NBS TECHNICAL NOTE

U.S. DEPARTMENT OF COMMERCE/ National Bureau of Standards

Detector Spectral Response

From 350 to 1 200 nm

Using a Monochromator Based

Spectral Comparator
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^

NaSorrai Bureau of Standard

JAN . 2 1979

etector Spectral Response From 350 to 1 200 nm

Using a Monochromator Based Spectral Comparator

Lntonio Corrons

Instituto de Optica

Madrid, Spain

Edward F. Zalewski

National Measurement Laboratory

National Bureau of Standards

Washington, D.C. 20234

*< °' c«

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

Dr. Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued December 1978
National Bureau of Standards Technical Note 988

Nat. Bur. Stand. (U.S.), Tech. Note 988, 21 pages (Dec. 1978) CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1978

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

Stock No. 003-003-02000-1 Price $1.20

(Add 25 percent additional for other than U.S. mailing).
TABLE OF CONTENTS

INTRODUCTION

APPARATUS

PAGE

DETERMINATION OF THE RELATIVE SPECTRAL RESPONSIVITY OF THE THERMOPILE

DETERMINATION OF THE RELATIVE SPECTRAL RESPONSIVITY OF OTHER DETECTORS

EVALUATION OF THE RELATIVE SPECTRAL RESPONSE MEASUREMENTS 13

CONCLUSIONS 14

ACKNOWLEDGEMENTS 16

m

DETECTOR SPECTRAL RESPONSE FROM 350 TO 120U nra USING A MONOCHROMATOR

BASED SPECTRAL COMPARATOR

Antonio Con.n.onA Instituto de Optica, Madrid, Spain

and

Edwan.d F. lalzwAkl

National Bureau of Standards

Washington, D. C. 20234

ABSTRACT

The. method o {, n.zlatlvz Apzctn.al detector KzAponAz mzaAun.zment baAzd on ^llteHA o ^ known tn.anAmlttance and a ApzctKal

ln.n.adlancz Atandan.d lamp uiaA uAzd to mea.Au.fie the HZAponAlvlty

o £ a thznmopllz. The thzn.mopllz waA then uAzd In conj unction

with a monochn.oma.toK baAzd Apec.tn.al companaton. to mzaAun.z the

n.zlatlvz Apec.tn.al n.zAponAz ^nom 350 to 1200 nm o& Azvznal othzn.

detecton.A . Seven.a.1 auxiliary zxpznlmzntA to evaluate the accunacy

o{> theAe tzchnlquzA an.e dzAcn.lbzd. The zAtlmatzd ac.cun.acif o&

nzlatlvz ApzctKal KZAponAz mzaAun.zmzntA uAlng theAe technlqueA

and thlA pan.tlculan. lnAtn.umzntatlon waA ^ound to nange fanom 3 to 71 depending upon the type oh dztzcton. being me.aAun.zd and thz

Apzctn.al n.zglon unden Atudy. Vlnally, the elective tn.anAmlttancz

o{ Azvzn.al filltzH-A waA mzaAun.zd to zvaluatz thz accuracy o^ thz

n.zlatl\)Z Apzctn.al dztzcton nzAponAz mzaAunzmzntA . It waA con- cludzd that thz z^zctlvz tn.anAmlttancz tzAt Ia not a Kzllablz

way to judgz thz accuracy o £ dztzcton H-ZAponAZ mzaAuH.zmzntA

.

KzyiMon.dA: Vztzcton.; dztzcton nadlomztn.y; dztzcton ApzctKal

companaton; dztzcton. ApzctKal KZAponAz; illtzn tKanAmlttancz tzAt;

photo dztzcton.; photomztzn.; nadlomztzn.; ApzctKal KZAponAlvltyv

INTRODUCTION

For many radiometric and photometric measurements it is necessary to

know the spectral response of the specific detector selected for the experiment. In order to obtain a detector's spectral response one may measure its

output relative either to a detector of known spectral response [1-4] * or to

a set of lamp and filter combinations of known spectral irradiance [5-8]. The

latter procedure is limited in resolution and accuracy by the size of the

obtainable bandwidths . It is also limited by the accuracy of the measurements of the spectral transmittance of the filters and the spectral irradiance

of the light source. The first method is by far the most accurate if one

uses an amplitude stabilized cw laser as the monochromatic source and an electrically calibrated radiometer as the reference detector [2,3]. However,

in most laboratories the detector comparison measurements are usually carried

out using a monochromator . Here the bandwidth restrictions are less severe

than is the case with the filter method; but the accuracy of this type of

measurement is limited by the fidelity of the comparison process (wavelength

accuracy, bandwidth and spectral purity of the monochromator ' s emission and

its beam uniformity) and the accuracy of the spectral response of the reference

detector.

Figures in brackets indicate the literature references at the end of this

paper. 1
ise

>and

In this study we have examined both the method of monochromator based

spectral comparison measurement and the method of detector spectral respom

measurement using a spectral irradiance standard lamp and several narrow-be

interference filters. This study was undertaken in order to evaluate these

techniques which have been used for many years to measure detector response.

It is most important to evaluate and understand the limitations of monochromator based spectral response comparators. Even though better monochromatic

sources are now available with the advent of amplitude stabilized cw lasers,

monochromator based comparators will still continue to be widely used for the

transfer of absolute spectral response.

The measurement of relative spectral response using a standard lamp and

filters was applied to a thermopile with a blackened receiver surface. Because

one would expect the response of such a thermopile to be a nearly constant

function of wavelength, it is the ideal detector for this type of response

determination. That is, one would expect to achieve the greatest accuracy from

the lamp and filter method for a detector whose response did not vary over the

bandwidth of each of the various filters. It was found that for the thermopiles available to us and suitable for use with the spectral comparator, the

spectral response was not wavelength independent -- variations on the order of

8% were observed. This is quite contrary to what one might reasonably assume from what is known about the reflectivity of a thick gold-black coating [9] and

the transmission of the quartz window used in the construction of these

thermopiles

.

