Chromatic opponent-response functions of anomalous trichromats

CHROMATIC OPPONENT-RESPONSE FUNCTIONS OF ANOMALOUS TRICHROMATS MARTHA RWESKIE’

Department

of Psychology. Brown University, Providence, Rhode Island. USA

(Received

21 June

1977; in revised

form

IO

February

1978)

Abstract-Chromatic valence functions for the red-green and blue-yellow opponent-response systems of normal and anomalous trichromats were measured psychophysically using the Jameson and Hurvich hue cancellation technique. Four protanomalous and two deuteranomalous observers with varying degrees of color discrimination loss, and fwo color-normal observers, served in the experiment. The color-normal data were in good agreement wiith the results reported by Jameson and Hurvich. Protanomalous and deuteranomalous observers differed with respect to the relative strengths of the two chromatic opponent systems: decreased red-green strength was correlated with poorer color dis-

crimination. Theoretical fits to the opponent-response data were calculated by assuming linear combinations of cone inputs for both chromatic systems and different sets of photopigments for the three classes of observer. Key Words-color vision; color blindness; anomalous trichromacy; maly; deuteranomaly.

INTRODUCTlON

Anomalous trichromacy is commonly defined on the basis of color matching behavior: anomalous observers require the same number of primaries for color matching as do normals, but in different proportions, for a given match. In the Rayleigh match (Rayleigh, 1881). for example, persons with normal color vision use a small range of ratios of the yellowish-red to yellowish-green primary to match the yellow standard. Those persons who require significantly more green than normal are classified as deuteranomalous, and those who need significantly more red are classified as protanomalous. These color matching data imply that in each class of anomalous trichromacy one or more cone photopigments differ from those of normal color vision. Because dichromats have been reported to accept the color matches of the corresponding form of anomalous trichromat as well as those of color-normal observers (Koenig and Dieterici, 1893), the inference has been made that only one pigment is deviant in each form of anomaly (von Kries, 1924). The prevailing notion is that protanomalous observers have the normal short-wave (z) and middle-wave (8) pigments, and a third, “anomalous pigment” whose peak absorption occurs at a wavelength shorter than the normal long-wave (p) pigment. Deuteranomalous observers are assumed to have the normal 5~and y pigments, plus an anomalous p pigment shifted toward the long-wave end of the spectrum. Recent psychophysical estimates of the protanomaious and deuteranomalous cone absorption spectra (Rushton. Powell and White, 1973; Piantanida and Sperling,

’ Present address: Department of Ophthalmology. York Medical College. Valhalla. NY 10592. U.S.A.

New

opponent-colors

theory; protano-

1973a, b) are consistent with that proposal. However, this reasoning is based on the assumption that all normal observers have the identical three photopigments; Alpern’s recent work (Alpern and Moeller, 1977; Alpern and Pugh, 1977; Alpem and Wake, 1977) suggests that it may not be a valid one and complicates speculation on the photopigment basis of anomalous trichromacy. Anomalous trichromacy also differs from normal color vision with respect to the ability to discriminate differences in hue and saturation. In both protanomaly and deuteranomaly, color discrimination ranges from essentially normal to nearly dichromatic (KGllner, 1929). even among observers with the same degree of color match deviance. This variation in color discrimination ability can be measured directly by determination of thresholds for wavelength discrimination (Engelking, 1926; Nelson, 1938; McKeon and Wright. 1940) and calorimetric purity discrimination (Nelson, 1938; McKeon and Wright, 1940; Chapanis, 1944). It is also evident in Rayleigh match data on the range of R/G ratios accepted as matches to the yellow standard (e.g. Willis and Farnsworth, 1952; Lakowski, 1968). The interobserver variability in color discrimination is a second important characteristic of anomalous trichromacy that requires explanation in any theoretical account of color vision. Within the opponent-process model (Hurvich and Jameson. 1955). it implies a reduction in strength of one or more of the neural opponent systems, which are postulated to receive input from the photopigments. This reduction could be merely a reflection of a narrowing of the separation between the middle- and long-wave pigment peaks, which would result in the generation of a smaller difference signal at the opponent level; different degrees of discriminative loss would then be due to varying separations of the photopigments (see

1521

Alpern and Moeller. 1977). Color match deviance should then be correlated with color discrimination ability. Alternatively. variations in opponent System strength may occur directly at the neural level. independent of alterations at the photopigment level (Jameson and Hurvich. 1956: Hurvich and Jameson. 1962: Hurvich. 1972. 1973: Pokorny and Smith, 1977). In this case. color match deviance and color discrimination might not covary. Unfortunately. the data on the degree of correlation between Rayleigh match midpoint and range have not been obtained with psychophysical procedures that reduce chances of response biases contaminating the data. and therefore they are of limited value in resolving this issue. Both cases predict the occurrence of variations in chromatic system strength that are correlated with color discrimination ability. In addition. the form of an observer’s opponent response functions should re-

flect that observer’s photopigments. The purpose of the present study was to measure psychophysically the red-green and blue-yellow chromatic opponentresponse functions for protanomalous and deuteranomalous trichromats having varying degrees of color

_.-._

-

P

NB

WL

-

JK

-

Jf

* MO .

