Chromatic Discrimination with Variation in ... - Semantic Scholar
Vision Res. Vol. 33, No. 13, pp. 1835-1845, 1993 Printed in Great Britain. All rights reserved
0042-6989/93 $6.00 + 0.00 Copyright 0 1993 Pergamon Press Ltd
Chromatic Discrimination with Variation in Chromaticity and Luminance: Data and Theory TSAIYAO YEH,*t
JOEL POKORNY,*$
VIVIANNE
C. SMITH*
Received 9 July 1992; in revised form 30 December 1992
Boy&on and Kambe developed a model of somatic ~~~~nation in which thresholds are mediated by two independent mechanisms: the short-wavelength sensitive (S-) cones (S-cone axis), and the middle-wavelength sensitive @I-) and long-wavelength sensitive (I_,-)cones (M/L-cone axis). In this study, we used a Maxwellian view optical system to investigate fundamental properties of the model as a fu~on of ~omatici~ and leak. We condom that ~~~a~o~ along the f&zone axis were dependent on S-cone excitation level. However, changes in chromaticity and changes in mean luminance were not described by a single threshold-vs-radiance (TVR) template. We developed a model to account for the different effects of changing S-cone excitation by varying mean chromaticity and by varying mean l~nance. M/L-cone donation showed a mourn at the L-cone excitation to white, indicating strong opponeucy. The thresholds increased with luminance approaching a Weber region and showing parallel functions for differing chromaticities. These data are fit by a model allowing retinal gain controls and spectral opponency. Color vision
Chromatic
discrimination
Psychophysics
The purpose of this study was to investigate how the differential sensitivities of the cone types regulate the ability of an observer to di~~minate two patches of light differing in chromaticity. Chromatic discrimination data are most frequently presented in the form of wavelength discrimination steps for spectral light, or in the form of di~~mina~on steps (Wright & Pitt, 1934; Wright, 1941) or discrimination ellipses (MacAdam, 1942; Brown & MacAdam, 1949; Wyszecki & Fielder, 1971) in the chromaticity diagram. Chromatic disc~~nation thresholds are affected by variation in luminance level. Wavelength discrimination functions deteriorate in the short wavelength region at low luminance levels (Weale, 1951; McCree, 1960; Stabell & Stabell, 1977). The effects of luminance on chromatic discrimination ellipses were described by Brown and MacAdam (1949), Brown (1951), and Wyszecki and Fielder (1971). The major axes of the ellipses rotated toward the blue corner of the chromaticity diagram as field luminance decreased. Clarke (1967) compared chromatic discrimination at different presentation intervals and luminance levels. Disc~mination steps along
*Visual Sciences Center, The University of Chicago, 939 East 57th Street, Chicago, IL 60637, U.S.A. 7Present address: Department of Ne~obiolo~, Max-Planck Institute for Biophysical Chemistry, Giittingen, Germany. /To whom reprint requests should be addressed.
the S-cone axis increased more than steps along the M/L-cone axis as luminance and field size decreased. Generally, it can be concluded that the discrimination sensitivity based on S-cones declines more than M- and L-cones at low luminance levels. One classical approach to represent chromatic discrimination data is the line element. Early line element theories used the differences of receptor excitation to express a change in color experience (Helmholtz, 1896; Schrodinger, 1920; Stiles, 1946). Le Grand (1949) analyzed MacAdam’s data and found that chromatic discrimination thresholds were mediated by only two independent variables: a S-cone pathway, and a M- and L-cone pathway. His analysis also suggested minimum discrimination thresholds near white for the M- and L-cone system. Later line element theories incorporated opponent stages in the model (Friele, 1961; Vos & Walraven, 1972a, b). In general, line element predictions were in agreement with experiment data, if the numerical parameters were adequately chosen. Boynton and Kambe (1980) followed Le Grand’s (1949) pioneering work. They measured chromatic discrimination along the cone excitation axes of the MacLe~-Boynton (1979) chromaticity space. Data from Boynton and Kambe (1980) showed that, at 120 td, discrimination ability dependent on S-cones changed slowly with S-cone excitation and approached the Weber region only at high levels of S-cone stimulation. Discrimination along the M/L-cone axis was near the Weber region. Their data also confirmed an opponent process
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contribution to discrimination along the M/L-cone axis. Boynton and Kambe further developed chromatic discrimination equations to describe their data. They noted however that the equation did not describe S-cone discrimination data for luminance levels higher than the 120 td constant luminance plane. A similar finding was reported for the analysis of the Brown and MacAdam (1949) data (Nagy, Eskew & Boynton, 1987). The purpose of the present study was to evaluate and extend the Boynton and Kambe model. We measured discrimination thresholds along the S-cone axis and the M/L-cone axis as a function of chromaticity and luminance level. The data were analyzed in units of S-cone trolands, and L-cone trolands, as specified by Boynton and Kambe (1980). At a constant luminance level, our data can be well described by Boynton and Kambe’s equations. However, the fitting parameters for this model varied as luminance level changed. These results suggested that quanta1 catch of the cones alone cannot explain the effect of luminance level on chromatic discrimination thresholds. We fit the data to a model of chromatic discrimination which includes gain control mechanisms and spectral opponency. EXPERIMENTAL
METHODS
Apparatus
The light source was a 450 W Xenon arc lamp (Osram XBO 450 W ofr) driven by a regulated power supply (Electronic Measurements Inc, model ELXE 1000 B). The light was split into four channels (Fig. 1). For three of the channels, light was collimated (by Ll), passed through a mask (Ml), and was then focused (by L2) on the mirror galvanometers (MG). The light passed through
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a second mask (M2). The amount of light passed by mask M2 depended on the angular position of the mirror galvanometers. After recollimation (L3), light from all three channels fell on a large Fresnel lens (L4) and was focused on the input port of an integrating sphere. In channel 4, light was collimated (Ll), passed through another Fresnel lens (L4), and was focused on the input port of a second integrating sphere. The exit ports of the integrating spheres served as sources for a Maxwellian view system with a lens (L5) placing images of the output ports in the plane of an artificial pupil. A 3 mm artificial pupil was used in the study (except for the MDB measurement for Expt 1). An ophthalmic lens (L6) could be placed adjacent to the artificial pupil to bring the image of the field stop into sharp focus. A chin-rest was used to position the observer’s head. The light from the two integrating spheres formed a bipartite field by means of a prism cube with half of the hypotenuse silvered. The right hemifield was illuminated by channel 4 and the left hemifield by the channels 1-3. The bipartite field could be changed to a uniform circular field illuminated by the output of the first integrating sphere (channels l-3), by adjusting the position of a field stop in front of the prism. The illuminance and chromaticity of each channel was adjusted by use of colored and neutral filters. In channel 1, a wheel with 13 chromatic filters and a 3 log unit neutral density wedge were used to control chromaticity and light level. The filter wheel included three-cavity interference filters (Ditric Optics) for middle-spectrum light. For short and long wavelengths, broad-band blocking filters [Ealing Electra-optics Inc, Balzers and “Russian Glasses” (Dobrowolski, Marsh, Charbonneau, Eng & Josephy, 1977)] were used. The CIE chromaticity
I\
CHANNEL4
INTEGRATING CHANNEL3
SPHERE
MIRROR
r
3
CHANNEL1
LIGHTSOURCE
L4
L -ROL
M2
FIGURE
1. Schematic of the four channel optical system. See text for details
CHROMATIC
DISCRIMINATION
coordinates of the channel 2 white were x = 0.3536, y = 0.3546. The device was controlled by a Macintosh II computer, and MacADIOS II digital input~output boards (GW Instruments). Two GW Instruments’ GWI-DAC 16-bit D/A daughterboards generated signals to move the mirror galvanometers and determined the wedge position by a d.c. servocontrol. The wedge could be also controlled manually and its position read by the MacADIOS. The interference filter wheel was run by a 12-bit D/A converter. A buzzer, used to alert the observer, was activated by a digital output port. Three switches were used to signal the observer’s responses. Switch responses were read by three bits of a digital input port. Calibrations The relative light output as a function of mirror galvanometer position was measured at the output of the integrating sphere using a PIN silicon photodiode (Silicon Detector Corp) and a current amplifier interfaced with the Mac II computer by a I%-bit A/D converter. The median of five readings for each of 109 positions was stored into a file for each galvanometer. Each galvanometer calibration was repeated three times and the median of the three was taken as the final value. A similar procedure was used to calibrate the neutral density wedge. The chromatic and white lights were calibrated for spectral energy distribution in the apparatus using a s~ctroradiometer (Intemational Light Inc, model IL 781). The spectroradiometer wavelength reading was referenced to a sodium lamp with a known spectral emission (589.6 nm). The calorimetric purities of the color filters ranged from 0.88 to 1.00. The luminance levels used were always referenced to the calibration for channel 2 white, which was measured by the EG&G photometer. Stimulus waveform and temporal frequency were measured at the D/A converter outputs using an oscilloscope and a digital counter/timer. Observers Five young observers (20-30 yr old) with normal color vision participated in the experiments. All observers were screened for color vision deficiencies using the Ishihara and Standard Pseudoisochromatic Plate tests, and the Neitz OT anomaloscope. All five observers showed superior discrimination for the FarnsworthMunsell loo-Hue test (errors ~40). Photometric matches between channels We measured chromatic discrimination thresholds in a constant luminance plane, so that the discrimination thresholds reflected the detection ability for chromatic differences. The technique of heterochromatic flicker photometry (HFP) was used to determine each observer’s sensation luminance match (Kaiser, 1988) for the various geld ~on~gurations. The median of three flicker photometric matches within a 0.05 log unit range was taken as the equiluminant match for each condition.
