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<0 NBS TECHNICAL NOTE 594"13

U.S. DEPARTMENT OF COMMERCE/ National Bureau of Standards
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards 1 was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and

technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to pro- mote public safety. The Bureau consists of the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology, the Institute for Computer Sciences and Technology, the Office for Information Programs, and the

Office of Experimental Technology Incentives Program.

THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United States of a complete and consist- ent system of physical measurement; coordinates that system with measurement systems of other nations; and furnishes essential services leading to accurate and uniform physical measurements throughout the Nation's scientific community, industry,

and commerce. The Institute consists of the Office of Measurement Services, and the following center and divisions: Applied Mathematics — Electricity — Mechanics — Heat — Optical Physics — Center for Radiation Research — Laboratory Astrophysics 2 — Cryogenics 2 — Electromagnetics 2 — Time and Frequency 2

. THE INSTITUTE FOR MATERIALS RESEARCH conducts materials research leading to improved methods of measurement, standards, and data on the properties of well-characterized materials needed by industry, commerce, educational insti- tutions, and Government; provides advisory and research services to other Government agencies; and develops, produces, and

distributes standard reference materials. The Institute consists of the Office of Standard Reference Materials, the Office of Air

and Water Measurement, and the following divisions:

Analytical Chemistry — Polymers — Metallurgy — Inorganic Materials — Reactor Radiation — Physical Chemistry.

THE INSTITUTE FOR APPLffiD TECHNOLOGY provides technical services developing and promoting the use of avail- able technology; cooperates with public and private organizations in developing technological standards, codes, and test methods; and provides technical advice services, and information to Government agencies and the public. The Institute consists of

the following divisions and centers: Standards Application and Analysis — Electronic Technology — Center for Consumer Product Technology: Product Systems Analysis; Product Engineering — Center for Building Technology: Structures, Materials, and Safety; Building

Environment; Technical Evaluation and Application — Center for Fire Research: Fire Science; Fire Safety Engineering.

THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts research and provides technical services designed to aid Government agencies in improving cost effectiveness in the conduct of their programs through the selection, acquisition, and effective utilization of automatic data processing equipment; and serves as the principal focus wthin the executive branch for the development of Federal standards for automatic data processing equipment, techniques, and computer

languages. The Institute consist of the following divisions: Computer Services — Systems and Software — Computer Systems Engineering — Information Technology.

THE OFFICE OF EXPERIMENTAL TECHNOLOGY INCENTIVES PROGRAM seeks to affect public policy and process

to facilitate technological change in the private sector by examining and experimenting with Government policies and practices in order to identify and remove Government-related barriers and to correct inherent market imperfections that impede

the innovation process. THE OFFICE FOR INFORMATION PROGRAMS promotes optimum dissemination and accessibility of scientific information generated within NBS; promotes the development of the National Standard Reference Data System and a system of in- formation analysis centers dealing with the broader aspects of the National Measurement System; provides appropriate services

to ensure that the NBS staff has optimum accessibility to the scientific information of the world. The Office consists of the following organizational units:

Office of Standard Reference Data — Office of Information Activities — Office of Technical Publications — Library —

Office of International Standards — Office of International Relations.

1 Headquarters and Laboratories at Gaithersburg, Maryland, unless otherwise noted; mailing address Washington, D.C. 20234.

5 Located at Boulder, Colorado 80302.
Optical Radiation Measurements:

The 1973 NBS Scale of

Spectral Irradiance

R. D. Saunders and J. B. Shumaker

Optical Physics Division

Institute for Basic Standards

National Bureau of Standards

Washington, D.C. 20234

<***" °P o0i

°*EM Of

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

Issued April 1977
National Bureau of Standards Technical Note 594-13

Nat. Bur. Stand. (U.S.), Tech. Note 594-13. 36 pages (Apr. 1977) CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1977

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C. 20402 - Price $1.40

Stock Number nns-nns-ni7nq^i
PREFACE

This is the thirteenth issue of a series of Technical Notes entitled OPTICAL

RADIATION MEASUREMENTS. The series will consist primarily of reports of progress

in, or details of, research conducted in radiometry, photometry and spectrophotometry in the Optical Radiation Section and the Radiometric Physics Section of the

Optical Physics Division.

The level of presentation in OPTICAL RADIATION MEASUREMENTS will be directed

at a general technical audience. The equivalent of an undergraduate degree in

engineering or physics, plus familiarity with the basic concepts of radiometry

and photometry [e.g., G. Bauer, Measurement of Optical Radiations (Focal Press,

London, New York, 1965)], should be sufficient for understanding the vast majority

of material in this series. Occasionally a more specialized background will be

required. Even in such instances, however, a careful reading of the assumptions,

approximations, and final conclusions should permit the non-specialist to understand the gist of the argument if not the details.

At times, certain commercial materials and equipment will be identified in

this series in order to adequately specify the experimental procedure. In no case

does such identification imply recommendation or endorsement by the National Bureau

of Standards, nor does it imply that the material or equipment identified is

necessarily the best available for the purpose.

Any suggestions readers may have to improve the utility of this series are welcome.

