unpolarized influx, the spectral transmittance () is given by 

  ( ,s) ( , p) 2

1

 ()      , (9) 

where s (perpendicular) and p (parallel) refer to the polarization of the beam with respect to the 

plane of illumination. This equation is equivalent to Eq. (1). 
23

 Reducing the data to final values for multiple source and detector combinations is usually 

accomplished using the combined files and a spreadsheet program. In general, each sample is 

measured once over a specified wavelength range, with the appropriate sources and detectors. If 

the sample is scanned more than once, the final values in a calibration report are obtained in a 

two-step process. First, the values measured multiple times under the same conditions are 

averaged in the combined file. Second, the final values for all source and detector combinations 

are plotted as a function of wavelength. 

3.6 Uncertainties 

The uncertainties for the calibration reports are calculated according to the procedures 

outlined in “Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement 

Results” [7]. There are several ways to classify the uncertainties in the transmittance values. 

Uncertainty can arise from systematic or random effects; the evaluation of the uncertainty can be 

classified as Type A or B; and the source of uncertainty can be sample-dependent or sampleindependent. The sources of uncertainty for the transmittance measurements are given in 

Table 6, along with their classification due to effect and their dependence on the properties of the 

sample. Repeatability is defined as the closeness of agreement between results of successive 

measurements of a sample using the same parameters. The repeatability of the transmittance of a 

sample can be obtained by simply starting another spectral scan at another point in time. An 

example of a factor that could affect the repeatability of a measurement is the stability of the 

lamp. In contrast, reproducibility is defined as the closeness of agreement between results for 

measurements of a sample using the same parameters, but under changed conditions. For 

example, the reproducibility of the transmittance of a sample can be obtained by removing the 

sample from the sample holder, restarting the lamp, and performing the measurement on 

different days. Sample uniformity and positioning can affect the reproducibility of a 

measurement. 

Table 6. Sources of uncertainty and classifications for transmittance measurements 

(S: Systematic; R: Random; I: Independent; D: Dependent) 

Source of Uncertainty Type of Effect Uncertainty 

Type 

Sample 

Dependence 

Wavelength S B D 

Stray Light S B D 

Detector Linearity (DL) S A D 

Detector Range Ratio (DRR) S B I 

Detector Gain Ratio (DGR) S B I 

Repeatability (RPT) R A D 

Reproducibility (RPD) S B D 

Note that most of the sources of uncertainty arise from systematic effects. 

The total relative uncertainty in the measured transmittance is given by the expression, 
24

       

    1/ 2 2 2

2 2 2 2 2

0

RPD

RPD

RPT

RPT

DGR

DGR

DRR

DRR

DL

( ) ( ) DL













 



  



 



 













 



  



 



  



 



  



 



  



 



 

u u

u u u u u u













, (10) 

where DL, DRR, DGR, RPT, and RPD are defined in the first column of Table 6 and 

       

   

1/ 2 2 2

2

,

,

2 2

,

,

2

0 ( )













 



  

  



 



  



























  

  



 



  



















  

  



 



  

 

c

c

s

s

c d

c d

c

c

s d

s d

s

s

u G

G

u G

G

u S

S

u S

S

u S

S

u S

S

u

 

   



. (11) 

In Eq. (10), the uncertainty contribution caused by wavelength, u/ , is evaluated by using 

the expression, 











 ( )

d

( ) d s i u u   , (12) 

where us() is the standard sample uncertainty in wavelength, ui() is the standard instrument 

uncertainty in wavelength, and the derivative of the transmittance is calculated from a cubic 

spline fit of transmittance as a function of wavelength. For the 600 groove/mm gratings, the 

standard instrument uncertainties in wavelength ui() are 0.05 nm for the one blazed at 200 nm 

(position A) and 0.10 nm for the one blazed at 1250 nm (position B). 

The sources of uncertainty and their uncertainty contributions, expressed in absolute 

terms, are provided in the calibration report. The sources of uncertainty due to wavelength and 

repeatability can be wavelength dependent, which can result in different uncertainty 

contributions for different wavelengths or wavelength ranges. In cases where the same detector 

range or gain setting is used for both the clear and sample signals, there is no uncertainty caused 

by detector range or gain ratios and these sources are not listed in the report. The uncertainty 

contribution due to repeatability is evaluated from the propagated uncertainties in the signals or 

from the standard deviation of repeat measurements, and is usually averaged over wavelength 

ranges. Finally, the expanded uncertainty is the combined (root-sum-square) uncertainty from all 

the uncertainty contributions, multiplied by a coverage factor k = 2. Typical uncertainty 

contributions for transmittance measured using a Si photodiode are given in Table 7, where 

percent signs refer to a percentage of the current value of the transmittance. 
25

Table 7. Sources of uncertainty and typical uncertainty contributions at 0.5 transmittance 

Source of Uncertainty Standard Uncertainty Uncertainty Contribution 

Wavelength (λ) 0.05 nm 0.0001 

Detector Linearity (DL) 0.05 % 0.0003 

Detector Range Ratio (DRR) 0.02 % 0.0001 

Detector Gain Ratio (DGR) 0.1 % 0.0005 

Repeatability (RPT) 0.02 % 0.0001 

Reproducibility (RPD) 0.035 % 0.0002 

Expanded Uncertainty (k = 2) 0.0012 

The sources of uncertainties for various detector systems used in transmittance 

measurements are listed in Table 8. 

Table 8. Sources of uncertainties for various detector systems 

Detectora

 Source of 

Uncertainty Gain Uncertainty Optical Electrical 

PMT DVM 

Linearity 0.2 % 

Range Ratio 0.02 % 

Reproducibility 0.03 % 

Si DVM 

Linearity 0.05 % 

Range Ratio 0.02 % 

Gain Ratio 7-8 0.01 % 

8-9 0.1 % 

7-9 0.1 % 

Reproducibility 0.035 % 

Si LIA 

Linearity 0.05 % 

Range Ratio 0.02 % 

Reproducibility 0.035 % 

Extended 

InGaAs LIA 

Linearity 0.075 % 

Range Ratio 0.1 %a

Reproducibility 0.03 % a

 PMT – photomultiplier tube; digital voltmeters DVM – digital voltmeter; Si – silicon 

photodiode; and LIA – lock-in amplifier 

3.7 Calibration Report 

The calibration report contains a description of the sample and the test performed. Also 

included are the data from the measurements and the associated uncertainties. Measurements of 
26

room temperature and sample dimensions are provided as reference and are not intended to be 

certified values. A plot of the data is also provided. The scale displayed on the plot may not be 

the best representation for the customer’s application. 

The calibration sample and a photocopy of the report are mailed together. Upon request, 

the report and the tabulated data in unencrypted form may be provided to the customer by email. 

The method of shipping will be determined by NIST unless the customer provides shipping 

account information and instruction. NIST does not provide any insurance above the free 

insurance offered by the shipping agent. Special arrangement can be made to pick up items in 

person. The original report is mailed separately from the sample. NIST maintains a file on the 

calibration for a period of three years. 