EXPERTS
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1: CHROMATIC DISCRI~NA~ON ALONG THE S-CONE AXIS
For discrimination dependent on S-cones, the first step was to determine pairs of chromatic lights that have different S-cone stimulation but identical M- and L-cone stimulations. Such pairs of lights pass through the tritanopic copunctal point in the chromati~ty diagram. Tritan pairs can be obtained by the method of minimally distinct border (MDB) (Tansley & Boynton, 1978; Zaidi, 1986). We used a bipartite field, with white light in one half of the field and equiluminous chromatic light in the other half of the field. The chromatic hemifield was composed of 560 and 580nm light. The observers changed the ratio of the 560 and 580 nm lights until the border disappeared or was ~nirni~d, culmination steps were measured along the tritan line from white to the 560/580 nm mixture and from the 560/580 nm mixture to white. The third data point for each observer was the disc~mination step from 448 nm light to white. Procedure A 2” bipartite field with a 2mm artificial pupil was used for the initial MDB protocol. One hemifield of the bipartite field consisted of channel 4 white, which was matched metametrically to channel 2 white by adjusting neutral density filters and inserting a small color correction filter (Kodak color compensating filter, CCOSR). The other half of the bipartite field was a mixture of light from channel 1 and channel 3. The filter wheel in channel 1 was set at 560 nm and a 580 nm interference filter (Ditric Optics) was placed in channel 3. The 580 and 560 nm lights were matched by HFP and set to give a 50: 50 ratio. The observer could change the proportion of 580/5~ nm light until the border between the white light and the chromatic light was maximally diminished. This procedure was repeated at least three times. The median for three trials that fell within a fairly narrow range (15% of the distance between 560-580 nm, equivalent to a wavelength range of 3 nm) was taken as the tritan metamer for white and the 560/580 nm mixture. For the chromatic discrimination experiment, a 2” circular field was used. White light from channel 2, the tritan metamer described above and 448 nm were used to study discrimination steps along the tritan line. Though 448 nm and the white are not on a tritan line, the change of M- and L-cone excitation was calculated to be 180-fold smaller than the change of S-cone excitation for the pair of stimuli at the discrimination threshold. The stimulus was presented as a 1 set temporal Gaussian waveform [e-(@-“.5)o.25~2], where t is time in seconds. The starting chromaticity and the experimental stimulus were presented in a three-alternative, temporal forced-choice paradigm. The control condition was 100% of the starting chromaticity. The experimental stimulus was the mixture of the starting and the discrimination color which was the appropriate ratio calculated in advance by a double random staircase procedure (Comsweet, 1962). One staircase started from 100% of the starting chromaticity and the other staircase started
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4 at 100% of the discrimination color. The up-and-down + JH transformed response rule (Wetherill & Levitt, 1965) was l-cSG used to diminish the influence of guessing: two correct * CL 440 NM responses were needed to move the staircase steps toward + FS 3 the starting chromaticity, but only one incorrect response u---w would shift the steps toward the discrimination color. I This rule provides an estimate of the 7 1% performance 3 2- 560/560 NM point on the psychometric function (Wetherill & Levitt, MIXTURE 1965). If the probability of guessing is taken into account, the calculated detection point on the psychometric function is 56% for the three-alternative, forced-choice lprocedure. Initially, the subject adapted to the starting chromaticity for 2 min. To start a trial, the subject pushed a button indicating readiness and the computer presented oI three intervals with the experimental stimulus occurring 1 4 2 3 -1 0 in one. A brief tone signaled the beginning of each LOG S TROLANDS interval. Each interval was 1 set in duration followed by a 0.5 set break. The subject viewed the test field con- FIGURE 2. The S-cone discrimination steps for five observers at tinuously. Three push buttons were used to signal the 110 td. Log AS is plotted as a function of the log S trolands at the starting chromaticity. interval changes by the subject. Between trials the observer adapted to the starting chromaticity. A discrimination was presumed to have occurred between the study for S-cone discrimination: the discrimination steps changed slowly as S-cone trolands increased and starting color and the experimental stimulus if the correct button was pushed. Using the calibration look-up table, approached the Weber region only at high S-cone stimulation levels. The limiting Weber fraction is about 3%. the necessary mirror galvanometer deflection positions were calculated for each desired step. The first step size The individual variance for S-cone absolute discrimination threshold spanned about 0.4 log unit. This range was 50% of the starting color. The step size was halved was smaller than for the Boynton and Kambe (1980) when a reversal response was obtained. The procedure observers. was continued until the step size was smaller than 0.1%. Figure 3 shows S-cone discrimination steps at four A tracking procedure with three reversals was then used luminance levels. Each data point represents the mean to obtain the discrimination threshold for a staircase. The average of the discrimination steps obtained by the for five observers for the 110 td condition, and the mean for three observers for the other luminance levels (290, two staircases was taken as the threshold. The procedure for measuring one threshold took about 15-20 min. We 29, and 2.9 td). For the 290 td field, only the two lower obtained data at three starting chromaticities (white, S-cone troland levels were measured because of a raditritan metamer, and 448 nm) and four luminance levels ance limitation of the calorimeter. The lines are fits of a model to be described below. The data show that as (2.9, 29, 110, and 290 td). A control experiment ensured that instrumental arti- luminance was increased from 2.9 to 290 td, the S-cone discrimination thresholds displaced along the 45” line. facts were not responsible for detection of the stimulus exchange. An interference filter, placed at the output port The horizontal asymptotic thresholds also increased of the integrating sphere, created isomeric lights from channels 1 and 2. Flicker photometry was used to obtain 3 -29lD equiluminance. Under these conditions, any difference in I 2.5 the output of these two channels need be due to optical artifact or miscalibration. The forced-choice double 2 random staircase procedure was run. No discrimination 1.5 thresholds were obtainable under these isomeric % 1 conditions. I
I
4
Results
The chromatic discrimination steps measured along the S-cone axis for a 110 td field are shown in Fig. 2. Symbols with solid lines represent data obtained by five observers. The data were plotted in units of S-cone troland differences as a function of the S-cone trolands at the starting chromaticity. The S-cone troland values for the 560/580 nm mixture, white light and 448 nm light were -0.34, 2.06 and 3.67 log S-cone trolands, respectively. The data showed similar trends as Boynton and Kambe’s
*
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100slRolaDs FIGURE 3. The mean S-cone discrimination steps for five (110 td) and three (290, 29, 2.9 td) observers. Error bars indicate standard errors of the means. The solid curves are the best fit of equation (15), where S,, = 1.0, S, = 0.04, and I, = 0.036.
CHROMATIC
1839
DISCRIMINATION
with luminance. That is, the absolute thresholds for the S-cone discrimination system depend on the mean luminance signal. Subsequent to the completion of this study, the differential effects of changing S-cone excitation by changing chromaticity and by changing luminance have been confirmed by Smith, Pokorny and Couropmitree (1993). Using a CRT display device, they measured discrimination steps for seven chromaticities along the tritan axis for retinal illuminance levels of 114 and 26 td. The data sets for the two luminance levels could not be fit with a single log AS vs log S-cone troland template.
chromaticity is relatively short, we assumed that gain of the discrimination chromaticity was dependent on S, only. Therefore, the output of the disc~mination chromaticity can be written as:
Analysis
that is:
02 = K(S,, + AS)G(S,).
(3b)
If the outputs of 0, and O2 are in the linear part of the signal-response curve and the observer has a criterion threshold (6) for disc~mination: 6 = 02 - 0, = K(S, + AS)G(S,)
- K(S,)G(S,) = K(AS)G(S,)
Boynton and Kambe (1980) described the S-cone disc~mination threshold by the following equation: AS = C,(S,,, + kB,)
G(&) = SN’(& + S,) = l/(1 + SaS,)
(2)
where S, (or l/S,) is a gain constant, the S-cone trolands where threshold is raised two-fold, and S, is the S-cone trolands at the starting chromaticity (cf. Hood & Greenstein, 1990). For a discrimination task in a constant luminance field, the output at the starting chromaticity is given by: 0, = Z=,G(Sti)
log AS = Iog(~~~) + log(l/G(S~)) = log S‘, + log (1 + S&,j)
(1)
where AS is the discrimination steps, C, is the limiting Weber fraction, S, is the S-cone troland at a given luminance level, B, is the “eigenblau” constant (44.5) and k is a dimensionless constant representing observer variance. If the quanta1 catch rate of S-cones is assumed to be the only factor that influences discrimination steps along the S-cone axis, the absolute threshold (k) and the Weber fraction in equation (1) should remain constant at different luminance levels. Our data indicate that this assumption does not hold: a common discrimination template does not describe S-cone discrimination changes with chromaticity and with mean luminance. To understand the mechanisms for the discrimination mediated by the S-cone, we rewrite the Boynton and Kambe (1980) equation to concur with a detection model which has been developed to incorporate the results of various increment threshold studies (Sperling & Sondhi, 1968; Pugh & Mollon, 1979; Geisler, 1981; Adelson, 1982; Hood & Greenstein, 1990). For one receptor type in one adaptation condition, there are two processes that control visual signal detection. The first process is transduction which translates the incoming light into neural system signals. This signal becomes the input to the second process, which contains a gain mechanism that produces Weber behavior. In the case of S-cone increment threshold, the elevation of threshold from dark adaptation to adapting excitation S, can be described by a gain control mechanism G(S,), equal to 1 at dark adaptation. The form of the gain control mechanism is:
(3a)
where K is a constant, Since the observer is always adapted to the starting chromaticity and the change from the starting chromaticity to the discrimination
(4)
(5)
where S, is the absolute discrimination threshold for S-cones. Equation (5) is algebraically equivalent to equation (1). There are two possible physiological sources which may account for the effect of mean luminance level. The first proposes that the S-cone output signal is attenuated by luminance information, Z (which is the sum of M- and L-cone activities). We modeled the luminance information either as a divisive or subtractive process from the S-cone system. Figure 4 (A-D) illustrates a scheme of these ideas. (A) Divisive process after the gain control: suppose the divisive process occurred after the gain control mechanism, then the signals are affected as: 0, = ~[S~~G(S~~)]/Z
@a)
0, = ZNS, + AS MWll~.