In the second part of this study the performance of a reasonably typical

monochromator based detector comparator was evaluated. The evaluation experiments were not elaborate but did serve to uncover some potential problems with

beam non-uniformity, image size at the detector aperture, monochromator bandwidth and wavelength uncertainties. The magnitude of the uncertainty in

spectral response arising from these effects was estimated. Finally the

thermopile, characterized in the first part of this study, and the detector

comparator instrument were used to measure the relative spectral response of

three detectors: a silicon photodiode, a silicon photodiode with a V(X)

[photopic] response, and a silicon photodiode fitted with an infrared cut-off

filter.

A common test of the accuracy of a relative spectral response calibration

has been to measure the effective transmittance of a set of filters [1] ; in a sense the converse of the lamp and filter response determination technique.

This test was applied to the three silicon detectors which had been measured

relative to the thermopile. Both narrow-band interference filters and broadband absorbing glass filters were employed. As one might expect, the narrowband filters provided the more sensitive test while the broad-band filter

results gave no indication of some pretty serious errors. APPARATUS

The thermopile was goldblack coated and mounted in an evacuated housing

with a quartz window. The radiation reaching the thermopile was chopped at a low frequency (less than 15 Hz) and the thermopile output was read using a synchronous ac amplifier.

In the measurement of the relative spectral response of the thermopile

17 interference filters covering the wavelength range from 350 to 1500 nm were used with a spectral irradiance standard lamp. The lamp was a 100 watt

quartz halogen incandescent lamp that had been calibrated at 26 wavelengths

from 250 to 1600 nm. Interpolated values of the spectral irradiance were obtained by fitting either an exponential or a quadratic function to the

experimental points depending on the spectral region. The transmittance of

each of the interference filters had been measured from 300 to 2300 nm on a double-beam recording spectrometer. In the region of the peak transmittance

readings were obtained at 1 nm intervals and in the other regions at 10 nm

intervals. The transmittance of four of these filters was also measured at

a few check wavelengths using the NBS high accuracy spectrophotometer [10].
./

+-c

Fig. 1: Measurement of the relative spectral

response of a thermopile. (A) Spectral irradiance standard lamp; (B) chopper; (C) baffle;

(D) interference filter; and (E) thermopile.

In both the transmittance measurements and the thermopile measurement,

the filters were aligned perpendicular to the optic axis of the radiation

source. To avoid possible interreflection errors from the thermopile window,

it was turned about 5° away from being perpendicular to the optic axis (see

Figure 1)

.

Detector-amplifier linearity was checked using a multiple aperture

technique [11] . Four apertures were employed to check linearity over approximately a factor of four and

overlapping measurements (by varying

the irradiance by less than four-fold)

were used to extend the range of these

measurements. Over the dynamic range

of our measurements the detector plus

amplifier non-linearities were found

to be less than 0.4% for both the

thermopile and the silicon photodiode

systems. This was about the limit of

the precision of these measurements.

The comparison of the silicon photodiode spectral response to that of the

thermopile was performed on an instrument that had been built at NBS several

years ago [12], see Fig. 2. It differed from the original in one major

aspect. For this study both the

reference and test detectors were placed in the same beam position and

the other beam from the partial mirror

(previously used to irradiate the

reference detector) was only used to

monitor the lamp fluctuations. Briefly the instrument consisted of a 100 watt quartz halogen lamp whose

coiled-coil filament was focused onto

the entrance slit of the monochromator

system. The monochromator system con- sisted of two 1/4 meter Ebert mount

grating instruments operated in tandem

to reduced stray (out-of -band) radiation. With the monochromator slit

widths that were used, the bandpass

(full width at half-height) was measured for each set of gratings and

found to be 3.8 nm from 350 to 800 nm

and 7.6 nm from 700 to 1800 nm. Two different sets of gratings were used in order to cover both the visible and infrared spectral regions. A

Corning No. 2-63 filter [13] was placed

at the entrance port of the monochromator to block the second-order diffraction for the long wavelength

measurements

.

The output from one of the directions of the beamsplitter was focused

onto a fixed silicon photodiode to measure the lamp fluctuations between

successive measurements. This monitor

detector had an extended ultraviolet

Fig. 2: Spectral Response Comparator:

(A) reference or test detector; (B) chopper;

(C) grating monochromator, 1/4 meter, Ebert

mount; (D) 100 W quartz halogen, coiled-coil

tungsten filament lamp; (E) stepping motor

wavelength drive; (F) shaft encoder wavelength readout; (G) monitor detector; and

(H) beamsplitter (mirror with hole through

center)

.
response in order to facilitate corrections in the blue spectral region down

to 350 nm. The infrared cut-off of this detector was approximately the same

as that of the other silicon photodiodes which were studied. This meant that

the lamp fluctuation corrections became increasingly unreliable at the longest

wavelengths. Because the stability of an incandescent lamp is usually better

at longer wavelengths than at the shorter ones [14] , this was judged to be a negligible error. The output from the other beamsplitter direction was used

to irradiate either the thermopile or the test silicon detector. The exit

beam of the monochromator was not homogeneous but was an image of the lamp

coils cropped by the jaws of the slit. At the focus it measured about 2 mm

by 20 mm. Silicon photodiodes were chosen for these measurements because, besides

their increasing commercial importance, they have several physical properties

that make them suitable for detector calibration transfer standards. They are typically more uniform in response across the active surface than vacuum photoemissive devices [15]. They do not exhibit the fatigue effects observed

in photoemissive [16] and selenium [17] detectors. And they can be made to

have a stable and linear response. The silicon detectors were operated in

the photovoltaic mode (zero reverse bias) using a very low input impedance

amplifier [18]

.

