Degree of Applicability and Consequences ofInappropriate Use of Units of Light

JoAnn S. Kinney

Since light is defined quantitatively as radiant energy evaluated according to the CIE photopic luminositycurve, ordinary light units are inappropriate whenever the organism's spectral sensitivity differs mark-edly from the CIE curve. Examples of differing spectral sensitivities include those of animals, of colordefective individuals, and curves for all individuals under low light levels or with large fields. Calcula-tions are presented of the amount of error involved when units of light are used for these inappropriateconditions; alternative solutions to the problem are discussed.

Most individuals in today's world probably realizethat light represents a portion of the electromagneticspectrum to which human beings are sensitive and thatit differs only in this respect from other general classesof energy such as x rays, uv, or radio waves. The factthat light is specifically and mathematically definedwith respect to human sensitivity is less well known andthe implications of this statement for the measurementof light probably have been considered by very fewindividuals indeed. This paper discusses the conse-quences of the definition of light for the measurementof light, specifically the errors introduced when the de-fined conditions are violated in the measurement.

Light is defined generally as radiant or electro-magnetic energy which has been evaluated accordingto the spectral sensitivity of the human eye. Mathe-matically represented, light is thus:

r70 0

K PxVxdX, (1)J400

where Px is a measure of the radiant energy or power ateach wavelength, in ergs or watts, etc., and V, is photo-pic luminosity curve standardized in 1924 by the Com-mission Internationale de L'Eclairage.

The results of this integration of energy and visi-bility, when multiplied by appropriate constants, yieldthe ordinary light units such as the foot-candle, milli-Lambert, or lumen per square meter.

The definition of light as a quantity not completelywithin the realm of physics, nor as a psychologicalresponse, but both-thus a psychophysical unit-isunique. Stimulus measurement in the other sense

The author is with the Naval Submarine Medical Center, NavalSubmarine Base New London, Groton, Connecticut 06340.

Received 14 June 1967.

modalities has generally been i terms of the physicalunits of the stimulus. However, this procedure leavesunanswered the question of whether a given physicalquantity will be perceived, since within each modalitythere is always a restricted range of possible physicalvalues to which the human being is sensitive. Thus.the stimuli for the sense of taste are measured in thephysical units of the chemist and one must be familiarwith the literature relating these to taste sensations toassess whether a particular quantity could be tasted or-not. Within audition, where a situation of differentialsensitivity to frequency analogous to the visual exists,the most common units of sound are ratios of energy orratios of pressure. These units are basically physicalwith the small concession to the psychological that thereference energy may represent the auditory threshold.

While the definition of light as a psychophysicalquantity was probably a historical accident, stemmingfrom the measurement of candlepower long beforeelectromagnetic energy was understood, it has severaldecided advantages. The stimulus for vision can bespecified by one number rather than the complete setof spectroradiometric values that would be required fora radiant energy specification. Furthermore, numer-ical equality implies equality of sensation, a fact thatnever could be inferred from the energy data alone.Finally, other things being equal, there is a monotonicrelation between light units and sensations of bright-ness.

Along with the numerous advantages which accrueto this system of specifying light, there are, of course,inherent disadvantages. Of major importance is thefact that the definition of light applies strictly to thecases in which the subject has the same spectral sensi-tivity as that specified according to the CIE 1924 data.i\'Jost of the problems or errors of measurement ariseout of the use of the CIE luminosity curve in situations

September 1967 / Vol. 6, No. 9 / APPLIED OPTICS 1473.

Table I. The Relative Luminance of Different Color Tem-perature Sources Calculated for Subjects Whose SpectralSensitivities Are Constitutionally Different from the CIE

Photopic Luminosity Curve

Color temperature

Condition 2042 0 K 2998 0 K 6486 0 K

CIE light unit 1.0 1.0 1.0Color defective subjects

Protanope 0.678 0.781 0.915Deuteranope 1.008 0.960 0.901

Possible corrections toCIE curve

100 Field size 1.039 1.057 1.099Judd's short wave-

length correction 1.001 1.002 1.007

u,U,aa0-C

U).!_

0-J

2000 3000 4000 5000 6000 7000Color Temperature

Fig. 1. The scotopic luminance increase over the 20420 Kstandard for various color temperature sources that are photopic-

ally equal. 9

to which it is not applicable. In other words, the sub-ject's spectral sensitivity is not the same, for one reasonor another, as the CIE V curve used for the definitionof light.