4. Transfer Instrument 

The transfer instrument is used for the majority of calibrations that require extended 

wavelength ranges or sets of multiple filters. The transfer instrument used is a commercial 

spectrophotometer that performs similar measurements to the RTS with less setup time and more 

rapid scan rates. It is a dual-beam instrument with a double monochromator, and it can operate 

in either a regular transmittance or diffuse reflectance mode. The uncertainties are larger than 

those of the RTS, but provide services at a considerable cost savings to the customer. 

While the RTS establishes the national scale for regular spectral transmittance by 

providing the highest accuracy, it requires significant time to set up and scan samples over large 

spectral regions. Therefore the RTS is typically reserved for use in establishing the scale using 

samples that can transfer the scale to transfer instruments. 

4.1 Instrument Description 

The overall wavelength range of the instrument is 185 nm to 3150 nm. Based on the 

transfer of the transmittance scale from the reference instrument, the calibration range is limited 

to wavelengths from 350 nm to 2500 nm. The monochromator uses two gratings, one to cover 

the UV-Vis (350 nm to 900 nm) range, and the other covering the NIR (700 nm to 2500 nm) 

range. A QTH lamp is used as the source. The scan rate can be selected between 0.004 nm/s 

and 2000 nm/s. 

The spectral bandwidth can be set to any fixed value between 0.01 nm to 5.00 nm in the 

UV-Vis, and 0.04 nm to 20.0 nm in the NIR. The minimum bandwidth may be limited 

depending on the available signal. 

The photometric range in the transmittance mode is 0 % to 100 %, while the photometric 

range in the transmittance density is 0 to 4.5. The transmittance density is defined as the 

common logarithm (base ten) of the reciprocal transmittance, 

 10 D  log . (13) 

The transmittance measurements are performed at ambient temperature and humidity. 

The temperature is noted at the time of the measurement. The allowable operating range of the 

instrument for relative humidity is 20 % to 80 %, based on the manufacturer’s specifications. 

The instrument is connected to the computer via GPIB. The computer is used to set the 

measurement parameters, and to display, collect, and analyze the data. Files of customer 

measurements are stored on a centralized server. 
27

4.2 Instrument Calibration 

Validation of the instrument operation is achieved by performing tests with the validation 

programs which are part of the instrument’s software package. These tests are run every year or 

before a critical measurement, such as a calibration that does not rely on master standards. 

The validation tests rely upon various standards. The wavelength scale is validated by 

scans of deuterium (D2) and mercury (Hg) lamps, which are internal to the instrument, and by a 

holmium oxide (Ho2O3) glass, which uses the master sample. The wavelengths of minimum 

transmittance for the master Ho2O3 sample are given in Table 9. The photometric scale is 

validated by scans of neutral-density glass filters, SRM 930 and SRM 1930. The regular spectral 

transmittance of these filters is determined quarterly on the RTS. A 2" x 2" sample holder or a 

cuvette holder can be used for the transfer standards. 

Table 9. Certified and measured wavelengths of minimum transmittance of a holmium oxide 

glass filter, for a spectral bandwidth of 1 nm [8, 9] 

Band Certified wavelengths [nm]

1 241.6 

2 279.3 

3 287.6 

4 333.9 

5 360.9 

6 386.0 

7 418.8 

8 453.6 

9 460.2 

10 536.5 

11 637.8 

4.3 Measurement Procedure 

Samples are cleaned with an air bulb to remove loosely attached dust particles only. 

They are kept in the container provided by the customer until the measurement is made, and are 

typically handled by the edges using powder-free gloves. 

The instrument is turned on and allowed to warm up for a period of one hour. The 

measurement parameters are input into the instrument software. These include the wavelength 

range, data interval, averaging time, spectral band width, and source and detector change-over. 

A 100 % transmittance baseline is obtained by scanning a blank sample holder. The 
28

blank sample holder is blocked with an opaque material for the 0 % transmittance baseline. A 

zero-baseline correction can either be calculated automatically by the software or manually by 

the user. 

4.4 Data Analysis 

The software accompanying the instrument reduces the data to percent transmittance and 

is saved in a CSV format. The data are plotted and analyzed for errors. Once the data have been 

analyzed, the data are formatted into the calibration report in the same manner as done for the 

RTS results. 

4.5 Uncertainties 

The uncertainties for transmittance calibrations on the transfer instrument are based on 

the uncertainties from the RTS. The scale of regular spectral transmittance is transferred from 

the RTS using check standards as transfer standards. The difference measured for the same 

sample between the two instruments is used as the estimate for the uncertainty ) ( r-t u  . The total 

expanded uncertainty for transmittance ) ( t u  as measured on the transfer instrument is 

calculated from the following expression, 

  2

r-t

2

t r u( )  u( )  u( ) , (14) 

where ( )r u  is the transmittance uncertainty for the RTS from Eq. (10). 

Acknowledgments 

The authors gratefully acknowledge Gerald Fraser, John Travis, Eric Shirley, and Robert 

Saunders for careful reading of this manuscript. 
29

References 

1. P. Y. Barnes, E. A. Early, and A. C. Parr, “Spectral Reflectance,” NIST Spec. Pub. 250-48, 

U. S. Dept. of Commerce (1998). 

2. M. E. Nadal, E. A. Early, and E. A. Thompson, “Specular Gloss,” NIST Spec. Pub. 1026, U. 

S. Dept. of Commerce (2006). 

3. K. L. Eckerle, J. J. Hsia, K. D. Mielenz, and V. R. Weidner, “NBS Measurement Services: 

Regular Spectral Transmittance,” NBS Spec. Pub. 250-6, U. S. Dept. of Commerce (1987). 

4. D. W. Allen, “Holmium Oxide Glass Wavelength Standards,” J. Res. Natl. Inst. Stand. 

Technol., 112, pp. 303-306 (2007). 

5. J. E. Stewart and W. S. Gallaway, “Diffraction Anomalies in Grating Spectrometers,” 

Applied Optics, 1, 421 (1962). 

6. K. D. Mielenz and K. L. Eckerle, “Spectrophotometer Linearity Testing using Double 

Aperture Method,” Applied Optics, 11, pp. 2295-2303 (1972). 

7. B. N. Taylor, and C. E. Kuyatt, “Guidelines for evaluating and expressing uncertainty on 

NIST measurement results,” NIST Technical Note, 1297 (1994). 

8. H. J. Keegan, J. C. Schleter, and V. R. Weidner, “Ultraviolet Wavelength Standard for 

Spectrophotometry,” J. Opt. Soc. Am., 51, 1470 (1961). 

9. “Standards for Checking the Calibration of Spectrophotometers (200 to 1000 nm),” Letter 

Circular 1017, U. S. Dept. of Commerce (1967). 

10. K. D. Mielenz and K. L. Eckerle, “Design, Construction, and Testing of a New High 

Accuracy Spectrophotometer,” NBS Tech. Note 729, U. S. Dept. of Commerce (1972). 

