foveal cone thresholds

vision Res. Vol. 29, No. 1, pp. 61-78, 1989 Printed in Great Britain. All rights WCrvcd

0042-6989/89 $3.00 + 0.00 Copyrigt Q 1989 Pcrgamon Press plc

FOVEAL CONE THRESHOLDS7

RAM L. PANDEY VIMAL,* JOEL POKORNY, ** VIVIANNE C. SMITH and STEVEN K. SHEVELL

The Eye Research Laboratories, The University of Chicago, 939 East 57th Street, Chicago, IL 60637, U.S.A.

(Received 14 December 1987; in revised form 26 May 1988)

Abstract-The method of constant stimuli was used to estimate the psychometric functions for detection of one or two flashes when two light pulses were presented. The test stimulus consisted of two simultaneous 0.5 msec, 1’ pulses separated by 17’. Observers reported seeing 0, 1 or 2 flashes. A computer-controlled direct-view apparatus allowed sampling of slightly different fovea1 locations on each trial. The data were analyzed assuming a binomial probability for sampling of L and M cones and Poisson distributed quanta1 fluctuation. Under these assumptions, the measurements imply that detection requires a minimum of 5-7 quanta absorbed per cone, and that the effective number of cones illuminated by the l’, 0.5 msec pulse is two. The estimated L/M cone ratio was 1.6 for one observer and 4.0 for the other; each observer’s ratio was in general agreement with the value estimated independently by heterochromatic flicker photometry.

Color vision Cones Fovea Detection threshold L/M Cone ratio Receptor mosaic

INTRODUCTION

Two fundamental types of information needed for modeling color vision are the ratio of the number of long wavelength sensitive cones to middle wavelength sensitive cones, that is, the L/M ratio, and the minimum number of quanta absorbed per cone for detection. Previous estimates of the L/M ratio for an average observer range from 1.5 : 1 to 2: 1 using the Weber frac- tion for the cones (Vos and Walraven, 19X), the relative heights of cone sensitivity functions (Walraven, 1974), and fits of the cone fundamentals to the luminosity function Vi (Smith and Pokorny, 1975).

Studies in the literature uniformly suggest that more than one quantum per cone is required at absolute photopic threshold. Bouman and colleagues estimated two or three quanta per cone (Bouman and van der Velden, 1948; Bouman and Walraven, 1957). Other estimates have been higher, at least five (Brindley, 1954, 1963; Marriott, 1963) or six (Cicerone and Nerger, 1985). Williams et al. (198 1 b) estimated a minimum of 10 quanta per cone at detection threshold for dark-adapted short-wavelength cones.

tThis research was presented at the Annual Meeting of the Optical Society of Amen& in Washington D.C. in 1985.

*Current address: Eye Research Institute of Retina Foun- dation, Neuroscience Unit, 20 Staniford Street, Boston, MA 02114, U.S.A.

**To whom reprint requests should be addressed.

An issue that is less well-resolved concerns the individual variability in L/M ratio. Rushton and Baker (1964) performed heterochromatic flicker photometric measurements on 197 color normal observers. Further, they used retinal densitometry to, evaluate a subset of these observers whose photometric matches were at the extremes of their population. The densitometry confirmed that observers who were “green sensitive” by photometry had more MWS pigment by densitometry than those who were photo- metrically “red sensitive”. Rushton and Baker, in what they term “only semi-quantitative study” (Rushton and Baker, 1964) estimated from densitometry that the range of variation of L/M ratio for their observers varied over a range from 1: 3-3: 1 (apparently with an assumed mean of unity, though they give no details of the analysis).

An upper bound for the variability can be obtained from flicker photometric matches. Within the CIE Standard Observer [and the Judd (1951) revised Standard Observer], the luminous efficiency function V, is represented as a linear combination of the color matching functions, and can be modeled as a weighted sum of the cone receptor sensitivities. Smith and Pokorny (1975) modeled the Judd Standard Observer Vi as a weighted sum of the LWS and MWS cone sensitivities. The L/M ratio for the Judd Standard Observer is 1.6: 1. If we assume that real observers share the spectral sensitivities of the cones of the Standard Observer but vary

61

62 RAM L. PANDEY VIMAL et al.

in the proportion of the various cone types, then individual flicker photometric spectral sensitivities may be modeled by varying the weights in the sums of the LWS and MWS sensitivity functions. Pokorny and Smith (1989) computed the possible range of cone ratios consistent with the variation of population flicker photometric spectral sensitivity data (Rushton and Baker, 1964; Adam, 1969; Lutze, 1988). The result of the calculation suggests that color-normal male individuals may have L/M cone ratios ranging from 0.5: 1 (2 MWS cones for each LWS cone) to 1O:I (10 LWS cones for each MWS cone). This calculation is an upper bound since minor variation in photopigment spectra and pre- receptoral filtering may contribute to HFP variability.

