JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

An Interpretation of the Bril Scale of Subjective Brightness*

WALTER C. MICHELSBryn Mawr College, Bryn Mawr, Pennsylvania

(Received September 23, 1953)

The bril scale, obtained from extensive experimental data by Hanes, represents an attempt to establisha subjective scale of brightness by the determination of particular luminances which produce specific ratiosof brightness. This scale, like other scales obtained from fractionation data, necessarily assumes a one-to-onecorrespondence between intensity of stimulus and magnitude of response-an assumption in conflict withknown facts regarding adaptation.

It is shown that the reformulation of the Fechner law proposed several years ago, aided by results obtainedfrom rating-scale techniques, can predict quantitatively all of the data used for the construction of the brilscale. Since this theoretical treatment takes explicit account of adaptation, it follows that each of the ratiosdetermined by fractionation techniques has meaning by itself, but that the combination of these ratiosinto a scale of wide range is not justified. The fallacy involved in such combination is the assumption thata given stimulus is psychologically equivalent to itself when it is presented under different conditions, and,therefore, under different states of adaptation.

1. INTRODUCTION

IT has become increasingly clear in recent years thatFechner's law, with its concept of the just noticeable

difference as a unit of measure and with its constantof integration fixed by the absolute threshold, is not asatisfactory statement of the relation between theintensity of a stimulus and the magnitude of theresponse. Two distinct approaches have been used inthe attempt to arrive at a satisfactory substituteformulation. In one of these, the response is expressedon a rating scale (e.g., very bright, bright, medium, dim,very dim) and ordinal numbers are assigned to thecategories of this scale. Experimental work along theselines has shown that the ratings are made relative to avariable intensity, determined by the conditions ofobservation and known as the adaptation level. Thesecond approach attempts to establish "ratio" scalesby a process of psychophysical fractionation. Anobserver, for example, is shown a light source of knownluminance, and is asked to adjust a second sourceuntil it appears one-half (or some other multiple) asbright as the standard. By successive applications ofthis technique, one can supposedly determine lumi-nances which correspond to any specified ratio ofbrightness.

In the field of vision, the ratio scale has been studiedvery carefully by Hanes.' Using ratios of , , 2, and 3,he has established the bril scale of subjective brightness.His relation between the brightness B and the lumi-nance L can be expressed, to a fair degree of approxi-mation, by the equation

B=constL L 0 3,,(1)in the range of L from 0.01 to 100 millilamberts. Onthe other hand, the present conclusion of the ratingscale work is that a functional relation between B and Lcan be written only for a limited range of luminance

* A preliminary report of this work was presented to the OpticalSociety of America at the Rochester meeting on October 15, 1953.

1 R. M. Hanes, J. Exptl. Psychol. 39, 719 (1949).

(about a hundredfold), and that it can be expressed,if the rating scale is appropriately chosen, by theequation

B=Bo+K' loge(L/A'), (2)

where Bo and K' are determinable functions of thenumber of categories in the rating scale and A' is theadaptation level.2 Since A' depends on the recent pastexperience of the subject and on the luminances of allparts of the field, Eq. (2) does not specify as definite arelation between L and B as does Eq. (1).

Equations (1) and (2) are so different, in both theirforms and their implications, that it is important thatthey be reconciled. Both are based on good experimentalevidence; the only hope of a reconciliation lies in anexamination of the theoretical considerations whichare used to combine the data into the relations givenpreviously. The chief difference in principle betweenthe two approaches is that Eq. (1) can be obtainedand has meaning only if there exists a one-to-onecorrespondance between stimulus and response, whereasEq. (2) implies that no such relation holds and thatthe response depends not only on the stimulus but alsoon the conditions of observation and on the pasthistory of the observer. It is the purpose of the presentpaper to show that all of the data used to obtain Eq. (1)can be explained quantitatively by the use of adapta-tion-level theory, and that the bril scale is thereforeneither a necessary nor a legitimate conclusion fromthese data.

2. THE REFORMULATED FECHNER LAW

The concept of adaptation level was used severalyears ago to develop a modified form of the Fechnerlaw.2 Because this and subsequent work, on whichthe present treatment depends, has appeared only inpsychological journals, a brief resum6 may be worthwhile.

The assumptions which underlie the treatment apply

2 W. C. Michels and H. Helson, Am. J. Psychol. 62, 355 (1949).

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VOLUME 44, NUMBER JANUARY, 1954

BRIL SCALE OF SUBJECTIVE BRIGHTNESS

not only to brightness judgments but also to judgmentsof the intensity of any stimulus. They are:

(1) The Weber law is valid within sufficiently broadlimits to be applicable.