VW
Following the logic developed above, log AS = log S,, -i- log Z + log{ 1 + S,S,,)
(7)
and the effect of Zis to shift the log AS vs log S, template vertically [Fig. 4(A)]. (B) Subtractive process after the gain control: if the luminance information is a subtractive process, the signal is attenuated as S,G(S,) - Z, then 0, = Z-W,G(S,)
@a)
- Z] - Zl
(gb)
log AS = log S,, -I-log( 1 + S,&,).
(9)
0, = JXSti + AS)G(S,) and
A plot of log AS vs log S,, shows the same template function as luminance level changes [Fig. 4(B)]. (C) Divisive process before the gain control: for the divisive process before the gain control, both the signal, &/I and the gain control G(S,/Z) are affected. 0, = K K&+/Z)lG (SJZ )
(loa)
02 =‘K [(Sti + AS >/OlGt&i/Z>
UW
log AS = log S,, + log Z + lo&l + &(&/I)].
(11)
The predicted log AS vs log S plot is shown in Fig. 4(C). As luminance level changes, the threshold is
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LOGS
Eq-Qi-
RESFONSE
NOISE
LOGS FIGURE 4. Schematic drawing of five possible S-cone discrimination mechanisms and the consequence for Scone discrimination thresholds as a function of luminance. The first step is a linear transduction in Scone receptors. The receptor output becomes the input to a gain control mechanism. Following the gain control, the signals are divided (A) or subtracted (B) by the luminance information, I. In (C) and (D), the S-cone signals are attenuated by the luminance information before the gain control. (E) An early stage noise occurs before the S-cone gain control mechanism.
raised by log Z and the threshold for the gain change increases as log(Z/S,). Thus, the curve would shift upward and to the right along the 45” diagonal when luminance increases. Data from Expt 1 support this type of model qualitatively. (D) Subtractive process before the gain control: as in (C), both the signal, and the gain control are affected: 0, = KU,
-
MWt, - 0
O,=K[(S,+AS)-Z]G(S,-I) log AS = log S,, + log[l + S&S,, - Z)].
(124 (12b) (13)
The predictions are shown in Fig. 4(D). The Weber fractions keep constant as Z changes. When the slope of the template is zero, an increase of luminance would decrease the thresholds and a decrease of luminance
would increase the thresholds. This prediction does not correspond to the data. (E) Internal noise: a second interpretation for the modification of the cone output signals is the notion of noise of the S-cone system. Possible sources of noise includes an early stage noise before the S-cone gain control mechanism and a late stage noise after the gain (Graham & Hood, 1992). The effect of late stage noise would shift the log AS vs log S template vertically. This prediction is contradicted by our data. The early source of noise includes physical noise and biological noise. The physical noise (quanta1 noise) is a probabilistic event and proportional to the mean light level. The S-cone absolute discrimination thresholds are predicted to increase in proportion to the square root of the luminance level, if the S-cone system is an ideal detector (cf. Hood &
CHROMATIC
DI!SCRIMINATION
Finkelstein, 1986). This latter prediction does not correspond to the data. The early stage biological noise can be described as an additive process: AS/(& + N) = C
(14)
where AS is the discrimination threshold, iV is the noise, and C is a constant. A change of C would alter the Weber fraction, and a change of N would shift the threshold above the absolute S-cone threshold. This formula has the same format as equation (l), if (k&J represents noise of the system. The data indicated (k&) increases with luminance changes. Therefore, if the noise model is applicable to the present results, the noise of the S-cone dis~mination system changes as a fiction of luminance level. The higher l~inance data would require higher noise. This type of mechanism is shown in Fig. 4(E). Potential sources of early stage biological noise might include dark current, and/or neural fluctuation (Barlow, 1957). The divisive process Our analysis indicated that typical detection models can be used to predict our S-cone discrimination data qualitatively. Our model postulated a divisive process before the gain control mechanism. Equation (11) predicts that the discrimination templates are scaled by I. However, the data show that the templates converge as Z decreases. We then further postulate a regulation of the luminance signal, which has the format: (1 + Z,,Z).Thus, equation (11) becomes: log AS = log S,, + log(l + Z,Z) + log[l + S&,/(1
+ ZoZ)]. (15)
Thus, the chromatic discrimination thresholds along the S-cone axis can be described by three terms: the first a S-cone absolute threshold (S,), the second a luminance gain (Z,) regulating the size of the luminance signal, and the third a S-cone gain (S,) regulating the cone output. The lines in Fig, 3 show the fit of equation (15) to the average data, giving estimates of S,, = 1.0, I, = 0.036, and S, = 0.04. Equation (15) describes the data for most observers, although careful examination of Fig. 2 indicates a minimum discrimination threshold at white for observers FS and TY. A similar phenomenon is observed in the mean data (Fig. 3). This minimum is an indication of an opponent process contribution to S-cone discrimination. We would expect a better fitted result if additional parameters incorporating an opponent effect were included in equation (15) (Miyahara, Smith & Pokorny, 1993). We did not attempt to incorporate an opponent process in the current data, since it would require estimating four parameters from limited data points.
nant test stimuli were in the long wavelength end of the spectrum, where the S-cone activity is essentially zero. The results were compared to the data of Boynton and Kambe (1980). Procedure All lights were set to equiluminance by HFP. A 2” circular field was used. Monochromatic light (560, 600, 630, and 656 nm) from channel 1 was used as the starting chromatic&y. A 580 nm filter was placed in channel 2 for the measurement of the discrimination step from the starting color. The channel 2 580 nm light was also used as a starting chromaticity and a discrimination threshold was measured as the step toward the channel 1 600 nm light. Luminance levels used were the same as Expt 1: 2.9-290 td in steps of 0.4 or 1 log td. The double random staircase forced-choice paradigm described for Expt 1 was used to obtain chromatic discrimination thresholds. Results Figure 5 shows chromatic discrimination steps along the M/L-cone axis for five observers at 110 td. For each starting wavelength, the amount of L-cone excitation expressed in L trolands is plotted on the abscissa. On the ordinate the discrimination steps (AL) are plotted. These were computed as the difference in L-cone excitation at the disc~ination threshold and the starting chromaticity. The data show a distinct V-shaped function, indicating an opponent effect of the M- and L-cone input. The discrimination thresholds were best near 570nm. The M/L-cone discrimination steps for four luminance levels are shown in Fig. 6. The data points are the average data for five observers at 110 td, and three observers at 2.9, 29, and 290 td. The lines are model fits to the data described in the next section. In Fig. 6(A), each V-shaped function represents data from a different hmrinance level. For each luminance level, AhLis plotted as a function of the starting chromaticity. The slopes of the V-shaped 0.5
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In this experiment, we studied chromatic discrimination mediated by M- and L-cone excitations. The equihuni-
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EXPERIMENT 2: CHROMATIC DISCRIMINATION MEDIATED BY M- AND L-CONES
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LOG L TROLANDS FIGURE 5. The M/L-cone axis discrimination thresholds for five observers at 110 td. Log AL is plotted as a function of the log L trolands at the starting chromaticity.
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Lo6 LTROIANDS FIGURE 6. The mean M/L-cone discrimination steps for five observers at 110 td and three observers at 290,29, and 2.9 td. Error bars indicate standard errors of the means. The solid curve is the best fit of equation (17), where L, = 0.015, La = 0.14, and L,, = 2.31. (A) The V-shaped functions from left to right represent data from 2.9,29, 110 and 290 td. (B) The mean data are plotted as a function of L-cone trolands. Each symbol represents a different chromaticity. The lines are the best fit of equation (17).
functions are similar as luminance level changes, indicating a constant opponent effect. The error bars represent the standard errors of the mean. The individual differences among observers did not change with luminance level. In Fig. 6(B), we replotted the data and the model fits as a function of mean chromaticity. Each line represents the data from a different starting chromaticity. For each starting chromaticity, the discrimination thresholds increased as luminance levels increased. The functions are parallel near the Weber region. This result suggest that the opponent signal is independent of luminance level near the Weber region.
Boynton and Kambe. (Lt., + Mtd) gives the test luminance level, and (L, - 2M,) is the L- and M-cone sensitivity difference. C, represents the Weber fraction of the data, C, the weighting of the M- and L-cone excitation differences for each chromaticity, and C, the weighting of the S-cone input. Boynton and Kambe’s (1980) data revealed C, to be 0.0105 and C, to be 0.8. These values vary between studies. S, is S-cone trolands at a given luminance level. The contribution of S-cones to detection along the M/L-cone axis, has not been verified in other studies (e.g. Krauskopf, Williams & Heeley, 1982; Stromeyer & Lee, 1988; Nagy et al., 1987; Miyahara et al., 1993). The Boynton and Kambe (1980) equation has the disadvantage of that it does not relate directly to possible physiological mechanisms, although our data can be well described by the equation. We chose to fit the data to a model developed to incorporate retinal gain control mechanisms and spectral opponency (Smith, Pokorny & Yeh, 1993). Like Boynton and Kambe (1980), we assume discrimination is mediated by L- and M-cone systems in a spectrally opponent channel. This spectral opponency is similar in form to the detection mechanism proposed by Wandell and Pugh (1980), Reeves ( 1981), and Stromeyer, Cole and Kronauer (1985). In developing the model, we noted that with adaptation to white the discrimination data show a minimum at the chromaticity of the white (Miyahara et al., 1993). With a dark surround, discrimination still show a minimum near equal energy white (Boynton & Kambe, 1980). We made the assumption that even when a chromatic stimulus is viewed in a dark surround, the primary factor determining cone adaptation is near equal energy white. In addition to the M- and L-cone spectral opponency, we proposed retinal gain controls before the opponency. Following the same logical development for the S-cone discrimination, we obtained: log AL = log Lth + log( 1 + L,L,) + log[l + LO,lL - L*IlU +
WA)l.