-

N

QY

c

-( MH --*

D

-

OR

weakness. METHODS Sirhjrcrs

Six anomalous trichromats and two color-normal observers served in this experiment. Diagnosis of type of color vision was made primarily on the basis of the midpoint of the acceptance range for the Rayleigh match. which was defined as the R/G ratio that bisected the measured range. Match ranges are shown in Fig. I. along with the median of three initial free settings. The apparatus and procedure used for the Rayleigh match are described in the Appendix. The AO-HRR pseudo-isochromatic plates. the Farnsworth D-15 test. photopic spectral sensitivity curves determined by flicker photometry, and comparison of brightness matches between the yellow. and green and red. Rayleigh match stimuli were also used for color vision evaluation: these measures were particularly useful when Rayleigh match midpoint and range scores did not provide a cleat diagnosis (see. for example. observers NB and DR). The four protanomalous observers were JF. who had a small range of acceptance on the Rayleigh match: JK and WL. with moderate-sized ranges: and NB, large-range. The deuteranomalous observers were MH and DR. with small and large acceptance ranges. respectively. MO and DY had normal color vision; they were run for comparison and to validate the apparatus and procedure by replication of the results of Jameson and Hurvich (1955). All subjects. with the exception of DY who was a practiced psychophysical observer. had little or no experience as observers in vision experiments. Each observer used his right eye. Apparatus Oprical s~srem. A complete description of the multiplechannel Maxwellian view optical system used in this study is available elsewhere (Romeskie. 1976). In brief. the stimuli consisted of mixtures of two monochromatic beams superimposed optically by a beam-splitting cube and passed through an achromatizing lens. The stimuli were presented in a foveally-viewed. circular I ’ field with a dark surround. The monochromatic beams were produced by Bausch & Lomb 500 mm grating monochromators. illuminated by a

Fig. I. Rayleigh match data for 16 color-normal, 7 protan. and 8 deutan observers. Each line represents the data of one observer: the vertical mark indicates the median free match setting: the horizontal line shows the range of acceptance (see Appendix). The zero point on the abscissa corresponds to the mean color-normal midpoint. loo0 W xenon arc lamp (Oriel Corp.). Entrance and exit slits were set at 2 mm. providing a nominal half-amplitude bandpass of 6.6 nm. Blocking filters reduced stray light and second-order spectra. Continuous control of radiance over a range of approximately 6 log units was provided by a neutral density wedge and filters in each channel; wedge position could be controlled by either observer or experimenter. The shutter was operated by a Grass stimubtor for single I set flashes and by a specially designed timing circuit for longer, repeated exposures. Mignmenr. Stable positioning of the observer’s head was achieved with a dental impression bite-bar and forehead rests: these were mounted on a stage that permitted adjustment of head position in three dimensions. Precise centering of the stimulus within the observer’s right pupil was accomplished with an auxiliary lens system containing a set of cross-hairs positioned concentric with the exit pupil of the optical system. The experimenter. looking through this system. viewed an image of the observer’s pupil superimposed on the cross-hairs: alignment was optimized by adjusting the observer’s head position until the pupil was centered on the cross-hairs and parallax was absent. To avoid possible adaptation and biasing effects. no fixation point was used (Jameson and Murvicb 1967). Calibration. The relative spectral energy distribution of ’ each channel was measured with a silicone photodiode (United Detector Technology Corp.1 that had been calibrated against a thetmopile;, placed at the exit pupil of the optical system The output of the photodiode was monitored wiih a linear readout system (t&ited Detector Technology Corp.). This system was also used to calibrate the neutral density filters and wedges. The wavelength drums of the monochromators were calibrated by adjusting them to produce maximum light

Opponent-response

1523

functions of anomalous trichromats

transmission through a 546.1 nm interference filter when the drums were set at 546nm. Following these adjustments. maximal transmission of the zero-order spectrum was observed to occur when each wavelength drum was set at OOOnm An additional calibration of one monochromator was performed by verifying that maximal transmission of a 632.8 nm laser beam occurred when the wavelength drum was set at 633 nm. Retinal illuminance of one channel with its monochromator set at 580nm was estimated by allowing its output to illuminate a MacBeth test plate. the luminance of which was measured with an SE1 photometer according to the method described by Westheimer (1966). Retinal illuminance of the other channel at 580 nm was determined by brightness matching between I’ fields provided by the two channels. Determination of chromatic valence functions for the redgreen and bk-yellow systems. The chromatic opponent-

response functions were measured with a hue-cancellation technique similar to that first used by Jameson and Hurvich (3955). The method makes use of the ability of the members of the hue pairs red and green. and blue and yellow, to cancel each other and rests on the assumption that the response of a chromatic system at a given wavelength is directly proportional to the energy of the light needed to cancel the hue coded by that system. Thus. for example. the function for the red system was determined by measuring the relative radiance of a green light (referred to as the “cancellation stimulus”) required to cancel the sensation of redness at each red-appearing wavelength (the “test stimulus”). The greater the radiance of the green light needed. the greater the response of the red system. To convert the results to an equal energy spectrum, at each test wavelength relative energy required for cancellation was multiplied by relative spectral sensitivity, as measured by flicker photometry (see Romeskie, 1976, for details of these measurements). This product was termed relative -‘chromatic valence”, in accordance with the terminology of Jameson and Hurvich (1955). The cancellation stimuli were each observer’s independently estimated unique blue, green and yellow wavelengths.’ and 670 nm for the red stimulus for all observers. The test stimuli were equated by flicker photometry for each observer to 2.0 log td at 580nm. At this luminance level subjects JK and DY were unable to make settings for the green and short-wave red branches of the red-green function. respectively. because they did not perceive sufficient amounts of the hue to be cancelled in the test stimuli. These data were obtained with test stimuli equated to I.0 log td at 580 nm, on the assumption that the shape of the red-green opponent-response function is invariant with luminance (see Larimer. Krantz and Cicerone. 1974: Krantz, 1975). Observers used the method of adjustment: they were instructed to set the radiance of the cancellation stimulus at the point where the hue to be cancelled ‘just disappeared”. It had been expected that as the radiance of the cancellation stimulus was increased the observed hue of the stimulus field would change from that of the test stimulus (for example, red) to that of the cancellation stimulus (green). perhaps passing through a “neutral” (neither-rednor-green) zone of finite width. The original intention was to instruct the observer to locate the boundary of the hue change. if sharp, or the middle of the “neutral zone”. However. in preliminary work all observers. particularly the colordefective. reported the following: with many testcancellation stimulus combinations. after cancellation of ’ The unique hue determination procedure and results are described in the Appendix: complete information is available in Romeskie (1976).

