Measurement of Relative Spectral SensitivityDistributions of Photoelectric Receivers

W. Budde and C. X. Dodd

An apparatus is described for the fully automatic measurement of the relative spectral sensitivity distri-butions of photoelectric receivers. A substitution method is used in which, after calibration of an auxil-iary photomultiplier against a reference thermopile, the sample receiver is mounted in the position for-merly occupied by the thermopile. Precision and accuracy of the measurements are discussed.

Introduction

The rapid development of new photoelectric receiversas well as increasing requests for highly accurate andreliable photometric and clorimetric instrumentationhave resulted in an increasing demand for accurate de-termination of the spectral sensitivity distributions ofphotoelectric receivers. Particularly, the recently de-veloped technique' of calculating the optimum thick-ness of glass filters for the construction of photoelectrictristimulus clorimeters and photometers is based onthe exact knowledge of the relative spectral sensitivitydistribution of a receiver. The necessity of studyingthe various parameters which may affect the sensitiv-ity distribution of a receiver not only imposes strin-gent conditions on accuracy and precision of spectralsensitivity measurements but also often requires alarge number of consecutive spectral sensitivity mea-surements, so that fully automatic instrumentationfor such measurements is advisable.

It is the purpose of this paper to describe an appa-ratus for the automatic determination of relative spec-tral sensitivity distribution [s(X) distributions] ofphotoelectric receivers for a wavelength range from350 nm to 800 nm and to give some applications.

ApparatusBasically two methods for the determination of s(X)

distributions have been described in the literature:

(1) The filter method, using light sources of knownspectral power distribution and sets of filters of known

The authors are with the Physics Division, National ResearchCouncil of Canada, Ottawa, KIA OS1.

Received 22 June 1971.

spectral transmittance. This method has been de-veloped theoretically to high perfection, 2 -4 but is sub-ject to practical instrumental difficulties' which im-pose limitations on its use.

(2) The thermocouple method, in which the responseof the test receiver is compared against that of a ther-moelectric receiver (thermocouple or thermopile) whichis assumed to be nonselective. For this method es-sentially two techniques have been employed. Inone technique the ratio of the signals from the testreceiver and the thermocouple is measured at eachwavelength regardless of the amount of radiation fall-ing on the thermocouple. 6 This technique has beenused mainly to modify existing commercial spectro-photometers for s(X) measurements. 7 -9 The othertechnique, described much more frequently in the lit-erature, may be called the equal power spectrum tech-nique. In this technique the thermocouple controls,by means of feedback circuits, either an optical attenu-ator, the light source, or the slits, so that the flux ofmonochromatic radiation on the thermocouple remainsconstant throughout the spectrum. A supposedlyconstant fraction of the flux is diverted to the test re-ceiver. Plotting the signal from the test receiver asfunction of wavelength yields directly its relative spec-tral sensitivity distribution.

This equal power spectrum technique affords ratherrapid measurements and is therefore a most desirabletechnique. However, the accuracy of this techniquedepends, among other parameters, on the beam-split-ting device which is assumed to divert to the test re-ceiver, independently of wavelength, a constant frac-tion of the radiant flux. This assumption is not neces-sarily met in some beam-splitting devices that havebeen described. Geometrical beam splitters, such asroof mirrors' 0 or mirror-comb arrangements, 9 whichdivert a geometrical fraction of the flux, are limited intheir nonselectivity because of effects reported byBauer." His investigation indicates that the density

December 1971 / Vol. 10, No. 12 / APPLIED OPTICS 2607

'A

of monochromatic radiation across an image of a mono-chromator prism is not uniform and that the densitydistribution changes with wavelength. This appliesalso in front of or behind the image, and therefore theratio of the monochromatic powers in the two beamsproduced by such a geometrical beam splitter mayvary with wavelength. Glass or quartz plates used asbeam splitters are selective because of polarizationeffects which are wavelength-dependent. Time-shar-ing beam splitters such as rotating semicircular mir-rors'2 '13 may be made nonselective so that the fluxratio in both beams remains constant throughout thespectrum. This method, however, usually involves,particularly in automatic instrumentation, the chop-ping of radiation and consequently other difficulties'4

are encountered which limit the usefulness of this typeof beam-splitting device.