(2) The judgment "neutral" or "medium" belongsto the stimulus L= A, where A is the adaptation level.

(3) The judgment scale and the stimuli encounteredare equivalent in the sense that the scale is broadenough to include judgments of all the stimuli en-countered and yet is so narrow that its extreme valuesdo not fall outside the range of judgments elicited byany of the stimuli.

(4) When an observer adjusts his responses to aseries of 2N+ 1 properly chosen categories, symmetri-cally placed about "neutral," he does so by choosing asthe first step below "neutral" the response correspond-ing to a stimulus of intensity (1- 1/N)A. In otherwords, he responds as if he had divided the stimulus Ainto N equal parts and had used all but one of thesefor his first step below "neutral."

(5) In forming his judgments, the observer can makecomparisons only in terms of his judgment scale. Thismeans that all subsequent steps will have the samesize on the judgment scale as the first step and thatthe adaptation level will be determined by a mean ofjudgments rather than by a mean of stimuli.

These assumptions have not, in general, been justifiedindividually; the successes of the theory in correlatingquantitatively a wide variety of psychophysical dataare their justification.

It follows rigorously from the assumptions of thepreceding paragraph that a stimulus L will evoke ajudgment J, expressed as the ordinal number of thecategory used to express the intensity, and runningfrom zero to 2N:

whereJ=N+K log(L/A),

K=-1/loge(1-1/N),

and A is the adaptation level. This quantity, in turn,is a weighted geometric mean of all stimuli, past andpresent, which may affect the judgment. These may begrouped, for convenience, into three categories, thefirst containing the stimulus L being judged, thesecond all other stimuli present in the field of view atthe time of judgment (i.e., the background), and thethird containing all stimuli experienced in the past(i.e., residuals). Assigning the respective weights p, q,and r to these three classes, and denoting the meanbackground and residual stimuli by Q and R, we maywrite

logA = p logL+q logQ+r logR.

For present purposes, we may group the last twoclasses of stimuli together to obtain

logA = p logL+ (1-p)logA', (5)

where A' is the weighted geometric mean of all back-ground and residual stimuli. Substitution of this valueof log A into Eq. (3) gives

f=N+K' 1oge(L/A'),where

K'= (1-p)K.

(6)

(7)

The weighting factor p is known as the self-adaptationcoefficient.

Equations (4) and (6) have been subjected to exten-sive experimental tests.3 The logarithmic relationbetween L and J, the dependence of K on N, and thedecreased value of the observed slope resulting fromself-adaptation have all been verified to the accuracyof the psychophysical data. We may, therefore, have afairly high degree of confidence in the validity of theassumptions on which the theory is based.

Experiments of the type used to establish the brilscale are not amenable to direct analysis by the use ofEq. (6), since they involve comparative judgmentswhereas the original theory deals with "absolute" judg-ments. Recently, however, the reformulated Fechnerlaw has been extended to comparisons.4 The argumentwhich allows this extension is that absolute judgmentsare made relative to the adaptation level; hence, wecan expect that comparative judgments will be maderelative to a comparative adaptation level, in thedetermination of which the standard offered theobserver will play a large part. The adaptation level Aof Eqs. (3) and (5) may be replaced by the comparativeadaptation level Ac, defined by the relation

logA, = s logS+ (1-s)logA, (8)

where S is the physical intensity of the standard.Equation (6) then is replaced by

J,=N+K' log6(L/A.), (9)

where J, is the magnitude of the comparative judgmentexpressed on a scale such as much brighter, brighter,equal, dimmer, much dimmer.

The success of Eqs (8) and (9), both in treatingcomparative judgment data4 and in explaining theorigin of time-order errors,5 gives new support to thereformulated Fechner law and therefore encourages oneto attempt its application to psychologically deter-mined "ratio" scales. A forthcoming article shows thatdata leading to the beg scale of apparent weight arecompletely consistent with Eqs. (8) and (9).6

3. APPLICATION TO THE BRIL SCALE

In his work on the bril scale, Hanes presented hisobservers with two light sources, each subtending anangle of about 4' degrees at the eye, and separated

3 E.g., see M. C. Nash, Am. J. Psychol. 63, 214 (1950).Helson, Michels, and Sturgeon, Am. J. Psychol. (to be pub-

lished).5 W. C. Michels and H. Helson, Am. J. Psychol. (to be published).6 W. C. Michels and H. Helson, Am. J. Psychol. (to be pub-

lished).