Henry J. Kostkowski, Chief

Optical Radiation Section

National Bureau of Standards

Jack L. Tech, Chief

Radiometric Physics Section

National Bureau of Standards

iii
TABLE OF CONTENTS

Page

1. Introduction 1

2. Derivation of Scale: An Overview 2

3. Measurement Apparatus 2

1. Lamp Image System 2

2. Monochromator fore-optics 6

a. Integrating Sphere 6

b. Imaging Optics . 6

3. Monochromator 7

4. Detection System 7

5. Data Acquisition 7

6. Lamp Mount and Power Supplies 7

4. Process of Realization 9

5. Data Reduction 13

6. Uncertainties 14

7. Conclusion 14

8. References 19

9. Appendix 20

LIST OF TABLES

1. Uncertainty (%) 18

LIST OF FIGURES

1. Block Diagram of the Measurement Setup used to Realize the Scale of Spectral

Irradiance from the Scale of Spectral Radiance 3

2. Measurement Setup for Calibrating the Radiance of the Image 5

3. Quartz-Halogen Type DXW Lamp used for Spectral Irradiance Standards 8

4. Tungsten Strip Lamps used for Radiance Standards 11

5. Typical Drift Curves for Type DXW Spectral Irradiance Standards 12

6. Spectral Irradiance Fit in Spectral Region 250 - 1600 nm 15

7. Spectral Irradiance Fit in the Spectral Region 250 - 350 nm 16

8. Spectral Irradiance Fit in Spectral Region 350 - 1600 nm 17
THE 1973 NBS SCALE OF SPECTRAL IRRADIANCE

R.D. Saunders and J.B. Shumaker

This note describes the measurement apparatus and techniques

used in deriving the 1973 scale of spectral irradiance. The un- certainty of this scale is believed to be less than 2% in the

spectral region 250 nm - 500 nm and less than 1% in the spectral

region 500 nm - 1600 nm. This uncertainty represents a threefold improvement over the previous NBS scale of spectral irradiance.

The complete derivation of the projected solid angle, which is

crucial when transferring from radiance to irradiance, is given.

Also described in this note is a model for interpolating the

spectral irradiance at wavelengths between the wavelengths measured.

Measurement details are presented and sources of error are discussed.

Key words: Calibrations; interpolation formula; irradiance drift

formula; projected solid angle; spectral irradiance; standards.

1. Introduction

Spectral irradiance, denoted E , is defined as the radiant flux incident on a surA face per unit wavelength and per unit area on the surface. Mathematically

E

A dA dA

where d

2

<j> is the element of flux and dA and dA are the elements of wavelength and area respectively.

In 1963, the National Bureau of Standards established a scale of spectral irradiance [l] 1 using a group of 200-watt, quartz-halogen, tungsten coiled-coil filament

lamps. Although these lamps were compact and relatively easy to use, the spectral irradiance below 400 nm was inadequate for many applications. For this reason, the scale was transferred to a group of 1000-watt, quartz-halogen lamps which increased the spectral irradiance by a factor of 5. The uncertainties assigned to this scale were about 3% in the

visible-infrared spectral region and 8% in the ultraviolet spectral region.

A widespread need for higher accuracy led NBS, in the early 1970 's to initiate development of an improved scale of spectral irradiance. The new scale, with estimated uncertainties about 1/3 that of the earlier scale, was first disseminated in September 1973. There

have been 10 realizations of the scale, and the scale was used in an international

figures in brackets indicate the literature references on page 19.

1
comparison involving 8 national laboratories [2] . The current Tech Note is a detailed

description of the realization of this new scale and of the uncertainties associated with

it.

2. Derivation of Scale: An Overview

The National Bureau of Standards scale of spectral irradiance is derived from its

scale of spectral radiance [3]. This is done by determining the average spectral radiance

of a tungsten strip lamp image which is formed by an optical system subtending a well defined and measurable solid angle. Since the spectral irradiance at this image can be calculated from its spectral radiance and the solid angle, this establishes a spectral irradiance scale. As a matter of convenience the scale is transferred to a group of four

1000-watt quartz-halogen lamps using an integrating sphere - monochromator combination designed for spectral irradiance measurements. These lamps, then, which are recalibrated at roughly 100-burning-hour intervals, embody the 1973 NBS scale of spectral irradiance.

3. Measurement Apparatus

Figure 1 shows a schematic block diagram of the measurement apparatus. For purposes

of discussion it is presented as consisting of the following six functional units:

1. Lamp Image System

2. Monochromator Fore-optics

a. Integrating sphere

b. Imaging optics

3. Monochromator

4. Detection System

5. Data Acquisition System

6. Lamp Mounts and Power Suppliers

1. Lamp Image System The lamp image system consists of a tungsten strip lamp in a holder and a spherical mirror in a three-point adjustable mount both attached to a threelegged adjustable table. An aluminum fast-coated (peak reflectance is obtained if

aluminized in less than 10 seconds) front surface mirror forms an image of the strip

filament of the radiance lamp with approximately unit magnification. Directly in front of

the spherical mirror is a calibrated aperture used to define the solid angle from which

the flux irradiates the sphere.

In the method developed for realizing the improved scale of spectral irradiance, the

current of the tungsten strip lamp is adjusted until the output signal from the measurement

apparatus is equal when observing either the irradiance lamp or the image of the strip

lamp. The equality of output signals is represented mathematically by

/.,/.. E, dA dA R = /.,/../ L. cosG d dA dA R,

J AA J AA A

; AA ; AAJ u) A in
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en
where

E.. = spectral irradiance at a particular point of the integrating sphere entrance

aperture.