Owing to these difficulties, a direct plotting methodbased on the equal power spectrum technique was con-sidered inadvisable and a substitution technique waschosen which allows the test receiver to be measuredunder exactly the same conditions as the reference re-ceiver (e.g., thermocouple) and, in fact, in the sameplace. A substitution technique has been describedby Krochmann,' 5 who combines it with the equal pow-er spectrum technique by using the thermocouple forthe empirical determination of the shape of a mechan-ical cam which controls an attenuator so that an equalpower spectrum is maintained. This particular sub-stitution technique requires high stabilities in thespectral properties of light source and optical compo-nents.

The above considerations and the additional require-ment that the measurements be made fully automatic-ally resulted in the construction of an apparatus whichis shown schematically in Fig. 1.

The dispersive element is a quartz prism doublemonochromator (Hilger D 121) with an added motordrive (X-drive motor). Also driven by this motor arethree electrical cams and the -disk. The light sourcelamp, a 200-W quartz-iodine lamp, is imaged by meansof a quartz lens at the entrance slit of the monochro-mator. Behind the exit slit a shutter is mountedwhich is operated from switch S by the solenoid R1.

omp-itler motor supply .asiosit dlve I|htte multiplier sample rectiver

lamp ( - quatta double s u bea _ _ _ I m splitter to replace

powe1 morochromolrt - -thetmopile the-pile

L ~~~~~~~~~~~~~~~."com _ ii amplifier

X- d o I

Fig.motor Sc tc dar of S4a Spar5ats

I I l f = 2 ~~~~~~~~~~~t R~

--5 t - digtal cor

Fig. 1. Schematic diagram of s(X) apparatus.

The monochromatic radiation leaving the monochro-mator is divided by a beam splitter so that about 90%of the radiation forms an image at the thermopile and10% at the auxiliary multiplier (EMI 9558B photo-multiplier). The signal from the thermopile is ampli-fied by means of the galvanometer amplifier by a factorof 100 and subsequently by a ,V amplifier by a factorof 5000 so that a total gain of 0.5 X 106 is achieved.The amplified thermopile signal is then available formeasurement and recording at switch S3. The signalfrom the auxiliary photomultiplier, which is connectedto a highly regulated HV power supply, is amplified bymeans of the mV amplifier and the amplified signal isavailable for recording at switch S4.

Cam 3 encodes the wavelength as a voltage so thatthe wavelength in nm is displayed numerically in mV.This signal is displayed on a small digital voltmeter(not shown in the diagram) and is also available for re-cording at switch S2. Cam 2 controls, via the slitservoamplifier, the slit motor. This motor drives theentrance and the middle slit of the monochromator sothat, with a constant exit slit, the bandwidth is constantthroughout the spectrum. Under normal operatingconditions this bandwidth is 5 nm.

Cam 1 controls the lamp power supply so that thesignal from the thermopile remains approximately con-stant within 410% throughout the spectrum. With-out this control, that is, with a fixed lamp current, thesignal from the thermopile would rise from about 2 b&Vat 350 nm to about 40 AV at 800 nm. This change ofsignal would require a high linearity of the galvanom-eter amplifier and the ,V amplifier over this range.Cam 1, however, makes the measurement nearly in-dependent of the linearity of these amplifiers becausethe whole thermopile circuit is operated on only twolevels: the dark signal of the thermopile and the sig-nal for a nearly constant spectral power.

The switches Si to S6 are closed or opened by camson the shaft of the cycle motor.

The procedure of the measurements starts with theX-drive motor, which drives the monochromator toincreasing wavelengths. The X-disk, consisting of alarge circular disk with a spiral groove with setscrewsat intervals related to the wavelengths of the mono-chromator,' 6 opens a microswitch which controls relayR2 so that the X-drive motor is stopped and the cyclemotor is started.

During one cycle the various switches SI to S6 areoperated as shown in Fig. 2, where the hatched barindicates that the switch is closed. While the shutteris closed (Si) the wavelength signal is routed to thedigital voltmeter (DVM) by closing S2 and the DVMis triggered by S5 to take one reading and record thisvalue by means of the card punch. Then the ther-mopile dark current is measured by closing S3 andtriggering the DVM again by S5. The shutter is nowopened (by opening S) and the light signal from theauxiliary multiplier is routed to the DVM by meansof S4; then the light signal from the thermopile is re-corded and after the shutter is closed again the darkcurrent of the auxiliary multiplier is measured. At

2608 APPLIED OPTICS / Vol. 10, No. 12 / December 1971

Time 0 5 10 15 20 25 sec.