(17)
According to equation (17) chromatic discrimination thresholds mediated by M- and L-cones are regulated by three terms: the first is the absolute threshold L,,, the second is a receptor gain term with constant L,, and the third is an opponent gain term with constant L,,. L, is the L-cone trolands near white. The lines in Fig. 6 show the fit of equation (17) to the average data, giving estimates of L, = 0.681 (576 nm), L, = 0.015, L, = 0.14, and L,, = 2.31. The data and predictions are in agreement. DISCUSSION
Analysis
Location of the gain mechanism for the S-cone system
Boynton and Kambe (1980) characterized M/L-cone discrimination thresholds by the following equation:
Zrenner and Gouras (1981) also Zrenner (1982) proposed a model hypothesizing sensitivity regulation of the S-cone signal by the L-cones via a horizontal cell. The model originated from the observation that the signal/spontaneous discharge ratio for a S-cone input ganglion cell increased from dark adaptation to bright
AL = C,U,, + Mtd) + C&d - 2J4,,I +
G&l (16)
where AL is the discrimination step along the M/L-cone axis, Mt,, and L, are the cone trolands as specified by
CHROMATIC
DISCRIMINATION
1843
BELOW 32 TD 48-90 TD lOO-200TD ABOVE 200 TD
0.5
1
1.5
2
2.5
3
106sTRoLANDs
B
1
0.5
i
O
-
5 TD TEMPLATE
------
BOTDTEMPlATE
-
14OTDTEMPlATE
----
24OTDTEMPlATE
-0.5
-1 0.5
1
1.5
2
2.5
3
lo6slRol.ANDs FIGURE 7. Brown and MacAdam’s (1949) data plotted in the format of log AS vs log Std. The lined are the model fit of equation (15) at 240,140,80, and 5 td. The best fit parameters are S,, = 0.0314, S, = 0.412, and I, = 0.114 for observer WRBG’s data, and S,, = 0.06, S, = 0.172, and 1, = 0.053 for observer DLM.
yellow adapting light, and there was an increase of the spontaneous discharge rate after the offset of the yellow background. The sensitivity enhancement by a yellow adapting light on this ganglion cell is opposite to the psychophysical result of Expt 1, and the result of other studies (Pugh & Mollon, 1979; Polden & Mollon, 1980; Wisowaty & Boynton, 1980; Yeh, Smith & Pokorny, 1989). This contradiction may be due to methodological differences between the Zrenner and Gouras study (1981) and the psychophysical experiments. However, if the Zrenner model is a proper description of the retinal ganglion cell reaction to a S-cone stimulus, then it implies that the gain control mechanism correlated to the psychophysical discrimination thresholds is located at a more central locus than the ganglion cell in the visual system. Pugh and Mollon (1979), and Polden and Mollon (1980) have developed a two-site detection theory to account for increment threshold data for the S-cone system. However, their model cannot explain our luminance data: it would require that the white field become progressively yellowish as luminance increases. The model in Fig. 4(C) is consistent with their theory in emphasizing the intluence of the M- and L-cones to the S-cone system, but our model postulates a divisive luminance input before the S-cone gain control.
Comparison
with Boynton and Kambe’s
(1980) result
Boynton and Kambe (1980) measured chromatic discrimination steps at 120 td. The discrimination mediated by S-cone excitation yielded an optimal Weber fraction of about 18%, and that for M/L-cone excitation of about 1.05%, indicating a 1% change in L-cone excitation with a concurrent 1% change in M-cone excitation. These values are six-fold larger than the estimates from our 110 td data (3 and 0.186%, respectively). We do concur however that limiting Weber behavior is about nine times higher for the S-cones than for L- and M-cones. Boynton and Kambe’s (1980) data suggested that major observer variation for chromatic discrimination threshold was the variance of the S-cone absolute thresholds. Our observers showed less inter-observer variation and in individual fits, this was mostly in IO. Miyahara et al. (1993) also emphasized observer variation in the amount of opponency that occurred in dark or dim surrounds. Boynton and Kambe (1980) showed that the individual variance among observers increased with mean luminance level for the discrimination along the M/Lcone axis. In our study, this was not the case. Our data also revealed a larger opponent gain than that of Boynton
TSAIYAO YEH et al.
1844
and Kambe (1980). A possible source of these differences is the difference of criterion due to variation in experimental design. Boynton and Kambe (1980) investigated supra-th~hold di~~mination steps. The observers had to report not only a change in color, but also the direction of the changes. We used a forced choice technique and this procedure yielded smaller discrimination steps. Comparison with Brown and ~acAd~~s
data
Figure 7 shows Brown and MacAdam’s (1949) S-cone discrimination data (tabulated by Nagy et al., 1987). Brown and MacAdam varied luminance level from 1.2 and 363 td between different chromaticities. We separated their data into four l~inance groups and plotted the discrimination thresholds in the log AS vs log S, format. The plot shows that the ASS converge along the 45” line at higher S-cone troland levels and confirms this aspect of our results. The conditions ran by Brown and MacAdam (1949) produced limited data at low S, levels. The few data points in the region are consistent with the effect we described for the effect of luminance on S-cone discrimination thresholds. We also looked at the Brown and MacAdam data along the M/L-cone axis. Their experimental conditions were such that the chromaticity and luminance level did not yield a spectrum of M/L-cone activity. Thus, the Brown and MacAdam data are not informative with the respect to the M/L-cone discrimination model developed here.
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Barlow, H. B. (1957). Increment thresholds at low intensities considered as signal/noise discrimination. Journal of Physiology, I36,469-488.
Boynton, R. M. & Kambe, N. (1980). Chromatic difference steps of moderate size measured along theoretically critical axes. Co/or Research and Application, 5, 13-23.
Brown, W. R. J. (1951). The influence of luminance level on visual sensitivity to color differences. Journal of the Optical Society of America, 41, 684-688.
Brown, W. R. J. & MaeAdam, D. L. (1949). Visual sensiti~ties to combined chromaticity and luminance differences. Journal of the OpticoI Society
of America, 39, 808-834.
Clarke, F. J. J. (1967). Colour measurement in industry. The effect of field-element size on chromaticity discrimination. Proceedings of a Symposium on Coiour Measurement in Industry (pp. 132-150). London: The Colour Group. Cornsweet, T. N. (1962). The stair~~-meth~ in psychophysics. American Journal of Psychology, 75, 485-491.
Dobrowolski, J. A., Marsh, G. E., Charbonneau, D. G., Eng, J. & Josephy, P. D. (1977). Colored filter glasses: An intercomparison of glasses made by different manufacturers. Applied Optics, 16, 1491-1512.
Friele, L. F. C. (1961). Analysis of the Brown and Brown-MacAdam colour di~~~nation data. Farbe, 10, 193. Geisler, W. S. (1981). Effect of bleaching and backgrounds on the flash response of the cone system. Journal of Physiofogy, London, 312, 413-434. Graham, N. & Hood, D. C. (1992). Quanta1 noise and decision rules in dynamic models of light adaptation. Vision Research, 3.?,779-787.
von Helmholtz, H. (1896). Hondbuch der Physiologischen Optik (2nd edn). Hamburg: Voss. Hood, D. C. & Finkelstein, M. A. (1986). Sensitivity to light. In Boff, K. R., Kaufman, L. & Thomas, J. P. (Eds), ~ondbook of~r~eption and human ~rforman~e, New York: Wiley.
Vol I: Sensory processes and perception.
Hood, D. C. & Greenstein, V. (1990). Models of the normal and abnormal rod system. Vision Research, 30, 51-68. Kaiser, P. K. (1988). Sensation luminance: A new name to distinguish CIE luminance from luminance dependent on an individual’s spectral ~nsitivity. Vision Research, 28, 455-456. Krauskopf, J., Wiltiams, D. & Heeley, D. (1982). Cardinal directions of color space. Vision Research, 22, 1123-113 I. Le Grand, Y. (1949). Les seuils differentiels de couleurs dans la theotie de Young. Reseoch d’opt, 28, 261-278. MacAdam, D. L. (1942). Visual sensitivites to color differences in daylight. Journal of the Opticai Society of America, 32, 247.-274. MacLeod, D. I. A. & Boynton, R. M. (1979). Chromaticity diagram showing cone excitation by stimuli of equal luminance. Journal of the Optical Society of America, 69, 1183-l 186. McCree, K. J. (1960). Colour confusion produced by voluntary fixation. Optic0 Acta, 7, 281-291. Miyahara, E., Smith, V. C. & Pokomy, J. (1993). How surrounds affect chromatic&y discrimination. Journal of the Optical Society of America. in press. Nagy, A. L., Eskew, R. T. & Boynton, R. M. (1987). Analysis of color-matching ellipses in a cone-excitation space. Journal of the Optical Society of America, 4, 756-768.
Polden, P. G. & Mellon, J. D. (1980). Reversed effect of adapting stimuli on visual sensitivity. Proceedings of the Royal Society of London, 2f0, 235-272.
Pugh, E. N. & Mellon, J. D. (1979). A theory of the ~1 and n3 color mechanisms of Stiles. Vision Research, 19, 293-312. Reeves, A. (1981). Transient desensitization of a red-green opponent site. Vision Research, 21, 1267-1277. Schrlidinger, E. (1920). Grundlinien einer Theorie der Farbenmetrik im Tagessehen. Annalen de Physik, 63, 481. [English translation in (1970) MacAdam, D. L., (Ed.), Sources of color science (pp. 134-182). Cambridge, Mass.: MIT Press.] Smith, V. C., Pokomy, J. & Couropmitree, N. (1993). S-cone discriminations as a function of luminance and background. Submitted for ARVO. Smith, V. C., Pokorny, J. & Yeh, T. (1993). Pigment tests evaluated by a model of chromatic discrimination. Journal of the Optical Society of America. In press. Sperling, H. G. & Sondhi, M. M. (1968). Model for visual luminance discrimination and thicker detection. Journal of the Optical Society of America, 58, 1133-l 145. Stahell, U. & Stabell, B. (1977). Wavelength discrimination of peripheral cones and its change with rod intrusion. Vision Research, i 7, 423-426.