L = spectral radiance of the strip lamp image at a particular point and direction

at the sphere entrance aperture.

oa = solid angle subtended by the calibration aperture at the sphere entrance

aperture.

AA = area of sphere entrance aperture.

AX = spectral band pass of monochromator

.

R = responsivity of measurement apparatus; that is, element of output signal per

element of flux incident on sphere entrance aperture.

6 = the angle between a ray from the mirror and the normal to the plane surface of

the entrance aperture.

This equation can be rewritten as

/a Jaa dAdXR = E> /aJaa/,, cose du dA dx R >

where E and L are average values weighted by the two integrands respectively. AssumA A ing that the responsivity is independent of the direction of incidence of an element of

flux and that / cos0 dtu has the same value at every point of AA,

/a Jaa dA dX R = h </a Jaa dA dA R) */M cos9 da))

and

E, = L, / cos6 du.

A A

; co

The projected solid angle, / cos0 do), has been numerically integrated with an estimated

calculation uncertainty of less than 0.01%. A detailed discussion of the evaluation of

this integral is given in the appendix. For the 75 cm radius of curvature and 14 cm aperture of the imaging mirror used in this work the projected solid angle varies by less

than .01% over the .06 x 5.6 mm area AA.

The average spectral radiance of the image, L , is determined by comparison to a

A calibrated tungsten strip lamp as shown in figure 2. Ideally in performing this measurement, AA and io should be the same as when making the spectral irradiance comparison

with the integrating sphere. Otherwise the averaged spectral radiance may be different

4
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in the two cases. The area AA was essentially the same but the solid angle was limited

by the entrance pupil of the monochromator rather than the somewhat larger aperture at the imaging mirror. However, it was experimentally demonstrated that the radiance of the

image was uniform over the larger solid angle to within 0.1% so that the two averages

would be identical regardless of the difference in solid angles. This uniformity was demonstrated by mapping the calibrated aperture.

2. Monochromator fore-optics

a. Integrating sphere The major problems in applying this method are related to the geometric size and shape differences between the irradiance and radiance sources and

the configurations in which they must be used. The irradiance sources are 1000-watt type

DXW coiled-coil tungsten filament quartz envelope halogen lamps placed at a distance of

approximately .5 meters from the point at which the irradiance is measured. These sources are used without imaging optics. The radiance source is a tungsten strip lamp and a spherical mirror for imaging the filament onto the area AA. These two sources may differ

in polarization, uniformity of field, and the solid angle of irradiation. Since the

transmittances of optical systems and the responses of detectors generally depend on these

factors, direct comparison of a radiance and irradiance flux generally has an uncertainty

of at least two or three percent and sometimes considerably more. These three areas of

difficulty are avoided by using an integrating sphere.

The integrating sphere is 2.5 cm in diameter with a .6 x 5.6 mm rectangular entrance

port and a 3 x 10 mm exit port located 90° from the entrance port. By rotating the sphere

about an axis through the exit port the radiometer can be made to view either of two sources as shown in figure 1. The inside sphere wall is coated with pressed high purity

BaSO^ using no binders (most binders lower the reflectance significantly in the UV) to insure a high sphere transmittance. The pressed BaSO^ approximates a Lambertian surface

(i.e., each incoming ray of flux is reflected diffusely). Because of multiple reflections

in the integrating sphere, entering radiation is randomized, producing uniform, depolarized

radiant flux at the exit port. Thus even a non-uniform source can be made uniform with the use of an integrating sphere. This was verified to within the measurement precision of 0.1%

by radiometrically scanning the exit port of the sphere. Depolarization was tested at 500 nm and 650 nm using an unpolarized source and a linear polarizer. As in the test for

uniformity, depolarization was complete within the precision of the measurements (0.1%).

The difference in solid angle of irradiation for the irradiance lamp and the radiance image

is only a problem when the reflectance of the integrating sphere wall is not uniform. The

high purity, 3 mm thick BaSO^ sphere coating provides this uniformity, and it was verified

by determining the spectral irradiance of one of the quartz-halogen lamps with different

sized apertures in front of mirror Ml. These apertures had diameters ranging from 2.5 cm

to 14 cm and simulated the difference in solid angles of irradiation for the irradiance

and radiance sources. No significant (>.1%) difference in the results was observed.

b. Imaging optics The exit port of the integrating sphere is imaged, using the

plane and spherical mirrors shown in figure 1, onto a polished stainless steel mask

6
(field stop) placed directly in front of the slits of the monochromator . The mirrors are

front surfaced with a fast coat of aluminum. The 45° plane mirror is used to divert flux

from the integrating sphere onto the spherical mirror, M2. The spherical mirror then images

the exit port of the integrating sphere onto the mask in front of the monochromator slits.

The exit port of the integrating sphere and the slits of the monochromator are at a distance from the spherical mirror approximately equal to its radius of curvature. The

monochromator slits and the 45° plane mirror are also kept as close as possible (3°) to the

axis of the spherical mirror to minimize aberrations.