DETERMINATION OF THE RELATIVE SPECTRAL RESPONSIVITY OF THE THERMOPILE

In the experiment depicted in Fig. 1 the output of the thermopile, V, is a function of its spectral responsivity , R(X) , the spectral irradiance of the

lamp, E(X), and the spectral transmittance of the filter, t- (X) ; V

i = /E(X) Ti (X) R(X) dX (1)

If we assume that R(X) is a constant through the principal transmission band

of the interference filters (typically 15 nm at the half-maximum transmission

points) , then the thermopile output is

V

i = R(Xi

) /E(X) Ti (X) dX (2)

The integral in the above equation can be evaluated using the lamp and

filter calibration values.

The spectral irradiance calibration of the lamp covered the 250 to 1600 nm

region and the interference filter calibrations covered the 300 to 2300 nm

region. The filters exhibited negligible transmission at wavelengths longer

than 1600 nm and the lamp output was negligibly small at wavelengths shorter

than 300 nm. The filter transmittance was measured every 1 nm within the

principal transmission region and the lamp spectral irradiance, measured at

26 wavelengths, was interpolated at 1 nm intervals. Some of the filters had

regions of very low transmittance outside of the principal band. In order

to account for this, the limits of integration in eq . 2 were from 300 to 1600 nm

in every case. Measurements of the thermopile voltage obtained with each of

the interference filters were normalized to the measurement using the filter

which peaked at 550 nm. This yields a measure of the relative spectral

responsivity of the thermopile at approximately the wavelength of the peak

transmittance of each filter.

R

i V

i /E(X) T 5 5o(X) dX

R777 ~ V777 /E(X) T7JJ) dx (3:i

The results are shown in Fig. 3 where the relative response is plotted

at the transmission peak of each filter. The line drawn through these data

is the approximation of the relative response that was used in subsequent

detector measurements . The thermopile has a flat response within a range

of ±1% across the visible and falls off in the near infrared. The decrease
in response is seen to be about 8% at 1200 nm. There also appears to be a sharp drop at 450 nm of about 5%. A second iterative calculation [5] of

eq. 3 using these variations in the relative values of R for the integration

outside the principal transmission band yielded essentially the same results.

Another thermopile of a similar

design from the same manufacturer was measured and a nearly identical relative response function was obtained.

Comparison of these thermopiles with

one having a cavity design and no window confirmed the variation of

response in the infrared (there was insufficient signal to check the

ultraviolet response) . Because its

greater sensitivity was needed for

the monochromator comparator measurements the windowed thermopile was used throughout the rest of the study.

It is our guess that the adhesives

used in the assembly of the windowed

thermopiles may have contaminated the

quartz windows, and that the adhesive

has absorption bands in the regions

where we observe a decrease of the

thermopile response. The actual cause

of the decreased response is not

important. It is important, however,

to note that the response of the

reference detector must be measured

and not simply assumed to be flat.

The accuracy of the spectral irradiance calibration is reported as about

±1% over the visible and near IR regions [14]. The transmission measurements

are much more accurate. However, they were done in collimated light whereas

in the thermopile measurements the light from the lamp subtends an angle of

about 4°. Rotation of the filters in the spectrophotometer by 4° produced

a 1% variation in transmittance . The linearity uncertainty (0.4%) and these

two uncertainties added in quadrature equals 1.5%. Adding to this the

imprecision of the thermopile measurements yields an estimated accuracy of

±2% for the relative response function shown in Fig. 3.

DETERMINATION OF THE RELATIVE SPECTRAL RESPONSIVITY OF OTHER DETECTORS

w«VEiE«eiH «•)

Fig. 3: Relative spectral response of gold

black coated, quartz windowed thermopile.

Data normalized to measurement at 555 nm; dashed line represents the approximate

response function used in subsequent

detector response measurements.

The relative spectral response function of

used to determine the relative spectral respons

spectral comparator instrument. There are seve thermopile response function which also affect

measurement. These other major sources of erro following experiments.

The wavelength accuracy of the monochromat

replacing the spectrally continuous incandescen

source such as a mercury or neon discharge lamp

drive and wavelength readout on an emission lin

spectral range, measurement of the wavelengths

spectrum from 313 to 878 nm were found to be wi

values. The error in responsivity , AR/R, intro

is proportional to the slope, dR/dX, of the res curve

.

the thermopile can now be

e of other detectors using the

ral factors other than the

the accuracy of the comparison

r have been examined in the

ors can easily be checked by

t light source by a line

After adjusting the grating

e near the center of the

of several lines spanning the

thin ±0.2 nm of the published

duced by this uncertainty, AX,

ponsivity versus wavelength

AR

R

M dR

R dX (4)

Of the three detectors studied, the one with the photopic response has the
Table 1 Approximate Slope of a Photopic Detector