Stiles, W. S. (1946). A modified Helmholtz line-element in brightnesscolour space. Proceedings of the Physical Society tendons, 58, 41-65.
Stromeyer, C. F. III & Lee, J. (1988). Adaptational effects of short wave cone signals on red-green chromatic detection. Vision Research, 28, 93 l-940. Stromeyer, C. F. I. III, Cole, G. R. & Kronauer, R. E. (1985). Second-site adaptation in the red-green chromatic pathways. Vision Research, 25, 219-237.
Tansley, B. W. & Boynton, R. M. (1978). Chromatic border perception: The role of red- and green-sensitive cones. Vision Research, f8, 683-697. Vos, J. J. & Walraven, P. L. (1972a). An analytical description of the line element in the zone-fluctuation model of colour vision-I. Basic concepts. Vision Research, 1.2, 1327-1344. Vos, J. J. & Walraven, P. L. (1972b). An analytical d~ription of the line element in the zone-fluctuation model of colour vision-II. The deviation of the line element. Vision Research, I2, 1345-1356. Wandell, B. A. & Pugh, E. N. (1980). Detection of long-duration, longwavelength incremental flashes by a chromatically coded pathway. Vision Research, 20, 625-636.
CHROMATIC
DISCRIMINATION
Weale, R. A. (1951). Hue-discrimination in para-central parts of the human retina measured at different luminance levels. Journal of Physiology, 113, 115-122. Wetherill, G. B. & Levitt, H. (1965). Sequential estimation of points on a psychometric function. British Journal of Mathematical and Statistical Psychology, 18, l-10. Wisowaty, J. & Boynton, R. M. (1980). Temporal modulation sensitivity of the blue mechanism: Measurements made without chromatic adaptation. Vision Research, 20, 895-909. Wright, W. D. (1941). The sensitivity of the eye to small colour differences. Proceedings of the Physical Society (London), 53, 93-112. Wright, W. D. & Pitt, F. H. G. (1934). Hue-discrimination in normal colour-vision. Proceedings of the Physical Society (London), 46, 459-473.
Wyszecki, G. & Fielder, G. H. (1971). New color-matching ellipses. Journal of the Optical Society of America, 61, 1135-l 152. Yeh, T., Smith, V. C. & Pokomy, J. (1989). The effect of background
1845
luminance on cone sensitivity functions. Investigative Ophthalmology and Visual Science, 30, 2077-2086.
Zaidi, Q. (1986). Adaptation and color matching. Vision Research, 26, 1925-1938. Zrenner, E. (1982). Electrophysiological characteristics of the blue sensitive mechanism: Test of a model of cone interaction under physiological and pathological conditions. Documenta Ophthalmologica Proceedings
Series, 33, 103-t 25.
Zrenner, E. & Gouras, P. (1981). Characteristics of the blue sensitive cone mechanism on primate retinal ganglion cells. Vision Research, 21, 1605-1609.
study was supported in part by NIH Research Grant EY07390 (Smith). This paper is based in part on material from the Ph.D. dissertation submitted by T. Yeh to the University of Chicago, 1991. Acknowledgements-This
0042-6989/93 $6.00 + 0.00 Copyright 0 1993 Pergamon Press Ltd
Chromatic Discrimination with Variation in Chromaticity and Luminance: Data and Theory TSAIYAO YEH,*t
JOEL POKORNY,*$
VIVIANNE
C. SMITH*
Received 9 July 1992; in revised form 30 December 1992
Boy&on and Kambe developed a model of somatic ~~~~nation in which thresholds are mediated by two independent mechanisms: the short-wavelength sensitive (S-) cones (S-cone axis), and the middle-wavelength sensitive @I-) and long-wavelength sensitive (I_,-)cones (M/L-cone axis). In this study, we used a Maxwellian view optical system to investigate fundamental properties of the model as a fu~on of ~omatici~ and leak. We condom that ~~~a~o~ along the f&zone axis were dependent on S-cone excitation level. However, changes in chromaticity and changes in mean luminance were not described by a single threshold-vs-radiance (TVR) template. We developed a model to account for the different effects of changing S-cone excitation by varying mean chromaticity and by varying mean l~nance. M/L-cone donation showed a mourn at the L-cone excitation to white, indicating strong opponeucy. The thresholds increased with luminance approaching a Weber region and showing parallel functions for differing chromaticities. These data are fit by a model allowing retinal gain controls and spectral opponency. Color vision
Chromatic
discrimination
Psychophysics
The purpose of this study was to investigate how the differential sensitivities of the cone types regulate the ability of an observer to di~~minate two patches of light differing in chromaticity. Chromatic discrimination data are most frequently presented in the form of wavelength discrimination steps for spectral light, or in the form of di~~mina~on steps (Wright & Pitt, 1934; Wright, 1941) or discrimination ellipses (MacAdam, 1942; Brown & MacAdam, 1949; Wyszecki & Fielder, 1971) in the chromaticity diagram. Chromatic disc~~nation thresholds are affected by variation in luminance level. Wavelength discrimination functions deteriorate in the short wavelength region at low luminance levels (Weale, 1951; McCree, 1960; Stabell & Stabell, 1977). The effects of luminance on chromatic discrimination ellipses were described by Brown and MacAdam (1949), Brown (1951), and Wyszecki and Fielder (1971). The major axes of the ellipses rotated toward the blue corner of the chromaticity diagram as field luminance decreased. Clarke (1967) compared chromatic discrimination at different presentation intervals and luminance levels. Disc~mination steps along
*Visual Sciences Center, The University of Chicago, 939 East 57th Street, Chicago, IL 60637, U.S.A. 7Present address: Department of Ne~obiolo~, Max-Planck Institute for Biophysical Chemistry, Giittingen, Germany. /To whom reprint requests should be addressed.
the S-cone axis increased more than steps along the M/L-cone axis as luminance and field size decreased. Generally, it can be concluded that the discrimination sensitivity based on S-cones declines more than M- and L-cones at low luminance levels. One classical approach to represent chromatic discrimination data is the line element. Early line element theories used the differences of receptor excitation to express a change in color experience (Helmholtz, 1896; Schrodinger, 1920; Stiles, 1946). Le Grand (1949) analyzed MacAdam’s data and found that chromatic discrimination thresholds were mediated by only two independent variables: a S-cone pathway, and a M- and L-cone pathway. His analysis also suggested minimum discrimination thresholds near white for the M- and L-cone system. Later line element theories incorporated opponent stages in the model (Friele, 1961; Vos & Walraven, 1972a, b). In general, line element predictions were in agreement with experiment data, if the numerical parameters were adequately chosen. Boynton and Kambe (1980) followed Le Grand’s (1949) pioneering work. They measured chromatic discrimination along the cone excitation axes of the MacLe~-Boynton (1979) chromaticity space. Data from Boynton and Kambe (1980) showed that, at 120 td, discrimination ability dependent on S-cones changed slowly with S-cone excitation and approached the Weber region only at high levels of S-cone stimulation. Discrimination along the M/L-cone axis was near the Weber region. Their data also confirmed an opponent process
1835
TSAIYAO
1836
contribution to discrimination along the M/L-cone axis. Boynton and Kambe further developed chromatic discrimination equations to describe their data. They noted however that the equation did not describe S-cone discrimination data for luminance levels higher than the 120 td constant luminance plane. A similar finding was reported for the analysis of the Brown and MacAdam (1949) data (Nagy, Eskew & Boynton, 1987). The purpose of the present study was to evaluate and extend the Boynton and Kambe model. We measured discrimination thresholds along the S-cone axis and the M/L-cone axis as a function of chromaticity and luminance level. The data were analyzed in units of S-cone trolands, and L-cone trolands, as specified by Boynton and Kambe (1980). At a constant luminance level, our data can be well described by Boynton and Kambe’s equations. However, the fitting parameters for this model varied as luminance level changed. These results suggested that quanta1 catch of the cones alone cannot explain the effect of luminance level on chromatic discrimination thresholds. We fit the data to a model of chromatic discrimination which includes gain control mechanisms and spectral opponency. EXPERIMENTAL
METHODS
Apparatus
The light source was a 450 W Xenon arc lamp (Osram XBO 450 W ofr) driven by a regulated power supply (Electronic Measurements Inc, model ELXE 1000 B). The light was split into four channels (Fig. 1). For three of the channels, light was collimated (by Ll), passed through a mask (Ml), and was then focused (by L2) on the mirror galvanometers (MG). The light passed through
YEH et al.