71January 1954

WALTER C. MICHELS

1000

a

100E

. 10.E

C I

0._0'

J 0.1

-J 0.01

) _

= 1/3

0.001 0.1 10 0o00Sfandord luminance S millilumberts)

FIG. 1. Luminances judged to yield brightnesses which arefixed multiples of the brightness of a given standard. The centercross marks on the vertical bars represent the mean luminancesjudged to be t times as bright as the standard, according toHanes, and the lengths of the bars indicate the standard deviationsof these means. The solid lines are plots of the predicted lumi-nances, according to the reformulated Fechner law.

by about 13 degrees, center to center.' One of these wasmaintained at a standard luminance, and the observerwas asked to adjust the other until it was one-third,one-half, twice, or three times as bright as the standard.The results obtained from the averaging of eightobservations by each of 24 observers with each standardare shown in Fig. 1. The vertical bars indicate thestandard deviations of the mean values of the lumi-nances chosen by the observers, and it is clear thatthe judgments for factors of 1 and 2 are significantlydifferent, as are those for factors of 2 and 3.

If we accept Eqs. (8) and (9), we can assign to thestandard, of luminance S, a brightness B1 , given byreplacing L by S:

B 1=N+K' log6(S/A.). (10A)

Further, we can predict that the observer will choose asn times as bright that luminance L which produces abrightness B,= nB1 . We therefore have

B, =nB1 =N+K' log (L/A). (10B)

Elimination of B1 from Eqs. (10) yields

log,(L/S)= (1-1) {N/K'+og(S/A ) }. (11)If N, K', and Ac can be found, this relation shouldagree with the data shown in Fig. 1.

Before we investigate the values of these quantities,it will be worth while to consider the range of it forwhich Eq. (11) is valid. If the weighting factor s inEq. (8) is close to unity, as it has been found to be for

lifted weights and as we shall later see it to be forbrightness, the comparative adaptation level A. willbe close to the standard S. Hence, log6 (S/A,) in Eq.(1OA) will be approximately zero, and Bln:N. Sincethe scale of brightness runs from zero to 2N, thepossible values of B, will fall in this range, and theonly values of n which make sense in Eq. (OB) willlie between zero and two. A further limitation appearsif we realize that there is a finite least count on thejudgment scale, and that all luminances for which

| log L-logA I > N/K'

invoke brightness judgments close to zero or 2N. Inthe absence of other data, we may accept Nash's valueof 4.6 for the judgment constant,7 so that the possiblerange of runs from about 0.2 to about 1.8. Hanes'ratios of 4 and 2 fall within this range, but his ratios of2 and 3 do not. We are therefore faced with a questionas to whether the fact that his observers were able toestimate brightnesses two or three times as great asthat of the standard is in conflict with Eq. (11).

This difficulty is easily resolved, and the answer tothe question is anticipated by part of the discussionin Hanes' paper, in which he says :8 "It might seem atfirst thought that estimating a ratio of 2:1 would bethe same whether fractional or multiple estimates arecalled for, since the observer is free to look back andforth in this situation and think either in terms of thevariable, in the case of multiple estimates, for example,as being the required multiple of the standard or in termsof the standard being the required fraction of thevariable."

He questioned his observers and found that only asmall fraction of them consciously interchanged theroles of standard and variable. Since the detailed waysin which quantitative judgments are made are seldomconsciously recognized by the observer, this evidencecannot be considered conclusive. We shall thereforesuppose that the brighter of the two sources is alwaystaken as the standard, and that only the ratios and2 should be used in Eq. (11). For values of n> 1, we canobtain a new equation by interchanging L and S to find

loge (L/S) = (1- 1/n) (N/K'+ log. (L/A )} (12)

The quantities N and K' always enter as a ratio,which may be rewritten, with the help of Eqs. (4)and (7), as

N/K'= -N loge,(I- 1/N)/(1-p). (13)

Although the fractionation experiments do not use arating scale explicitly, and hence do not give an im-mediate determination of N, a close correspondencebetween fractionation and rating-scale techniques maybe established. When a judgment of one-half as brightis required, the simplest rating scales that could be

7 See reference 4. The judgment constant C is related to theleast count I.c. on the response scale by the relation. I.c.=N/C.