11. K. L. Eckerle, “Modification of an NBS Reference Spectrophotometer,” NBS Tech. Note 913, 

U. S. Dept. of Commerce (1976). 

12. IUPAC Compendium of Chemical Terminology, 

http://www.chemsoc.org/chembytes/goldbook/index.htm. 

13. “Standard Practice for Computing the Colors of Objects by Using the CIE System, ASTM 

E308-95,” American Society for Testing and Materials, West Conshohocken, PA (1995). 

14. Z.M. Zhang, R.R. Gentile, A.L. Migdall, and R.U. Datla, “Transmittance Measurements for 

Filters of Optical Density between One and Ten,” Applied Optics, 36, pp. 8889-8895 (1997). 

15. K. L. Eckerle, J. J. Hsia, and V. R. Weidner, “Transmittance MAP Service,” NIST SP692, 

U.S. Government Printing Office, Washington, D.C. (1985). 
30

Appendix A: Transmittance Theory and Measurement Equation 

When radiant flux (optical radiation) interacts with matter, it may be reflected, absorbed, 

or transmitted. For purposes of the regular spectral transmittance measurement service, the 

following definitions [10, 11] apply. 

Transmission is the process whereby radiant flux passes through a material or object 

without a change in wavelength of its monochromatic components. Therefore, 

photoluminescence – luminescence produced by the absorption of radiant flux – is not 

considered here. Diffusion is a change of the angular distribution of a beam of radiant flux by a 

transmitting material or a reflecting surface, such that flux incident in one direction is 

continuously distributed in many directions. The process does not conform on a macroscopic 

scale to the laws of Fresnel reflection and refraction and does not change the wavelength of the 

monochromatic components of the flux. Regular transmission is transmission in accordance 

with the laws of geometrical optics, without diffusion, while diffuse transmission is transmission 

in which diffusion occurs, independently of the laws of refraction. Mixed transmission is a 

combination of regular and diffuse transmission. 

The transmittance  of an object is the ratio of the transmitted radiant flux t to the 

incident radiant flux i, under specified geometrical and spectral conditions, and is given by 

i

t





  . (A1) 

Transmittance depends on wavelength, polarization, and on the angles of incidence and 

collection. The internal transmittance i of an object is the ratio of the radiant flux reaching the 

exit surface to the radiant flux that penetrates the entry surface. The reflectance  of an object is 

the ratio of the reflected radiant flux r to the incident radiant flux, under specified geometric 

and spectral conditions, and is given by 

i

r





  . (A2) 

The absorptance  of an object is the ratio of the absorbed radiant flux a to the incident radiant 

flux, under specified geometric and spectral conditions, and is given by 

i

a





  . (A3) 

By conservation of energy, the transmittance, reflectance, and absorptance sum to one. That is, 

    1 . (A4) 

Relating the measured transmittance of an object, which is an extrinsic property, to its 

intrinsic properties requires consideration of both the interaction of the radiant flux with the 

boundary of the object and with the material composing the interior. Since in nearly all cases for 
31

which regular transmittance is measured, the object is semi-transparent and non-conducting, the 

following equations are applicable for a homogeneous dielectric, linear, isotropic, and nonmagnetic medium. 

For the boundary interaction, a ray of radiant flux is incident upon the boundary of an 

object, as shown in Fig. A1. The angles between the normal of the boundary and the incident, 

reflected, and transmitted rays are i, r, and t, respectively. The material from which the ray is 

incident has index of refraction ni, while the material into which the ray is transmitted has index 

of refraction nt. The plane of incidence is the plane containing the surface normal and the 

incident ray. 

Figure A1. Interactions of incident radiation with a surface boundary. 

The law of reflection states that the reflected ray is in the plane of incidence and the 

angles are related by 

 r   i . (A5) 

The law of refraction, or Snell’s Law, states that the transmitted ray is also in the plane of 

incidence and the angles are related by 

t t i i n sin  n sin . (A6) 

The Fresnel equations for the reflection and transmission of the ray at the boundary are obtained 

from Maxwell’s equations and the boundary conditions for the electric and magnetic fields at the 

boundary. These equations depend on the polarization  of the incident ray, with s and p 

polarization having the electric field perpendicular and parallel to the plane of incidence, 

respectively. The amplitude reflection coefficients r depend on the angle of incidence, the 

wavelength , and the polarization, and are given by 

θi θr

θt

ni

nt

normal 
32

i i t t

i i t t

i ( ) cos ( ) cos

( ) cos ( ) cos ( , ,s)    

     

n n

n n

r



  and (A7) 

t i i t

t i i t

i ( ) cos ( ) cos

( ) cos ( ) cos ( , ,p)    

     

n n

n n

r



  . (A8) 

The angle of the transmitted ray can be eliminated from Eqs. (A7) and (A8) by using Eq. (A6). 

Similarly, the amplitude transmission coefficients t are given by 

i i t t

i i

i ( ) cos ( ) cos

2 ( ) cos ( , ,s)       

n n

n

t

  and (A9) 

t i i t

i i

i ( ) cos ( ) cos

2 ( ) cos ( , , p)       

n n

n

t

  . (A10) 

The radiant flux of a ray is given by the irradiance, the magnitude of the Poynting vector, 

multiplied by the illumination source area projected onto the sample plane. The reflectance and 

transmittance at the boundary are the ratio of the reflected and transmitted radiant flux, 

respectively, to the incident radiant flux. In terms of the amplitude coefficients, the boundary 

reflectance b is given by 

( , , ) ( , , ) i

2 b i    r    , (A11) 

and the boundary transmittance b is given by 

( , , )

cos

cos ( , , ) i

2

i i

t t

b i   





    t

n

n  . (A12) 

Within the object, the radiant flux interacts with the medium. According to Bouguer’s 

law, the internal transmittance, an extrinsic property of the object, is given by 

d d e ( )

i( , )       , (A13) 

where () is the spectral attenuation coefficient, an intrinsic property of the medium, and d is 

the distance through the object, i.e., thickness of object. The attenuation coefficient is the sum of 

the absorption coefficient a(λ) and the scattering coefficient s(λ). The mean penetration distance 

dm(λ), an intrinsic property of the object, is given by 

( )

1 ( ) m  

d   , (A14) 

while the optical thickness , an extrinsic property of the object, is given by 
33

 

  

  

m

( ) d

d  . (A15) 

Expressing the spectral attenuation coefficient as a product of the concentration c of the 

absorbing medium and the medium’s extinction coefficient (λ) yields Beer’s law form of 

Eq. (12), given by 

c d

i d e ( ) ( , )       . (A16) 

Sometimes, absorbance measurements are requested by the customer. The transmission 

(optical) density D(λ) is given by 

     10 D  log , (A17) 

while the absorbance Ai(λ), or just optical density, is given by 

Ai    log10  i  . (A18) 

Note that the transmission density depends on the total transmittance from Eq. (A1), whereas the 

optical density is a function of the internal transmittance from Eq. (A13). Internal transmittance 

refers to energy loss by absorption only, whereas the total transmittance is that due to absorption, 

reflection, scatter, and other processes [12]. Conversely, the transmittance calculated from the 

absorbance is given by 

    