the test hue was achieved. further increases in the radiance of the cancellation stimulus produced only the sensation of increasing brightness; the hue of the cancellation stimulus could not be perceived at any radiance level. With some other combinations. observers could perceive the hue of the cancellation stimulus on the brighter side of the neutral zone. but at that point the cancellation hue was so desaturated that they could not judge the transition point between “neutral” and the cancellation hue with any precision. The only setting all observers could readily make with all four cancellation stimuli at all test wavelengths was the point at which the hue of the test stimulus to be cancelled first disappeared. This point corresponds to the cancellation/ test hue boundary for combinations where a sharp transition from one hue to the other existed. The observer was instructed to approach the point to be set from both sides at least once each before making the final setting. Each 2--i hr s&on began with a IOmin period ofdarh adaptation following pupil alignment. The observer was told the hue to be cancelled; only one of the four color systems was measured in each session. The stimuli were presented for 7sec. followed by a 5sec dark interval; this cycle was repeated as often as necessary for the observer to be confident of the setting. Test stimuli were presented in wavelength order. every IO-20nm. A l-2 min dark adaptation period followed each setting. The observer made four adjustments for each test-cancellation pair: two during traverses of the spectrum from short to long wavelengths, and two during reverse-order traverses. Traverses in a single session were separated by 5-10 min dark adaptation periods. For the blue and green curves. all four runs were completed in the same session; the red and yellow functions were determined in two sessions each. Thus six sessions were required to obtain a complete set of functions. Each observer had several practice sessions on each function before the data reported below were collected. Determination opponent systems.

of

relarice

strength

of

the

chromatic

The basic cancellation experiment determines only the shapes of the four chromatic system functions and not the relative strengths of the different systems; the relative heights of the functions in Figs 2-J are arbitrary. Additional data are needed to adjust the heights of the four chromatic valence curves so that they correspond to perceived hue at a given luminance level. The general procedure described by Jameson and Hurvich (1955) was used here; the blue function was fixed relative to yellow by assuming that activity in these two systems is equal when the perceived hues blue and yellow are cancelled. For each observer, blue- and yellow-appearing wavelengths were chosen, such that the perceived hue of their mixture changed from blue to neither-blue-nor-yellow to yellow as the radiance of one of the wavelengths was varied. The energy of one wavelength was set at the flicker photometry-determined equivalent of 2.0 log td at 580 nm; the observer was instructed to adjust the radiance of the other stimulus to either the blue/neutral boundary or the yellow/ neutral boundary. Each of these points was determined five times, and the mean of the ten settings was calculated. The relative heights of the blue and yellow functions at these two wavelengths were then hxed in inverse relation to the difference in log relative energy at the mean cancellation point. For example, if 0.3 log units more energy of 470 nm than of 570 nm was present at the mean blueyellow cancellation setting, then the blue and yellow functions were adjusted so that the yellow curve at 570nm was 0.3 log units higher than the blue curve at 470nm. The same procedure was used for an analogous pair of red- and green-appearing wavelengths in order to lock the red curve with respect to the green curve. The relative strengths of the blue-yellow and red-green opponent systems at one luminance level were established on the basrs of perceived hue judgments The strengths of the two opponent systems were assumed to be equal

Table I. Spectral regton Judged an equal mtxture and )ellow by color-normal. protanomslous. and anomalous

of red deuter-

observers

Observer

LOCUS (nmj

MO

6OC610 605 6X-650 610-640 -

DY JF JK WL NB MH DR

to obtarn stable hue judgments observer k’L: therefore. hts data further analysis

The log relative two color-normal

680-700 6x-630 660-690

redness and yellowness were equal. The hue was judged an equal mixture of redness and yellowness was determined for each observer. and the relative heights of the blue-yellow and red-green functions were adjusted to cross at that point. These relative heights are correct for the luminance level at which the ‘-half-red. half-yellow” locus is measured: theoretical hue coefficients derived from chromatic cancellation data scaled on the basis of these assumptions accord well with experimental measures of perceived hue (Hurvich and Jameson. 1955: Wooten. 1970). In the present study each observer judged monochromatic flashes as either “more red than yellow” or “more yellow than red”. The stimuli were equated by flicker photometry to 1.0 log td at 580nm. The observer was darkadapted: the stimulus duration was I sec. with an intertrial interval of 20 sec. Initially. wavelengths from 580 to 700 nm in IOnm steps were judged twice each. in random order. On the basis of these data. four to six wavelengths, each separated by j-10 nm. were selected to bracket the region of change from perceived reddish-yellow to yellowish-red. locus

whose

I

I

from were

protanomaious excluded from

RESULTS

when perceived

spectral

Each srtmuius %a3 then pwsented iour or fi\~ :..XCS:r, random order. The mcasursd “half-red. hAIf-!ellow” !oc‘i dtffered ac‘ross obssr\:rs: the data are presented tn Table I. Despite numerous prscrtce sessions. tt *as not possible

chromatic

valence functions

/

I

/

/

DY

I

10

500

for the

observers are shown in Fig. 2. The data for ,A40 and DY are similar in their general features. The red. green and blue functions are nearly identical in shape; maxima occur at about 440nm and 610-620 nm for red, at approximately 530 nm for green, and at 440nm for blue. The only prominent difference between the data of the two subjects occurs in the yellow functions. DY’s curve has a much steeper long-wave slope: when the functions for MO and DY are locked at their peaks (SO-560nm). the curves begin to depart at about 600nm. and in the 660-700 nm region the difference is about 1.0 log unit. The protanomalous data are shown in Fig. 3. The mean log relative chromatic valence values for all four observers have been plotted together and the ranges have been omitted in order to facilitate comparisons between subjects: the variability of these data will be described below. The averaged color-normal red. green and blue functions are shown by solid lines: because the yellow functions for these two observers differ systematically for i. > 590 nm. smoothed curves for MO and DY are shown separately by solid and

400 WAVELENGTH,

500

600

701

nm

Fig. 2. Log relative chromatic valence functions for color-normal observers MO and DY. Wavelength of the test stimulus is shown on the abscissa. The ordinate represents log relative energy of the cancellation stimulus required to cancel the test stimulus hue designated by the letter below each curve. minus log relative energy of the test stimulus at minimal flicker. Each data point represents the mean of four measurements; error bars denote the range of the four settings. The smooth curves have been fitted to the data by eye. The relative heights of the four functions for each observer are arbitrary.