3. Monochromator The double monochromator is a prism-grating instrument (2 nm/mm

dispersion at 250 nm to 4 nm/mm at 1600 nm and wavelength error about .1 nm) exhibiting

very low spectral scattering. The optical chain of the monochromator consists of a collimating mirror, a quartz prism predisperser, an intermediate slit, a grating and a second mirror which forms an image at the exit slit.

4. Detection System A thermoelectrically cooled (-15°C) EMI 9558QB (S-20 cathode)

photomultiplier tube is placed behind the exit slit of the monochromator to measure flux in

the spectral region 250 nm - 800 nm. The photo current is converted to a 0-1 volt signal

by a picoammeter. A photo current of less than 10~ 8 amperes is maintained by adjusting the

voltage across the dynode chain of the photomultiplier. Past experience has demonstrated

that the photomultiplier will remain stable (0.1%) and linear (1%) under these conditions.

For the spectral region 700 nm - 1600 nm, a concave ellipsoidal mirror is used to collect

the flux from the exit slit. The monochromator exit slit is located at one focus of the

ellipsoidal mirror and a demagnified image (factor 7) of the slit appears at the other

focus. A PbS detector is placed at this focus to measure the flux. The signal from the

PbS detector is amplified to a 0-1 volt signal by a phase sensitive lock-in type voltmeter.

A sector disk operating at a modulating frequency of 78 hertz is placed at the entrance

slit of the monochromator. The signal-to-noise ratio of the detector is optimized by

cooling the detector to liquid freon temperature (-113°C) . It was found that further cooling decreased the signal while the noise remained at approximately the same level.

5. Data Acquisition The data acquisition system consists of a capacitor type

integrator ? MIDAS [4] data acquisition system and a S^-digit voltmeter. Depending on which detector is being used, the picoammeter output or the lock-in voltmeter output is

integrated. Integration times can be set to any desired interval; typically

60 seconds is used. The integrated signal, lamp current, lamp voltage, and ambient temperature are measured and recorded by the MIDAS system. The MIDAS system under control of

a minicomputer, operates the integrator, sets the wavelength drive and positions the

integrating sphere. The data collected is sent directly to the minicomputer for processing.

6. Lamp Mount and Power Supplies The irradiance sources (type DXW quartz-halogen

lamps) are mounted in U-shaped holders as shoim in figure 3. Each irradiance lamp has its own holder including a recessed lamp socket which is spring loaded to allow the lamp to expand and contract when heating and cooling.
-o (/) CD T3

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The radiance lamps are mounted in holders that can be adjusted in height, pitch, yaw,

x direction, and y direction. These adjustments are necessary to align and keep aligned

the radiance lamp during measurements.

Both radiance and irradiance lamps are operated at a constant direct current (.01%

measurement accuracy .001% current regulation).

4. Process of Realization

In order to avoid making any critical assumptions about the linearity of the detector

response, the spectroradiometer is used in a null mode, i.e., the test source and reference

source produce equal output signals. In practice, the sources are matched to within 2%.

Since the detector non-linearity has been shown to be less than 0.5%, and this non-linearity

applies only to the differences in output signals, the error due to the 2% mismatch is

negligible.

One gas-filled strip lamp (250 - 800 nm) and one vacuum strip lamp (700 - 1600 nm) are used to represent the scale of spectral radiance. A second gas-filled lamp and a second vacuum lamp are used with spherical mirror Ml to form the radiance image. These lamps

have been selected from a larger group of lamps that were specially designed to maximize

radiance stability and the selected lamps have been checked for radiance stability, radiance

gradient, and polarization.

Radiance stability was checked by operating the lamps continuously for approximately

30 hours and checking the radiance during this time. The drift rate for the gas-filled

lamps was approximately .01%/hr at 654.6 nm. No drift in radiance of the vacuum lamps

could be detected. Similar vacuum lamps have exhibited a radiance drift rate of about

0.0001%/hr at 654.6 nm.

A well-defined .6 x 5.6 mm filament area on each of the radiance lamps was mapped for

radiance. The lamps were first mapped vertically by dividing the defined filament area into seven . 6 by . 8 mm areas. Using the measurement configuration shown in figure 2, the

spectral radiance of each area was measured and normalized to the center area. Depending

upon the filament brightness temperature and the wavelength, the radiances over this area

for the gas-filled lamps varied by 2% to 10% while those for the vacuum lamps varied by

1% to 5%. The radiances horizontally across the filament were also mapped by dividing the

defined area into six .1 mm by 5.6 mm areas. The variations of the spectral radiance

horizontally across the filament of all the lamps were about 1%. In all cases the radiances were smooth functions of position.

The selected lamps were also chosen such that their directions of polarization were

approximately the same. In general the radiances of strip lamps are slightly polarized.

Measurements with a polarization sensitive instrument (such as a monochromator) can therefore yield incorrect results. Possible errors due to polarization have been minimized by

selecting, for comparison, those lamps which had nearly identical polarization.

The gas-filled strip lamps have a plane quartz window so that they can be used in the

9
UV spectral region. These lamps are operated at brightness temperatures up to 2400 K. Although the radiance of these lamps fluctuates about 1.5% in a few seconds, the average

radiance over ten seconds is repeatable to a few tenths of a percent. Some of this

fluctuation is thought to be caused by the snout on the lamp envelope (see fig. 4) which

disrupts the normal flow of gas around the filament causing changes in refraction and in

the filament temperature. In the spectral region 700 - 1600 nm, the vacuum strip lamps are used. Because there is no gas in these lamps, the radiance fluctuations are very

small (<.l%/s).