There are, of course, a number of organisms, which, forgenetic reasons, possess spectral sensitivity differentfrom the standard CIE curve. Such a statement prob-ably applies to most infrahuman animals, invalidatingthe use of light units for many experimental purposeswith animals. However, this fact seems to be rathergenerally recognized; numerous investigators attemptto determine brightness equivalents behaviorally fortheir animal subjects before using light as an experi-mental variable.

Certain human beings are likewise equipped con-stitutionally witl different spectral sensitivities. Mostnotable are the protanopes, the color defective in-dividuals seriously insensitive to the longer wavelengthsof radiation. Other color defective individuals, deuter-anopes and tritanopes, may also display sensitivitiesdistinct from the OIL, but to a lesser extent.

Still smaller variations are found in the population ofcolor-normal individuals. Since the CIE curve is anaverage of the data for a larger number of individuals,it is highly unlikely that it will apply precisely to thesensitivity of any one given individual. Such normalvariation is of little importance in most practical situa-tions. There are, however, some instances requiringprecise measurement for which it is necessary tospecify a given subject's spectral sensitivity rather thanuse the norm.

It is possible to assess the importance of these genet-ically determined spectral sensitivities by comparingvalues of light, determined on the basis of the CIEcurve, with those calculated using the spectral sensi-tivity curve appropriate to the given individual. Thishas been done for three different color temperaturesources in Table I for protanopes, using Pitt's data,2 andfor a deuteranope 3 at our laboratory for whom we havespectral sensitivity data.

If there were only one source of energy available toproduce light, problems arising from individuals withdifferent spectral sensitivities would be minor and couldbe corrected by the use of a simple constant. Thetroublesome errors of measurement arise in evaluatingthe effectiveness of different spectral distributions ofenergy for different individuals, since some distributionsmay be more effective in producing light and others lesseffective than for the normal subject.

NE

B1

Ir3

I

Ld

Fig. 2. Spectral sensitivity of the 10° periphery as a function ofintensity level."

1474 APPLIED OPTICS / Vol. 6, No. 9 / September 1967

_ ~ ~ ~~~0~~~~~

.1 .01 .001 .0001 .00001

LIGHT LEVEL Mf-L)

Fig. 3. Increase in luminous efficiency at different photopicallydefined light levels for various color temperature sources:6486'K (X); 5489'K (); 4491°K (); 2998'K (); 238°K(+). The value in ft-L times 3.426 yields the value in cd/ml.

This is illustrated in the values in Table I; comparedwith the normal subject, a distribution of 2042°K isslightly overevaluated for the deuteranope and seriouslyunderevaluated for the protanope. Distributions ap-proximating daylight on the other hand are under-evaluated for both types of color defective subjects.

Calculations for two other unusual conditions areincluded in the table. The first is that the spectralsensitivity displayed by normal subjects for largevisual fields is somewhat different from that for thesmaller, 2 field specified by the CIE curve. The CIEis currently considering a specification for a 10° curve4which could be used in place of the 2 curve if the ap-plication warranted it. Calculations of relative lumi-nance based on this provisional, 10° luminosity curve, inTable I, show that some slight differences would ensue.The difference is largest for the daylight source sincethe major distinction between the 2 and 10° curves isheightened sensitivity to the short wavelengths for thelarger field.

Second, during the course of the more than fortyyears since the adoption of the standard curve by theCIE, it has been noted that there are a number of minorinaccuracies in the original curve. These are welldocumented by now'-' but are of more theoretical thanpractical interest. The largest single discrepancy is anunderevaluation of sensitivity to the extreme short endof the spectrum, particularly for young subjects; in1951, Judd proposed new values to correct for this.'Calculations based on his values are also included inTable ; compared to the size of other errors con-sidered here they are of minor importance.

The factors considered thus far yield errors of mea-surement that become insignificant in size compared withthe effects which can be produced when ordinary lightunits are employed under environmental conditions forwhich they are not applicable. This refers, of course,to the fact that the curve used to specify light is a day-light or photopic curve and applies only to foveal, light-adapted vision. If the light is viewed peripherally,by a dark-adapted eye, or at an intermediate illumina-

tion level, the photopic curve cannot be used and thecurve appropriate to the specific conditions should besubstituted instead. This fact becomes doubly im-portant when it is considered that it applies to everyoneand not just a limited percentage of the population.