Wavelength V(A) c1 ,AV\ -i Slope CtvJ nm

Fractional

Change ( AV

j nm

- 1

400 .0004 0.4 x 10"" 0.100

410 .0012 1.6 x 10" 4 0.133

420 .0040 5.1 x 10" 4 0.128

430 .0116 9.5 x 10" 4 8.19 X IO' 2

440 .0230 1.3 x 10" 3 5.65 X IO" 2

450 .0380 1.82 x io -3 4.79 X IO" 2 460 .0600 2.59 x 10" 3 4.32 X IO" 2

470 .0910 3.87 x 10 -3 4.25 X IO" 2 480 .1390 5.67 x io

-3 4.08 X IO" 2 490 .2080 8.93 x IO

-3 4.29 X IO" 2

500 .3230 1.487 x io

-2 4.60 X IO" 2

510 .5030 2.009 x io' 2 3.99 X IO" 2

520 .7100 1.85 x io -2 2.61 X IO" 2

530 .8620 1.217 x 10" 2 1.41 X IO" 2

540 .9540 6.54 x IO

-3 6.86 X IO" 3

550 .9950 1.99 x 10

-3 2.00 X IO" 3

560 .9950 -2.16 x IO" 3 -2.17 X IO" 3

570 .9520 -6.32 x 10 -3 -6.64 X IO" 3

580 .8700 -9.91 x IO

-3 -1.14 X IO" 2

590 .7570 -1.214 x IO

-2 -1.60 X IO" 2

600 .6310 -1.281 x 10" 2 -2.03 X IO" 2

610 .5030 -1.256 x IO" 2 -2.50 X IO" 2 620 .3810 -1.202 x IO" 2 -3.15 X IO" 2

630 .2650 -1.04 x IO" 2 -3.92 X IO" 2 640 .1750 -7.88 x 10" 3 -4.50 X IO" 2

650 .1070 -5.66 x 10' 3 -5.29 X IO" 2

660 .0610 -3.70 x io" 3 -6.07 X IO" 2

670 .0320 -2.14 x 10" 3 -6.69 X IO" 2

680 .0170 -1.13 x 10" 3 -6.65 X IO" 2

690 .0082 -6.20 x IO"

1* -7.56 X IO" 2

700 .0041 -2.80 x io" 4 -6.83 X IO" 2

710 .0021 -1.40 x 10"" -6.67 X IO" 2

720 .0010 -8.00 x 10" 5 -8.00 X IO" 2

730 .0005 -3.00 x IO" 5 -6.00 X IO" 2

740 .0003 -2.00 x IO" 5 6

-6.67 X IO" 2
greatest slope in regions of appreciable response (greater than 10% of peak)

(see Table 1) . In the region around 500 nm and again around 650 nm the

fractional change in response is about 5% per nm. The corresponding uncer- tainty would be on the order of ±1%. At the extremes this error approaches

or exceeds ±2% but then the relative response is on the order of one percent

of the maximum value. For a silicon detector the greatest fractional change

in response occurs near 1100 nm (about -2% per nm) and again near 400 nm

(about II per nm) . The corresponding uncertainties in response would be ±0.4%

and ±0.2% respectively.

The presence of out-of-band radiation can be checked at specific wave- length settings by measuring the instrument output with and without a filter

that blocks these wavelengths. Significant out-of-band radiation may be

expected at the blue and ultraviolet wavelength settings since an incandescent

source is more intense in the other spectral regions. At longer wavelengths,

second order diffraction effects are expected unless adequately blocked. The

results of measurements made with several blocking filters and a silicon photo

diode as the detector are shown in Table 2. The amount of stray radiation is seen to be below 0.04% in each case except in the vicinity of 300 nm. Measure

ments with the thermopile yielded similar, but noisier, results. For detectors having identical spectral response functions, stray radiation effects

cancel out, of course. In other situations an error of ±0.04% would be the

worst case expectation. For this instrument it appears that stray light

errors will be negligible.

Table 2 Out-of-Band Radiation Test

DETECTOR OUTPUT

Wavelength

Setting

300nm

350

400

450

500

600

700

Blocking

FilterO)

Without

Filter

With

Filter

Percent

Stray

Radiation( b )

600 nm blazed gratings

0-51 0.0423 0.0001 0.2±0.2

0-51 0.6432 0.0002 0.03

3-72 3.5918 0.0000 0.00

3-66 3.2899 0.0003 0.00

3-66 5.6744 0.0000 0.00

5-57 8.1494 0.0000 0.00

5-57 6.4814 0.0000 0.00

1200 nm blazed gratings

Plus Corning 2-63 order sorting filter

800

900

1000

4-97

4-97

4-97

10.3122

10.2633

7.6068

0.0019

0.0011

0.0032

0.02

0.01

0.04

Blocking filters designated by the manufacturer's (Corning) number.

Estimated uncertainty is approximately ±0.01% unless otherwise indicated,

7
Since the other detectors are not measured simultaneously with the thermopile, drift in the lamp output between measurements may be a potential problem.

As stated previously the fixed detector was used to monitor these changes and

a correction was made for them. The question remains as to how well the

monitor and test detectors track any lamp fluctuations. This was checked by

varying the voltage on the lamp. The measurements over as much as a ±25%

change in lamp output are shown at four wavelengths in Fig. 4. Perfect tracking would be a straight line of 45°

slope. It is seen that the monitor

and thermopile track well at 450 and

1100 nm but not at 600 and 900 nm. The non-tracking may be due to several

effects. The non-uniformity of the

monochromator is probably wavelength

dependent, since the spectral output

varies over the image of the filament

coils and the spectral output is also

a function of lamp voltage. This

effect coupled with either (1) the

non-uniformity of response of the

thermopile, (2) the variability of the

slit image on the monitor detector

(its aperture was overfilled) or

(3) the variability of the beamsplitter

ratio with slit image (it was a mirror

with a hole through the center) could

be the cause of the result shown in

Fig. 4. We don't believe such a large

effect could arise from the detector

non-linearities which were very small.

>

1 / /

20 D O/

/ - /+ o"/

/ /

+ /

/o

s

• 450 nm — // O

Q o

a

600 nm

900 nm

/

/ 1

+

1

1100 nm

1 -20 20 CHANGE IN THERMOPILE READOUT (%)

Fig. 4: Tracking of thermopile and monitor

detector readings as a function of lamp out

put and wavelength.

i i 1 1 r "i i r

It would appear that if lamp stability is a potential problem then the

detector and thermopile should be

measured simultaneously; one in each

separate beam from the beamsplitter.

This is not a practical solution since, as we have seen, the results in Fig. 4 may indicate that the beamsplitter has some spectral selectivity. This spectral selectivity can be more explicitly demonstrated by measuring each beam

with the same detector in successive runs. The results of such a measurement

(using a silicon detector) are shown in Fig. 5. Here the beamsplitter ratio

varies by about 22%. Obviously the two beams are not spectrally identical

and any arrangement where the reference detector is in one beam while the

test detector is in the other should be avoided.