RATIONALE

There is a diverse history of the use of punctate stimuli to explore the receptors constituting the retinal mosaic. Significant modern con- tributions have been made by Bouman and Walraven (1957), Krauskopf (1964; 1978) Krauskopf and Srebro (1965), Williams et al. (1981 b) and Cicerone and Nerger (1985). The present study employs very small stimuli (1’) briefly presented at an eccentricity of 8.5’ from the central fovea. The exposure duration was sufiiciently short so that eye movements were unlikely to smear the retinal image during a stimulus presentation. In this analysis we con- sider only the LWS and MWS cones; it is unlikely that SWS cones play a role in fovea1 threshold detection. Both anatomical (Marc and Sperling, 1977; DeMonasterio et al., 1981; De- Monasterio et al., 1985) and psychophysical (Williams et al., 1981b) studies indicate that the SWS cones represent less than 10% of the total number of cones in the primate retina and that they are much scarcer in the central fovea1 region (Stiles, 1949; Wald, 1967; Williams et al., 1981a). Additionally we chose our stimuli (A > 520 nm) to minimize SWS cone stimu- lation.

We can outline the rationale of our approach by developing a hypothetical retinal mosaic and then exploring the consequences of change in the major independent variable, wavelength. Figure 1 shows an idealized mosaic of LWS and MWS cones arranged in a regular triangular array. The cone types have been assigned to locations in a random manner, with an L/M ratio of 2 : 1. The successive panels from left to

right show how the relative probability of quan- tal catch would change as a function of wavelength. Here, probability of quanta1 catch is represented by a grey scale, with higher reflectances indicating higher probabilities. For the purpose of demonstration, the LWS-cone probability of quanta1 catch is represented by the same grey for all the wavelengths. For the shortest wavelength, 520 nm, the MWS cones have a slightly higher probability of quanta1 absorption than the LWS cones. For a wavelength where the two cone types have similar probability of absorption, 546 nm, all of the receptors in the mosaic have equal probability of quanta1 catch. With a further increase in wavelength, 580 nm, the mosaic is constructed of LWS cones and “probability troughs” at the locations of the MWS cones. Finally, at a long wavelength, 650 nm, the MWS “probability troughs” are very dense. Therefore it may be seen that the distribution of the probability of quanta1 catch by the cones which lay under the retinal image of a stimulus will vary with wavelength,

In this study the stimuli were small, 1’ in dia. With sufficiently small retinal stimuli, the change in the relative probability of quanta1 catch for the two cone types will be revealed by changes in the shapes of threshold psychometric functions, with shallower functions being associated with stimuli of longer wavelength (the actual stimulus situation we used is a bit more complicated than this, but the logic is the same). Mosaics composed of different L/M cone ratios will have different frequencies of “probability troughs”, the depth of which vary with wavelength. Specifically, the greater the proportion of MWS cones, the greater the expected change in the shape of the psychometric function with wavelength. Figure 2 (left panels) shows the predicted psychometric functions for two wavelengths (546 and 650 nm) as a function of the average number of quanta absorbed when the stimulus consists of one point of light (other modeling parameters are given in the figure caption). The upper left graph is for a mosaic with a L/M ratio of 1: 1 (PL = 0.5), the middle left graph is for a ratio of 2: 1 (PL = 0.67) and the lower left graph is for a ratio of 3: 1 (PL = 0.75). As can be seen, with an increase in the density of “probability troughs” (created in the locations of the MWS cones at long wavelengths), the 650 nm psychometric functions change shape, and for the specific modeling parameters, the 1: 1 L/M cone ratio predicts a

-1 -

\ \

. \

-2 - '\ \

-3 I I I

500 550 600 650

WAVELENGTH

Fig. 1. The lower panel shows the Smith and Pokomy (1975) LWS and MWS fundamentals normalized to equal sensitivity at their peaks. The upper panels all represent the same mosaic of LWS and MWS cones with the successive panels from left to right showing how the relative probabilities of quanta1 catch for MWS and LWS cones would change as a function of wavelength. The cone types have been assigned to locations in a random manner, with an L/M ratio of 2: 1. The grey scale is used to represent probability of quanta1 catch with higher reflectances indicating higher probabilities. For the purpose of graphical presentation, the LWS-cone probability of quanta1 catch has been assigned the same grey for all the

wavelengths.