St shutter closed - - - - - - - - - -/////////////////S2 X-encoder to DVM _

S3 thermopile to DVM -- ---- --- -S4 multiplier to DVM -- ----- - ---S5 DVM- trigger -- …---- 13 _

S6 start X-drive motor …_

measurement of: wovelengthl thermopileaux.mult.Ithermopilel aux. mult.zero ig gnoat |igna I dark current

or :sample j smple Ireceiver receivordark curren Signal

Fig. 2. Contact closures during one cycle. The hatched barindicates the period of closure of the switch.

the end of this cycle 86 is closed, which stops the cyclemotor and starts the X-drive motor to proceed to thenext wavelength, where the cycle is repeated. Inthis manner the apparatus scans the spectrum from350 nm to 800 nm in steps of 5 nm. As indicated inFig. 2 the time required for one cycle is about 25 sec.The whole spectrum is scanned in about 50 min. Theparticular timing shown in Fig. 2 gives the thermopileand its electronics at least 9 sec to settle to its final val-ue. Although the thermopile has a response time of1 sec the response time of the associated electronicshas been increased by some RC filters (not shown inFig. 1) at the output of the MV amplifier to suppressnoise from the galvanometer amplifier.From the data obtained with the thermopile in the

apparatus the ratio r of the auxiliary multiplier re-sponse to that of the thermopile is calculated for eachwavelength after corrections for dark signals are ap-plied. This is, of course, not the s(X) distribution ofthe auxiliary multiplier, because the properties of thebeam-splitting device are still inherent in these data.

After the spectrum has been scanned in the mannerdescribed, the thermopile is removed and a sample re-ceiver mounted in its place and the associated elec-tronics connected to switch S3. The spectrum isscanned again according to the same program but nowthe sample receiver takes the place of the thermopile.From these measurements the ratio r2 of the responseof the sample receiver to that of the auxiliary multi-plier is calculated.

The product of the two ratios r and r2 yields theratio of the response of the sample receiver to that ofthe thermopile. The properties of the beam splitterare completely canceled out. If the thermopilewere nonselective, this ratio, plotted as function ofwavelength, would represent the relative spectralsensitivity distribution of the sample receiver. Com-parisons of the thermocouples with black receiv-ers 14,17,18 show that thermocouples may be selective andthat changes of a few percent may occur in the rangefrom 350 nm to 800 nm. For this reason the thermo-pile used in this apparatus (Hilger-Schwarz model FT16) was compared against a blackbody receiver.'9 Theresults show that the sensitivity of this thermopile at350 nm is about 2% lower than that at 800 nm. Cor-

rections for this deviation are incorporated in the cal-culations.

In this apparatus the most important condition isthat the s(X) distribution of the auxiliary multiplierand the spectral properties of the beam splitter re-main constant for the time required for the calibrationof the auxiliary multiplier and the measurements ofthe sample receiver. Various experiments have shownthat these components are stable enough for at leastone week, so that a considerable number of sample re-ceivers may be measured after the auxiliary multiplierhas been calibrated against the thermopile.

Precision and Accuracy

An obvious procedure for the determination of theprecision of a measuring device is to measure repeatedlya quantity whose inherent variations are small com-pared to the resolving power of the device. If eachmeasurement yields a different result, an average andthe standard deviation can be calculated, the latterbeing a measure for the precision of the device.

It is rather difficult to apply this procedure to thespectral sensitivity apparatus because the responses ofmost photoelectric receivers are not very stable.Noise, temperature effects, the low sensitivity in cer-tain wavelength regions, and other parameters makethe fluctuations in the receiver response comparableto the resolving power of the apparatus, and the stan-dard deviation obtained from repeat measurements withsuch receivers does not reflect the true precision of theapparatus itself.

The experiments described below will illustrate thesedifficulties but will nevertheless result in an indicationof the precision of the apparatus.

For the first series of measurements the thermopilewas mounted in its normal position and eight consecu-tive scans throughout the spectrum were made withoutremoving the thermopile. The first scan was used forthe calibration of the auxiliary photomultiplier andthe other seven were treated as sample scans. Theaveraged s(X) values (arbitrarily normalized) and thestandard deviations in percent are given in columns2 and 3 of Table I. The s(X) values show the expectedhorizontal distribution.