Four 1000-watt, type DXW quartz-halogen lamps were selected as irradiance sources. The lamps were chosen from a group of lamps that had been screened for emission lines and

absorption bands. At the time this group was chosen, there were very few DXW quartz-halogen

lamps that had no absorption bands and emission lines. Lamps with the weakest absorption

bands and emission lines were chosen. The average drift rate of the four lamps is less

than .02%/hr at 654.6 nm (see fig. 5).

With the irradiance lamp and strip lamp image positioned as in figure 1, the flux

entering the integrating sphere from the irradiance lamp at a single fixed current can be

matched by the flux from the radiance lamp only if the radiance lamp current is varied with

wavelength. Therefore, before the scale realization process was started the reverse of the

process was carried out to determine the strip lamp current needed at each wavelength to match the flux from the irradiance lamp.

The measurement process is now performed in three basic steps at each wavelength.

First, the spectral radiance of the lamp image at the lamp current determined above is

measured in the measurement configuration shown in figure 2 using the other strip lamp

carrying the spectral radiance scale as the reference lamp. Second, the radiance image is

positioned on the mask (0.6 x 5.6 mm) of the integrating sphere as in figure 1 and one of

the four irradiance lamps is placed at a distance of 50 cm on the opposite side of the

rotatable integrating sphere. Using the relationship E = L (/ cosQ dco) S„/Sj

(where s /S is the ratio of the irradiance signal to the radiance image signal) the

E L spectral irradiance of the irradiance lamp is measured. Third, the radiance image system

is replaced by an irradiance lamp chosen from one of the remaining three irradiance lamps,

and the four irradiance lamps are intercompared using the following measurement scheme:

Left Side Right Side

X K

X K+1

IK+2

XK

XK ""k+s

IT,.-, i„ K+l K

At each repetition, a different irradiance lamp is calibrated using the radiance image.

(In the above measurement design a repetition is equivalent to selecting a different value

for K. I, . is used whenever K + j > 4). The complete process yields five independent

10
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or

-a

sfl3 T3c

on

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1 1 1 1

10

I600nm

—

+ +

+ + —

J- _

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-10 —

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2

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<r

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O

or io —

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•

„ •

•

•

•

—

-10

J _L [

250nm

100 200 300 400 500

TIME (hours)

Figure 5. Typical Drift Curves for Type DXW Spectral Irradiance Standards.

12
measurements on each irradiance lamp.

5. Data Reduction

Twenty-six wavelengths were chosen for this realization. Eight of the wavelengths in

the UV spectral region, however, were used to check the validity of an equation (discussed

below) defining spectral irradiance as a function of wavelength and computed blackbody

temperature. These eight wavelengths (260 nm, 270 nm, 280 nm, 290 nm, 310 nm, 320 nm,

330 nm and 340 nm) have only been measured twice. The gas-filled strip lamps are used at the wavelengths 250 nm, 300 nm, 350 nm, 400 nm, 450 nm, 500 nm, 555 nm, 654.6 nm, 700 nm

and 800 nm. Vacuum strip lamps are used at the wavelengths 700 nm, 800 nm, 900 nm, 1050 nm, 1150 nm, 1200 nm, 1300 nm, 1540 nm, and 1600 nm.

Because of stabilization times (20 min) and the integration time required to smooth

short-term radiance fluctuations, the total time for each wavelength is approximately an hour for the first two steps of the realization. In step 3 (irradiance to irradiance) the

measurement time for all wavelengths on an irradiance lamp is approximately two hours. The

large number of operating hours involved means that lamp drift cannot be ignored. Therefore, for each lamp an equation was developed to allow its spectral irradiance to be calculated at any time t.

Based upon the drift data exemplified by figure 5 an adequate model for the drift of

spectral irradiance of constant current tungsten halogen lamps is given by the equation

E, = X~ 5 exp (A, + Ct + (D + Bt)/A),

A A

Comparing this equation with Wien's law for a gray body: E eA 5 exp (C2/AT) one sees

A that exp (A + Ct) represents the effective emissivity (and envelope transmission) which

A is assumed to change with time. The term (D + Bt) represents C2/T, again assumed to change with time. D was set at 4.7 ym corresponding to T = 3061 K. The remaining

coefficients (B, C, and one A for each of the twenty-six wavelengths) were determined by

A least-squares fitting techniques.

In a similar way an interpolation formula was developed for calculating the spectral

irradiance of tungsten-halogen lamps at wavelengths intermediate between the 26 calibrated

wavelengths. This formula is:

E, = (A + A X A + A2 A

2 + . . . + A An

) A

5 exp (a + b/A)

A n

The quantities a and b are determined by fitting the data to ln(E A

5

) a + b/A in

A which it will be recognized that exp (a) is an effective gray-body emissivity and b is closely related to the reciprocal of the distribution temperature. With a and b thus fixed

13
A , Ai , . . .A are least squares fitted using 1/E2 weighting (assuming constant pern a centage measurement error). In practice it has been found that the final fit is con- siderably improved if the spectrum is broken into two spectral regions, 250 - 400 nm and

350 - 1600 nm, for separate fitting.