63

Fovea1 cone thresholds 65

ONE POINT PRESENlATlON PL I 0.s

LOD RELATIVE OUANTA

PL I 0.67

0 t *

LOQ WAllVE QUANTA

PL = 0.75

0 I 2

LOD RELAllVE OUANTA

TWO POlNT PRESENTATION PLs0.s

i i P

LOO INCIDENT OIJANTA

PL 3 0.67

1 0

LOO INCIDENT OUAN’lA

PL t 0.75

LOD INCIDENT OllAN7A

Fig. 2. Predicted detection functions for wavelengths 546 nm and 650nm based on the model. The probability of detection for the one point presentation paradigm (left panels) is plotted as a function of log relative quanta (i.e. average number of quanta absorbed at the photoreceptor) to allow comparison of the slopes. The probability of detection for the two point presentation paradigm (right panels) is plotted as a function of log average number of quanta incident at the photoreceptor, to allow separation of the 546 and 650 nm functions. The average number of quanta, C, is assumed to be 5; the number of cones attaining this average number, N, is 2; the parameter PL is the proportion of LWS cones. The upper panels show predictions for a PL of 0.5 (L/M ratio of 1.0); middle panels for Pr of 0.667 (L/M ratio of 2.0) and lower panels for PL of 0.75 (L/M ratio of 3.0). The dashed lines in the right panels are a replot of

the predictions for one point presentation.

duplex psychometric function. In this situation, tense so that the MWS cones in the mosaic each to achieve a probability of detection ap- approach a 1.0 probability of reaching the de- proaching 1.0, stimuli need be sufficiently in- tection criterion.

66 RAM L. PANDEY VIMAL ef al.

The experimental paradigm we used involves measurement of a pair of psychometric functions at each of a series of wavelengths presented to the dark-adapted fovea. Since the adapting conditions are identical for all measurements, any changes in the shape of the psychometric functions may be attributed to wavelength specific effects. At any given wavelength, each trial consists of simultaneous brief presentation of two point sources.* The observer reports seeing 0, 1 or 2 stimuli. Psycho- metric functions for the detection of both stimuli, and either one or both stimuli were constructed. From probability theory, the two psychometric functions are related (the under- lying assumptions are more fully discussed later). If the probability of detecting one stimulus (given that only one is presented) is P, then the probability of seeing neither, seeing exactly one, or seeing two points is (1 - P)2, 2(1 - P)P and P*. If we assume a psychometric function for detection when the stimulus is a single point, we can derive the pair of psychometric functions associated with detection when the stimulus is two points-the probability of seeing either one or two points [P(2 - P)], and of seeing two points (P2). From this analysis it may be seen that the pair of psychometric functions for “1 or 2” and “2” are associated; their separation will covary with the slope. A close separation is associated with steep psychometric functions. The right hand panels of Fig. 2 show the relation between the psychometric functions derived for a two point presentation experiment (solid lines) from those for an experiment in which only one point of light is the stimulus (dashed lines). In this figure we plot detection as a function of average quanta incident at the receptor, so that the 546 and 650 nm predictions are separated.

What is the biological significance of the pair of psychometric functions? On each trial the two points of light stimulate two clusters of cones. From Fig. 1 it can be seen that sufficiently Small stimuli could sometimes stimulate clusters composed totally of LWS cones, sometimes stimulate clusters with both cone types and sometimes

*O’Brien (1951) first used a two dot presentation technique to explore an aspect of the retinal mosaic. Thou@~ the purpose of his experiment is not of current interest (to evaluate Hecht’s theory for the change in visual acuity with illumination), O’Brien realized some of the consequences of presenting two stimuli rather than one on each trial.

