, ,

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RESEARCH DEP.ARTMEUT

PHOTOELECTRIC TRISTIHULUS COLORHIETER

Investigation by:

WoUo Sproson

Report No. T.034

Serial Ho. 1952/16

,Report written byg

W o liT • Sproson

~~,--JO'v /0:.~,~

-------(Wo Proctor Wi1son)

)

FOREWORD

This report is ooncerned with a partioular aspect of a

highiy speoialised subject. It is not 'self-explanatory, and

should be read in conjunction with Researoh Report No. T.027,

or alternati-vely any standard work describing, the C.I'.E.

system of colorimetry, e.g., 'Wright, W.D., liThe Measurement

of Colour", (Adam Hilger, 1944) 0

(Researoh Repo~t No. T.034)

Section

1

2

3

4

5

REPORT llTO. T. 034

PHOTOELEOTRIC TRISTI1UJLUS OOLORlllmTER

Title

INTRODUCTION _ - - - _ _ _ _ _ _ __ _

DESCRIPTION OF THE INSTRUMENT - _ _ _

PERFORMA.1ITCE OF THE COLORHIETER - __ _

~

1

2

3

301 Linearity of Responso - - - - - - 3 3.2 Fatigue and Temperature

Coefficient - - - - - - - - - 4 3.3 Accuracy of Chromaticity

Measurements - - - - - - - - - 4

ATTEMPTS TO CORRECT THE INACCURACIES OF THE COLORITh~TER - ______ _

CONCLUSION - - ____ , _______ _

APPENDIX - - - - - - - - - - - - - -TABLES 1 to 3.

FIGS 0 1 to 9 •

••• ••• 000 .... • ••

5

6

1

r

Research Department REPORT NO. T.034

(Serial No. 1952/16)

, CONFIDENTIAL

July, 1952.

Fig. Nos. 1 to 9.

PHOTOELECTRIC TRISTIMULUS COLORIMETER

A: photoelectric colorimeter is nn instrument which shall replace a visunl co'lorimoter and stp.ndard obsorver. An observer will still be required with the photoelectric instrument, but his function will in the main consist of taking pointer readings - no knowledge is required of his colour vision.

\ '

Since human colour vJ.Sl.on me.y be regarded as substantially tri­chromatic~ the instrument will be required to give three readings for each colour - 'corresponding to the red ,green and blue rosponses of the eye. In setting up an. addi ti ve (visue.l) tricolorimeter any three primaries can be used and the results can be transferred to the standard C .LIt system. It is convenient in practice to use fairly saturated red, greon and blue primaries, because 'relatively small quantities of negative prinaries vdll be required to cover the whole possible colour domain. However, in the case of a photoelectric colorimeter, the three spectral response functions must be theC.I.E. X, y ~nd z curves or linear transformations thereof. No other sot of responses can give correct and unambiguous answers.

There ar,e two possible wiws of achieving an instrument giving x, y r:md z responses

a) by the use of et dispe,rsing' system with threo masks to select the proper intensities at each wavelength,

b) by the uso of throe colour filters in conjunction with a photocell of known spectral response.

The first method is capable of achieving a very high order of accuracy provided the instrumentation is carried out properly. rrho difficul tics lie in the complexity of tp.e apparatus, \since it must contain a prism or diffraction grating dispersing system, also highly stabilised a.mplification of the doc. signals from the photocoll.

The socond method is much simpler, since all that is required

~ Commission Internationale d'l'Eclairago, 1931.

-- -----------~=----;;-------=-,-""="....,..." .--...."..".-"';"'~~~'"

- 2 -

is P_ set of tlJ.ree filtors, a photooell I'1.nd a mioroammeter. Its main dofect is that it is impossible to obtain the desired spectral responses wi th a' high degree of precision. ,The present ,work was undertaken to see whether a, useful and practical instrument of t~is second class could be constructed, also to determine the IJ,ccur(1,cy and reliability.