Table I. Precision of s(X) Apparatus

Thermopile RCA 6217 Photocell VB 59

X 0O0r0

(nm) s(X) (%) s(X) (%) s(X) (%)

350 1.102 0.5 0.400 0.3 0.869 1.3400 1.098 0.2 1.244 0.2 1.732 1.1450 1.097 0.1 1.626 0.3 1.882 0.9500 1.097 0.1 2.137 0.4 1.879 0.6550 1.102 0.2 2.022 0.4 1.657 0.7600 1.098 0.2 1.579 0.6 1.258 1.2650 1.100 0.2 0.804 0.6 0.732 1.4700 1.094 0.2 0.238 0.7 0.271 2.8750 1.099 0.4 0.034 1.4 0.044 9.1800 1.080 2.3

December 1971 / Vol. 10, No. 12 / APPLIED OPTICS 2609

(n

z0

a.

20

15 -

.0 .A .. . . . ....iou 400 500 600

WAVELENGTH (nm)700 800

Fig. 3. Averaged spectral sensitivity distribution of photocellVB 59.

For the second series of measurements the auxiliaryphotomultiplier was again calibrated against the ther-mopile. Then the thermopile was replaced by an RCA6217 photomultiplier and ten spectrum scans weremade within two days. The averaged s(X) valuesand their standard deviations in percent are given incolumns 4 and 5 of Table I.

The third series of measurements was compiled fromten measurements in which a vacuum photocell VB59 was used as sample receiver. The measurementswere made over a period of about three months. Inthis series each measurement is based on a separatecalibration of the auxiliary photomultiplier. Theaveraged s(X) distribution is shown in Fig. 3; someaveraged s(X) values and their standard deviationsgiven in columns 6 and 7 of Table I.

For the last two series the increase of a- toward thered end of the spectrum is typical of the situation wherethe s(X) value decreases and approaches the resolvingpower of the data acquisition system of the apparatuswhich is determined by the maximum of the s(X) dis-tribution. In both cases noise from the sample re-ceiver and its associated electronics contribute to theuncertainty of the measured value, particularly at lowvalues. The standard deviations at these wave-lengths, therefore, do not indicate the precision of theapparatus.

One important difference between these two series isnoteworthy. In the RCA 6217 series all measure-ments are related to the same calibration of the auxili-ary photomultiplier, whereas in the VB 59 series eachmeasurement is based on a separate calibration of theauxiliary photomultiplier. The results indicate thatfor investigations where small differences betweens(X) distributions are of major importance, a higherprecision is obtained if the measurements are madewithin about two weeks so that the same calibrationof the auxiliary photomultiplier can be used.

The thermopile measurements, exhibiting the bestprecision, are not affected by a relative lack of sensitiv-

ity in a certain spectral region. It may be concludedthat the standard deviations shown in column 3 ofTable I are typical for the apparatus itself. Theincrease of a at either end of the spectral range occursbecause the sensitivity of the auxiliary photomulti-plier is rather low in these regions.

The accuracy of a measuring device can be giveneither if the true value of a standard is known, and thedifference between the measured and the true value isdetermined, or if a very careful assessment of the sys-tematic errors can be made.

Neither of these methods lends itself readily to thes(X) apparatus. Standards, such as blackbody orcavity receivers, which have known spectral absorp-tivities, 7 8 are difficult to make. Comparisons withthe results obtained in other laboratories may, if theresults agree, tend to increase the confidence in theaccuracy but are still no absolute confirmation. Toestimate the effects of systematic errors in a rathercomplex process of measurement, such as the presentone, is very difficult and open to argument becausesources of error may easily be missed.

Therefore an effort was made to estimate the accuracyfrom an application where transmittance values ofglass filters, predicted by calculation from the mea-sured s(X) distribution, are compared with actualmeasurements of the filter transmittances.

For these transmittance measurements an incan-descent lamp of known relative spectral power distribu-tion Eo(X) and a fixed glass filter of known spectraltransmittance T(X)' 0 were mounted on a photometerbench. Also mounted on the bench were a filter wheeland a photocell whose s(X) distribution had been deter-mined in the s(X) apparatus. The filter wheel con-tained five apertures covered with glass filters of knownspectral transmittances Ti(X), i 1.. .5 (see Fig. 4)and an open aperture. The purpose of the fixedfilter between light source and filter wheel is to modify

1.0

0.8

0.6

E _ <~~~~~~E

I0.4 -GRE

0.2

300 400 500 600 700 nm 800Wavelength

Fig. 4. Spectral transmittances of filters for the filter test andspectral power distribution E(X) of light source + fixed filter

combination.

2610 APPLIED OPTICS / Vol. 10, No. 12 / December 1971

oE(X) so that a light source, E(X) = Eo(X) -Tf(X), isobtained with E(X) = 0 outside the range 350-800nm. E(X) is also shown in Fig. 4.