  Ai

i

 10 . (A19) 

Suppressing λ-dependence from Eq. (A18), the uncertainty in absorbance, u(A), in terms of u() 

is given by 



( ) ( ) 0.434 u

u A   . (A20) 

Likewise from Eq. (A19), the uncertainty in transmittance, u(), in terms of u(A) is given by 

 ) u( ) 2.303 10 u(A A       . (A21) 

For two absorbances A1 and A2 corresponding to two thickness d1 and d2 of the same medium, 

Lambert’s law is given by 

2

2

1

1 A

d

d A  . (A22) 
34

Although the luminous transmittance is not often requested, sometimes it is needed. The 

luminous transmittance V for CIE standard illuminant C and for both the CIE 1931 (2o) standard 

observer color-matching function y and the CIE 1964 (10o) supplemental standard colormatching function 10 y is given by 





 

  







  

    



( ) ( )

( ) ( ) ( )

V S y

S y

 , (A23) 

where  is the wavelength, S() is the spectral power distribution of CIE standard illuminant C, 

() is the regular spectral transmittance of the calibration item, y() is the appropriate colormatching function, and  is the spectral bandwidth. Values for S() and y() were obtained 

from the ASTM E308 documentary standard [13]. 

An expression for the measured transmittance of an object of finite thickness in terms of 

the properties of the boundary and medium is obtained by considering the inter-reflections as 

radiant flux passes through the object in Fig. A2. If a ray is incident upon the boundary of the 

object, part of the ray is reflected by the boundary, while the remainder passes into the interior. 

The ray is attenuated as it passes through the object, and is both reflected and transmitted by the 

other boundary. The fraction of the ray that is reflected is further attenuated as it passes through 

the object to the original boundary. This process of reflection, transmission, and attenuation is 

repeated, and the total radiant flux that is transmitted through the object is measured. The 

measured absorptance, in terms of the boundary reflectance and transmittance and internal 

transmittance is given by 

 

i b

i b

3

i b

2

i i b i b i b

1

(1 )

( , , , ) (1 ) 1 ( ) ( )

 

 

           

 

  

d           

 , (A24) 

where the dependences on incident angle, wavelength, polarization, and thickness on the righthand-side of the equation have been suppressed for clarity. Likewise, the measured reflectance 

is given by 

 





 





 

    

   

           

2

i b

2

b

2

i

2 b

i b

b

2

b

2

i

b

6

i b

4

i b

2

b i b

2

b

2

i b i

1 ( )

1

1 ( )

( , , , ) 1 ( ) ( ) ( )

 

 



 

   

    d           

 (A25) 

and the measured transmittance is given by 

 

2

i b

2

i b

6

i b

4

i b

2

i b

2

i i b

1 ( )

( , , , ) 1 ( ) ( ) ( )

 

 

           

 

 

d          

 . (A26) 
35

The above formulas neglect coherence effects important when the coherence length of the 

incident light, 

  







n

L

2

 , (A27) 

is on the order of or larger than the sample thickness. For λ = 1000 nm, Δλ = 1.5 nm, and 

n = 1.5, the coherence length is 0.44 mm. Zhang et al. discusses the effects of complete and 

partial coherence for transmittance measurements of optical filter using a Nd:YAG laser. [14] 

The sum of Eqs. (A24) to (A26) is one, as required by the conservation of energy. The 

application of Eqs. (A24) to (A26) is illustrated by several examples. First, consider two 

extreme cases. For an opaque object, i = 0, which yields  = 1 – b = b,  = b, and τ = 0. For 

a perfectly transparent object, i = 1, which yields  = 0, 

b

b

1

2



 

  , and (A28) 

b

b

1

1



 



  . (A29) 

Figure A2. Interactions of incident radiation within a layer. 

For a more realistic case, consider an object composed of glass with a thickness of 2 mm. 

The measurement is performed in air, so ni = 1, and the index of refraction of the glass is 

nt = 1.5. The attenuation coefficient is  = 0.005 mm−1

, yielding an internal transmittance at 

normal incidence of i = 0.99005, a mean penetration distance of dm = 200 mm, and an optical 

thickness of  = 0.01. For a given angle of incidence, the path length is given by 

θi θr

b

 i b 1 

i b  

b 

2

i b   2

b

2

b

3  i   

 i i b b 1    

b

2

b

2  i    3

b

2

b

4  i   

  2

b b

2 1 i  i   

4

b

2

b

5  i   

  3

b b

3 1 i  i   

  4

b b

4 1 i  i   

  5

b b

5 1 i  i   
36

t cos

2 mm



d  . (A30) 

The transmittance as a function of incident angle for s and p polarizations and for unpolarized 

incident radiant flux is shown in Fig. A3. 

0 15 30 45 60 75 90

0.0

0.2

0.4

0.6

0.8

1.0

Polarization

Transmittance

Incident Angle [deg]

 s

 p

 none

Figure A3. Transmittance as a function of incident angle for the indicated polarizations of the 

incident radiant flux of a sample with an index of refraction of 1.5, thickness of 

2 mm, and attenuation coefficient of 0.005 mm−1

. 

The Reference Transmittance Spectrophotometer (RTS) typically measures the regular 

transmittance of a sample at normal incidence (i = 0°) as a function of wavelength and 

polarization of the illumination beam. Measuring at normal incidence eliminates effects from 

polarization and path length through the sample. This appendix derives the measurement 

equation corresponding to the operation of the RTS, which relates measured quantities to the 

transmittance. 

As detailed in Section 3.1, the RTS operates by polarizing a collimated, monochromatic 

illumination beam and passing it through the sample carriage. The beam continues on to the 

receiver, whose optical detector measures a signal proportional to the radiant flux of the beam. 

The sample carriage consists of two incident positions for the beam: clear and sample. In each 

position a shutter is used as a light trap for a dark signal. At each wavelength and polarization, 

signals are measured from the clear, dark, sample, dark, and clear positions, in order. Signals for 

the clear and sample positions are proportional to the incident and transmitted radiant fluxes, 

respectively. Net signals for the clear and sample positions are obtained by subtracting the dark 
37

position signals. Since the beam emerging from the collimating mirror is not completely 

polarized, measurements are made for two orthogonal polarizations of the illumination beam, 

and the resulting transmittances are averaged to obtain the transmittance for unpolarized incident 

radiant flux. For typical samples measured so far, the variation due to polarization is within the 

expanded uncertainty. 