8 R. M. Hanes, J. Exptl. Psychol. 39, 726 (1949).

72 Vol. 44

-0101 �, I 10

-A II 11 II T 1 I

BRIL SCALE OF SUBJECTIVE BRIGHTNESS

used by the observer, subject to the condition of equalintervals, would involve one of the two following setsof categories below "equal":

4 as bright, 4 as bright, 4 as bright, very dim;2 as bright, very dim.

For the first of these N=4, for the second, N=2.Similarly, for a judgment of one-third as bright, thesimplest scale is:

22 as bright, l as bright, very dim,

with N= 3. If very fine judgments are being attempted,a larger number of categories may be used, but thejudgment constant of 4.6 quoted above indicates thatN is never greater than about five. Further, the value ofthe ratio N/K' is insensitive to changes in N for N> 3,as may be seen from Eq. (13). Approximating thelogarithm as - 1/N, we find that N/K'= 1/(1-p) forlarge N. We shall therefore not go far astray if wetake N= 3.

The value of the self-adaptation coefficient in visionand its dependence on the size of the source has beenrecently investigated by Scovil.9 She has obtainedevidence that p varies with size of the source in themanner indicated in Fig. 2 and that its value liesbetween the limits shown by the dashed lines. We maytherefore take 0.70 as a value appropriate to the 4-degree source used by Hanes. Inserting this value andN=3 into Eq. (13), we find that N/K'=4.06.

The value of the comparative adaptation level A,depends on the weighting factor s, according to Eq.(8). No independent measurements have yet beenmade of this factor, but it can be estimated by usinga single one of the twenty sets of observations shownin Fig. 1. Self-adaptation, i.e., the effect of the weakerof the two sources, has been taken into account throughp; the only other stimuli which can effect the adaptationlevel are the stronger of the two sources and the"residual stimulus," which is determined by thephysiology of the observer and by his experiences priorto the experiment. This residual stimulus is the A ofEq. (8), and may be taken as a constant for the averageobserver. If S= A, it is clear from that equation thatA c=S, independent of the value of s. Fortunately,Hanes includes in his paper a report of brightnessmatches of the two sources.10 The mean values obtainedfor standard luminances of 5, 50, and 500 millilambertsare, respectively, 5.28, 50.02, and 472.2 millilamberts.This is exactly the behavior which would be predictedfrom Eq. (8), since the effect of the residual stimulus isto make AC>S when S<A and to make A,<S whenS>A. The fact that essentially perfect matching wasobtained for 50 millilamberts indicates that we cantake this luminance as the value of A. We may nowdetermine s from any one of Hanes' points, exceptthose which use a standard luminance of 50 milli-

9Adeline Scovil, unpublished data (private communication).10 R. M. Hanes, J. Expt]. Psychol. 39. 721 (1949).

la

12

4-

0

U)

0.00 I I I10 ~ 0 30Angle subtended by source (degrees)

FIG. 2. Dependence of the self-adaptation coefficient on theangle subtended by the source. The solid line shows mean values asobtained by Scovil; the dashed lines indicate the limits of theestimated uncertainties in these values.

lamberts. With S=0.5 millilamberts and n= 4, themean value of L was 0.118 millilamberts. Substitutionof these values into Eq. (11) gives A0 for these con-ditions as 1.66 millilamberts. This quantity may beused in Eq. (8) to give s= 0.74.

The solid lines of Fig. 1 are plots of the functionalrelationship between L and S, computed from Eqs. (11)and (12), with N/K'=4.06 and with A. computedfrom Eq. (8). A has been taken as 50 millilamberts ands as 0.74. Only one of the experimental points (= 0.5,L= 0.118) has been used in fitting the theoreticalcurves. The fit for =2 and =3 is nearly perfect,

with seven of the remaining experimental points fallingwithin the standard deviation of the means rm of theprediction, and the other two departing by less than2am. For n= 2, the fit is satisfactory except for thelowest value of S. A breakdown of the theory here isnot unexpected, since the standard luminance (0.005millilamberts) is close to the absolute threshold forphotopic vision. The fit for n= 3 is not as good as mightbe desired, particularly at the extreme values of S.The departures of the theory from experiment here arein the direction which would result if S, as well as L,plays a role in determining the comparative adaptationlevel. Further experimental work on comparativejudgments of brightness should clarify this point andmay result in the slight modification of the theorynecessary for good agreement with the experimentalresults.

In combining his data to form the bril scale, Hanesfound inconsistencies among the various runs whichwere at least as serious as are the departures of thepresent theory from the experimental observations.