a second mask (M2). The amount of light passed by mask M2 depended on the angular position of the mirror galvanometers. After recollimation (L3), light from all three channels fell on a large Fresnel lens (L4) and was focused on the input port of an integrating sphere. In channel 4, light was collimated (Ll), passed through another Fresnel lens (L4), and was focused on the input port of a second integrating sphere. The exit ports of the integrating spheres served as sources for a Maxwellian view system with a lens (L5) placing images of the output ports in the plane of an artificial pupil. A 3 mm artificial pupil was used in the study (except for the MDB measurement for Expt 1). An ophthalmic lens (L6) could be placed adjacent to the artificial pupil to bring the image of the field stop into sharp focus. A chin-rest was used to position the observer’s head. The light from the two integrating spheres formed a bipartite field by means of a prism cube with half of the hypotenuse silvered. The right hemifield was illuminated by channel 4 and the left hemifield by the channels 1-3. The bipartite field could be changed to a uniform circular field illuminated by the output of the first integrating sphere (channels l-3), by adjusting the position of a field stop in front of the prism. The illuminance and chromaticity of each channel was adjusted by use of colored and neutral filters. In channel 1, a wheel with 13 chromatic filters and a 3 log unit neutral density wedge were used to control chromaticity and light level. The filter wheel included three-cavity interference filters (Ditric Optics) for middle-spectrum light. For short and long wavelengths, broad-band blocking filters [Ealing Electra-optics Inc, Balzers and “Russian Glasses” (Dobrowolski, Marsh, Charbonneau, Eng & Josephy, 1977)] were used. The CIE chromaticity
I\
CHANNEL4
INTEGRATING CHANNEL3
SPHERE
MIRROR
r
3
CHANNEL1
LIGHTSOURCE
L4
L -ROL
M2
FIGURE
1. Schematic of the four channel optical system. See text for details
CHROMATIC
DISCRIMINATION
coordinates of the channel 2 white were x = 0.3536, y = 0.3546. The device was controlled by a Macintosh II computer, and MacADIOS II digital input~output boards (GW Instruments). Two GW Instruments’ GWI-DAC 16-bit D/A daughterboards generated signals to move the mirror galvanometers and determined the wedge position by a d.c. servocontrol. The wedge could be also controlled manually and its position read by the MacADIOS. The interference filter wheel was run by a 12-bit D/A converter. A buzzer, used to alert the observer, was activated by a digital output port. Three switches were used to signal the observer’s responses. Switch responses were read by three bits of a digital input port. Calibrations The relative light output as a function of mirror galvanometer position was measured at the output of the integrating sphere using a PIN silicon photodiode (Silicon Detector Corp) and a current amplifier interfaced with the Mac II computer by a I%-bit A/D converter. The median of five readings for each of 109 positions was stored into a file for each galvanometer. Each galvanometer calibration was repeated three times and the median of the three was taken as the final value. A similar procedure was used to calibrate the neutral density wedge. The chromatic and white lights were calibrated for spectral energy distribution in the apparatus using a s~ctroradiometer (Intemational Light Inc, model IL 781). The spectroradiometer wavelength reading was referenced to a sodium lamp with a known spectral emission (589.6 nm). The calorimetric purities of the color filters ranged from 0.88 to 1.00. The luminance levels used were always referenced to the calibration for channel 2 white, which was measured by the EG&G photometer. Stimulus waveform and temporal frequency were measured at the D/A converter outputs using an oscilloscope and a digital counter/timer. Observers Five young observers (20-30 yr old) with normal color vision participated in the experiments. All observers were screened for color vision deficiencies using the Ishihara and Standard Pseudoisochromatic Plate tests, and the Neitz OT anomaloscope. All five observers showed superior discrimination for the FarnsworthMunsell loo-Hue test (errors ~40). Photometric matches between channels We measured chromatic discrimination thresholds in a constant luminance plane, so that the discrimination thresholds reflected the detection ability for chromatic differences. The technique of heterochromatic flicker photometry (HFP) was used to determine each observer’s sensation luminance match (Kaiser, 1988) for the various geld ~on~gurations. The median of three flicker photometric matches within a 0.05 log unit range was taken as the equiluminant match for each condition.
EXPERTS
1837
1: CHROMATIC DISCRI~NA~ON ALONG THE S-CONE AXIS
For discrimination dependent on S-cones, the first step was to determine pairs of chromatic lights that have different S-cone stimulation but identical M- and L-cone stimulations. Such pairs of lights pass through the tritanopic copunctal point in the chromati~ty diagram. Tritan pairs can be obtained by the method of minimally distinct border (MDB) (Tansley & Boynton, 1978; Zaidi, 1986). We used a bipartite field, with white light in one half of the field and equiluminous chromatic light in the other half of the field. The chromatic hemifield was composed of 560 and 580nm light. The observers changed the ratio of the 560 and 580 nm lights until the border disappeared or was ~nirni~d, culmination steps were measured along the tritan line from white to the 560/580 nm mixture and from the 560/580 nm mixture to white. The third data point for each observer was the disc~mination step from 448 nm light to white. Procedure A 2” bipartite field with a 2mm artificial pupil was used for the initial MDB protocol. One hemifield of the bipartite field consisted of channel 4 white, which was matched metametrically to channel 2 white by adjusting neutral density filters and inserting a small color correction filter (Kodak color compensating filter, CCOSR). The other half of the bipartite field was a mixture of light from channel 1 and channel 3. The filter wheel in channel 1 was set at 560 nm and a 580 nm interference filter (Ditric Optics) was placed in channel 3. The 580 and 560 nm lights were matched by HFP and set to give a 50: 50 ratio. The observer could change the proportion of 580/5~ nm light until the border between the white light and the chromatic light was maximally diminished. This procedure was repeated at least three times. The median for three trials that fell within a fairly narrow range (15% of the distance between 560-580 nm, equivalent to a wavelength range of 3 nm) was taken as the tritan metamer for white and the 560/580 nm mixture. For the chromatic discrimination experiment, a 2” circular field was used. White light from channel 2, the tritan metamer described above and 448 nm were used to study discrimination steps along the tritan line. Though 448 nm and the white are not on a tritan line, the change of M- and L-cone excitation was calculated to be 180-fold smaller than the change of S-cone excitation for the pair of stimuli at the discrimination threshold. The stimulus was presented as a 1 set temporal Gaussian waveform [e-(@-“.5)o.25~2], where t is time in seconds. The starting chromaticity and the experimental stimulus were presented in a three-alternative, temporal forced-choice paradigm. The control condition was 100% of the starting chromaticity. The experimental stimulus was the mixture of the starting and the discrimination color which was the appropriate ratio calculated in advance by a double random staircase procedure (Comsweet, 1962). One staircase started from 100% of the starting chromaticity and the other staircase started
1838
TSAIYAO
YEH et al.
4 at 100% of the discrimination color. The up-and-down + JH transformed response rule (Wetherill & Levitt, 1965) was l-cSG used to diminish the influence of guessing: two correct * CL 440 NM responses were needed to move the staircase steps toward + FS 3 the starting chromaticity, but only one incorrect response u---w would shift the steps toward the discrimination color. I This rule provides an estimate of the 7 1% performance 3 2- 560/560 NM point on the psychometric function (Wetherill & Levitt, MIXTURE 1965). If the probability of guessing is taken into account, the calculated detection point on the psychometric function is 56% for the three-alternative, forced-choice lprocedure. Initially, the subject adapted to the starting chromaticity for 2 min. To start a trial, the subject pushed a button indicating readiness and the computer presented oI three intervals with the experimental stimulus occurring 1 4 2 3 -1 0 in one. A brief tone signaled the beginning of each LOG S TROLANDS interval. Each interval was 1 set in duration followed by a 0.5 set break. The subject viewed the test field con- FIGURE 2. The S-cone discrimination steps for five observers at tinuously. Three push buttons were used to signal the 110 td. Log AS is plotted as a function of the log S trolands at the starting chromaticity. interval changes by the subject. Between trials the observer adapted to the starting chromaticity. A discrimination was presumed to have occurred between the study for S-cone discrimination: the discrimination steps changed slowly as S-cone trolands increased and starting color and the experimental stimulus if the correct button was pushed. Using the calibration look-up table, approached the Weber region only at high S-cone stimulation levels. The limiting Weber fraction is about 3%. the necessary mirror galvanometer deflection positions were calculated for each desired step. The first step size The individual variance for S-cone absolute discrimination threshold spanned about 0.4 log unit. This range was 50% of the starting color. The step size was halved was smaller than for the Boynton and Kambe (1980) when a reversal response was obtained. The procedure observers. was continued until the step size was smaller than 0.1%. Figure 3 shows S-cone discrimination steps at four A tracking procedure with three reversals was then used luminance levels. Each data point represents the mean to obtain the discrimination threshold for a staircase. The average of the discrimination steps obtained by the for five observers for the 110 td condition, and the mean for three observers for the other luminance levels (290, two staircases was taken as the threshold. The procedure for measuring one threshold took about 15-20 min. We 29, and 2.9 td). For the 290 td field, only the two lower obtained data at three starting chromaticities (white, S-cone troland levels were measured because of a raditritan metamer, and 448 nm) and four luminance levels ance limitation of the calorimeter. The lines are fits of a model to be described below. The data show that as (2.9, 29, 110, and 290 td). A control experiment ensured that instrumental arti- luminance was increased from 2.9 to 290 td, the S-cone discrimination thresholds displaced along the 45” line. facts were not responsible for detection of the stimulus exchange. An interference filter, placed at the output port The horizontal asymptotic thresholds also increased of the integrating sphere, created isomeric lights from channels 1 and 2. Flicker photometry was used to obtain 3 -29lD equiluminance. Under these conditions, any difference in I 2.5 the output of these two channels need be due to optical artifact or miscalibration. The forced-choice double 2 random staircase procedure was run. No discrimination 1.5 thresholds were obtainable under these isomeric % 1 conditions. I
I
4
Results
The chromatic discrimination steps measured along the S-cone axis for a 110 td field are shown in Fig. 2. Symbols with solid lines represent data obtained by five observers. The data were plotted in units of S-cone troland differences as a function of the S-cone trolands at the starting chromaticity. The S-cone troland values for the 560/580 nm mixture, white light and 448 nm light were -0.34, 2.06 and 3.67 log S-cone trolands, respectively. The data showed similar trends as Boynton and Kambe’s
*
I
I
1
0.5
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
100slRolaDs FIGURE 3. The mean S-cone discrimination steps for five (110 td) and three (290, 29, 2.9 td) observers. Error bars indicate standard errors of the means. The solid curves are the best fit of equation (15), where S,, = 1.0, S, = 0.04, and I, = 0.036.