Opponent-response

1525

functions of anomalous trichromats

.

400

500

600

700

500

400

WAVELENGTH,

600

7oc

nm

Fig. 3. Comparison of protanomalous and color-normal log relative chromatic valence functions. The symbols represent the mean data of the four protanomalous observers (H JF: l JK; A NB; V WL). For all observers the maxima of the four chromatic functions have been arbitrarily assigned the same ordinate value. The solid lines shown with the blue, red and green data represent average functions for the two color-normal observers (MO and DY); the yellow functions for MO and DY are shown separately by solid and dashed lines, respectively.

lines. respectively, in that region of the spectrum. The blue functions for the protanomalous observers are essentially identical and have the same shape as the color-normal function. For the yellow system, the peak occurs at about 540 nm for every protanomalous observer, which is 10-20nm shorter than the normal peak. When locked at their A,,, the curves of the protanomalous subjects differ systematically in steep ness of the long-wave slope, beginning at about 600 nm; the difference in mean log relative chromatic valence between the most- and least-sensitive subjects is about 0.7 log units at the long-wave end of the spectrum. The protanomalous yellow functions are intermediate in slope relative to the two color-normal curves. The green functions for JF, WL and NB are similar in shape. The peak occurs at 530-54Onm. which is the same as for the color-normal observers; however, these protanomalous functions are broader than the color-normal functions on both sides of the peak. JK’s green function is quite different. The peak occurs at 5OOnm and chromatic valence decreases steadily to 540nm the longest wavelength at which green measurements could be obtained; the functions of the other protanomalous observers increase in that region. For JK, WL and NB, no short-wave red response was measurable by this cancellation procedure at either 2.0 or 1.0 log td. These observers reported that virtually all test stimuli in the extreme shortwave region of the spectrum appeared “pure blue”. JF’s short-wave red function is slightly broader than the color-normal function on the long-wave side. The dashed

long-wave red curves for JF, JK and NB all peak at approximately 59Onm and have somewhat different long-wave slopes. For WL, the maximum occurs at 570 nm and falls off more steeply on the long-wave side compared to the other protanomalous functions. The entire long-wave red function of every protanomalous observer is shifted toward shorter wavelengths relative to the normal function. When the functions are locked at their peaks, the red valence of protanomalous observers is about 1.0 log unit lower than that of the color-normal observers from 630 to 700 nm. The mean data for MH and DR, the deuteranomalous observers, are given in Fig. 4. The blue functions for the two observers do not differ systematically and appear to be slightly broader than the color-normal function on the long-wave side. The yellow functions for MH and DR do not differ across most of the spectrum but deviate by about 1.3 log units between 660 and 7OOnm. The yellow maximum occurs in approximately the same spectral region as for the color-normals but the deuteranomalous curves are considerably broader on the long-wave side. Both components of MH’s red function, and the green function, closely resemble those of the colornormal subjects. The long-wave red function for DR declines more rapidly for 1 > 620 nm; the short-wave red function could not be measured. DR’s green func-

tion could not be measured at 1 > 54Onm; on the basis of the relatively few data points obtained, it appears that the curve is narrower and shifted toward shorter wavelengths compared to MH’s curve. The range of the four separate measures at each

MARTHA

ROMESKIE

L

400

500

600

700

400

WAVELENGTH,

Fig. 4. Comparison

500

6ocl

700

nm

of deuteranomalous and color-normal log relative chromatic Same as Fig. 3. W MH: l DR.

valence functions.

wavelength averages approximately 0.2 log units for the color-normal observers. The variability of the

anomalous data is generally about the same, with the exceptions of the green function for all anomalous observers. and all data for MH, for which the range averages about 0.3 log unit. The chromatic vaknce functions are shown in arithmetic form in Figs 5-7. The relative heights of the chromatic systems in these figures have been adjusted according to the method described in Procedures. Complete tabular data are available ekewhere (Romeskie, 1976). The relative magnitudes of the chromatic systems. as plotted in these figures, are appropriate for a flicker-equated retinal illuminance level of 2.0 log td at 580nm. The red and yellow functions have been arbitrarily assigned positive values and the blue and green functions negative values in order to emphasize the opponent nature of the chromatic systems. The solid lines in these figures will be discussed in the next section. The peak of the smoothed blue function has been arbitrarily assigned a value of - 10 for each observer. The blue function was selected as the basis for normalization across subjects because, of the four chromatic systems. it is almost certainly the one least likely to manifest inter-observer dif!brences associated with anomalous trichromacy. The ‘absolute height of the blue function probably does vary across observers. due to differences in such ftiors as the number of short-wave pigment-containing cones, and hs and macutar pigmentation density: therefore, the absolute strength ofa given system cannot be compared across subjects. However, it is important to tealite that interobserver differences in absolute strength of the blue system would not a&a the ratios of the heights of the four functions for a given observer, and different subjects may be compared on that basis.