The spectral variability of the

non-uniformity in the output beam of

the monochromator can lead to another

error in detector comparison measurements. A non-uniform detector such

as the thermopile or an over-filled

detector aperture will sample different portions of the beam at different wavelengths. Thus it will

appear as if the response of the

detector is varying while in reality

it is the distribution of the spectral

irradiance that is changing. Short

of mapping the variations in the mono- chromator output as a function of

wavelength and then correlating these

measurements with a map of the detector uniformity, there is no other way

of measuring the error introduced by

J I I L J L

too WAVELENGTH Inn I

Fig. 5: Comparison of the two reflections

of the beamsplitter. "Test beam" refer to readings taken at position A of Fig. 1 and

"monitor beam" refers to position G.
this effect. As a qualitative measure of this effect a much simpler experiment was performed. The thermopile was moved in four directions away from

its normal position (rotation by approximately ±20° and ±5mm translation

away from the focal plane) and the change in the relative output of the

monochromator was measured. This is, in effect, a measurement employing

five detectors of different uniformity of response across their surfaces but

having the same relative spectral response. If there were no spectral variability of the uniformity of the monochromator output, then the output of

"each" detector would read the same spectral variations of the output of the

monochromator. That this is not the case is shown in Fig. 6. Here the

thermopile readouts from each of the five measurements of the spectrum were

area normalized (to adjust the readings to the same scale) and then averaged.

Figure 6 is a plot of the deviations from the average at each wavelength

versus wavelength -- the results for both sets of gratings are presented.

The larger deviations in the blue are not unexpected because the uniformity of

the output of the lamp, and consequently that of the monochromator, would have

greater spectral variability at shorter wavelengths . Although this test is by

no means quantitative, it appears that the non-uniformity effect could add an uncertainty of at least ±1%, with a much greater uncertainty in the blue

spectral region.

The bandwidth of the monochromator

output also adds an uncertainty when

the test and reference detector

response curves do not have the same

slope. The error can be approximated

as follows. The output of the x detector, I x , at the monochromator

-*w-lwavelength setting

•Aq+6

A is given by

I X(X„) /An-6R

x

(X) E(X) T(X), (5)

700 700 100 WAVELENGTH In.)

900 1000 1100

Fig. 6: Apparent variations in the relative

spectral output of the monochromator as the

thermopile position is varied. Measurements

with the two different grating sets were made

at different times and precise repositioning

of the thermopile was not possible. Meaningful correlations between the individual

curves in each set is, therefore, not practical and consequently the various positions

described in the text are not identified in

this figure.

where 26 is the width of the bandpass

(to the zero transmission points), Rx

is the detector spectral response, E is the spectral irradiance of the lamp

and T is the transmittance of the

monochromator. Within this small

wavelength interval let us approximate

the spectral response of the x detector

as a straight line

R (X) x

v J R

x

(x ) (X-Xo)

dR

x

(X ) ~dX (6)

Then

I (X ) = R (X ) /

Xn+6

E(X) T(X) dX

X -6

dR

x

(X ) d A /

Xn+6

(X-X ) E(X) T(X) dX

Xn-6

(7)

If we approximate the response of the reference detector as a constant over

the bandpass of the monochromator then the corresponding equation for its

output is
I S (A ) = R

s Uo) /

An+6

E(A) T(X) dX (8)

Xo-6

Dividing eq . 8 by eq . 7 yields the response of the test detector

•Xo + 6

I dR

X

(X.)

R

x Uo) " I (X ) R

s (Ao) " —dl 7-TT^

X o " <5 /

(9)

E(X) T(X) dX

Xn-6

To integrate the term on the right-hand side of the above equation it is

convenient to transform the coordinates so that

y = X-X,

Then

/

X +6 r6

(X-X ) E(X) T(X) dX = I ye(y) t(y) dy ; Xo-6

(10)

(11)

with a similar result for the other integral. Let us assume that the irradiance varies linearly over the bandpass , so that

e(y) = e (1 + by)

and that the bandpass is triangular. For -5 < y < 0,

t(y) = t (l + })

and for _< y <_ 6

t(y) = t (i - £)

Therefore, eq. 11 is

/X + 6 (X-X ) E(X) T(X) dX = e t b6 3 /6

ao-6

and similarly for the other integral

/Xo +6

E(X) T(X) dX = e t 6 ao-6

Equation 9 is then

I x Uo) b6 2 dR

x

(X ) R

x Uo) " I (Xo)

R

s (Xo) ~6 dX

(12)

(13)

(14)

(15)

(16)

(17)

10
For an incandescent source, b is largest in the blue. At 400 nm it is

about 0.02 nm" 1 for a 3000 K blackbody. A photopic detector has a slope of

101 per nm at this wavelength. Therefore, an instrument with a 3.8 nm bandpass will be in error by about 0.5%. At 500 nm, b is about 0.01 nm" 1 and the

detector slope is about 5% per nm, yielding an error of 0.1%. The slope of

the irradiance spectrum at the detector is, of course, not just due to the

spectrum of the lamp. The reflectance and transmittance of the various optical

components will alter the lamp spectrum. Therefore, in order to apply a correction for the effect of the bandpass one must measure the spectral distribution at the output of the particular lamp and monochromator combination

employed. Furthermore, as we have seen the response of the reference detector

may not be a constant function of wavelength and will further add to the

uncertainty of the measurement. It is relatively easy to rederive eq. 17 to

include the effect of a reference detector with a spectrally variable response

function. The result is

R

x Uo) =j

i Uo)

TX^T [R Uo) + b6 a dR

s (A ) b6 2 dRx

(X ) dA dX (18)

Optimally the effect of the instrument bandpass on the detector spectral

response should not be treated as an uncertainty of the measurement. It is

preferable to apply it as a correction in the manner indicated above. However, since in our case it appears to be a small correction compared to the

uncertainty due to non-uniformity we will assume it to be a small error in our measurement: on the order of ±0.5%.