stimulate clusters composed totally of MWS cones. If the sampling of the retinal mosaic is random from trial to trial (as is accomplished by changing the retinal locus of the two stimuli from trial to trial), then the two point stimuli will randomly strike clusters composed of cones whose constitution will be related to the overall frequency of the LWS and MWS cone types. The psychometric function for seeing “1 or 2” is weighted toward the average detection probability function for the more-sensitive of the two stimulated patches of retina while the psychometric function for seeing “2” is weighted toward the average detection probability function for the less-sensitive patch of retina. As can be seen, the pair of psychometric functions represent sampling of two different populations of cone clusters, with one (“1 or 2”) being more heavily weighted with the clusters containing the more sensitive cone type, and the other (“2”) with clusters containing the less sensitive cone type. From the HFP data discussed above, it appears that a typical observer’s L/M ratio will be greater than 1.0. For mosaics composed of a majority of LWS receptors, the psychometric function for seeing “2” ensures that we often sample the population of MWS cones and allows a better estimate of the L /A4 ratio. This can be seen from the plots of Fig. 3. The top graph shows theoretical psychometric functions for an experiment in which the stimulus consists of one point. Functions are shown for one wavelength, 650 nm, and for seven values of P,: 1.0, 0.875, 0.75,0.67,0.50,0.25 and 0.00. The axis is shown as log average quanta incident at the receptor. The 546 nm predictions superimpose since all the cones in the mosaic have the same probability of quanta1 catch and are not shown. For 650 nm, the successive functions differ with the differences being associated with density of “probability troughs” at the locations of the MWS receptors. The lower graphs show a par- allel set of theoretical functions for the experimental condition in which the stimulus consists of two point sources. The 650 nm “1 or 2” psychometric functions cluster more closely than the functions for a single point stimulus, as would be expected if the proportion of LWS cones contributing to the “1 or 2” psychometric function was greater than for the single point stimulus shown above. The “2” psychometric functions are spread further apart, as expected if the proportion of LWS cones was less than for the single point stimulus. The two point presentation data allow a greater distinction


ONE POINT PRESENTATION

0 i i

LOQ INCIDENT QUANTA

TWO POINT PRESENTATION PROBABILITY OF SEEING ONE OR TWO

Od

Od

LOO INCIDENT QUANTA

PROBABiUIY OF SEEING TWO l.O-

0 1 i

LOG INCIDENT QUANTA

Fig. 3. The effect of varying PL on the predicted functions for 650 mn, plotted as a function of log average incident quanta. The values for C (5) and N (2) are as in Fig. 2. The upper panel shows the probability of detection for the one point presentation paradigm. The lower pair of panels show data for the two point presentation paradigm: the probability of seeing “one or two” (left) and the probability of seeing “two” (right). The values of PL are 1.0, 0.875, 0.75, 0.667, 0.5, 0.25 and 0.0; as Pr is decreased, the

functions move systematically toward the position for a PL of 0 (shown in the lower tight panel).

between the various PL values. For our experimental situation, the two-point design provides a richer data set than would paradigms using detection of a single stimulus (e.g. Marriott, 1963; Cicerone and Nerger, 1985) and better serves to restrict the acceptable range of model parameters.

Overview of the model

The model we develop gives an estimate of the L/M cone ratio. Additionally, estimates of two other biologically important parameters are derived: the minimum number of quanta absorbed per cone for detection, and the effective number of cones participating in the detection process

for a 1’ stimulus presented to the dark-adapted fovea. Detection data were fit with a model positing Poisson distributed stimulus quanta1 fluctuation. By making these measurements at a number of different wavelengths, it was possible to estimate the L/M ratio assuming a binomial probability for L and M cone sampling. The model parameters were optimized to fit for each wavelength the pair of psychometric functions and their separation on a relative radiance axis. The model has three major estimated parameters: PL (the probability of any single cone being an L cone), C (the minimum number of quanta that must be absorbed by a single cone for detection) and N (the effective number of


SCHEMATIC DIAGRAM OF THE APPARATUS

-I - AP

FIELD OF VIEW

2” 2 TEST STIMULI

I .

4 FIXATION POINTS

Fig. 4. Schematic diagram of the apparatus and the field of view. Top panel: A: two apertures with two shutters, AP: 2 mm artificial pupil, BS: beam splitter, D: diffuser, FB: filter box, FL: Xenon arc flash lamp, FS: field stop, L: lens, ND: neutral density, P: Pechan prism image rotator. Bottom panel: Two 1’ test stimuli separated by 17’ from each other and centered within four fixation points. The dotted circle

indicates the path of the two test stimuli as a function of the rotation of the Pechan prism.

cones illuminated by a stimulus). These three quantities do not depend on wavelength and therefore are highly constrained by measurements taken at many different wavelengths. Additionally, we estimated scaling factors that allow us to convert from units of relative radiance to units of average number of quanta absorbed per cone.

Apparatus

METHODS

A schematic diagram of the apparatus is shown in the top panel of Fig. 4. The stimuli

were generated by a computer controlled, direct-view apparatus with a Xenon arc flash lamp FL (U.S. Scientific 2CP-2) as the source. The input energy per flash was 1.5 J. The tempo- ral waveform of the light was a virtually instan- taneous pulse followed by an exponential decay, with half power occurring at 0.5msec. The spectral content of each of the test stimuli was determined by a three-cavity interference filter (Ditric Optics) with a half-bandpass width of 10-l 2 nm. A 2.7 log unit neutral density wedge allowed variation in stimulus radiance. The two test stimuli were 1’ in dia. (&fined by two 0.4 mm pinholes), and were separated by 17’.