Figures 6, 7 and 8 show the different fittings to the equations given above. This

method is only valid for the continuous spectrum and does not predict the emission lines

and absorption bands.

6. Uncertainties

The significance of this new method for determining the spectral irradiance is best

appreciated by examining the basic uncertainties associated with the method. These are listed in Table 1. The total absolute uncertainties in the last two lines of the table are obtained by adding all the uncertainties at a given wavelength in quadrature.

The systematic uncertainty in the radiance-to-irradiance transfer (line II a) is obtained by adding in quadrature estimated contributions from a number of error sources. Each

of the following error sources contributed 0.01% or less: Non-linearity of the detectoramplifier system, wavelength error, stray light, lamp polarization, lamp current measurements,

and the integrating sphere response to the different solid angles of the radiance image and

irradiance sources. Each of the following contributed less than 0.05%: The projected solid

angle determination, uniformity of mirror Ml, and spectral light scattering due to the slit

function wings. Finally, the non-uniformity of the radiance sources over the viewing area contributes an uncertainty varying from 0.12% in the UV to .05% in the IR.

The uncertainties listed in Table 1 are the uncertainties assigned to the mean value

of the four working standards at the time that the standards are calibrated. Because lamps

drift with time, the spectral irradiance at any other time is obtained from the spectral

irradiance vs. time formula described above for the working standards group. The possibility

that this drift model may be wrong introduces an additional uncertainty not included in

Table 1. This model uncertainty for a particular lamp is estimated as 0.8%. This un- certainty was obtained by comparing the calculated extrapolated spectral irradiance with

further scale realizations. When the working group is used between scale realizations,

this 0.8% uncertainty must be combined in quadrature with the total uncertainties in Table 1.

7. Conclusion

The method described in this report has made the frequent realization of the spectral

irradiance scale feasible. This, in turn, has significantly reduced the uncertainty of the

scale by eliminating the reliance upon long-term predictability of the NBS working lamp

standards. The method is valid for generating a spectral irradiance scale of any magnitude;

the magnitude can be altered either by changing the radiance levels or by changing the solidangle-defining aperture at mirror Ml. At present a scale realization requires about 40 hours

to complete. Most of this time is spent stabilizing the strip lamps, which must be done

because the lamp current is changed for each wavelength. Other sources of spectral radiance

are being investigated which will require less stabilization time. A radiance source requiring

14
0.

I I

I I I

I I I I I I I I I I

I I I I

I I I I

• Measured spectral irradiance

A.

Ex =e a

(e b/X )/X5

(A + A| X... A 5 X

5

)

1111111111 i 250 500 800 MOO 1400 1600

WAVELENGTH (Nanometers)

Figure 6. Spectral Irradiance Fit in Spectral Region 250 - 1600 nm.

15
l E

o

I

4-

4-

D

UJ

o

z

<

<

<ra:

<

enho

LU

Q.

</)

i r 1 r

250

• Measured spectral irradiance

E,=_ e°(e b/x

) (A + A,X...A 5 X

5

)

300 350

WAVELENGTH (Nanometers)

Figure 7. Spectral Irradiance Fit in Spectral Region 250 - 350 nm.

16
250

O

<

a

<

or<

or

ho

a.

i i i i

i i i i i I i i i i i i i i i i i i • Measured spectral irradiance

e

a (e b/x

)

«-. 200

10

i E

a

l

o

150

100

(A + A,\...A 5 X*)

350

Figure 8.

600 800 1000 1300

WAVELENGTH (Nanometers)

1600

Spectral Irradiance Fit in Spectral Region 350 - 1600 nm.

17
o s csl rH o c • • vo

rH

00 CM

O >~ CM rH Q • • ro

rH

vO CM

O 6 < CM O C • • oo

vO U~l VO • s vO CM o- c • • m

vO

m o m B vO CO

LO c • • m

•-s CO

H

r?-? o b o> vO v^ in B • • rH -* W £ J 3

PQM o vO < <! o e CM r^ H H m c • • Prf en rH WU

C§ vO VO o B vO o m C • • CN rH rH

l~- o O 00

r-~ o o oo

00 rH O LO

00 <f o m o VO

rHm o en

rH

m

vo

m

rH

m

VO CM

rH r-.

m

oom

oo

o>vo

oo

VO

oo

CM00

VO

inoVO

vO

rH

oom

o>

vo

CM I •Ha3

>^ T)

4-1 CO

O c 4J n

•H

H acO e 0) 4J 3 u U

0)M s o 00 rH a cu 3 o

4-1

4-1

CU 60

4-1 4J fl 3 o o >> rH CU rH 4J o O. •H

en CO C/> i-H

,£> <u

m -h

<!

u 3 rQ

r>> CU 1 4-1 xi <-> c TJ 4-J H

•rl CU

cfl 4J l*H 4J Cfl O CO u B X)

cu •H >>

u o 4J 4-1 Cfl cl CO •H T3 3 CU rH C *^* •H cfl CJ -o -u •H C •H CD 4J o a

cfl •H 3 4H B CO XI O

cu •H o

4-1

O r-l

C '-V

CO CU P-, cfl o

;>• r-l CU <U 1 O0 PM u B ci

•H

CO rQ

4-1 cfl •H a c 3 3 XI >-, O 4-1 M U «H

C/3 P-, rH

CU -H

O rH rQ

4-1 •H B a

4J Vj 3 O cu -a

cu 4-1 o

P- rH

CO 60 Pu

cu

C <u

MO r-l rH

x

B

4J CO r-l •H ffl <U & 2: 4-i

18
little or no stabilization would decrease the scale realization time to about 8 hours

for four working standards.