Before giving (1, detailed d esoription of the instrument we may list the essential roquiremonts8

i) accurate linearity of response (output current vs. incident light flux) 0

ii) zero fatigue and temperature coefficient of the ~10tocell.

iii) the combined spectral rosponses of tho colour filters and tho photocell shall be C.I.E. x, y and z functions (or linear transformations).

iV) the instrument shall have adequate sensitivity for direot measuremonts on a colour television monitor (i,e. peak whi tes of approximp.toly 5 ft .-,lamberts).

2. DESCRIPrION OF THE IUSTRID>mNT

The photoeleotric tristimulus colorimeter is illustrated in Fig.l. It oonsists of

a) the barrier iayer photocell •

. b) a whoe 1 wi th srx filter po si tions mounted in front of the photocoll.

c) the box together ~tith hood - housing the photocell and wheel.

The output'from the rhotocell goes te a mioroammeter giving a full-soale reading with 7'2 mioroR.mps. For greater sensitivity this .' oan be changed for a Cambridge Instrument Company's spot galvo giving full-scale defleotion of 1 microamp.

The instrunent can be easily mounted on an optioal bench or usod wi th a retort stand as support.

The method of using the instrument is as follows3

The instrument is first stl',ndardised by using white light of known colour temperature. The radiation from an N.P.L. standardised

~ Only three filter positions are required for this instrument, the remaining three arc used for otller pm;'poses.

- 3 -

lamp is arranged to fall normally on. to the photocell surface. The photocell currents due to the radiation as modified by passe~e through the X, y and z colour filters in turn' are noted·... Since the chromaticity co-ordinates o'f the. white iight are known , the relative values that these currents should have are also known~ thus the actual current readings may be corrected either by multiplying factors or by the interposition. of neutral filters on' either side of the colour filters. The device having been adjusted so that the three currents are each proportional to the three chromaticity co-ordinates of the known ste.ndard white, an illumination of unknovm chromaticity may be measured by noting the throe current ,readings obtainod by interposing in turn the three coloUr, filters. between the soUrce and the photocell.

The spactrp,l sansi tivi ty of the photocell was determined· using the Unicam spectrophotometer' as a dispersinguni t to produce substantially monochromatic radiations of known relative intensity. Tho result is shovv'u as the broken lino curve in Fig. 2, which also contn,ins data obtn,ined by tho N .P.L. on the sn,me type of colI. The results ofeur men,su.remont are' seen to be net too dissimilar to the N.P.L. measurements •

. The threo colour filters used were Chromex 692,- 693 and 694 -. filtors specially designed to be used with this type of photocell to giv~ good n,ppro:dmations to the 3f, y rmd z responses. Figs. 3, 4 and 5 show the extent to which this is achieved. It will be observed that th<;: experimentally realised y curve. is quite .closo to tho theoretical requirements~ The x curve is most difficult to n,chieve as i·t involves a doublo pe2,k filtor. Tho aGreement hero is only modorate (although it was tho best of about thirty attempts to produce a filter "vi th the required transmission curve). The z curve is fairly good~ improvement in its characteristics might well be possible, but until 2. much better x filter is available, there is no point in improving 'io Incidentally thore is good reason for having 11 good y responso, sinc.e quite apart from tho x and z the instrument can be used as 'a photometer for' comparison of light sources of different·colour temperature, because as is well known the y response is ident:1cal with the standard luminosity (photopic) curvo.

3. PERFORj)jJANCE ciF . THE COLORIMETER

3.1 Linearity of Response

This was tested in applying the inverse square law using a light source of constant output and varying tho distance to the photocell. Fig. 6 shows the results of three sots of readings in which the correction to the actual microammeter reading to giv~ a value con­sistent with the inverse square law is plotted against the. observod

I I

- 4-

reading. Some variationsvdll be not~ced but the error appears to be limited to about 0.7 of a division.