Foveal cone thresholds 69

Each had its own shutter. The two test Stimuli were centered within four fixation dots as shown in the bottom panel of Fig. 4. A Pechan prism image rotator (P) was used to sample various fovea1 locations from trial to trial. The dotted circle indicates the possible locations of the two test stimuli on successive trials. A 2 mm artificial pupil with chin and head rest was used. The neutral density wedge was calibrated using a tungsten source and an EG&G photometer/ radiometer. The lens, the diffuser and the pinholes were adjusted to make the two stimuli identical to each other in all respects. This was verified by comparing the psychometric functions obtained for two interleaved one point presentation trials.

For heterochromatic flicker photomet~ (HFP) a separate apparatus (Lutze et al., 1987) allowing a 1.8” field was used. A mirrored two sectored disc provided alternation of light from a low color temperature tungsten source (the standard) and light from a Bausch and Lomb grating monochromator (500 mm focal length) in M~wellian view. The radiance of the narrowband light could be varied with a neutral density wedge. The relative radiances of the stimuli were measured at the eyepiece with the EG&G photometer/radiometer with the “flat” filter and confirmed with a thermocouple (Dexter Research) and lock-in amplifier.

Procedure

The method of constant stimuli was used for the detection experiment. The observer was positioned close to the exit aperture of the instrument (with the cornea less than 5 mm from the artificial pupil) and aligned on the photopically visible fixation dots. Following 7 min dark adaptation the observer initiated a trial and reported seeing 0, 1 or 2 points. First, 60 random trials using two-point presentation were given to find the appropriate stimulus range for the main ex~~ment. That is, a lower radiance level was determined for which the percent seen was near zero and a higher radiance level was determined at which both points were seen nearly 100% of the time. After about 5 min of additional dark adaptation, 580 ran-

dom trials were presented. Of these 60 were blank trials (both shutters closed), 120 were one-point presentation trials (one shutter open, the other closed), and 400 were two-point presentation trials. Each session lasted l-l 5 hr. Each observer was tested using 6 different wavelengths, with one or two sessions per wave-

length. The rni~rn~ time interval between sessions was at least 4 hr, and usually was a full day. A few practice sessions were allowed.

Heterochromatic flicker photometry was performed at 10 nm intervals between 510 and 670nm using the method of adjustment. The standard was a low color temperature tungsten “white” of 50 td retinal illuminance. The observer had control of both the flicker rate and the radiance of the test field.

Observers RV (38 yr, male, one of the authors) and RP (30 yr, female) both had normal color vision as assessed by the Rayleigh equation (Neitz anomaloscope midpoints, RV: 40, RP: 42) and Moreland equation, and showed normal color disc~mination on the FM- 100 hue test. Each observer used the right eye for the measurements; the left eye was patched. The blank trials and the one-point presentation trials were used to check for false positives. There was a total of 11 sessions for observer RV and 9 for RP. For RV, three sessions had false positives greater than 1.7% and for RP, 2 sessions had false positives greater than 2.8%; data from these sessions were excluded from analysis.

RESULTS

The detection experiment

The psychometric functions for two-point presen~tion trials are shown in Figs 5 (Observer RP, test wavelengths between 546 and 680 run) and 6 (Observer RV, test wavelengths between 520 and 650 nm). In each panel the percentage seen is plotted against relative wedge transmittance; the open squares represent the percentage seen for the detection of two points, open circles the percentage seen for the detection of either one or two points. The solid and dashed lines are the corresponding best fits using our model that will be described later. In each panel, the percentage seen increased with wedge transmittance, and the psychometric function for detection of both stimuli required higher wedge transmittances than the function for detection of either one or two stimuli. As the wavelength of the stimuli was increased, the distance between the two psychometric functions increased, and the slopes of the psychometric functions decreased. This result agrees qualitatively with Figs 2 and 3, suggesting that long wavelength stimuli excited fewer cones than the shorter wavelength stimuli. Although the results for the two observers were similar,

70

i3 ”

w I

w H

RAM L. PANDEY VIMAL et al.