CHROMATIC
1839
DISCRIMINATION
with luminance. That is, the absolute thresholds for the S-cone discrimination system depend on the mean luminance signal. Subsequent to the completion of this study, the differential effects of changing S-cone excitation by changing chromaticity and by changing luminance have been confirmed by Smith, Pokorny and Couropmitree (1993). Using a CRT display device, they measured discrimination steps for seven chromaticities along the tritan axis for retinal illuminance levels of 114 and 26 td. The data sets for the two luminance levels could not be fit with a single log AS vs log S-cone troland template.
chromaticity is relatively short, we assumed that gain of the discrimination chromaticity was dependent on S, only. Therefore, the output of the disc~mination chromaticity can be written as:
Analysis
that is:
02 = K(S,, + AS)G(S,).
(3b)
If the outputs of 0, and O2 are in the linear part of the signal-response curve and the observer has a criterion threshold (6) for disc~mination: 6 = 02 - 0, = K(S, + AS)G(S,)
- K(S,)G(S,) = K(AS)G(S,)
Boynton and Kambe (1980) described the S-cone disc~mination threshold by the following equation: AS = C,(S,,, + kB,)
G(&) = SN’(& + S,) = l/(1 + SaS,)
(2)
where S, (or l/S,) is a gain constant, the S-cone trolands where threshold is raised two-fold, and S, is the S-cone trolands at the starting chromaticity (cf. Hood & Greenstein, 1990). For a discrimination task in a constant luminance field, the output at the starting chromaticity is given by: 0, = Z=,G(Sti)
log AS = Iog(~~~) + log(l/G(S~)) = log S‘, + log (1 + S&,j)
(1)
where AS is the discrimination steps, C, is the limiting Weber fraction, S, is the S-cone troland at a given luminance level, B, is the “eigenblau” constant (44.5) and k is a dimensionless constant representing observer variance. If the quanta1 catch rate of S-cones is assumed to be the only factor that influences discrimination steps along the S-cone axis, the absolute threshold (k) and the Weber fraction in equation (1) should remain constant at different luminance levels. Our data indicate that this assumption does not hold: a common discrimination template does not describe S-cone discrimination changes with chromaticity and with mean luminance. To understand the mechanisms for the discrimination mediated by the S-cone, we rewrite the Boynton and Kambe (1980) equation to concur with a detection model which has been developed to incorporate the results of various increment threshold studies (Sperling & Sondhi, 1968; Pugh & Mollon, 1979; Geisler, 1981; Adelson, 1982; Hood & Greenstein, 1990). For one receptor type in one adaptation condition, there are two processes that control visual signal detection. The first process is transduction which translates the incoming light into neural system signals. This signal becomes the input to the second process, which contains a gain mechanism that produces Weber behavior. In the case of S-cone increment threshold, the elevation of threshold from dark adaptation to adapting excitation S, can be described by a gain control mechanism G(S,), equal to 1 at dark adaptation. The form of the gain control mechanism is:
(3a)
where K is a constant, Since the observer is always adapted to the starting chromaticity and the change from the starting chromaticity to the discrimination
(4)
(5)
where S, is the absolute discrimination threshold for S-cones. Equation (5) is algebraically equivalent to equation (1). There are two possible physiological sources which may account for the effect of mean luminance level. The first proposes that the S-cone output signal is attenuated by luminance information, Z (which is the sum of M- and L-cone activities). We modeled the luminance information either as a divisive or subtractive process from the S-cone system. Figure 4 (A-D) illustrates a scheme of these ideas. (A) Divisive process after the gain control: suppose the divisive process occurred after the gain control mechanism, then the signals are affected as: 0, = ~[S~~G(S~~)]/Z
@a)
0, = ZNS, + AS MWll~.
VW
Following the logic developed above, log AS = log S,, -i- log Z + log{ 1 + S,S,,)
(7)
and the effect of Zis to shift the log AS vs log S, template vertically [Fig. 4(A)]. (B) Subtractive process after the gain control: if the luminance information is a subtractive process, the signal is attenuated as S,G(S,) - Z, then 0, = Z-W,G(S,)
@a)
- Z] - Zl
(gb)
log AS = log S,, -I-log( 1 + S,&,).
(9)
0, = JXSti + AS)G(S,) and
A plot of log AS vs log S,, shows the same template function as luminance level changes [Fig. 4(B)]. (C) Divisive process before the gain control: for the divisive process before the gain control, both the signal, &/I and the gain control G(S,/Z) are affected. 0, = K K&+/Z)lG (SJZ )
(loa)
02 =‘K [(Sti + AS >/OlGt&i/Z>
UW
log AS = log S,, + log Z + lo&l + &(&/I)].
(11)
The predicted log AS vs log S plot is shown in Fig. 4(C). As luminance level changes, the threshold is
TSAIYAO
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YEH et al.
P
LOW
!
HIGH
I
LOGS
Eq-Qi-
RESFONSE
NOISE
LOGS FIGURE 4. Schematic drawing of five possible S-cone discrimination mechanisms and the consequence for Scone discrimination thresholds as a function of luminance. The first step is a linear transduction in Scone receptors. The receptor output becomes the input to a gain control mechanism. Following the gain control, the signals are divided (A) or subtracted (B) by the luminance information, I. In (C) and (D), the S-cone signals are attenuated by the luminance information before the gain control. (E) An early stage noise occurs before the S-cone gain control mechanism.
raised by log Z and the threshold for the gain change increases as log(Z/S,). Thus, the curve would shift upward and to the right along the 45” diagonal when luminance increases. Data from Expt 1 support this type of model qualitatively. (D) Subtractive process before the gain control: as in (C), both the signal, and the gain control are affected: 0, = KU,
-
MWt, - 0
O,=K[(S,+AS)-Z]G(S,-I) log AS = log S,, + log[l + S&S,, - Z)].
(124 (12b) (13)
The predictions are shown in Fig. 4(D). The Weber fractions keep constant as Z changes. When the slope of the template is zero, an increase of luminance would decrease the thresholds and a decrease of luminance
would increase the thresholds. This prediction does not correspond to the data. (E) Internal noise: a second interpretation for the modification of the cone output signals is the notion of noise of the S-cone system. Possible sources of noise includes an early stage noise before the S-cone gain control mechanism and a late stage noise after the gain (Graham & Hood, 1992). The effect of late stage noise would shift the log AS vs log S template vertically. This prediction is contradicted by our data. The early source of noise includes physical noise and biological noise. The physical noise (quanta1 noise) is a probabilistic event and proportional to the mean light level. The S-cone absolute discrimination thresholds are predicted to increase in proportion to the square root of the luminance level, if the S-cone system is an ideal detector (cf. Hood &
CHROMATIC
DI!SCRIMINATION
Finkelstein, 1986). This latter prediction does not correspond to the data. The early stage biological noise can be described as an additive process: AS/(& + N) = C
(14)
where AS is the discrimination threshold, iV is the noise, and C is a constant. A change of C would alter the Weber fraction, and a change of N would shift the threshold above the absolute S-cone threshold. This formula has the same format as equation (l), if (k&J represents noise of the system. The data indicated (k&) increases with luminance changes. Therefore, if the noise model is applicable to the present results, the noise of the S-cone dis~mination system changes as a fiction of luminance level. The higher l~inance data would require higher noise. This type of mechanism is shown in Fig. 4(E). Potential sources of early stage biological noise might include dark current, and/or neural fluctuation (Barlow, 1957). The divisive process Our analysis indicated that typical detection models can be used to predict our S-cone discrimination data qualitatively. Our model postulated a divisive process before the gain control mechanism. Equation (11) predicts that the discrimination templates are scaled by I. However, the data show that the templates converge as Z decreases. We then further postulate a regulation of the luminance signal, which has the format: (1 + Z,,Z).Thus, equation (11) becomes: log AS = log S,, + log(l + Z,Z) + log[l + S&,/(1
+ ZoZ)]. (15)
Thus, the chromatic discrimination thresholds along the S-cone axis can be described by three terms: the first a S-cone absolute threshold (S,), the second a luminance gain (Z,) regulating the size of the luminance signal, and the third a S-cone gain (S,) regulating the cone output. The lines in Fig, 3 show the fit of equation (15) to the average data, giving estimates of S,, = 1.0, I, = 0.036, and S, = 0.04. Equation (15) describes the data for most observers, although careful examination of Fig. 2 indicates a minimum discrimination threshold at white for observers FS and TY. A similar phenomenon is observed in the mean data (Fig. 3). This minimum is an indication of an opponent process contribution to S-cone discrimination. We would expect a better fitted result if additional parameters incorporating an opponent effect were included in equation (15) (Miyahara, Smith & Pokorny, 1993). We did not attempt to incorporate an opponent process in the current data, since it would require estimating four parameters from limited data points.
nant test stimuli were in the long wavelength end of the spectrum, where the S-cone activity is essentially zero. The results were compared to the data of Boynton and Kambe (1980). Procedure All lights were set to equiluminance by HFP. A 2” circular field was used. Monochromatic light (560, 600, 630, and 656 nm) from channel 1 was used as the starting chromatic&y. A 580 nm filter was placed in channel 2 for the measurement of the discrimination step from the starting color. The channel 2 580 nm light was also used as a starting chromaticity and a discrimination threshold was measured as the step toward the channel 1 600 nm light. Luminance levels used were the same as Expt 1: 2.9-290 td in steps of 0.4 or 1 log td. The double random staircase forced-choice paradigm described for Expt 1 was used to obtain chromatic discrimination thresholds. Results Figure 5 shows chromatic discrimination steps along the M/L-cone axis for five observers at 110 td. For each starting wavelength, the amount of L-cone excitation expressed in L trolands is plotted on the abscissa. On the ordinate the discrimination steps (AL) are plotted. These were computed as the difference in L-cone excitation at the disc~ination threshold and the starting chromaticity. The data show a distinct V-shaped function, indicating an opponent effect of the M- and L-cone input. The discrimination thresholds were best near 570nm. The M/L-cone discrimination steps for four luminance levels are shown in Fig. 6. The data points are the average data for five observers at 110 td, and three observers at 2.9, 29, and 290 td. The lines are model fits to the data described in the next section. In Fig. 6(A), each V-shaped function represents data from a different hmrinance level. For each luminance level, AhLis plotted as a function of the starting chromaticity. The slopes of the V-shaped 0.5
I +a.?