5 :

0

z

-5

2 ” -10 5

3 5

10

0 5

5

k :

0 -5 -10 400

500 WAVELENGTH,

600

700

nm

Fig. 5. Relative chromatic valtnce functions for color-normal observers MO and DY. The heights of the systems relative lo each other have been ad&&d according to the procedures described in the text. Each symbol (0 blue: A yellow; 0 red; V green) represents the mean of four measurements. The smooth curves are described in the text.

Opponent-response

1527

functions of anomalous trichromats

The deuteranomalous data are shown in Fig. 7. MH is the observer with a narrow Rayleigh match range. comparable to protanomalous observer JF; DR’s range was large, similar to that of protanomalous observer NB (see Fig. 1). Despite the variability in MH’s data, results analogous to those obtained with the protanomalous group are evident. Comparing the two deutan subjects, the red, green and yellow systems are much lower relative to blue for DR than for MH. Both observers show lower than normal strength of the red system relative to yellow for 1>6OOnm. To summarize these data. the major finding is that the relative strengths of the chromatic opponent systems at one luminance level differ among normal and anomalous trichromatic observers in a pattern that is correlated with their performance on the Rayleigh match. Increasing Rayleigh match range is associated with both decreasing strength of the red-green opponent system and with decreasing strength of the yellow system relative to blue.

z

DISCUSSION I

I

I

NB'

1

1

5 t

-5 -10

Comparison

with earlier

data

The present study provides the first measurements of the chromatic opponent-response functions of color-defective observers. These functions have been measured previously for two color-normal observers by Jameson and Hurvich (1955). Their procedure was

tti

I

I

I

400

500 WAVELENGTH,

Fig. 6. Relative

I

700

600 nm

chromatic

valena functions for protanomalous observers JF, JK. and NB. Same as Fig. 5.

The color-normal data are presented in Fig 5. The relative heights of the four color systems for the two observers are quite similar overall. However, the short-wave branch of the red function is lower for DY: the height of the long-wave red peak is about 1.67 times that of the short-wave peak for MO but approximately 4 times the short-wave maximum for DY. A second difference between the two sets of functions is the ratio of yellow to red valence for i. > 610nm: it is consistently higher for MO. Figure 6 shows the data for the protanomalous observers, arranged, from top to bottom, in order of increasing Rayleigh match acceptance range (see Fig. 1). Considering the red-green system first, there is a progressive decrease in the height of the red-green function relative to the blue-yellow function proceeding from the observer with the smallest Rayleigh match range to the observer with the largest range. The blue-yellow functions of the three protanomalous observers also show systematic differences: increasing Rayleigh match range is associated with decreasing height of the yellow branch relative to blue. The strength of the red system relative to the yellow system for i. > 600nm is considerably lower than normal for all three protanomalous observers. even though the ratio of peak red to peak yellow strength is similar for JF, JK and the color-normal observers.

._

I

I

400

500 WAVELENGTH,

600

700 nm

Fig 7. Relative chromatic valence functions for deuteranomalous observers MH and DR. Same as Fig. 5.

MARTHA ROWWE

O.

0

0

o

.

0 0 .

400

500

600

700

500

400

WAVELENGTH,

600

700

nm

Fig. 8. Comparison of log relative chromatic valence functions for color-normal observers MO (e) and DY (m) with the data reported by Jameson and Hurvich (1955) for color-normal observers J (0) and H (Cl). The maxima of the four chromatic functions for all observers have been arbitrarily assigned the same ordinate value. Data points for MO and DY represent means of four measurements: for J and H. means of twenty measurements.

the model for the one used here. but differed in certain details. The major differences are: (1) the observers in the Jameson and Hurvich experiment were tight-adapted to a “chromatically-neutral white”: (2) the temporal parameters of stimulation, which were not specified by Jameson and Hurvich, were probably somewhat different: and (3) for testcancellation wavelength pairs for which a relatively wide “neutral zone” exists, their measurements may represent different points in that zone. These procedural differences do not seem to affect the shapes of the chromatic system functions, as shown in Fig. 8. Overall. the agreement between the two studies is quite good. The blue. green and red functions of all four observers are nearly identical in shape. Significant variation is evident only in the yellow system data: both the peak wavelength and the long-wave slope differ among observers, in both studies. Essentially identical procedures were used here, and by Jameson and Hurvich. to establish the levels of the four chromatic systems relative to each other. The ratios of the peaks of the blue and yellow functions. and the ratios of the red and green peaks, are nearly the same for all subjects. The most obvious difference in the data of the two studies is in the estimated relative strengths of the two opponent systems. The redgreen system appears to be stronger relative to the blue-yellow system for observers H and J than for MO and DY. This discrepancy may appear puzzling at first, because both studies were done at comparable luminance levels. However, in the Jameson and Hurvich study. test stimuli were viewed in a white surround field, which. through simultaneous brightness contrast. should induce darkening of the test field and

therefore reduce the perceived brightness of the test stimuli relative to the brightness of stimuli of equal luminance viewed with no surround field. Coren and Keith (1970) have demonstrated that monochromatic lights identical in wavelength and luminance but differing in brightness (because of the presence of a bright surround field around one of the monochromatic lights) will differ in perceived hue. The nature of this diflerence in hue is the same as the change in hue that occurs when the luminance of a monochromatic tight is varied (the Bezoki-Briicke hue shift): the perceived yellowness or blueness of a monochromatic light increases as its energy and/or brightness is increased; conversely, perceived redness or greenness increases as stimulus energy and/or brighmess decreases. Since Jameson and Hurvich’s test stimuli should therefore have appeared less bright than those of the present study. their stimuli should have appeared greener and redder, resulting in a shift of the WA red. soo/, yehow locus toward shorter wavelengths; this would account for the differences in the relative strengths of the red-green and blueyellow systems in the two sets of data Implications for the physiological lous rrich~omacy

mechanism

of anoma-

Color matching data impfy that at least one photopigment differs from the normal compkznent in both protanomaly and deutcrmonsaly. By assuming a particular relation betwenn the photopigment absorption spectra and the chr@tn&tic opponent-response functions. it is possible to generate theoreti~al curves for the chromatic system data using different sets of photopi_nments. Then, by examining the goodness of fit