I I I I I I 1

0.003 0.010 0.032 0.10 0.32 1.0

0.003 0.010 0.032 0.10 0.32 1.0

I 1 I 1 I I

I , 1 I 1 I

0.003 0.010 0.032 0.10 0.32 1.0 MEL&E TRRt5tlITTME

I , , I I I lW-W5(1oM 1

0 ;

/- 0

80 70 ::,

60 / o

. . . . . . .._.......i . . . . . . . . . 40 30 1

M 10 J: c

i I

0

I 1 1 I I , i

0.003 0.010 0.032 0.10 0.32 1.0

I I I I,

IO0 - Rp 90- W- 70 - EO-

40- 30- m- 10 - 0 -

I 1 I 1 8 I 0.003 0.010 0.032 0.10 0.32 1.0

I 1 , I I I I I 0.003 0.010 0.032 0.10 0.32 I.0

YEDGE TMITT~CE

Fig. 5. The psychometric functions for observer RP for two-point presentation trials. The open squares represent the percentage seen for the detection of both points and open circles indicate the detection of either one or two stimuli. The solid line is the theoretical fit for seeing both points; the dashed line is the theoretical fit for seeing either one or two points. Top left: 546 nm stimulus, top right: 560 nm, center left: 580 nm, center right: 600 nm, bottom left: 620 nm, bottom right: 680 nm (520 nm results not shown).

the changes in slope and separation were smaller for RV; thus we may predict that the L to M ratio is larger for RV than for RP.

Heterochromatic flicker photometric spectral sensitivity

Each observer’s measured flicker-photometric spectral sensitivity was compared to a systematically incremented series of linear combi- nations of the Smith and Pokorny (1975) LWS and MWS sensitivity functions. We used a least-squares fitting procedure to estimate the goodness of fit of the various L/M ratios. Figure 7 shows the root mean square deviations of the fits as a function of the L/M ratio. For observer RP the L/M ratio for best fit to the

HFP measurements was 1.1; for RV, the L/M ratio was 3.4. These ratios can be expressed in terms of the proportion of L cones, PL. For RP the HFP data yielded a proportion of 0.52; for RV the proportion was 0.77. The HFP functions are shown for the two observers (RP on the left, RV on the right) in Fig. 8. The solid lines are the best fits to the WFP data, the dashed lines are the Judd Vi (Wyszecki and Stiles, 1982). RP is more “green sensitive” and RV is more “red sensitive” than the Judd Observer but both RP and RV fell within + 2 SD of expected population variance (re- viewed by Pokorny and Smith, 1988). We calculated and compared the log R/G values for our observers with the data of Rushton and Baker


0.003 0.010 0.032 0.10 0.32 1.0 0.003 0.010 0.032 0.10 0.32 1.0

I L 1 L t l L

0.W3 0.010 0.032 0.10 0.32 1.0

0.003 0.010 0.032 0.10 0.32 1.0 0,003 0.010 0.032 0.10 0.32 1.0

MEMX l~f~l~ UEKE T~S~ITT~E

loo 90 80 70 60

I........... . . . . . . . . . . .

40 30 20 10 0

~ 1.0

Fig. 6. The psychometric functions for observer RV. Top left: 520 nm stimulus, top right: 546 nm, center left: 580 nm, center right: 600 nm, bottom left: 620 nm and bottom right: 69 nm, For details refer to

Fig. 5 (56Onm results not shown).

(1964), Adam (1969) and Lutze (1988). Observer RP is 0.66 SD more “green sensitive” and observer RV is 1.3 SD more “red sensitive” than an average male observer.

Model

MODEL AND ANALYSIS

We make six assumptions in our model. (I) The proportion of illuminated L and M

cones in a given I’ test follows a binomial sampling dist~bution.

(2) The stimulus quanta1 fluctuatjon obeys the Poisson probability distribution.

(3) L-cone and/or M-cone detection are independent processes,

(4) The 17’ separation of the two 1’ test points is sufficient for detection of each point to be independent of the other,

(5) The sensitivities of the M and L cones are that of the Smith-Pokomy MWS and LWS cone fundamentals (Smith and Pokorny, 1975).

(6) The photosensitivity at &,,, of the L and M cones are similar.

We assumed the contribution of rods and short wavelength sensitive cones to be negligible given the wavelength range and 0.5 msec, 1’ fovea1 stimuli. Thus the total effective number of illuminated cones (N) is the sum of the effective number of long-wavelength sensitive cones (Nd and the effective number of middie- wavelength sensitive cones (Nln). The notation defined below is essential for the development of the model.

I 1 I

0.30 1.00 3.00 e t/M RRTiO *

30.0

Fig. 7. Root mean square deviations of the fits of linear sums of Smith-Pokorny (1975) LWS and MWS fundamentals expressed as a function of L/M ratio. For observer RP the L/M ratio for best fit to the HFP measurements was 1.1; for RV, the L/M ratio was 3.4. Arrows indicate L Jh4 ratios (RP: 1.6; RV: 4.0) estimated from the detection

experiment.