In this experiment, we studied chromatic discrimination mediated by M- and L-cone excitations. The equihuni-
JH
-a “VFS 0.0- I
TY
d a 2 -0.5-
-1.0 1.0
EXPERIMENT 2: CHROMATIC DISCRIMINATION MEDIATED BY M- AND L-CONES
lslll
8.. 1.5
.
*
I.. 2.0
.
.
i
LOG L TROLANDS FIGURE 5. The M/L-cone axis discrimination thresholds for five observers at 110 td. Log AL is plotted as a function of the log L trolands at the starting chromaticity.
TSAIYAO YEH et al.
1842
A ‘L 0.5
0 I -0.5 ‘I i
d
-1;
Y v
-1.5 -
-2.;Y an~.“‘:“‘.:““:““:““:““I 0 0.5
1
1.5
0
560nm
n
58Onm
0
6OOnm
0
63Onm
A
6!55nm
2
2.5
3
2
2.5
3
LOG LTROIANW
B 1 0.5 0 -0.5 i
-1 -1.5 -2
0
0.5
1
1.5
Lo6 LTROIANDS FIGURE 6. The mean M/L-cone discrimination steps for five observers at 110 td and three observers at 290,29, and 2.9 td. Error bars indicate standard errors of the means. The solid curve is the best fit of equation (17), where L, = 0.015, La = 0.14, and L,, = 2.31. (A) The V-shaped functions from left to right represent data from 2.9,29, 110 and 290 td. (B) The mean data are plotted as a function of L-cone trolands. Each symbol represents a different chromaticity. The lines are the best fit of equation (17).
functions are similar as luminance level changes, indicating a constant opponent effect. The error bars represent the standard errors of the mean. The individual differences among observers did not change with luminance level. In Fig. 6(B), we replotted the data and the model fits as a function of mean chromaticity. Each line represents the data from a different starting chromaticity. For each starting chromaticity, the discrimination thresholds increased as luminance levels increased. The functions are parallel near the Weber region. This result suggest that the opponent signal is independent of luminance level near the Weber region.
Boynton and Kambe. (Lt., + Mtd) gives the test luminance level, and (L, - 2M,) is the L- and M-cone sensitivity difference. C, represents the Weber fraction of the data, C, the weighting of the M- and L-cone excitation differences for each chromaticity, and C, the weighting of the S-cone input. Boynton and Kambe’s (1980) data revealed C, to be 0.0105 and C, to be 0.8. These values vary between studies. S, is S-cone trolands at a given luminance level. The contribution of S-cones to detection along the M/L-cone axis, has not been verified in other studies (e.g. Krauskopf, Williams & Heeley, 1982; Stromeyer & Lee, 1988; Nagy et al., 1987; Miyahara et al., 1993). The Boynton and Kambe (1980) equation has the disadvantage of that it does not relate directly to possible physiological mechanisms, although our data can be well described by the equation. We chose to fit the data to a model developed to incorporate retinal gain control mechanisms and spectral opponency (Smith, Pokorny & Yeh, 1993). Like Boynton and Kambe (1980), we assume discrimination is mediated by L- and M-cone systems in a spectrally opponent channel. This spectral opponency is similar in form to the detection mechanism proposed by Wandell and Pugh (1980), Reeves ( 1981), and Stromeyer, Cole and Kronauer (1985). In developing the model, we noted that with adaptation to white the discrimination data show a minimum at the chromaticity of the white (Miyahara et al., 1993). With a dark surround, discrimination still show a minimum near equal energy white (Boynton & Kambe, 1980). We made the assumption that even when a chromatic stimulus is viewed in a dark surround, the primary factor determining cone adaptation is near equal energy white. In addition to the M- and L-cone spectral opponency, we proposed retinal gain controls before the opponency. Following the same logical development for the S-cone discrimination, we obtained: log AL = log Lth + log( 1 + L,L,) + log[l + LO,lL - L*IlU +
WA)l.
(17)
According to equation (17) chromatic discrimination thresholds mediated by M- and L-cones are regulated by three terms: the first is the absolute threshold L,,, the second is a receptor gain term with constant L,, and the third is an opponent gain term with constant L,,. L, is the L-cone trolands near white. The lines in Fig. 6 show the fit of equation (17) to the average data, giving estimates of L, = 0.681 (576 nm), L, = 0.015, L, = 0.14, and L,, = 2.31. The data and predictions are in agreement. DISCUSSION
Analysis
Location of the gain mechanism for the S-cone system
Boynton and Kambe (1980) characterized M/L-cone discrimination thresholds by the following equation:
Zrenner and Gouras (1981) also Zrenner (1982) proposed a model hypothesizing sensitivity regulation of the S-cone signal by the L-cones via a horizontal cell. The model originated from the observation that the signal/spontaneous discharge ratio for a S-cone input ganglion cell increased from dark adaptation to bright
AL = C,U,, + Mtd) + C&d - 2J4,,I +
G&l (16)
where AL is the discrimination step along the M/L-cone axis, Mt,, and L, are the cone trolands as specified by
CHROMATIC
DISCRIMINATION
1843
BELOW 32 TD 48-90 TD lOO-200TD ABOVE 200 TD
0.5
1
1.5
2
2.5
3
106sTRoLANDs
B
1
0.5
i
O
-
5 TD TEMPLATE
------
BOTDTEMPlATE
-
14OTDTEMPlATE
----
24OTDTEMPlATE
-0.5
-1 0.5
1
1.5
2
2.5
3
lo6slRol.ANDs FIGURE 7. Brown and MacAdam’s (1949) data plotted in the format of log AS vs log Std. The lined are the model fit of equation (15) at 240,140,80, and 5 td. The best fit parameters are S,, = 0.0314, S, = 0.412, and I, = 0.114 for observer WRBG’s data, and S,, = 0.06, S, = 0.172, and 1, = 0.053 for observer DLM.
yellow adapting light, and there was an increase of the spontaneous discharge rate after the offset of the yellow background. The sensitivity enhancement by a yellow adapting light on this ganglion cell is opposite to the psychophysical result of Expt 1, and the result of other studies (Pugh & Mollon, 1979; Polden & Mollon, 1980; Wisowaty & Boynton, 1980; Yeh, Smith & Pokorny, 1989). This contradiction may be due to methodological differences between the Zrenner and Gouras study (1981) and the psychophysical experiments. However, if the Zrenner model is a proper description of the retinal ganglion cell reaction to a S-cone stimulus, then it implies that the gain control mechanism correlated to the psychophysical discrimination thresholds is located at a more central locus than the ganglion cell in the visual system. Pugh and Mollon (1979), and Polden and Mollon (1980) have developed a two-site detection theory to account for increment threshold data for the S-cone system. However, their model cannot explain our luminance data: it would require that the white field become progressively yellowish as luminance increases. The model in Fig. 4(C) is consistent with their theory in emphasizing the intluence of the M- and L-cones to the S-cone system, but our model postulates a divisive luminance input before the S-cone gain control.
Comparison
with Boynton and Kambe’s
(1980) result
Boynton and Kambe (1980) measured chromatic discrimination steps at 120 td. The discrimination mediated by S-cone excitation yielded an optimal Weber fraction of about 18%, and that for M/L-cone excitation of about 1.05%, indicating a 1% change in L-cone excitation with a concurrent 1% change in M-cone excitation. These values are six-fold larger than the estimates from our 110 td data (3 and 0.186%, respectively). We do concur however that limiting Weber behavior is about nine times higher for the S-cones than for L- and M-cones. Boynton and Kambe’s (1980) data suggested that major observer variation for chromatic discrimination threshold was the variance of the S-cone absolute thresholds. Our observers showed less inter-observer variation and in individual fits, this was mostly in IO. Miyahara et al. (1993) also emphasized observer variation in the amount of opponency that occurred in dark or dim surrounds. Boynton and Kambe (1980) showed that the individual variance among observers increased with mean luminance level for the discrimination along the M/Lcone axis. In our study, this was not the case. Our data also revealed a larger opponent gain than that of Boynton
TSAIYAO YEH et al.
1844
and Kambe (1980). A possible source of these differences is the difference of criterion due to variation in experimental design. Boynton and Kambe (1980) investigated supra-th~hold di~~mination steps. The observers had to report not only a change in color, but also the direction of the changes. We used a forced choice technique and this procedure yielded smaller discrimination steps. Comparison with Brown and ~acAd~~s
data
Figure 7 shows Brown and MacAdam’s (1949) S-cone discrimination data (tabulated by Nagy et al., 1987). Brown and MacAdam varied luminance level from 1.2 and 363 td between different chromaticities. We separated their data into four l~inance groups and plotted the discrimination thresholds in the log AS vs log S, format. The plot shows that the ASS converge along the 45” line at higher S-cone troland levels and confirms this aspect of our results. The conditions ran by Brown and MacAdam (1949) produced limited data at low S, levels. The few data points in the region are consistent with the effect we described for the effect of luminance on S-cone discrimination thresholds. We also looked at the Brown and MacAdam data along the M/L-cone axis. Their experimental conditions were such that the chromaticity and luminance level did not yield a spectrum of M/L-cone activity. Thus, the Brown and MacAdam data are not informative with the respect to the M/L-cone discrimination model developed here.
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study was supported in part by NIH Research Grant EY07390 (Smith). This paper is based in part on material from the Ph.D. dissertation submitted by T. Yeh to the University of Chicago, 1991. Acknowledgements-This