Opponent-response

functions of anomalous trichromatr

obtained with each set. tentative inferences can-be drawn regarding the number of pigments that differ. and the direction of the shift(s). Jameson and Hurvich (1968) have postulated that the chromatic opponent-response functions are determined by linear combinations of the outputs of the three cone systems, as expressed in the following

equations: R-G = (k,z - k,B + k,y)

(1)

BY

(2)

= (-k,z

+ k,B + key)

where r, B and y are the spectral absorption functions of the short-, middle-, and long-wave cone photopigments, and k,-k6 are weighting constants. For the chromatic valence functions reported here, curves were obtained by the method of least-squares deviation using a specially-written computer program, and assuming the linear relations expressed in Eqns 1 and 2. For a given set of photopigment absorption spectra, the program generated values for the k, coefficients that produced the best-fitting functions. Relative goodness of fit was assessed by the average squared deviations. The normal photopigments were assumed to absorb maximally at 435,530 and 562 nm. The 435 MI short-wave peak was chosen because it corresponds to the maximum of the photopic spectral sensitivity curve of those monochromats who are believed to possess only the short-wave cone photopigment (Blackwell and Blackwell, 1961; Alpern. Lee and Spivey, 1965; Daw and Enoch, 1973). The &,,,. for the middle- and long-wave pigments are consistent with the peaks of the spectral sensitivity curves of protanopes and deuteranopes (Pitt, 1935; Hecht and Shlaer, 1936; Hecht and Hsia, 1947; Hsia and Graham. 1957). respectively, whose luminosity curves are probably determined by the normal middle- or long-wave pigment in the region of maximal sensitivity. Also. these I,,, are close to the peaks of the Vos and Walraven (1971) primaries, deduced from linear transforms of color-mixture functions, and they are consistent with increment threshold data reported by Wald (1964) and Wooten and Wald (1973). The photopigments were assumed to have the same shape as the absorption spectrum of iodopsin (Wald Brown and Smith, 1955) when plotted on a frequency scale. For use in the least-squares analyses. the absorption spectrum of each photopigment was calculated by shifting the iodopsin nomogram to the appropriate spectral locus, converting from a frequency to a wavelength abscissa and from a quanta1 absorption to an energy absorption ordinate, and adjusting for absorption by the ocular media according to Table 2.8 in Wyszecki and Stiles (1967). to represent relative sensitivity at the cornea. The corrected absorption curves were then normalized with the peaks set at 1.0 Fits to the anomalous data were generated using the normal pigments, and varying degrees of shift of J and y. For the protanomalous observers, the following sets of photopigments were used: y shifted 10, 22 or 27 nm toward fi; and /t and y both shifted 10 nm toward z. The following fits were calculated for the deuteranomalous subjects: /3 shifted 5, 10. 22 and 27nm toward y; and B and y shifted IOnm toward longer wavelengths.

The theoretical curves obtained for the two colornormal observers are shown in Fig. 5 by the solid lines. The different-shaped yellow functions of the two observers are fitted by the same photopigments, but with a much lower value of the y weighting constant (k6) for DY. The differences in short-wave red strength for MO and DY are accommodated by different values of k, . For the anomalous observers, comparable fits to

1529

the blue-yellow system data were obtained with at least one of the sets of photopigments tested; but equally good fits to the red-green data were not always obtained. The normal photopigments did not provide the best fit to the data of any of the anomalous observers. Successively better fits to the protanomalous red-green functions were obtained as 7 was shifted closer to /I: for all protanomalous observers. the best fits were obtained with z = 435, /J = 530 and y = 535. These fits are shown in Fig. 6. The deuteranomalous data were poorly fitted by an equal-magnitude shift of /3 toward p. The normal pigments provided better fits to the deuteranomalous functions than to the protanomalous functions, but the best fits. shown in Fig. 7. were obtained with a small shift of /? toward longer wavelengths: z = 435, /? = 535. y = 562. Thus. the best fits to the anomalous data were provided by assuming the presence of a single anomalous pigment (&,, = 535 nm) in combination with the normal short- and middle-wave pigments for protanomaly, and the normal short- and long-wave pigments in deuteranomaly. In these theoretical fits, the interobserver differences in relative strengths of the chromatic systems are accommodated by variations in the derived values for the photopigment weighting constants. It must be emphasized that the suggestion of a single “anomalous pigment” is based on the outcome of a limited number ofphotopigment combinations. using a single cone absorption spectrum shape, and data from a relaticely small number of obsercers. The cancel-

lation data reported here, though adequate to demonstrate the red-green weakness effect, are not sufficiently stable to justify more exhaustive photopigment analyses. Assuming, at least, that in both protanomaly and deuteranomaly the /3 and y cone photopigments are closer together than those of normal color vision, it might be argued that the pigment shift itself causes the observed red-green system decrease because the presumed subtractive interaction between fl and 7 for the red-green system would produce a smaller signal. However, there is a compelling argument against this notion: the short-wave red component of the system is reduced as well (see Figs 6 and 7). If this branch is determined largely by the z pigment, then the spacing of the B and 7 pigments should have little effect on its height. The fact that it is decreased. and that the relative heights of the red and green branches are similar for the normal and anomalous observers. suggest a uniform compression of the entire red-green system. One way this might occur physiologically is by a decrease in the number of red-green opponent cells relative to the number of blue-yellow opponent cells at some level of the visual system. Electrophysiological evidence for such a mechanism has been reported for the squirrel monkey, Saimiri, whose behaviorally-assessed color vision resembles that of the protanomalous human (Jacobs and De Valois, 1965; De Valois and Jacobs, 1968). In conclusion, the chromatic opponent-response functions measured here, and the finding of orderly differences in the relative strengths of the two systems among protanomalous and deuteranomalous trichromats. provide new information about the color vision