N: the effective number of cones illuminated by a stimulus.

NL: the effective number of L cones. NM = (N - NJ: the effective number of M

cones. PL: the probability of any single cone being an

L cone. By the binomial assumption, this is also the proportion of L cones in the central fovea; thus the fovea1 cone ratio, L/M, is NL/NM or

P,lU -PA

QLd: the probability that a given L cone does not reach the criterion for detection of a stimulus at wavelength A.

PM>.: the probability that a given A4 cone does not reach the criterion for detection of a stimulus at wavelength 1.

The probability P of detecting a point stimulus by one or more cones for one-point presentation trials is 1 -y, where

_V = Pr[No single cone reaches the criterion],

= (Pr[exactly NL of N cones of the L type] x

[none of NL L cones reaches criterion] x

[none of (N - N&I4 cones

reaches criterion])

= P;4;(1 - PJ(N-NL)Q~~Q~;NL)

Thus

P = 1 - V’LQLi + (1 - PL)QMJ”. (1)

Assumption 2. Poisson probability distribution

The expressions for QLI and QMi of equation

for the ~ti~u~u~ qua~ta~ ~uctuation

(1) can be derived by assuming that the quantum fluctuation of a stimulus obeys the Poisson probability dist~bution. The notation used is given below.

C: the minimum number of quanta that must be absorbed by a single cone for detection (assumed to be equal for both A4 and L cones).

r

.2.0 i 450 550 850

wh~~~n(~

Fig, 8. Heterochromatic flicker photometric spectral sensitivity functions for RP (left panel) and RV (right panel). The &id CircIes represent the HFP data. The solid lines arc the best fits to the HFP data with the L/M ratios = I, 1 for RP and 3.4 for RV. The dashed lines represent the Judd V, (Wysxecki and Stiles,

1982).

Fovea1 cone thresh&k

X,: the average number of quanta absorbed by an L cone at 1.

X,,: the average number of quanta absorbed by an M cone at A. ~o~bili~es Qtk and Qddd are thus (LeGrand, 1957; Wyszecki and Stiles, 1982).

C-l (2)

Let T be the transmittan~ of the neut~l attenuating wedge {the units on the X-axes of Figs 5 and 6). Scaling factors U,, and U,, are defined to convert wedge transmitt~~~~ values to average number of quanta absorbed per cone (X,, and X,,) for a stimulus of wavelength 1.

The expression for P (equation 1) assumes the pro~~lity of detection by one cone type (lw or L) is inde~ndent of detection by the other cone type. We also assume that the two 1’ stimuli are s~ciently separated (17’) so that they are detected independently (Graham et al., 1939; Will- mer, 1950; Hillmann, 1958). The probability of seeing neither, seeing exactly one, or seeing two points is therefore (1 - P)‘, 2fl - P)P, and P2, res~tive~y, where P is given in equation (I).

The cone scaling factors U,, and Vti com- pensate for filter transmittance at each wavelength as well as convert from units of relative wedge transmittance to average number of quanta absorbed per cone. Two scahng factors may be meaningfully compared only in ratio, and only when both factors are for the same wavelength. The ratio ~~~/~~~ is relative MWS- cone to LWS-cone sensitivity, scaled by a single unknown that represents the absolute heights of the MWS-cone and LWS-cone sen~tivity functions. The heights may be factored out by dividing each ~~~~U~ ratio by a similar ratio for some fixed wavelength (560 nm is used here). This allows the scaling factors to be related to cone fundamentals by the equation

where V,,, V,, U,, and U,, are the scaiing __ . factors as defined in equations (4) and (5) and Iw,, Lnt Mm, and I.., are the observer’s MWS-cone and LWS-cone spectral sensitivities. Assuming the Smith and Pokorny (1975) LWS and MWS fundamen~ls and r~arran~ng terms,

therefore the UMA scaling factors may be determined from the U,,s and W,,.