8. References

[1] Stair, R. , Schneider, W. E. , and Jackson, J. K. , Appl. Opt. 2, 1151 (1963).

[2] Suzuki, M. and Ooba, N., An International Intercomparison of Spectral Irradiance

Scales, to be published.

[3] Waters, W. R. , - Nat. Bur. Stand. (U.S.) Tech Note, Spectral Radiance Scale,

to be published.

[4] Popenoe, C. H. and Campbell, M. S. , - MIDAS Modular Interactive Data Acquisition

System, Nat. Bur. Stand. (U.S.) Tech Note 790, 42 pages (August 1973).

19
9 . Appendix

Evaluating the Projected Solid Angle at the Image Point

The Projected Solid Angle Integral

0(0,0,0)

Consider a spherical mirror of radius of curvature (r) whose center of curvature is at . The center of the mirror aperture and point define the z axis of a rectangular coordinate system. The point A is the center of the mirror surface; the point

P is an arbitrary point on the mirror; and the point I is an image point in the yz plane.

The projected solid angle is

/

cos6 d co (1)

where go is the solid angle subtended at I by a portion of the mirror and 9 is the

angle between AI and the solid angle element d oo. This can be expressed as Ifcos AIP

cos OPI dS PI 2 (2)

20
where S is the surface of the mirror, OPI is the angle between the viewing direction and

the normal to the mirror surface, and PI is the distance to the surface element dS. The

x, y and z coordinates of the four labeled points are

0: o, o, o

A: o, o, r

I: o, y , z (The assumed position at the image point)

P: x, y, z (where z = */r 2 -x2 -y2

)

.

The following vectors

IA = -v j + (r-zQ

) k

u ~r -?

IP = xi + (y-y ) j + (z-z ) k

PO = xi + yj + zk

T -7 T

and the distances

PI = (x2 + (y-y ) 2 + (z-z ) 2

)

Js

IA = (y 2 + (r-zo) 2 )^2

PO = r

are needed.

Now since V"i V2 = ViV2 cos 9 the cosine factors appearing in (2) can be calculated.

IA • IP cos AIP = — ~

IA • PI

yQ

( yo-y) + (r-z )(z-z >

\!(y 2 + (r-z

Q

) 2 )(x2 + (y-y

Q

) 2 + (z-z

o

) 2

)

IP • PO 2 j. r \ j_ 1 \ x^ + y(y-y ) + z(z-z ) cos OPI = —- = - —

PI • PO

r yj x

2 + (y-yQ

) 2 + ( z_z ):

The element of surface area is given by

21
ds = dx dy 4/1 + 4

r 9z] 2 3z

3yJ

^

= dx dy \/l + % + \ (using z = (r 2 -x2 -y 2

) 2

= dx dy

Now integral (2) can be expressed as:

[y„(y«~y) + (r-z )(z-z )][x2 + y(y-y ) + z(z-z )] dx dy

I 2 S

° 2 2 2

(3) If

V yl + (r-z ) 2 [x* + (y-y ) 2 + (z-z ) 2

] z 00 w } z o o

in which the notation z is simply a shorthand for (r 2 -x2 -y2

)

2

. The limits of integration, S, remain to be defined.

The Integration Limts : The area S

Consider an aperture plane perpendicular to the z axis which cuts the mirror surface

in a circle with radius b. The equation of this plane is

z = ^-b2.

The line PI to an arbitrary mirror point

(temporarily denoted as x , y , z ) is

:

m m m

22
7.-7. O X = X z-z m m o

z-z y-y = (y -y ) o z-z 'm J m o

The intersection of this line and the aperture plane is;

x = u xm

y-y = u (y -y ) o 'm o

Vr2 -x2 -2 mmy- -z

o

Writing g and n for the x and y coordinates in the aperture plane and dropping the

subscript m for coordinates on the mirror surface gives:

5 = u x

n-y

Q = u (y-y ) (4)

4

r^h2" -z

Vr2 -x2 —2 y

- z

as the relation connecting any point 5 , n in the aperture plane to the corresponding

point x,y on the mirror surface defined by the ray from the image point, I, through

E, , r). For a circular aperture with radius a the image point can "see" all mirror points

x,y which satisfy £

2 + n2

<. a

2

. Similarly the object point will illuminate all mirror

points x',y' which satisfy £

2 + n2

<_ a

2 with

23
n-y

Q = u'(y'-y'

o

) (5)

\/r 2 -b 2 -z*

_^ o Vr2 -x' 2 -y* 2 -z'

where y' and z' are the coordinates of the object point.

If the mirror is viewed from the origin with the source to the left and image to the

right the areas "seen" by object and image will look like*

The area over which the integration is to be performed is the central area common to both

object and image viewing.