1530

MARTHA

of such observers; these results confirm the predictions made by Jameson and Hurvich (1956). Finally. any set of photopigments proposed for protanomaly and deuteranomaly must also be able to account for these anomalous opponent-system functions. wish to thank Bill Wooten. Lorrin Riggs and Dean Yager for invaluable asistance throughout the course of this research. Bill Wooten and Dean Yager for a critical reading of this manuscript. and Dorothea Jameson and Leo Hurvich for several helpful discussions. This research was completed under the tenure of a predoctoral fellowship from NIH. Acknowkdgumrnrs-I

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Blackwell H. R. and Blackwell 0. M. (1961) Rod and cone mechanisms in typical and atypical congenital achromatopsia. Vision Res. 1. 62-107. Chapanis A. (1944) Spectral saturation and its relation to color-vision defects. J. exp. Psychol. 34. 2444. Coren S. and Keith B. (1970) Bezold-Briicke effect: pigment or neural locus’! J. opr. Sot. Am. 60. 559-562. Cornsweet T. 1962) The staircase method in psychophysics. rltt~. J. Psychol. 75, 485-491. Daw N. W. and Enoch J. M. (1973) Contrast sensitivity. Westheimer function and Stiles-Crawford effect in a blue cone monochromat. Vision Res. 13. 1669-1680. De Valois R. L. and Jacobs G. H. (1968) Primate color vision. Science 162. 533-540. Engelking E. (1926) uber die spektrale Verteilung der Unterschiedsempfindlichkeit ftir Farbentiine bei den verschiedenen Formen der anomalen Trichromasie. KIin. Mhl. Augenheilk 77. 61-75. Hecht S. and Hsia Y. (1947) Colorblind vision. I. Luminosity losses in the spectrum for dichromats. J. gen. Physiol. 31. 141-152. Hecht S. and Shlaer S. (1936) The color vision of dichromats. J. gen. Ph.uio/. 20. 57-93. Hsia Y. and Graham C. H. (1957) Spectral luminosity curves of protanopic. deuteranopic. and normal subjects. Proc. Narn. Acad Sci. 43. I01 I-1019. Hurvich L. M. (1972) Color vision deficiencies. In Handbook of Sensor?_ Physiology (edited by Jamaon D. and Hurvich L. M.). Vol VlL’4. Sorinzer-Verlae Berlin. Hurvich L. M. (1973) Color v&ion-deficien&. In Co/or Vision. pp. l-33. National Academy of Sciences, Washington. Hurvich L. M. and Jameson D. (1955) Some quantitative aspects of an opponent-colors theory. II. Brighmiss. saturation, and hue in normal and dichromatic vision. J. opr. Sqc. Am.

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Hurvich L. M and Jameson D. (1962) Color theory and abnormal red-green vision. Dot. Ophrhal. 16. 409-442. Jacobs G. H. and De Valois R. L. (1965) Chromatic opponent cells in squirrel monkey lateral geniculate nucleus. Nature. Land. 206. 487-489. Jameson D. and Hurvich L. M. (1955) Some quantitative aspects of an opponent-colors theory. I. Chromatic responses and spectral saturation. J. opr. Sot. Am. 45. 546552.

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Nelson J. H. (1938) Anomalous trichromatism and its relation to normal trichromatism. Proc. Phys. Sot. 50. 661-697. Piantanida T. and Sperling H. G. (1973a) isolation of a third chromatic mechanism in the protanomalous observer. vision Res. 13. 2033-2048. Piantanida T. and Sperling H. G. (1973b) Isolation of a third chromatic mechanism in the deuteranomalous observer. Vision Res. 13, X49-2058. Pitt F. H. G. (1935) Characteristics of dichromatic vision. Med. Res. Council Spec. Rep. Ser. No. 200. H.M. Stationery Office. London. Pokorny J. and Smith V. C. (1977 Evaluation of singlepigment shift model of anomalous tricbromacy. J. opt. Sot. Am. 67. Il96-1209. Rayleigh Lord (Strutt J. W.i (1881) Experiments on colour. tiatrrre 25. 64-66. Romeskie M. (1976) Chromatic opponent-response functions of anomalous trichromats. Ph.D. thesis. Brown University. University Microfilms. Ann Arbor. Rushton W. A. H.. Powell D. S. and White K. D. (1973) Pigments in anomalous trichromats. vision Res. 13. 20 17-203 I. Vos J. J. and Walraven P. L. (1971) On the derivation of fovea1 receptor primaries. Vision Res. 11. 799-818. Wald G. (1964) The receptors of human color vision. Science 145. 1007-1017. Wald G.. Brown P. K. and Smith P. H. (1955) Iodopsin. J. gen.