A component of the uncertainty of any measurement is the precision with

which the measurement can be repeated. Table 3 is a list of the estimated

standard deviations for two different silicon detectors being compared to the same thermopile. Each detector was measured three times during different runs

on different days. The average precision from 450 to 950 nm is 0.6%. Outside

these limits the average precision is 1.7%.

Table 3 Precision (Estimated Standard Deviations for a Single

Measurement) of Silicon Detector to Thermopile Comparisons at Several Wavelengths

350 nm 1.9%

400 1.1

450 0.6

500 0.5

550 0.5

600 1.0

650 0.6

700 0.5

750 nm 0.5%

800 0.2

850 0.4

900 0.7

950 0.9

1000 1.6

1050 2.3

1100 1.3

In summary, it is difficult to estimate the overall accuracy of the

detector response transfer measurements made with this spectral comparator

instrument, principally because of the crude estimate we made of the effect

of the non-uniformity of the thermopile response and the spectrally variable

non-uniformity of the monochromator output. Also, since the silicon detectors

are overfilled by the image of the output slit of the monochromator they are

not uniformly sampling the monochromator output thereby contributing a non-uniformity type of error. If we assume that the non-uniformity contribution to the uncertainty is on the order of ±1% everywhere except in the blue

where it is about ±4%, then we can combine this in quadrature with the

11
1 1 1 1 1 1 1 A

/

-v[ I I I 1 1 I 1 i i _ \ ¥ (XI S' i ~ — \ /

- _ / \ \ / - - /

/ \ V - -

/ - - // K\

- -

/ _ / / vv - _ /

/ v ^^~~- z -

1 L_-r'\ 1 1 1 1 i / i i iVi i ~~i ~

10 I I I I I I \ 1 \ 1 1 1 1 1 i

'

' 3 /

N

\

v W

8 / \

' v^

~ / * ~

6 - \\ / / \

'

04 \l / \

_ A / \

2 \ \

-

rra-n I I iN^t^-^j—il2><-.\ 1 1 1 500 600 WAVELENGTH |nm)

Fig. 7: Comparison of the visible transmittance

of the four calibrated absorbing glass filters

and a photopic detector. The curves are:

(1) selenium red glass; (2) copper green glass;

(3) cobalt blue glass; (4) carbon yellow glass;

and V(A) is the relative response curve for an

ideal photopic detector.

Table 4 Difference Between Observed and Calculated Transmittance

of Absorbing Glass Filters -- Responsivity Determined

with the Corrected Thermopile Response Function

Filter Type Silicon Photodiode Photopic Detector

Photodiode with

Silicon - IR Cut-off

Blue -0.5% -0.7% -1.4%

Green 0.2 -0.3 -0.5

Yellow 0.3 0.3 0.5

Red 0.03 1.0 1.2

Table 5 Difference Between Observed and Calculated Transmittance

of Absorbing Glass Filters -- Responsivity Determined

with an Uncorrected (Flat) Thermopile Response Function

Filter Type Silicon Photodiode Photopic Detector

Photodiode with

Silicon - IR Cut-off

Blue 0.1% -0.2% 0.0%

Green -0.4 -0.4 -0.4

Yellow 0.05 0.4 0.3

Red 0.1 1.1 0.9

12
uncertainties due to the relative thermopile response (±21) , the non- linearity (±0.41), the bandpass (±0.5%) , and the wavelength error (±0.1 to

±21) to obtain an overall uncertainty. Adding this result to a 3a estimate

of the precision yields accuracy limits of ±3% to ±4% in the mid-spectral

range (500-100Cnm) and ±6 to ±7% in the blue and near infrared for the

determination of relative spectral response.

EVALUATION OF THE RELATIVE SPECTRAL RESPONSE MEASUREMENTS

A commonly used technique to check the accuracy of the relative spectral

response of a detector is to measure the effective transmittance of a filter [1]. That is, the transmission of a specific irradiance function, E(A),

by a filter whose spectrophotometrically measured transmittance is x(A). For

a detector of relative spectral response, r(A), the effective transmittance,

T, is computed as follows:

T

_ /E(A) x(A) r(A) dA nq . T 7ETT) r(A) dA (- iyj

The comparison of the calculated and measured values of T is then taken to be

a measure of the accuracy of the r(A) function.

We obtained from the NBS Spectrophotometry Group four calibrated absorbing

glass filters [19] . The visible transmittance for each of these filters plus

the relative response of a photopic detector is depicted in Fig. 7. Table 4 lists the differences between the calculated and measured effective transmittances of each of these filters using the three silicon detectors measured

above. The agreement is remarkable. The effective transmittance errors are everywhere less than 1.5%; typically they are about 0.5%. Whereas the estimated uncertainty of the relative response ranged from 3 to 7%.

If the relative responsivities of the three silicon detectors are recom- puted using a wavelength independent response function for the thermopile,

a different set of results is obtained from the computation in eq . 19. The

effective transmittance errors obtained using a flat thermopile response as the reference detector are shown in Table 5. Although we have changed the.

relative spectral responsivities by 5% in the blue and 8% in the near infrared,

the changes in the effective transmittance measurements, especially those of

the (bare) silicon photodiode, do not indicate this. The reason that they do

not becomes clear if we examine eq. 19 in a little detail.