The integration over x is straightforward: the integral is symmetric about x = o

so, for a given y, the integral runs from o to the smaller of x and x' where

x = x(y

o

,zo

,y)

x' = x(y^,z^,y)

*In this illustration the image point is assumed closer to the mirror than the object point,

thus resulting in a slightly larger area "seen" by the image point.

24
are solutions of ?

2 + n2 = a2 using (4) for x and (5) for x' . The integration over y

runs from the negative branch of the solution y' = y(y',z',0) to the positive branch of

the solution y = y(y , z ,0) where these are solutions of the same equations (£ 2 + n

2 =

a

2

, etc.) with x = 0.

Numerical Evalution

For the numerical calculation of F, equation (3) can be rewritted so as to leave

terms of order y /r and z /r as correction terms:

o o

o o, . y+

x (y) F =

2 f dy f (1 + p)(l + q) dx

Vy2 r \ +

z + (r-z )- o o

f dy f (1 + p)(l +

oy_

p =

q =

(z 2 -z (2z + r) +y2 -y y) (r-z) + y yz

o o ^o J o

J * o

J

z (r 2 -2yy + y

2 -2zz + z

2

) o •'o o o

z o

(z- z o

) + y ( y-y )

(r 2 -2yy + y

2 -2zz + z2

) o o o

= >P~ p _x -y

The limits of integration are determined by numerical solution of equations like:

C

2 (x,y) + n2 (x,y) = a

5

or u

2 x

2 + u2 (y -y (1-1/u)) 2 = a

2

x/r 2 -b 2 -z

* o wi th u = Vr 2 -x2 -y2 -z

o

25
If u were known the equations would be simple; hence the technique is to assume a trial

value for the unknown (x or y) in u, then solve for an improved value of the unknown,

etc. Specifically

x (y) = Min (x ,x')

3. 3.

where

x

a

= JaW -(y-y

o (1-1/u)) 2

and

x'a

= JaW 2 -(y-y^ (1-1/u')) 2

Jr*-b2 -z \ o u — u \r2 -x -y 2 -z " a

J o

f*=bT -z'

yr2^:x -y^ -z

a o

and xaaand x denote trial values of x and x'. x and x are replaced by x

a a a a a and x' and new values for x and x' are computed; the process being repeated to cona a a vergence. For the y limits set x = o and solve the following equations

y° = Max (y~,y~')

a. ci

y° = Min (ya

.ya

')

where

ya

= yo (1-1/u) -a/u , y&= y^ (1-1/u') -a/u'

y+

= y (1-1/u) +a/u , y+ ' = y' (1-1/u') + a/u' +

'

. y

a o a o

26
and

\

r "y

a

" zo

* -*

TT

y and y are trial values which are repeatedly refined to convergence,

a a

Geometrical Relationships

The distances r, b, y , z , y

1 , and z' which appear in the expressions for F

are difficult to measure. Therefore, the following equations are used to calculate them

from the more easily measured quantities, s, I, l\ t, and a. s is the distance

from the image point to the closest point of the aperture opening; % is the distance to the most remote point of the aperture opening. £' is the distance from the object point

to the most remote point of the aperture opening as seen from the object point, t is the

distance from the plane of the aperture to the center of the mirror surface, a is the

radius of the aperture.

27
£

2 -s 2 yo

" 4a

= ^s2 -(4a2 -*2+s 2

) 2 /16a2

y

o tan Y " i+T

y

2 + (e+t) 2 P/cos y

= e+t

= t - a tan y +

J£ ,z /cos 2 y -(a+t tan y) : cos y

2 / P P' P/cos y + P'/cos y I cos 2 y

V

b = Jrz -(r-t)-

y' = -y P'/P

•'o o

z = r -e -t

o

z' = r -(r-z ) P'/P.

o o

28
HBS-114A (REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBS Technical Note 594-13

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

OPTICAL RADIATION MEASUREMENTS:

The 1973 NBS Scale of Spectral Irradiance

5. Publication Date April 1977

6. Performing Organization Code

7. AUTHOR(S)

R. D. Saunders and J. B. Shumaker

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No.

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Same as no. 9

13. Type of Report & Period Covered Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

This note describes the measurement apparatus and techniques used

in deriving the 1973 scale of spectral irradiance. The uncertainty

of this scale is believed to be less than 2% in the spectral region

250 nm -500 nm and less than 1% in the spectral region 500 nm - 1600 nm. This uncertainty represents a threefold improvement over the previous

NBS scale of spectral irradiance. The complete derivation of the

projected solid angle, which is crucial when transferring from

radiance to irradiance, is given. Also described in this note is a model for interpolating the spectral irradiance at wavelengths between

the wavelengths measured. Measurement details are presented and sources

of error are discussed.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons)

Calibrations; interpolation formula; irradiance drift formula;

projected solid angle; spectral irradiance; standards.

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The following current-awareness and literature-survey

bibliographies are issued periodically by the Bureau:

Cryogenic Data Center Current Awareness Service. A

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Superconducting Devices and Materials. A literature survey issued quarterly. Annual subscription: $20.00.

Send subscription orders and remittances for the pre- ceding bibliographic services to National Bureau of Standards, Cryogenic Data Center (275.02) Boulder,

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