When the highest accuracy is required, observed readings can be corrected inaccordanco with Fig. 6 be,fore being used to calculate a chromatibity. '

3.2 ,~j:~!l!_T_p!ll~~~~~.J __ Q.~~:f..f}~_i..0J'~"t

The photocell definitely suffors from a fatigue effect. Fig. 7 shows the results of continuously irradiating the cell surface with tungsten lighting for over eighty minutes. It is apparent that if ,~ high accuracy is aimod at, then the reading must be taken vdthin one minute of illuminating the coIl, the 0011 being kept in tha dark except for the time taken in actual measurement. If conditions are steady then one minute is very ample time in which to ,take aroading.

Infra-rod radiation is known to give rise 1;0 fatigua effects in some photocells - possible effocts of this kind have been roduced by using a shoet of infra-red absorbing glass. This is permanently in the optical path for all six disk positions. A shoet of ultra-:-violet absorbing filter material is A.lso kept pormanently in tho optical path as the cell has Cl, rather high sensitivity to near ultr~violot light 0

No measurements of the temperature coefficient of the ,cell ,have been taken, but the makers quote a figure of 0.3% perdegroe C. As yet no inconsistencios in the porformanae of the instrument have been traced to, temperature variations. In any caso, the usual procodure is t,ochock the colorimeter 1'I.gainst an N .P.L. standardised lamp either immediatoly before or immediately after a particular measurement, or series of measurements.

3'.3 Accuracy of Chromaticity Measurements

It weuld be possible to calculate from Figs.' 3, 4 and 5, tho errors' which must arise in a chromaticity measurement for any given sp0ctral distribution of sourco or source 'and filter combination, in fact ,a more direct A.pproach was used. This consisted of a measuremont of the chromaticities of a number of colour filters with the photoelectric tricolorimeter and a comparison with theircomputQd values derived from measurements of their spectrophotometric curves~

I Two sories of filters were invostigatod'- the Ilfard spectrum sorios and 8 sot of tricolours and complomentary tricolours. Tho results 'arc shown on th.:l Standard C .LE. diagram in Figs. 8 and 90 Before a series of measurements the instrument was standardisod by the measure­ment of El. v,hi to of known colour temperaturo as indicEl.ted previously,

- 5 -

and the X, Y, Z readings of the tricolorimeter were then scaled to fit the chromaticity of the white point.

The accuracy of the instrument on the tricolours and complement­ary tricolours is seen (Fig. 8) to vary in different parts of the diagram. Since the colorimeter is intended to replace a standard observer operating a visual colorimeter, the desirable accuracy should be at least as good as the discrimination of a human observer. This varies over the colour diagram - or expressed in a different way, the C .LE. diagram is not a uniform chromaticity diagram. In the most critical,region (which is near the spectrum locus in the 380 - 470 m~ ,range) the minimum perceptible chromaticity change for a 20 fiEild is about"O.OO1. :The limiting case for large area comparison might well involve changes as low as 0.0001 for a skilled colour matcher. However, 0.001 is probably a reasonable level of acouracy to attempt. In the green region of the C.I.E. diagram, the minimum perceptible change can be as large' as 0.020.

An examination of Fig. 8 shows that only the yellow chromaticity approaches the desired accuracy. The full results are given in Table 1, which quotes the, luminance Y in addition to the chromaticity co-ordinates x and y. The agreement between directly measured and computed values of Y varies from about 1 per cent upwards. The direct measurement of transiu~ent or transparent colours which trans­mit less than 5% of the incident light becomes very difficult as the chromaticity is deduced from three small readings, none of, which can be taken ~rlth great accuracy. This is particularly so in the case of the spectrum filters (Fig. 9). '

4. ATTEMPTS TO CORRECT THE INACCURACIES OF THE COLORIMETER

The results quoted in Table 1 show that although the instrument gives very approximately the proper chromatiCity (and luminance) of a colour with an integrated transmission of 5% or greater, there is no doubt that a considerablo improvement in its performance is required if it is to replace satisfactorily the standard obsorver operating a visual colorimeter.