To derive the measurement equations, several definitions are needed. Since the 

illumination beam of the RTS is linearly polarized, all of the following polarizations of the 

radiant flux are assumed to be along either the s or p direction. Expanding upon the definition of 

transmittance given by Eq. (A1), the transmittance for polarized incident and transmitted radiant 

flux is given by 

( , )

( , , ) ( , , )

i i

t i t

i t  

  

   



 , (A31) 

where  is the wavelength of the radiant flux, and i and t are the polarization of the incident 

and transmitted radiant flux, respectively. Note that the polarization of the transmitted radiant 

flux can be different from that of the incident radiant flux. In most cases, the total transmitted 

radiant flux for a given polarization of the incident radiant flux is required, given by 

( , )

( , ,s) ( , , p)

( , )

( , , t) ( , ,t)

i i

t i t i

i i

t i

i  

   

 

 

  



    

 , (A32) 

where t denotes the total transmitted radiant flux. The transmittance for unpolarized incident 

radiant flux and polarized incident radiant flux is also useful, and is given by 

( ,s) ( ,p)

( ,s, ) ( ,p, )

( ,u)

( ,u, ) ( ,u, )

i i

t t t t

i

t t

t  

   



 

  

  

     , (A33) 

where u denotes unpolarized incident radiant flux. Note that the incident radiant fluxes for each 

polarization have to be equal. Finally, the transmittance for unpolarized incident radiant flux and 

the total transmitted radiant flux is given by 

( ,s) ( ,p)

( ,s,s) ( ,s,p) ( ,p,s) ( ,p,p)

( ,u)

( ,u,t) ( ,u,t)

i i

t t t t

i

t

 

   





 

  

        

 . (A34) 

The radiant flux is not measured directly. Rather, a current I [A] from the optical 

detector is measured, which is proportional to the radiant flux  [W] by 

I(,)  (,) R(,) , (A35) 

where R [A/W] is the responsivity of the detector, which depends on the wavelength and 

polarization of the radiant flux. Following the progression for transmittance given by Eqs. (A31) 

to (A35), the currents corresponding to polarized, total, and unpolarized incident and transmitted 

radiant fluxes are given by 
38

( , ) ( , ) ( , ) i   i i   i R   i I    , (A36) 

 ) ( , , ) ( , , ) ( , t   i  t t   i  t R   t I    , (A37) 

 ) It (, i ,t)  t (, i ,s) R(,s)  t (, i ,p) R(,p , (A38) 

( ,u) ( ,s) ( ,s) ( ,p) ( ,p) Ii   i   R   i   R  , (A39) 

and 

( ,p,s) ( ,s) ( ,p,p) ( ,p).

( ,u,t) ( ,s,s) ( ,s) ( ,s,p) ( ,p)

t t

t t t

   

    

R R

I R R

    

      

 (A40) 

The transmittances given in Eqs. (A31) to (A34) can now be expressed in terms of the 

measured currents and known responsivities. Solving Eqs. (A36) and (A37) for the radiant flux 

and substituting into Eq. (A31) yields 

( , )

( , )

( , )

( , , )

( , )

( , )

( , )

( , , )

( , , )

t

i

i i

t i t

i

i i

t

t i t

i t  

 

 

  

 

 

 

  

   

R

R

I

I

R

I

R

I

   . (A41) 

Calculating (, i, t) from the measured currents is therefore possible only if the receiver is 

able to discriminate the polarization of the radiant flux, by having a polarizer between the sample 

and the detector, and knowing the ratio of the responsivities for the two polarizations, or by 

having no change in polarization of the radiant flux that is transmitted by the sample. 

The transmittance for the total transmitted radiant flux, from Eqs. (A32), (A36), and 

(A38), is 

( , ,s) ( , ,p)

( ,p)

( , )

( , )

( , ,p)

( ,s)

( , )

( , )

( , ,s) ( , ,t)

i i

i

i i

i t i

i i

t i

i

     



 

 

 



 

 

 

  

 

   

R

R

I

I

R

R

I

I

 . (A42) 

This expression for (, i, t) is valid if the receiver is able to discriminate the polarization of the 

radiant flux. If there is no change in the polarization of the radiant flux that is transmitted by the 

sample, then Eq. (A42) reduces to Eq. (A41) without the ratio of the responsivities. Finally, if 

the receiver is not sensitive to the polarization of the radiant flux, we have 

R(,s)  R(,p) , (A43) 

and Eq. (A42) becomes 
39

( , )

( , ,t) ( , ,t)

i i

t i

i  

 

  

I

I  , (A44) 

where the current from the optical detector It(, i, t) includes both polarizations of the 

transmitted radiant flux. 

The transmittance for unpolarized incident radiant flux, from Eqs. (A33), (A37), and 

(A39) is 

( , p)

( , p)

( ,s)

( ,s)

( , )

( , p, )

( , )

( ,s, )

( , u, )

i i

t

t t

t

t t

t









 

 

 

 

  

R

I

R

I

R

I

R

I





 . (A45) 

To make the incident radiant fluxes for both s and p polarizations equal, the terms in Eq. (A45) 

for the p polarization of the incident radiant flux are multiplied by a factor of 

(Ii(, s)/R(, s))/(Ii(, p)/R(, p)). Multiplying both the numerator and denominator by 

R(, s)/Ii(, s) then yields 

  ( ,s, ) ( ,p, ) . 2

1

( , )

( ,p)

( ,p)

( ,p, )

( , )

( ,s)

( ,s)

( ,s, )

2

1 ( ,u, )

t t

i t

t t

i t

t t

t

     

 





 

 





 

  

 





 



    

R

R

I

I

R

R

I

I

 (A46) 

As discussed above for Eq. (A42), Eq. (A46) is valid only if the receiver is able to discriminate 

the polarization of the radiant flux or there is no change in the polarization of the radiant flux that 

is transmitted by the sample. Applying the same procedure to Eqs. (A34), (A39), and (A40) 

yields 

 

  ( ,s,t) ( ,p,t) . 2

1

( ,s,s) ( ,s,p) ( ,p,s) ( ,p,p) 2

1

( ,p)

( ,p)

( ,p)

( ,p,p)

( ,s)

( , )

( ,p)

( ,p,s)

( ,p)

( ,s)

( ,s)

( ,s,p)

( ,s)

( ,s)

( ,s)

( ,s,s)

2

1 ( ,u,t)

i

t

i

t

i

t

i

t

   

       

































 

 

   

























  

   



R

R

I

I

R

R p

I

I

R

R

I

I

R

R

I

I

 (A47) 

As with Eq. (A42), this expression is valid if the receiver is able to discriminate the polarization 

of the radiant flux. If there is no change in the polarization of the radiant flux that is transmitted 

by the sample, or the receiver is not sensitive to the polarization of the radiant flux, then 

Eq. (A47) reduces to 
40

  ( ,s,t) ( ,p,t) . 2

1

( ,p)

( ,p,t)

( ,s)

( ,s,t)

2

1 ( ,u,t)

i

t

i

t

   









 

 





 



  

I

I

I

I

 (A48) 

If the receiver is sensitive to polarization, but the ratio of the responsivities to the two 

orthogonal linear polarizations s and p is not known, (, i, t) and (, u, t) can still be 

determined, but with an increase in the number of required measurements. A set of 

measurements is obtained with the polarization-sensitive component of the receiver rotated 0° 

from its normal position, then a second set of measurements is performed at a rotation of 90° 

about the axis of the radiant flux. This introduces an additional variable r = 0° or 90° for the 

responsivity and hence the current. Summing the measured currents for the case of polarized 

incident radiant flux and total transmitted radiant flux yields 

  

  ( , ,0 ) ( , ,90 ) ( , )

( ,s,0 ) ( ,s,90 ) ( , ,s) ( ,p,0 ) ( ,p,90 ) ( , ,p)

( , ,0 ) ( , ,90 )

( , ,s,0 ) ( , ,p,0 ) ( , ,s,90 ) ( , ,p,90 )

( , ,0 ) ( , ,90 )

( , ,t,0 ) ( , ,t,90 )

i i i i

t i t i

i i i i

t i t i t i t i

i i i i

t i t i

     

       

   

       

   

   

   

         

  

       

  

  

R R

R R R R

I I

I I I I

I I

I I

 (A49) 

Now, while ) R(, t ,0)  R(, t ,90 because of the sensitivity of the receiver to polarization, 

1 R(,s,0)  R(,p,90)  R and 2 R(,p,0)  R(,s,90)  R because of the orthogonality of 

the linear polarizations and the 90° rotation of the receiver. Therefore, Eq. (A49) reduces to 

   

 

( , ,t).