With this setup the integral transmittances Tm, ofthe five filters were measured for this particularsource-receiver combination. Then from the knownspectral data the integral transmittances T werecalculated according to

TCi= fE(X)Ti(x)s(X)dX/fE()s()dx.

The ratios R, = Tc,i/Tm,i and the percentage errorsRit' = (1 - R1) 100 were also calculated.

The following values were obtained for the photocellYB 59 mentioned above:

Filter

1 Blue2 Green3 Yellow4 Orange5 Red

Ri1.0020.9921.0000.9891.000

Ri' (%)

+0.2-0.8

0-1.1

0

Similar measurements with other receivers such asphotomultipliers or silicon photodiodes show that thesevalues are typical for all s(X) measurements made inthis apparatus. But these values do not reflect exclu-sively the accuracy of the s(N) measurements becausein the calculation of T,, other spectral data are usedwhich are subject to systematic errors.

The accuracy of the Ti measurements is of theorder of 0.2%, which is comparatively small com-pared to the above errors.

However, this filter test can be used to study theinfluence of wavelength errors on the accuracy of thes(X) measurements, as follows.

An s(X) distribution, which is measured in wavelengthincrements of 5 nm, was interpolated for wavelengthincrements of 1 nm. New distributions were thencalculated according to

s'(X) = s(X + AX),

with AX ranging from -5 nm to +5 nm. This pro-vides shifts of the whole s(X) distribution in steps of1 nm to either side of the given measured distribution.With these shifted distributions T was calculatedagain and new R,' values were determined. For apositive and a negative shift of 1 nm the percentageerrors were found as follows:

Filter

1

2345

(Ri') I

Ri'(AX = -1nm) %

-0.3-1.0+0.2-0.5+1.0

2.38

Ri'(A = 0) RI'(A = +1% nm) %

+0.2 +0.7-0.8 -0.7

0 -0.2-1.1 -1.70 -1.01.89 4.67

The sum of squares of the R' values shows a min-imum value for the given measured data (AX = 0),which indicates that if there is a constant wavelengtherror in the s(X) measurements, this wavelength

error must be less than 1 nm. Similar studies with asilicon photodiode confirm this conclusion.

One the basis of the various results obtained with thefilter test it is estimated that the relative spectralsensitivity distributions measured in the apparatusdescribed above are accurate to better than i4 2%from 400 nm to 700 nm, with larger tolerances towardeither end of the total range.

The authors appreciate very much many helpfuldiscussions with G. Wyszecki and C. L. Sanders. Manypractical and most valuable contributions came fromDenis Gignac and Frank McNeely. Ron Burtonwrote the programs for the evaluation of the raw data.All this help is gratefully acknowledged.

References1. H. Wright, C. L. Sanders, and D. Gignac, Appl. Opt. 8, 2449

(1969).

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

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

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

5. D. Hahn and J. Weidermann, P.T.B.-Milleilunger 4/65, p.323.

6. T. F. Young and W. C. Pierce, J. Opt. Soc. Am. 21, 497(1931).

7. J. T. Tykociner and L. R. Bloom, J. Opt. Soc. Am. 31, 689(1941).

8. A. R. Boileau, J. Opt. Soc. Am. 51, 1457 (1961).

9. S. Licht, Rev. Sci. Instrum. 35, 1027 (1964).

10. E. H. Stupp, Rev. Sci. Instrum. 33, 1215 (1962).

11. G. Bauer, Z. Phys. 145, 279 (1956).

12. D. G. Avery and P. H. Hammond, J. Sci. Instrum. 30, 400(1953).

13. H. Mitsuhashi and T. Nakayama, J. Phys. Soc. Japan 11, 308(1956).

14. R. Stair et al., Appl. Opt. 4, 703 (1965).

15. J. Krochmann, Lichttechnik 17, 79A (1965).

16. C. L. Sanders and W. Gaw, Appl. Opt. 6, 1639 (1967).

17. K. Bischoff, Optik 21, 521 (1964).

18. W. L. Eisenmann, R. L. Bates, and J. D. Merrian, J. Opt.Soc. Am. 53, 729 (1963) and 54, 1280 (1964).

19. She authors are greatly indebted to K. Bischoff, Physikalisch-Technische Bundesanstalt, Braunschweig, Germany, formaking this comparison and for valuable discussions.

20. The spectral transmittances of the glass filters were measuredin a Cary model 14 spectrophotometer. Eo(X) was deter-mined in the apparatus described in Ref. 16.

December 1971 / Vol. 10, No. 12 / APPLIED OPTICS 2611