Two methodswero attempted to improve the accuracy of the instrument and these are described in some detail in the appendix. The conclusion from these attempts was that good accuracy can be achioved from the instrument only if it is used as a comparator in a substitution measure­ment. To do this tho unknown colour is measured end one, then produces a v~own chromaticity by moans of colour filters and a standard light source which give a similar sot of ratios of readings X g Y g Z.

I, it X for example is the oorrected instrument reading when the x filter

is in the light path.

- 6

Instead of using a tungsten lamp of known chromaticity as' a standard­ising point for the whole of the colour diagram, a standardising point is selected in the region of the unknown colour. This unfortunately takes much more time than the direct method of using the instrument, but it is considered well worth the trouble, particularly as there are some measurements, such Pl.S the determination of the cb.romatic~ty of light sources,for which we have at present no other method availabte in this Department.

As an example of the comparative method, the determination of the chromaticity of Cl. colour temp~rature reising filter is compared with ~ the proper value in Table 3, which gives full details of the calculation. A neutral filter was used with the X and Y values so that the basic conversion factors for X, y'and Z are not too dissimilar. A correction for non-lino1".rity has been applied in f1.ccordance with Fig. 6. The result is seen to be ef quite good accurMY. In practice ono would choose a stA.ndardising point much noaror to the ohromaticity in quostion than is illustrated in Table 3. '

5. CONCLUSION I

The possibility of , constructing a simple :tristimulus photoelectric colorimeter has _ been investigated. Wh~n usod' wi th one centrnl calibrating point, the accuracy is found to vary over the C.I .E. di~gram and to giVG only a rough approximation to the correct chromaticity~ the main reason for the;) 0rrors is the difficulty in securing the correct x, y, z responses with availl?ble colour filters. If more accurate filters could be made, the performance would then be limited by non-linearity of the photocell response, but it is truo to say that these limitations are instrumental rather than fundamental.

A 'comparison method is suggested when results of a high order of e.ccuracy are requirod and when used in this way the colorimoter is a useful and practicr.l instrUITlent. An advantage is that it may be used for the direct measurement' of tho'chromaticity of primary sourceA, such as lf1mps and cathodo ray tubes.

~ - - - - -WJJS/DC

e·

- 7 -

APPENDIX

Let the spectral response of the photocell as modified by the three filters be 11.(/..), B(/..) and C(/..). For the moment we make no assumptions about these three fmlctions.

We wish to measure the chromaticity of an unknown source of illumination whose spectral energy distribution is B(/..).

Then the three instrumental readings will be

,:~oo. .. .,·00 _00

f()..) B()..) " / - ,-

/ E(~) C(~) / E(/..) A()..) d).. , dil. and d)"

~ <"0 \.io

It is desired that these three values (with appro.priate mul tiply­ing factors) shall give the tristimulus values X, Y and Z of the illumination. We shall denote the modified instrumental readings, which are attempts to give the tristimulus values, by XI, yl and Z' •

Thus . r oo J

X' kl / E(~) 1.C;,) d/..

I Vo ..,co

Y' "" k lE(\) BCiI.) d/.. 2 / .

i. /~'OO zr ... k3 I B(\) C(,)~) dA.

~ .... 0

where RI' R2 and R3 are the directly obsorved instrumental rea.dings

and kl , k2 and k3 the multiplying factors.

Now lot us write down the expression for the tristimulus values of the illumination BC/..) as defined by the C.I.E.

- 8 -

" !

f X = i E(?") x.diu

; (,,/

.1i

I Y.c i E(?") Y.d?.

I ....

It is obvious t~a.t if A("1I.) = k4 x, B(iI.) "" k5 Y and C (iI.) "" 1<:6 Z t

where k4 , 1<:5 and 1<:6 . are num7,l'ipal constants.