( , )

( , ,t)

( , )

( , ,s) ( , ,p)

( , ,0 ) ( , ,90 )

( , ,t,0 ) ( , ,t,90 )

i

i i

t i

1 2 i i

1 2 t i 1 2 t i

i i i i

t i t i

  

 

 

 

   

   

   







 

        

  

R R

R R R R

I I

I I

 (A50) 

Similarly, 

 

( ,u,t).

( ,s,t) ( ,p,t) 2

1

( ,s,0 ) ( ,p,0 ) ( ,s,90 ) ( ,p,90 )

( ,s,t,0 ) ( ,p,t,0 ) ( ,s,t,90 ) ( ,p,t,90 )

i i i i

t t t t

 

   

   

   



        

      

I I I I

I I I I

 (A51) 

The current from the optical detector is usually not measured, but is converted to a 

voltage S [V] for measurement, given by 
41

S(, )  I(, )G , (A52) 

where G [V/A] is the gain of the transimpedance amplifier. For the RTS, the receiver is 

insensitive to the polarization of the radiant flux, so the total transmitted flux is measured. Sets 

of signals are recorded as a function of wavelength and polarization of the incident radiant flux 

twice for the clear position and once for the sample position of the sample carriage. In addition, 

dark signals are recorded for each position. A single recorded signal is given by S(, , i), where 

 and  are the wavelength and polarization of the incident radiant flux, respectively, and i

designates the number in the set. The average signal is given by 





n

i

S i

n

S

1

( , , ) 1 (, )   . (A53) 

With the sample carriage at the clear position, the first average signal is designated by Si1, the 

second by Si2, and the dark signal by Sid. At the sample position, the signal is designated by St1, 

and the dark signal by Std. The net signals are obtained by subtracting the dark signals, so 

  ( , ) ( , ) 2 ( , ) 2

1 ( , ) Si    Si1    Si2    Sid   and (A54) 

 ) ( , ) ( , ) ( , St    St1    Std   . (A55) 

Using the expressions for the signals, Eqs. (A52) to (A55) with Eq. (A44) yields the 

measurements equation for the total transmitted radiant flux for a given wavelength and 

polarization of the incident radiant flux, given by 

( , )

( , )

( , )

( , ) ( , ,t)

t i

i i

i i

t i

i  

 

 

 

  

G

G

S

S   , (A56) 

where Gt and Gi are the gains of the transimpedance amplifier when measuring the transmitted 

and incident radiant fluxes, respectively. The measurement equation for the total transmitted 

radiant flux at a given wavelength for unpolarized incident radiant flux is derived from 

Eqs. (A48) and (A56) and is given by 





 



     ( ,p)

( ,p)

( ,p)

( ,p)

( ,s)

( ,s)

( ,s)

( ,s)

2

1 ( ,u,t)

t

i

i

t

t

i

i

t

















 

G

G

S

S

G

G

S

S . (A57) 

In the calibration reports, this quantity is rewritten in a simpler form as 

2

( ,0 ) ( ,90 ) ( )        

  , (A58) 

where 
42

( , )

( , )

( , )

( , )

( , )

( , ) ( , )

i i

t i

t i

i i

i i

t i

i  

 

 

 

 

 

  

S

S

G

G

S

S    , (A59) 

because for most calibrations, the gains, Gt(λ, σ) ~ Gi(λ, σ), do not vary much. 
43

Appendix B: Sample Report 

REPORT OF CALIBRATION 

38061S Regular Spectral Transmittance 

for 

Six Neutral Density Filters 

Submitted by: 

Any Company, Inc. 

Attn.: Ms. Jane Doe 

123 Calibration Street 

Measurement City, MD 20800-1234 

(See your Purchase Order No. 12345, dated January 1, 2010) 

1. Description of Calibration Items 

Six neutral density filters, 51 mm square, serial numbers F1-001, F1-002, F1-003, F2-001, F2-

002, and F2-003, submitted by Any Company, Inc. 

 

2. Description of Calibration 

The regular spectral transmittance  is the ratio of the radiant flux transmitted by the item, 

without diffusion, to the radiant flux incident on the item at normal incidence as a function of 

wavelength. For normal incidence, the axis of illumination is parallel to the normal of the front 

surface of the item. 

The items were measured using the NIST Reference Transmittance Spectrophotometer. This 

instrument has undergone significant modifications for automation, but the design is similar to 

the one described in [1]. A spherical mirror focuses radiant flux from a source onto the entrance 

slit of a prism-grating monochromator. The beam emerging from the exit slit of the 

monochromator is collimated by an off-axis parabolic mirror, passes through a Glan-Taylor 

polarizer, and is incident on an iris to provide a circular illumination beam. The beam passes 

through the sample carriage, is collected by a fold mirror, and is focused by a spherical mirror 

into an averaging sphere. A signal proportional to the radiant flux of the beam is measured by an 

optical detector attached to the averaging sphere. The sample carriage consists of two incident 

positions for the beam: clear and sample. In each position a shutter is used as a light block for a 

dark signal. At each wavelength and polarization, signals are measured from the clear, dark, 

sample, dark, and clear positions, in order. Signals from the clear and sample positions are 
44

proportional to the incident and transmitted radiant fluxes, respectively. Net signals for the clear 

and sample positions are obtained by subtracting the dark position signals. 

Individual items were cleaned with an air bulb and mounted in a commercial lens holder with the 

illumination beam centered on the front surface of the item at normal incidence. This was 

achieved by adjusting tilts and translations of the sample holder and carriage until a laser beam at 

a wavelength of 632.8 nm, propagating collinear to the beam from the monochromator, was 

centered on the front of the item and retroreflected. 

The sampling aperture, defined by the illumination beam, had a diameter of 20 mm and was 

located at the center of the calibration item. The maximum deviation of any ray within the 

illumination beam from the normal direction was 0.81. The maximum deviation of any ray 

within the receiver beam from the normal direction was 2.7. 