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Opponent-response

functions of anomalous trichromats

Wooten B. R. (1970) The effects of simultaneous andsuccessive chromatic contrast on perceived hue. Ph.D. thesis, Brown University. University Microfilms, Ann Arbor. Wooten B. R. and Wald G. (1973) Color-vision mechanisms in the.peripheraI retinas of normal and dichromatic observers 1. gen. Physiol. 61, 125-145. Wyszecki G. and Stiles W. S. (1967) Color Science. Wiley, New York. APPENDIX I. Rayleigh match The Maxwellian view optical system described in the main text was used. The observer viewed two circular 1” fields, separated by 20’. in a dark surround. The left field was illuminated by a mixture of 670 and 546 nm, and the right field by 589 nm. The observer was instructed to fixate between the fields. Matches were made in a dark room. Following pupil alignment, the observer familiarized himself with the operation of two knobs, which controlled the luminance of the 670 and 589 nm channels. Luminance in the 546nm channel was fixed at 2.14 log td in order to simplify the matching task. The observer first made “free matches”. The 670 and 589 nm luminances were set to predetermined starting points, and the observer was instructed to turn one or both knobs in order to obtain a perfect match. The fields were illuminated for Ssec and dark for 5sec. in order to reduce fading; the observer was allowed to work as long as necessary. After a match was reported, the observer was required to verify it at the next stimulus onset. Three such “free matches” were obtained. The median of these three settings was used as the starting point for determination of the range of accepted matches. The observer was shown a series of R/G ratios in the left field and was required to determine, for each, whether or not a perfect match could be obtained by adjusting the luminance of the 589nm field only. A total of 114 different R/G ratios, ranging from entirely red to entirely green, could be presented, all at a level of 2.40 log td. The experimenter began with an R/G ratio five steps above or below the observer’s median free match; if no match could be obtained, ratios successively closer to the free match setting were presented, alternating randomly from the “redder” and ‘greener” sides. until the observer reported perfect matches on each side. The endpoints of the accepted range were then rechecked If the observer could make matches to the first R/G ratios presented by the experimenter, ratios successively farther away from the free match were shown in an attempt to locate ratios that the observer could not match; it was possible to find such points for all observers except protanopes and deuteranopes. The experimenter then proceeded as described above.

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Following the range determination the observer made brightness matches by adjusting the right side (589nm) to match 546 or 670nm on the left. each presented at 2.40 log td. Three matches to each light were obtained. in alternating order. This procedure for the Rayleigh match is similar to the one recommended by Linku (1964. pp. 190-197). II. Unique hue loci Unique blue, green and yellow wavelength estimates were obtained with a forced-choice. double randomly aiternating staircase procedure (see Comsweet, 1962). To determine unique green. for example, the observer was required to respond “blue” or “yellow” after viewing a monochromatic stimulus in the green-appearing part of the spectrum. If the response was “yellow”, the next stimulus was shorter in wavelength; if “blue”. a longer wavelength was presented next. The direction of the staircase was reversed after each change of response. In order to prevent the observer from anticipating the next stimulus, two such staircases were run simultaneously, and the experimenter alternated between them randomly trial-by-trial The starting points for the staircases were chosen on the basis of previously obtained hue judgments: the observer was shown 1 set flashes of monochromatic light, equated to 2.0 log td at 580 nm, and was asked to describe each light in terms of red. green, blue and yellow in any combination. These judgments were made at every IO nm from 420 to 700 nm. These data provided approximate indications of the unique hue loci; the starting points for the two staircases were always chosen to be at least 20 nm longer and shorter than the wavelengths estimated for the unique hues. The desired wavelength step size was one that reliably produced a reversal of response after 3-4 steps. Typically. a relatively large step size (4-8 nm) was used at the beginning of each determination; step size was reduced to 1-4nm when the reversal-of-hue zone was more precisely located. The fir&step size used depended upon the color discrimination capacity of the observer and upon the hue .being determined. It was generally larger for anomalous trichromats than for color-normals and was smallest for unique green for the colordefectives and smallest for unique yellow for color-normals. The apparatus used for these measurements is described in the main text. After pupil alignment. subjects were darkadapted for 10min. Stimuli were presented for I set with an interflash interval of 20 sec. All wavelengths were equated by flicker photometry for each observer to a retinal illuminance of 2.0 log td at 580 nm. Estimates of unique hue wavelengths were based on the data collected after the first reversal of response in each staircase: the procedure was continued for approximately 20 reversals. Only wavelengths for which at least three responses had been obtained were used in the calculations. To determine a unique green wavelength, for example, the relative percentages of “blue” and “yellow” responses at

Table 2. Estimates of unique hue loci and the wavelengths corresponding to a change of the psychometric function from 25% to 75% of one hue response for color-normal, protanomalous, and deuteranomalous observers Blue

Observer

Locus (nm)

Interval (nm)

Locus (nm)

MO DY JF JK WL NB MH DR

476 476 475 484 473 474 483 489

2.0 2.5 1.5 2.0 1.0 1.5 2.5 2.5

498 496 497 501 491 497 509 504

Green Interval (nm) 2.5 2.0 1.0 1.0 1.5 1.0 1.0 1.0

Locus (nm) 573 580 572 567 587 -

Yellow Interval (nm) 3.0 1.0 4.0 8.0 4.5 -

I532

MARTHAROMEWE

each wavelength presented three times or more were graphed. The unique green locus was defined as the nearest whole nanometer corresponding to 50“; blue. 5OO;yellow judgments. found by interpolation. The estimated unique blue. green and yellow wavelengths for the eight observers are presented in Table 2. To provide an index of the precision of each determination. the wavelength distance. in nanometers. within which the psychometric function changed from 25:; to 75”/, of one hue response is also given. A unique yellow locus could not be determined for anomalous observers WL. NB and DR. presumably due to their poor color discrimination in that spectral region. These subjects gave approximately equal numbers of “red” and “green” responses from about 530 to 600 MY. The yellow cancellation stimulus used for WL and NB was 570nm. the wavelength intermediate between the unique yellow loci of the two other protanomalous observers. For

DR. deuteranomalous observer MH’s unique yellow wavelength was used. Since the unique hue values given in Table 2 are based on relatively few observations. they are considered here to identify the unique hue loci to a rough approximation only. The unique hue data permitted the selection of et% cient cancellation stimuli for measurement of the chromatic opponent-response functions, since wavelengths near unique hue loci are essentially selective stimuli for the individual chromatic systems. The exact choice of wavelengths to be used as cancellation stimuli is not critical: if the chromatic valence of a given system {e.g. green) were measured with each of two cancellation wavelengths (e.g. 620 and 670nm). the IWO resulting functions would not differ in shape: the difference in relative energy of 620 and 670nm at the neither-red-nor-green point would be constant as a function of wavelength (see Larimer er al.. 19741.