Suppose that r(A) is the true detector response function while our mea- surements are in error by a wavelength dependent function 6(A). The calculated

iffective transmittance is then

T = /e(A) x(A)[r(A) + 6(A)] dA f2 , calc /E(A) [r(A) + 6(A)] dA lZUJ

and T is given by eq. 19. If we make the following assumption

/E(A) r(A) dA >> /E(A) 6(A) dA

then eq. 20 can be approximated as

T r /E xr dA IE x6 dA n n /E6 dA -. calc ' L /E r dA /E r dA J l /Er dA J

The indication of dependence on A has been omitted to simplify the form of

the equation. The difference between the calculated and observed effective

transmittance would be

13
Tcalc " T expt _ ri /ExddX -. n _ /E6dA -. . ±

r 23)

T

L /ExrdX J Li /ErdX J k J expt

The ratio of integrals in the first bracket is an estimate of the error within

the filter transmission band, and the ratio in the second bracket is the

estimate over the entire response range of the detector. If these two ratios

are of the same order of magnitude, that is, if the errors within the filter

transmission band are approximately the same as those throughout the detector

response band, then the product of the two brackets in eq . 23 is approximately

equal to one. Actually

T calc " T expt /ExSdX /E6dX /Ex6dX . /E6dX (2A)

T /ExrdX /ErdX /ExrdX /ErdX

expt

The estimate of the spectral response error, the first term on the right,

will be increased or diminished depending on the errors throughout the rest

of the response range. The effective transmittance test can be a qualitative

indication of relative spectral response errors if two conditions are met.

First the transmission band of the filter must be small with respect to the

response range of the detector. And second, the relative response errors within the transmission band must be large with respect to the errors throughout the rest of the response range. The correct magnitude of the error cannot

be determined by this test.

The first condition is met by the interference filters that were used

in the first part of this study to measure the relative spectral response of

the thermopile. The result of an effective transmittance test using some of

these filters is given in Table 6. Two things are immediately obvious. First

the variations of relative spectral response for the silicon photodiode and

the silicon photodiode plus ir cut-off filter are on the order of the estimated uncertainties of the previous section. Second, the variations of the

photopic response indicate substantially greater errors than expected. This

may be due simply to the failure of the effective transmittance test as noted in eq. 24. That is, the estimate of the spectral response error has

been substantially increased in the blue and decreased in the red spectral

regions. On the other hand, the bandpass errors and wavelength errors may

have been greater than expected since our detector did not have the same slopes as the ideal photopic detector, nor was the monochromator output

spectrum the same as a 3000 K blackbody. In any event, it is obvious that

the broadband effective transmittance test failed completely to indicate

the presence of some pretty large errors in all three detectors.

CONCLUSIONS

Small improvements beyond the ±2% uncertainty level can possibly be

made in the lamp and filter method of measuring the relative spectral response

of a thermopile. But these are hardly worth the effort considering the

accuracy that can be obtained with a characterized electrical substitution

radiometer [2,3] (ESR) . Pyroelectric ESR's are now commercially available

that have uncertainties of about one percent in absolute response throughout

the wavelength range from the near uv to the near ir. Furthermore, their

sensitivity and uniformity surpasses that of thermopiles. Use of the lamp

and filter method to measure other detector response functions will almost

certainly have uncertainties exceeding ±3%. Spectral comparison to a reference detector of an accurately known response provides a more accurate

method of detector measurement.

Several conclusions can be drawn regarding the improvement of the mono- chromator based spectral comparator used in this study. The largest source

14
Table 6 Difference Between Observed and Calculated

Transmittance of Interference Filters

Filter

Transmittance

Peak

Silicon

Photodiode

-0.81

Photopic

Detector

a

Silicc

with

m Photodiode

IR Cut-off

350 nm

a

400 -3.4 a 0.4%

450 -3.8 9 3.2% 4.2

500 1.1 19.6 0.5

550 0.4 1.2 -0.7

580 0.8 -1.1 -0.4

600 -0.4 -8.2 -1.6

650 0.6

a -0.4

750

800

850

3.5

-1.7

-2.1

a

a

a

-2.0

a

a

1000 0.8 a a

1200 0.9 a a

Nearly zero detector output.

of uncertainty was due to the lack of spatial uniformity in the monochromator

output and the detector response. The monochromator output can be made more uniform by using a more uniform light source such as a strip lamp or an entrance diffuser on the monochromator itself. Thermopiles can not be made

more uniform without a loss in sensitivity. Hence another type of reference

detector is called for, such as, a pyroelectric detector or a silicon photodiode. Also, if it is at all possible one should underfill the detector

apertures rather than overfill them.

The uncertainty due to the monochromator bandpass can be reduced by

using eq. 18. One needs to know the relative spectral distribution of the

monochromator output and the relative spectral response of the reference and

test detectors. Since the response of the test detector is an unknown,

obtaining a bandpass correction is an ex post-facto calculation. The error

due to such an iteration should be smaller than the magnitude of the bandpass

correction itself.

The use of a monitor detector is a reasonable way to improve measurement precision. However, use of a partially reflecting mirror is preferable

to the pierced mirror used in this study. This would insure that the monitor

detector views the same portion of the monochromator output as the reference

and test detectors.

The major source of imprecision in these measurements was the thermopile. It has already been recommended that it be replaced by either a pyroelectric on a silicon detector. From the standpoint of repeatability and

sensitivity a silicon photodiode would be the preferred reference detector.

However, if wide spectral range is required then a black-coated pyroelectric

is the detector of choice.

15
Given the incre

substantially reduce

the bandpass correct

the wavelength error requires mechanical

Finally we do n

a filter as a reliab

ment. The cancellat

erroneous estimation

ased sensitivity of the silicon

the instrument bandpass. This

ion (and its corresponding unce somewhat. Further reduction o improvements of the wavelength

ot recommend the effective tran

le test of the accuracy of a sp

ion of errors as shown in eq. 2 of the error within the filter

photodiode one can

will, of course, reduce

rtainty) and decrease

f the wavelength error

drive and readout.

smittance measurement of

ectral response measure4 clearly indicates an transmission band.