All items were measured at wavelengths from 380 nm to 770 nm every 10 nm. The spectral 

bandwidth of the illumination beam was 3 nm. The source was a QTH incandescent lamp, and 

the detector was a silicon photodiode. Each item was measured three times at two polarizer 

orientations rotated 90 from each other about the direction of the illumination beam. 

3. Results of Calibration 

The transmittance  at each wavelength  and polarization  is given by 

( , )

( , ) ( , )   

  

i

t

S

S  , 

where St is the net signal from the transmitted radiant flux in the sample position and Si is the net 

signal from the incident radiant flux in the clear position. The regular spectral transmittance for 

an unpolarized illumination beam is given by 

2

( ,0 ) ( ,90 ) ( )        

  . 

The final regular spectral transmittance was obtained by averaging the values from both 

polarizations and is plotted in Fig. B1. The certified regular spectral transmittances of the 

calibration items, measured according to the details given above, are given in Tables B1 to B6. 

Uncertainties were calculated according to the procedures outlined in [2]. Sources of uncertainty 

due to random effects are source stability and detector noise. The uncertainty contribution 

caused by these sources was evaluated from the standard deviation of repeat measurements of 

each item. 

Sources of uncertainty due to systematic effects are the wavelength of the monochromator and 

linearity of the receiver. The uncertainty contribution caused by the wavelength uncertainty was 

evaluated from the derivative of the transmittance. The uncertainty contribution caused by 
45

linearity, which was determined in the characterization of the RTS facility, includes effects from 

both the detector and the signal electronics. All uncertainty components were assumed to have 

normal probability distributions. 

The sources of uncertainty and uncertainty contributions are given in Tables B7 to B12 for the 

items. The expanded uncertainty in regular spectral transmittance is obtained from the root-sumsquare of the uncertainty contributions multiplied by a coverage factor k = 2. 

4. General Information 

1) The items were measured in the “as received” condition, after cleaning with an air bulb. 

2) The data in Tables B1 to B6 apply only to the central 20 mm diameter area of the calibration 

item. 

3) This calibration report may not be reproduced except in full without the written consent of 

this Laboratory. 

Prepared by: Approved by: 

Catherine C. Cooksey Eric L. Shirley 

Optical Technology Division For the Director, 

Physical Measurement Laboratory National Institute of 

(301) 975-6208 Standards and Technology 

 (301) 975-2349 

References: 

[1] K. L. Eckerle, J. J. Hsia, K. D. Mielenz, and V. R. Weidner, “NBS Measurement Services: 

Regular Spectral Transmittance,” NBS Special Publication 250-6 (1987). 

[2] B. N. Taylor and C. E. Kuyatt, “Guidelines for Evaluating and Expressing the Uncertainty 

of NIST Measurement Results,” NIST Technical Note 1297 (1994). 

 
46

Figure B1. Regular spectral transmittance as a function of wavelength  of neutral density 

filters. 

 

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

360 410 460 510 560 610 660 710 760

Wavelength [nm]

Transmittance

F1-001

F1-002

F1-003

F2-001

F2-002

F2-003
47

Table B1. Regular spectral transmittance as a function of wavelength  of a neutral density 

filter, serial number F1-001. 

 [nm]   [nm] 

380 0.9067 580 0.9123 

390 0.9077 590 0.9124 

400 0.9082 600 0.9125 

410 0.9087 610 0.9126 

420 0.9090 620 0.9126 

430 0.9092 630 0.9126 

440 0.9095 640 0.9127 

450 0.9097 650 0.9128 

460 0.9101 660 0.9130 

470 0.9104 670 0.9131 

480 0.9106 680 0.9132 

490 0.9107 690 0.9133 

500 0.9110 700 0.9134 

510 0.9112 710 0.9134 

520 0.9114 720 0.9136 

530 0.9116 730 0.9136 

540 0.9117 740 0.9137 

550 0.9120 750 0.9138 

560 0.9120 760 0.9138 

570 0.9121 770 0.9140 
48

Table B2. Regular spectral transmittance  as a function of wavelength  of a neutral density 

filter, serial number F1-002. 

 [nm]   [nm] 

380 0.7956 580 0.8367 

390 0.7999 590 0.8376 

400 0.8034 600 0.8386 

410 0.8066 610 0.8394 

420 0.8095 620 0.8402 

430 0.8119 630 0.8410 

440 0.8143 640 0.8418 

450 0.8164 650 0.8425 

460 0.8183 660 0.8432 

470 0.8201 670 0.8438 

480 0.8218 680 0.8445 

490 0.8235 690 0.8451 

500 0.8251 700 0.8457 

510 0.8267 710 0.8463 

520 0.8281 720 0.8468 

530 0.8295 730 0.8474 

540 0.8310 740 0.8478 

550 0.8322 750 0.8484 

560 0.8334 760 0.8489 

570 0.8346 770 0.8491 
49

Table B3. Regular spectral transmittance  as a function of wavelength  of a neutral density 

filter, serial number F1-003. 

 [nm]   [nm] 

380 0.6582 580 0.6694 

390 0.6600 590 0.6697 

400 0.6612 600 0.6700 

410 0.6623 610 0.6703 

420 0.6631 620 0.6707 

430 0.6637 630 0.6709 

440 0.6642 640 0.6712 

450 0.6646 650 0.6716 

460 0.6650 660 0.6720 

470 0.6653 670 0.6723 

480 0.6656 680 0.6726 

490 0.6659 690 0.6729 

500 0.6664 700 0.6732 

510 0.6668 710 0.6735 

520 0.6671 720 0.6738 

530 0.6675 730 0.6742 

540 0.6680 740 0.6745 

550 0.6683 750 0.6747 

560 0.6687 760 0.6750 

570 0.6690 770 0.6753 
50

Table B4. Regular spectral transmittance  as a function of wavelength  of a neutral density 

filter, serial number F2-001. 

 [nm]   [nm] 

380 0.7931 580 0.8330 

390 0.7973 590 0.8341 

400 0.8008 600 0.8351 

410 0.8041 610 0.8359 

420 0.8069 620 0.8368 

430 0.8094 630 0.8377 

440 0.8116 640 0.8383 

450 0.8137 650 0.8391 

460 0.8157 660 0.8399 

470 0.8175 670 0.8405 

480 0.8192 680 0.8412 

490 0.8209 690 0.8418 

500 0.8225 700 0.8425 

510 0.8240 710 0.8431 

520 0.8254 720 0.8435 

530 0.8269 730 0.8441 

540 0.8282 740 0.8446 

550 0.8296 750 0.8451 

560 0.8308 760 0.8457 

570 0.8320 770 0.8462 
51

Table B5. Regular spectral transmittance  as a function of wavelength  of a neutral density 

filter, serial number F2-002. 