Then

., X I :. = kl 1<:4 X = kl RI

Y' ... kZ/k5

Y = k2 R2

zr =1<:3 k6 Z = k3 R3

Thus X, Y and Z are directly obtainable from t~e instrumentai readings by multiplying the latter by the factors k' k and k respectively. 4 5 6

In the instrument, an attempt was made to ensure this, but Figs. 3, 4 and 5 show that the result is only a very rough approximation.

There is, however, a more general solution to the problem.

'If A(?") '" k11 x + k12 y + k13 Z

B(\) = k21 x + 1<:22 r + k23 z (

C(\) ::: k31 X + 1<:32 y + k33 Z whero the kij's arc positiv~ numerical constants

".'. "

- 9 -

Then / "

X' f

~ 1 kl ! B(\) x + k12 Y +k13 z dll. f

Ll~ I I

i -!

similarly

Vfuenoe it is olear that' X Y Z oan be expressed preoisely and unambiguously in terms of X' Y' and Z' by a related nine ooeffioient system of equations.

Thus X "" mll X' + ml2 yl + ml3 Zt

Y = m21 X' + m22 Y' + m23 Z'

Z ""'m 31

X,, + m32

Y' + m33 ZI

where the m .. I S are numerical constants whioh can be written down, if required~Jin terms of the previous k

l, k

2, k3 and kij'so

The first of the two methods whioh a+.tempt to improve the accuraoy of the, oolorimeter, utilisos this more general solution., It is striotly valid only if theourves shown in Figs. 3, 4 and 5 are linear transform3.tions of the true x, y and z funotionso' Al though this was not thought to be so, it was oonsidered worth a trial to compute the nine ooeffioients for the case of the three trioolours. The resulting set of equations is ~

X O.9282X' + 0.2005Y' - 0.106lZ'

Y = 0.0337X' + 1.007Y' - O.Ol48Z'

Z = - 0.0165X' - 0.0289Y' + 0.9435Z'

Sinoe we have attempted the simplest type of solution, the diagon[>'l coeffioients should be unity and the others zero. The above equation can be regarded as indioating the extent to which yvohavo suooeeded in achieving the desired x, y and z rosponses. Thus X requires the largest corrections, Y is fairly good and Z requires an intermediato amount of correotion. This qualitatively agrees with the deviations shown in

,-

- 10 -

Figs. 3, 4 and 5.

If we 'use this set of -equations to compute the known whi tp point, an approciable error is introduced and we see that in effect we have succeoded in correcting the corners of the rod-green-blue triapgle at the expense of the centre. The results are quoted in Table 2, which shows the effect of recalculating the chromaticity of the complementary tricolours as well as the whito point. No improvement is achieved -on balance, the accuracy may in fact bo slightly inferior. Tpese calculations show that the performance of the colorimeter cannot be substantially improved by this somewhat more complicated way of ~ dealing wi th the results. . ..

The second method is based on the results of the chromaticity measurements of the spectrum series of filters. The idea was to .provide a second order correction factor which is read off on a graph vdth the apparent hue as ,abscissa. The apparont saturation was ",Iso taken into' considoration. In this way, the whi to point of the diagram is unaltered. However, the ~pplication of this purely empiricp.l mothod to correct some practical results showo,d the."Ii it w",s of no value.

vmS/DC

TABLE 1

"

'Series Filter Colour No.