A ***** *

ACKNOWLEDGEMENTS

We would like to express our appreciation to Kenneth Eckerle and

Victor Weidner for the spectrophotometric measurements on the interference

filters and for the loan of the absorbing glass filter standards, and to

John Jackson and Donald McSparron for the loan of a spectral irradiance

standard lamp.

16
REFERENCES

1. W. Budde and C. X. Dodd, Appl. Opt. 10, 2607 (1971).

2. J. Geist, B. W. Steiner, A. R. Schaefer, E. F. Zalewski and A. Corrons

,

Appl. Phys. Lett. 26, 309 (1975).

3. M. A. Lind, Proc . of the Electro-Optical and Laser Conference 1976,

p. 55 (Industrial and Scientific Conference Management, Chicago, 111.

1976).

4. G. Eppeldauer, J. Graner, J. Schanda and U. M. Vanyek, Appl. Opt. 16,

255 (1977).

5. H. S. Moran, J. Opt. Soc. Am. 45, 12 (1955).

6. G. Wyszecki, J. Opt. Soc. Am. 50, 992 (1960).

7. N. Mori, J. Opt. Soc. Am. 51, 1015 (1961).

8. H. E. Fleming and D. Q. Work, Appl. Opt. 4, 337 (1965).

9. W. R. Blevin and W. J. Brown, Metrologia 2, 139 (1966).

10. K. D. Mielenz, K. L. Eckerle, R. P. Madden and J. Reader, Appl. Opt. 12,

1630 (1973).

11. K. D. Mielenz and K. L. Eckerle, Appl. Opt. 11, 2294 (1972).

12. D. G. Goebel, NASA Preprint No. X-732-72-169 (NASA Goddard Space Flight

Center, Greenbelt, MD, May, 1972); D. G. Goebel, E. W. Poole and R. G. Hartsock, Appl. Opt. 8, 1749 (1969).

13. Commercial materials and equipment are identified to specify experimental

procedure. In no case does such indentification 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.

14. R. D. Saunders and J. B. Shumaker, NBS Technical Note 594-13, 1977

(U.S. Government Printing Office, Washington, D. C. 20402, SD Cat. No.

013.46:594-13) . 15. I. Reif, R. N. Kniseley and V. A. Fassel, Appl. Opt. 9, 2398 (1970);

G. S. Birth and D. P. DeWitt, Appl. Opt. 10, 687 (1971); and E. A. Ballik,

Appl. Opt. 10, 689 (1971).

16. 0. Youngbluth, Jr., Appl. Opt. 9, 321 (1970).

17. K. Mohan, A. R. Schaefer and E. F. Zalewski, NBS Technical Note 594-5,

June 1973 (U.S. Government Printing Office, Washington, D.C. 20402,

SD Cat. No. C13. 46:594-5)

.

18. E. F. Zalewski, A. R. Schaefer, K. Mohan and D. McSparron, NBS Technical

Note 594-2, 1972 (U.S. Government Printing Office, Washington, D.C.

20402, SD Cat. No. C13 . 46 : 594-2)

.

19. H. J. Keegan, J. C. Schleter and M. A. Belknap, J. Opt. Soc. Am. 54,

69 (1964)

.

17

ft U. S. GOVERNMENT PRINTING OFFICE : 1978 281-067/328
NBS-114A (REV. 11-77)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBS TN 988

2. Gov't Accession

No.

4. TITLE AND SUBTITLE

Detector Spectral Response From 350 to 1200 nm Using a Monochromator Based Spectral Comparator

7. AUTHOR(S)

Antonio Corrons and Edward F. Zalewski

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

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

3. Recipient's Accession No.

5. Publication Date number 1 978

6. Performing Organization Code

8. Performing Organ. Report No.

10. Project/Task/Work Unit No.

11. Contract/Grant No.

13. Type of Report & Period Covered

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

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

bibliography or literature survey, mention it here.) The method of relative spectral detector response measurement based on filters of known transmittance and a spectral irradiance standard lamp was used to

measure the responsivity of a thermopile. The thermopile was then used in

conjunction with a monochromator based spectral comparator to measure the relative specti

response from 350 to 1200 nm of several other detectors. Several auxiliary experiments

to evaluate the accuracy of these techniques are described. The estimated accuracy of

relative spectral response measurements using these techniques and this particular

instrumentation was found to range from 3 to % depending upon the type of detector

being measured and the spectral region under study. Finally, the effective transmittance of several filters was measured to evaluate the accuracy of the relative

spectral detector response measurements. It was concluded that the effective transmittance test is not a reliable way to judge the accuracy of detector response

measurements.

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) Detector; detector radiometry; detector spectral comparator;

detector spectral response; filter transmittance test; photodetector; photometer;

radiometer; spectral responsivity.

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Consumer Information Series—Practical information, based on NBS research and experience, covering areas of interest to the consumer. Easily understandable language and

illustrations provide useful background knowledge for shopping in today's technological marketplace.

Order above NBS publications from: Superintendent of Documents, Government Printing Office, Washington, D.C.

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Federal Information Processing Standards Publications (FIPS PUB)—Publications in this series collectively constitute the Federal Information Processing Standards Register.

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pursuant to the Federal Property and Administrative Services Act of 1949 as amended, Public Law 89-306 (79 Stat. 1127), and as implemented by Executive Order 11717

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BIBLIOGRAPHIC SUBSCRIPTION SERVICES

ic following current-awareness and literature-survey bibli- raphies are issued periodically by the Bureau:

Cryogenic Data Center Current Awareness Service. A litera- ture survey issued biweekly. Annual subscription: Domestic, $25.00; Foreign, $30.00.

'iquified Natural Gas. A literature survey issued quarterly. Annual subscription: $20.00.

Superconducting Devices and Materials. A literature survey

issued quarterly. Annual subscription: $30.00. Send subscription orders and remittances for the preceding bibliographic

services to National Bureau of Standards, Cryogenic Data

Center (275.02) Boulder, Colorado 80302.
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