 [nm]   [nm] 

380 0.7384 580 0.7999 

390 0.7451 590 0.8015 

400 0.7504 600 0.8029 

410 0.7549 610 0.8044 

420 0.7589 620 0.8057 

430 0.7626 630 0.8069 

440 0.7661 640 0.8081 

450 0.7694 650 0.8093 

460 0.7727 660 0.8105 

470 0.7756 670 0.8115 

480 0.7785 680 0.8126 

490 0.7811 690 0.8136 

500 0.7837 700 0.8146 

510 0.7860 710 0.8155 

520 0.7885 720 0.8164 

530 0.7906 730 0.8173 

540 0.7927 740 0.8182 

550 0.7946 750 0.8191 

560 0.7964 760 0.8199 

570 0.7983 770 0.8207 
52

 

Table B6. Regular spectral transmittance  as a function of wavelength  of a neutral density 

filter, serial number F2-003. 

 [nm]   [nm] 

380 0.5337 580 0.5059 

390 0.5323 590 0.5053 

400 0.5307 600 0.5047 

410 0.5289 610 0.5042 

420 0.5270 620 0.5037 

430 0.5250 630 0.5032 

440 0.5232 640 0.5028 

450 0.5213 650 0.5024 

460 0.5195 660 0.5020 

470 0.5178 670 0.5018 

480 0.5162 680 0.5015 

490 0.5148 690 0.5012 

500 0.5134 700 0.5010 

510 0.5122 710 0.5008 

520 0.5110 720 0.5005 

530 0.5100 730 0.5003 

540 0.5091 740 0.5001 

550 0.5082 750 0.4999 

560 0.5074 760 0.4998 

570 0.5066 770 0.4996 

 
53

Table B7. Uncertainty contributions and expanded uncertainty (k = 2) of the regular 

transmittance of a neutral density glass filter, serial number F1-001. 

Source of Uncertainty Standard Uncertainty Uncertainty Contribution 

Wavelength 0.1 nm 0.0000 

Receiver Linearity 0.05 % 0.0005 

Repeatability 0.0001 0.0001 

 Expanded Uncertainty (k = 2) 

 0.0010 

Table B8. Uncertainty contributions and expanded uncertainty (k = 2) of the regular 

transmittance of a neutral density glass filter, serial number F1-002. 

Source of Uncertainty Standard Uncertainty Uncertainty Contribution 

Wavelength 0.1 nm 0.0000 

Receiver Linearity 0.05 % 0.0004 

Repeatability 0.0001 0.0002 

 Expanded Uncertainty (k = 2) 

 0.0009 

Table B9. Uncertainty contributions and expanded uncertainty (k = 2) of the regular 

transmittance of a neutral density glass filter, serial number F1-003. 

Source of Uncertainty Standard Uncertainty Uncertainty Contribution 

Wavelength 0.1 nm 0.0000 

Receiver Linearity 0.05 % 0.0003 

Repeatability 0.0001 0.0001 

 Expanded Uncertainty (k = 2) 

 0.0008 
54

Table B10. Uncertainty contributions and expanded uncertainty (k = 2) of the regular 

transmittance of a neutral density glass filter, serial number F2-001. 

Source of Uncertainty Standard Uncertainty Uncertainty Contribution 

Wavelength 0.1 nm 0.0000 

Receiver Linearity 0.05 % 0.0004 

Repeatability 0.0001 0.0001 

 Expanded Uncertainty (k = 2) 

 0.0008 

Table B11. Uncertainty contributions and expanded uncertainty (k = 2) of the regular 

transmittance of a neutral density glass filter, serial number F2-002. 

Source of Uncertainty Standard Uncertainty Uncertainty Contribution 

Wavelength 0.1 nm 0.0000 

Receiver Linearity 0.05 % 0.0004 

Repeatability 0.0001 0.0001 

 Expanded Uncertainty (k = 2) 

 0.0008 

Table B12. Uncertainty contributions and expanded uncertainty (k = 2) of the regular 

transmittance of a neutral density glass filter, serial number F2-003. 

Source of Uncertainty Standard Uncertainty Uncertainty Contribution 

Wavelength 0.1 nm 0.0000 

Receiver Linearity 0.05 % 0.0003 

Repeatability 0.0001 0.0001 

 Expanded Uncertainty (k = 2) 

 0.0006 
55

Appendix C: Sample Data 

Figure C1. Transmittance as a function of wavelength of the color filters. 

Figure C2. Transmittance, on a logarithmic scale, as a function of wavelength of the MAP 

(Measurement Assurance Program) filters [15]. Nominal transmittance values and 

materials for the MAP filters are given below in Table C3. 
56

Table C3. Nominal transmittance values at 548.5 nm and materials for the MAP filters. 

Filter No. Nominal  Material 

1-1 0.9 Borosilicate crown glass 

1-2 0.7 Schott NG-11 

1-3 0.5 Schott NG-11 

1-4 0.25 Schott NG-4 

1-5 0.10 Schott NG-4 

1-6 0.01 Schott NG-9 

1-7 0.001 Schott NG-9 

Figure C4. Measured spectral transmittance of the holmium oxide glass filter for a spectral 

bandwidth of 1 nm. 

Holmium oxide filter serial number H-050630

0

10

20

30

40

50

60

70

80

90

100

230 280 330 380 430 480 530 580 630 680

Wavelength [nm]

Transmittance [%]
57

Appendix D: How to Request Regular Spectral Transmittance Calibrations 

1. Prepare a purchase order with the following (discuss with technical contact prior to 

submitting a formal request): 

 a. Service ID number requested (include range and points): 38061S. 

 b. Clear identification of calibration item(s), including any model or serial numbers. 

 c. Company name and address and name and phone number of contact person to receive the 

calibration report(s). 

 d. Billing and shipping addresses. 

 e. Return shipping instructions (prepay and add, COD, charge to account with shipper) 

 i. Test fee does not include shipping; customers are responsible for all shipping costs. 

ii. Without instructions, NIST will return test item by common carrier, collect, and uninsured. 

 f. Special handling instructions. 

2. Send the purchase order to: 

 Calibration Services 

 National Institute of Standards and Technology 

 100 Bureau Drive, Stop 2330 

 Gaithersburg, MD 20899-2330 

 Tel.: (301) 975-2002 

FAX: (301) 869-3548 

E-mail: calibrations@nist.gov 

3. Send the test item(s) to: 

Catherine C. Cooksey 

National Institute of Standards and Technology 

100 Bureau Drive, Stop 8442 

Gaithersburg, MD 20899-8442 

Tel.: (301) 975-6208 

FAX: (301) 975-6991 

E-mail: catherine.cooksey@nist.gov

 WWW: http://www.nist.gov/pml/div685/ grp03/staff/cooksey.cfm 

After receipt of purchase order, calibration services are scheduled to be completed in 90 days. NIST 

policy requires prepayment of all calibration services performed for non-U.S. organizations. Please 

contact the Calibration Program office to arrange payment. Despite best efforts sample may in rare 

instances incur damage during routine handling. Customers should consider a contingency or 

replacement plan to minimize any disruption prior to submitting samples. 

Please note that the Analytical Chemistry Division calibrates the following SRMs: 930, 1930, 

2930, and 2031. For recalibration of these SRMs, please contact: 

Melody Smith 

Phone: 301-975-4115 

FAX: 301-977-0587 

Email: melody.smith@nist.gov