Tricolours' W26 Red

W58 Green

W48 Blue

Complementary 302 Cyan Tricolours

Tristimulus Oolorimeter

x x.. y

0.685 0.281 19.4

0.215 0~696 23.5

0.185 0.061 0.80

503 Magenta 0.629 0.221,1l.2

110 Yellow

Spectrum 601 Violet Filters

0.253 0.006 0.02

602 IllUG 0.189 0.074 0.12

603 Blu.e- 0.093 0.413 0.63 green

604 Green' 0.022 0.911 1.76

605 Yo11ow- 0.276 0.677 0.93 green

606 Yellow 0.566 0.429 2.80

607 Orange 0.659 0.339 4.97

608 Red 0.741 0.192 2.44

609 Deep red 0.683 0.128 0.44

Rc,port No. T.034

S£ectr0I'h.otometri~ Measurements

x x.. Y

0.7004 0.2996 16.2

0.3069 0.6614 23.3

0.1247 0.0902 0.98

0.1647 0.3935 22.2

0.5907 0.2493 12.7

0.5374 0.4583' 78.4

0.1590 0.0164 0.07

0.1150 0.0926 0.14

0.0412 0.4554 0.53

0·1l42 0.7937 1.61

0.3392 0.6549 0.97

0.51:35, 0.4855 2.85

0.657 0.343 5.61

0.7224 0.2776 2.58

0.7324 0.2676 0.66

TABLE 2 RepodNo ~. T .034,

Filter Colour ~eot1y Measured "Correoted" ~ 9 a,oaff. E.9..uati..£!:,. !2..

x Y z x Y z

Whit: 109.8 100.0 35.6 0.448 0.407 118.2 103.9 28.9 0.4710.414

110 YeJ,low 90.1 77 .2 2.0 0.532 0.456 98.9 80.7 -1.8 0.556 0.454

503 Magenta 31.9 il.2 7.6 0.629 0.221 31.0 12.2 6.3 0.626 0.246 e 302 Cyan 10.6 24.9 '25 .. 4 0.174 0.409 12.1 25.0 23 .. 1 0.201 0.415

Fil ter ' Colour 90mputed from S~ectroEhotometric Curve No.

X Y Z x if.. -110 Yellow 91.91 18~39 0.74 0.5374 0.4583

503 Magenta 30.17 12.73 8.17 0.5907 0.249:3

302 Cyan 9.31 22.25 24.97 0.1647 0.3935

ii White is the oalibra1iing point '(2848(,K)

.'

TABLE 3 Report No. T.034

I Actual Measurements

o Calibration vtithlcnown light source of 2700 K. Microammeter Read.ings

,,~ y" Z .t~

1st set .... · .. • •• . . . · .. · .. 77.7 / 94.0 31.8 2nd set .... • •• ••• " ... • •• • • 0

17 .8 93.9 31.7

Measurements on unknown chromaticity (2700° K lamp + 0.464 CTR 1st set . . . • •• ••• .. .. • •• o •• 32.6 42.1 22 .. 4 2nd set • • • .... ••• • •• • •• • •• 32.8 42.3 22.1

n Calculations

III

a) Correction for non-linearity as per Figure 6 - mean values. o

2700 K source ••• ••• .... ••• 77.75 o 2700 K source +0.464 CTRfiltor 33.4

93.95 42.8

32.45 23.25

b) Determigation of correction factors to fit standard 2700 K source vdth Y value made equal to 100.

o 2700 K source 82.76 100.0

~Since true values for a 27000 K source ar08-

111.98 100.0

Corroction factors are 1.353 1.000

34.54

31.72

0.918

Using these factors on the experimental results (corrected for non-linearity) we qbtain

45.2 42.8 21.8 I \----.,....-----" 'ro.tal 109 .. 8

Rence trichromatic co-ordinates of the 27000 K source and 0.464 CTR filter are

0.390 0.198

Y value is 42.8/93.95 ~ 45.5%.

Comparison with Chrom1'..ticity Derived ~- - from Spectrophotometrz

Colorimeter •••••• ," •••• Computed value •••••••••

2S. :LX 0.412 0.390 '45.5% 0.407 0.395 45.3%

filter)

~ X and Y readings vYoret.'1.k:en wit]:l a 0.4 noutrnl density filter in front of the colorimeter ,'Z ha:iriilg no extra filter.

1 1 - 10- 51

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FIG.l GENERAL ARRANGEMENT

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LIGHT FLUX OF UNKNOWt

CHROMATICIT

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ACTUAL READING

FIG.6 EEL LINEARITY CORRECTION CURVE

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FIG.7 FATIGUE EFFECT

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