A number of years ago I suggested that the seeminglywide range of absolute thresholds for night visioii foundin the literature was probably an artifact owing to theuse of photopic light units in order to assess the thresh-olds.9 Calculations of the size of the effect for variouscolor temperature sources were made at that time andare reprinted in Fig. 1. Two sources equated photo-pically, thus having the same foot-candle (or meter-candle) value, may be of very different intensity at thescotopic level; a daylight source of 6486'K is 2.5 timesas intense, or 0.4 log unit greater, than the standard20420 K source.

The procedure for calculating scotopic luminances isnow well established; the CIE has standardized ascotopic luminosity curve, has specified the 2042'Ksource as having unit luminance at photopic andscotopic levels, and scotopic luminances can now becalculated in a manner completely analogous to thosedone for the photopic system."

The remaining, rather thorny question, concerns theintermediate or mesopic intensity levels at whichneither the photopic nor the scotopic curves completelyapply. Figure 2 shows the type of curves obtained atlevels between scotopic and photopic thresholds, for a 20field located at 10° in the periphery." In this region,the state of adaptation, the absolute intensity level, andthe retinal position are of major importance in deter-mining the spectral sensitivity curve obtained. In the100 periphery there is an almost continual shift inspectral sensitivity from the purely scotopic curve atthreshold in the direction of the photopic curve; how-ever, even at fairly high light levels, the purely photopiccurve is not obtained." For a large retinal area whichincludes the fovea, the shift is complete by approxi-mately 0.1 ft-L (0.34 cd/m); the curve obtained is thesame as the 10° CIE photopic curve.' 2 For a 20 fovealfield, of course, the scotopic curve is never found.

Obviously the use of either photopic or scotopic lightunits in this region will yield errors under certainconditions, the size of the error depending, once again,on the spectral distribution of the source. One possi-ble solution is to calculate the luminous efficiencies forvarious sources using the appropriate spectral sensi-tivity curves. These efficiencies, when compared withthe photopic value, yield the amount of error introducedby the use of the inappropriate photopic curve.

Figure 3 is a sample of such calculations utilizingspectral sensitivity data obtained with a 20 field locatedat 100 in the periphery." All luminous efficiencieshave been calculated relative to 1.0 (log unit iiicrease0) for 20420K. Since the major difference in the spec-tral sensitivity curves is a shift toward the shorterwavelengths as intensity is reduced, the resulting familyof curves shows the greatest increase in efficiency, or

September 1967 / Vol. 6, No. 9 / APPLIED OPTICS 1475

Table II. Relative Luminous Efficiencies for Various ColorTemperature Sources in the Mesopic Region

Color temperature

Condition 20420K 29980 K 6486'K

20 field1.0 ft-L (3.4 cd/in') 1.( 1.0 1.00.1 ft-L (0.34 cd/ml) 1.0 1.002 1.0240.ol ft-L (0.034 d/m) 1.0 1.059 1.201

100 field1.0 ft-L (3.4 cd/ml) 1.0 1.017 1.0580.1 ft-L (0.34 cd/m) 1.0 1.045 1.1610.01 ft-L (0.034 cd/m) 1.0 1.172 1.549

Scotopic threshold(CIE curve) 1.0 1.524 2.512

greatest relative error, forsources.

the higher color temperature

It is obviously impractical to attempt such a solutionfor the myriad number of conditions under which lightsmight be viewed in the itensity range below photopicvision. However, specific conditions could be selectedand specified as standards for the mesopic region.*

Table II shows aii example of this type of solution.Calculations of the relative luminous efficiency of variouscolor temperature sources have been performed for twocentrally viewed field sizes, 2 and 100 at differentlight levels. The spectral sensitivity curves upon whichthe calculations are based were obtained under thesespecific conditions with the eye completely adapted tothe light level in question. ' 2 " All luminous efficienciesare relative to the 20420 K source whose efficiency isdefined as 1.0. Errors introduced in the mesopicregion by different sources are relatively small for the20 field size. The increasing sensitivity of normalsubjects to the short wavelengths, found for the 100field as the light level is reduced, begins to show a