73January 1954

WALTER C. MICHELS

We may, therefore, conclude that the reformulatedFechner law, which is consistent with known factsabout adaptation, will account for the data obtainedfrom fractionation experiments at least as well as willthe assumption of a one-to-one correspondence betweenstimulus and response. If the present treatment beaccepted, there must be an error in the reasoning whichleads from the fractionation experiments to a ratioscale. This error apparently lies in the assumption thata given luminance invokes the same psychologicalresponse when it is presented as a standard as it doeswhen it is presented as a multiple of a standard. Thus,suppose that one defines 100 brils as the brightness ofa 1-millilambert source and that it is found that a0.22-millilambert source is judged to be half as bright.This determines that the brightness of a 0.22-milli-lambert source is 50 brils. A further measurement,using the 0.22-millilambert source as a standard,

establishes the brightness of a 0.060-millilambert sourceat 25 brils, if we suppose that the 0.22-millilambertsource evokes the same response under the two condi-tions of presentation. According to Eq. (8), the com-parative adaptation level is 2.82 millilamberts withthe 1-millilambert standard, and 0.91 millilambertswith the 0.22-millilambert standard. Equation (11)yields, as the brightness judgments of the 0.22-milli-lambert source, the two values 1.11 and 1.95, respec-tively. Only by assuming the identity of these twodiscordant brightnesses can one arrive at an extendedratio scale.

This work was done as part of a psychophysicalresearch program being carried out with the help ofgrants made from the income of a Carnegie Corporationgift to Bryn Mawr College for the coordination of thesciences. The author wishes to express his gratitudefor this assistance.

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA VOLUME 44. NUMBER I JANUARY, 1954

Note on the Electrical Response of the Human Eye During Dark Adaptation*MATHEW ALPERN AND JOHN J. FARISPacific University, Forest Grove, Oregon

(Received October 16, 1953)

Measurement of the magnitude of the principal component of the electrical response of the human eyeto an intense flash of light, as a function of time in the dark following five minutes of light adaptation toan extremely bright field, shows an increasing response as a function of time in the dark. The curve levelsoff at a plateau before a second abrupt rise at about seven minutes in the dark. This break in the curveresembles the rod-cone break in the psychophysical dark-adaptation curve, in that a decrease in the levelof prior light adaptation reduces the prominence of the break or even eliminates it. The variation in theinitial dark electrical response after various time intervals of prior light adaptation resembles the variationin cone threshold after various durations of light adaptation.

INTRODUCTION

THE study of the human electroretinogramfurnishes the possibility of advancing under-

standing in both theoretical' and applied' physiologyof vision. One approach in such studies has been thecorrelation of the variations in electrical responses withcertain psychophysical data. While it is important topoint out that such correlations should not be expectedto be one to one,3 such an approach has been helpfulin defining a number of variables of the electroretino-gram. For example, on such a basis it has been possibleto relate the major component of the usual electro-retinogram more closely to the light scattered withinthe eye rather than to the focal illumination of the

* Assisted by grants from the Tektronix Foundation and theTheta Chapter of Omega Epsilon Phi.

I G. W. Bounds, Arch. Opthalmol. 49, 63-89 (1953).2 H. M. Burian, Arch. Opthalmol. 49, 241-256 (1953).3 E. P. Johnson and L. A. Riggs, J. Expt]. Psychol 41, 139-147

(1951).

retina,4 following a speculation originally proposed in1935 by Fry and Bartley.5

Similarly, it has become rather axiomatic to regardthe principal component of the electroretinogram asmirroring rod activity because: (a) the effectivenessof moderately intense lights of the various wavelengthsin arousing the electrical response follows the scotopicluminosity curve6 ; and (b) the electrical sensitivityto a moderately intense flash as a function of time in thedark following moderate light adaptation variescontinuously (whether the criterion is the height ofthe response7 or the logarithm of the intensity requiredto produce a specific height response') with time in

4 R. M. Boynton and L. A. Riggs, J. Exptl. Psychol. 42, 217-226(1951); R. M. Boynton, J. Opt. Soc. Am. 43, 442-449 (1953).

6 G. A. Fry and S. H. Bartley, Am. J. Physiol. 111, 335-340(1935).

6 Riggs, Berry, and Wayner, J. Opt. Soc. Am. 39, 427-436(1949).

7 G. Karpe and K. Tansley, J. Physiol. (London) 107, 272-279(1948).

8 E. P. Johnson, J. Exptl. Psychol. 39, 597-609 (1949).

74 Vol. 44