* This solution is based upon the assumption that the integra-tion of energy and luminosity (or the area under the curve) will befunctionally related to the perceived light intensity at the mesopiclevels, just as it is for photopic and scotopic vision. While such anassumption certainly seems reasonable on the surface, there is onecomplication: at either photopic or scotopic levels, only one systemof receptors is involved, while in the mesopic region, the spectralsensitivity curve may be determined by the rods for one region ofthe spectrum and by the cones for another. Thus, for the integra-tion of spectral sensitivity and energy to be effective in the mes-opic region, we must assume that activity from rods and conessummate in the response to white light. The empirical verifica-tion of this assumption obviously deserves careful study. Whilesuch an investigation is beyond the scope of this paper, I havemade a few empirical checks. Subjects compared the brightnessof a 2042 0 K source with that of a 6486 0 K source in a 100 field atdifferent mesopic light levels; comparisons of the empirical andcalculated ratios were then made. The data were insufficient tomake any statement other than no gross error was indicated. Asimilar empirical verification is presented by Yurov for three dif-ferent energy distributions in the progress report of Comm. 1.4.1of the CIE (see Ref. 13, pp. 214-215).

sizable increase in luminance for the higher colortemperature sources.

Calculations such as this could be performed, assum-ing appropriate spectral sensitivity data were available,for certain discrete steps and for certain defined condi-tions throughout the range of mesopic and scotopicvision. The advantage is, of course, that, once done,appropriate corrections could be applied to the photopicunits of any light source to predict its efficiency atlower levels.

A second alternative is to specify mesopic luminanceswith respect to a visual match to a standard. Thissolution, currently under study by a working com-mittee of the CIE, has the following features: (1) Theconcept of equivalent luminance is established and de-fined as "the standard luminance of another field whichhas the color temperature of 20420 K and which, inparticular photometric conditions seems to be equallybright to the first field". (2) The "particular photo-metric conditions", i.e., the field size, retinal position,state of adaptation, method of making the visual ob-servations, must be carefully specified and adhered to,for these are the essential operational characteristicswhich influence mesopic light measures."

This solution, too, would have a number of ad-vantages. The system can be used for any light byspecifying its visual equivalence. Thus, the layman

Table Ill. Relative Luminance of Different WavelengthsCalculated for Subjects Whose Spectral Sensitivities Are

Constitutionally Different from the CIEPhotopic Luminosity Curve

Wavelength (mu)

Condition 450 520 580 650

CIE light unit 1.0 1.0 1.0 1.0Color defective subjects

Protanope 2.105 1.267 0.701 0.093Deuteranope 0.737 0.591 1.137 1.290

Possible corrections toCIE

100 field size 2.355 1.073 0.998 1.006Judd's blue correction 1.232 1.000 1.000 1.000

Table IV. Luminous Efficiences for Various Spectral Sourcesin the Mesopic Region Calculated Relative to a Luminous

Efficiency of 1.0 for 20421K

Wavelength (mg)

Condition 450 520 580 650

20 field1.0 ft-L (3.4 cd/m) 1.0 1.0 1.0 1.00.1 ft-L (0.34 cd/m) 1.652 0.997 0.997 0.9970.01 ft-L (0.034 cd/m) 7.233 1.131 0.777 1.087

100 field1.0 ft-L (3.4 cd/ml) 2.267 1.033 0.960 0.9680.1 ft-L (0.34 cd/m2) 6.918 1.184 0. 834 1.0810.01 ft-L (0.034

cd/M2) 16.891 1.374 0.737 0.599Scotopic threshold 30.624 3.366 0.355 0.012

1476 APPLIED OPTICS / Vol. 6, No. 9 / September 1967

need not worry about whether or not the light level inquestion is within the range of photopic, mesopic, orscotopic vision. If, by chance, it lies in the photopicrange, the luminance of the unknown field, the standardluminance, and the equivalent luminance would all benumerically the same.

Thus far the discussion of the problems involved inthe measurement of light has considered only themeasurement of white light, i.e., various continuousdistributions of spectral energy which do not departtoo markedly from subjective neutrality. The mea-surement of nonselective radiations does constitute themore important practical task since these are the dis-tributions most available, either commercially ornaturally.

However, there are many lighting applications inwhich selective radiations such as fluorescents, arc lights,and light reflected from a variety of colored materialsor surfaces must be measured. All of the possiblereasons for the inapplicability of the CIE photopicluminosity curve apply as well to the measurement ofselective radiations, but the inherent error is usuallymany times magnified. It is a useful generalizationthat the closer to an equal energy spectrum a givenenergy distribution comes, the less the chance for mea-surement deviation; conversely, the measurement ofspectral radiations allows for gross errors if specifiedmeasuring conditions are violated. For example, cor-recting the CIE photopic luminosity curve in the shortwavelengths makes little difference to the measurementof continuous distributions. If, however, the applica-tion involved a source of violet light, correcting for thisso-called insignificant error could easily change thelight measurement by a factor of five.

Tables III and IV give the calculated luminances fora number of sample conditions involving inappropriateuse of the CIE curve for four spectral lights. Varia-tions occur both in the direction and magnitude, be-coming more extreme as the ends of the spectrum are

reached. The effects of bumps and other irregularitiesin the sensitivity curves are also apparent in the cal-culated luminances.

It should be noted that very similar types of errorsare found when using photocells to measure light fromspectral or highly selective sources at the ends of thespectrum. While most commercial instruments doan excellent job of duplicating the CIE luminosity curvethroughout most of the spectrum, it is extremely diffi-cult to match exactly the tiny values required on eithertail. A difference in spectral sensitivity between 0.02and 0.04 will go unnoticed on the linear graph of theinstrument's spectral response and will likewise makeno difference to the accuracy of measurement of whitelight. If measuring violet or red wavelengths, however,the error involved is likely to be intolerable, even forthe most casual application.

References1. Y. Hsia and C. H. Graham, in Vision and Visual Perception

C. H. Graham, Ed., (John Wiley & Sons, Inc., New York,1965), pp. 402-403.

2. F. H. G. Pitt, Med. Res. Council, Spec. Rept. Ser. No. 200(1935).

3. J. A. S. Kinney, J. Opt. Soc. Am. 57, 1149 (1967).4. CIE, Compt. Rend., 14th Session, Bruxelles, 1959 (Central

Bureau of CIE, Paris, 1960), Vol. A, p. 95.5. Y. Hsia and C. H. Graham, Proc. Natl. Acad. Sci. (U.S.)

38, 80 (1952).6. L. C. Thompson, Proc. Phys. Soc. (London) B62, 787 (1949).7. H. R. Blackwell and 0. M. Blackwell, Vision Res. 1, 62

(1961).8. Report of the Colorimetry and Artificial Daylight Commit-

tee, CIE, 12th meeting, Stockholm, 1951 (Central Bureau ofCIE, New York, 1951), Vol. I, Tech. Cmtte No. 7.

9. J. A. S. Kinney, J. Opt. Soc. Am. 46, 1093 (1956).10. L. E. Barbrow, J. Opt. Soc. Am. 41, 734 (1951).11. J. A. S. Kinney, J. Opt. Soc. Am. 48, 185 (1958).12. J. A. S. Kinney, J. Opt. Soc. Am. 54, 671 (1964).13. CIE, Compt. Rend. 15th Session, Vienna, 1963 (Central

Bureau of CIE, Paris, 1964), Vol. B, p. 216.

This column is compiled partly from information sent in by APPLIED OPTICS Reporters in various centers of opticsacross the world, but the Editorial Consultant welcomes news from any source. It should be addressed to

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CI[

The Commission International de l'Eclairage, better knownin the States as the International Commission on Illuminationor the CIE, was founded in 1913 as an organization devoted tointernational cooperation in all phases of illumination and to es-tablishing international agreement. Essentially a technicalbody, with a large percentage of its membership being scientistsand academics in both the research and evaluation fields, anever-growing number of members is now coming from the area oflighting practice. Membership in CIE is by countries ratherthan individuals, each of the member countries having a NationalCommittee whose work is under the direction of locally electedofficers. Currently, twenty-six countries have National Com-mittees, and in addition, twelve smaller countries are Associates

September 1967 / Vol. 6, No. 9 / APPLIED OPTICS 1477