As a further constraint, we assumed that the photo~nsitiv~ty at &= (product of the quantum efficiency and the extinction coefficient at peak wavelength) of the L and M cones are similar. This assumption is consistent with measurements on diverse Vitiman A, based photopigments (~a~nall, 1972). Given the relatively small possible variation in the spectral positions of normal cone action spectra (Smith et al., 1976; Alpern and Pugh, 1977; Eisner and Mac- Leod, 1981; MacLeod and Webster, 1983; Netz and Jacobs, 1986), this additional constraint could be implemented by restricting solutions for each observer to those for which U,, and V,,, did not vary over a wide range. Conser- vatively, we used a range of 2: 1,

Results for each observer were analyzed separately. The set of measurements from an observer was analyzed simult~~eousiy for six wavel~~gtbs, providing 120 values to be fitted (6 wavelengths x 2 psychometric functions x 10 points per psychometric function). The model has three ~rn~~ant estimated parameters, PLI C and N. We used ~uations (2) and (3) to calculate QLi and & using a possible value of C; and equation (1) to calculate P and thus give the probability of detection of “1 or 2” or “2” spots, using possible values of N and PL, Parameters were estimated by least squares using Chandler’s STEPfT procedure (Chandler, f 976).

The scaling factors U, and V,, allow us to convert from units of relative radiance to units of average number of quanta absorbed per cone. The analysis was performed on the 12 psycho-


Table 1. Least squares estimates of C, N, PL, L/M (values estimated from HFP for Pt and L/Mshown in parentheses) and the scaling factors U, and U,, (equations 4 and 5) for

observers RP and RV

Parameter

c N pi.

RP RV

7 5

Ohl~OS2) 2

0.80 (0.77) L/M 1.6 (1.1) 4.0 (3.4)

i (nm) r/,, r;i,, ULi UJfi 520” 105.5 129.5 36.0 40.0 546 102.6 104.0 110.0 110.0 560 68.6 63.0 119.0 105.0 580 85.0 105.5 90.5 600 545.0 2% 109.0 64.0 620 43.0 18:O 64.0 22.0 650 - 13.6 1.9 680 8.6 .S - -

“Values at 520 nm were determined using the C, N and L/M estimates derived from the other six wavelengths.

metric functions for wavelengths > 520 nm, there are 12 scaling factors: six tJ,, s and six UMis (one V,, and one U,, for each of the six wavelengths tested). The model can fit the psychometric functions quite well, but the solutions obtained were not decisive with respect to the parameter values. Many different parameter values gave comparable and excellent fits, although not all solutions were sensible. For example, predicted MWS and LWS sensitivities might be exchanged on the wavelength axis.

The problem of multiple solutions required that the number of estimated parameters be reduced from 15 (PL, C, N and 12 scaling factors) to 10. We accomplished the reduction using the relation between the scaling factors and the cone fundamentals described in As- sumption 5. The 10 estimated parameters were PLY C, N, six values of U,, (one for each wavelength), and U,,*. The M-cone scaling factors for the five other wavelengths were calculated by use of equation (7).

The best-fitting values of the parameters are summarized in Table 1. Fits to the psychometric functions in Figs 5 and 6 were optimal when the minimum number of quanta absorbed per cone for detection, C, was 7 for observer RP and 5 for observer RV. The probability of a cone being an L cone, PL, was estimated to be 0.61 for RP and 0.80 for RV. The ratio of the number of L cones to the number of M cones, P,/(I - PL), was thus 1.6 for observer RP and 4.0 for observer RV. The effective number of cones (i.e. those receiving on average the neces- sary C quanta), N, was estimated to be 2 for both observers.

The original goal of fitting all 15 parameters was completed by analyzing separately the measurements at each wavelength, holding fixed P,, C and Nat the values shown in Table 1 (thus two scaling parameters, U,, and U,, were fit to 20 points in each analysis). The psychometric functions predicted by the 15 parameters are plotted in Figs 5 and 6 as solid and dashed lines; they show a very good fit to the detection data. The root mean square difference between experimental measurement and theoretical predic- tion for 120 data points was 0,058 for observer RP and 0.044 for RV,

As a check on internal consistency, we exam- ined whether the scaling factors determined in the last step of the analysis recovered correctly the LWS-cone spectraf sensitivity. Obviously this is not an unconstrained assessment, since the Smith-Pokorny fundamentals were used in the initial analysis that gave the values for PL, C and iV. Scaling factors derived separately however, in the subsequent least squares fits to the psychometric functions at each wavelength, with PL, C and N held fixed at previously determined values, optimize the fit to the raw data and may fail to reconstruct the correct properties of cones. Rearranging the equation in Assumption 5 gives

where i is predicted LWS-cone spectral sensitivity. Predicted LWS-cone sensitivity is plotted in Fig. 9 for both observers (RP on the left, RV on the right). The solid circles represent LWS- cone sensitivity derived from the estimated scaling factors; the solid and the dashed lines are LWS and MWS fundamentals, respectively, for a 15’ stimulus (2” Smith-Pokorny fundamentals adjusted to reflect the estimated optical density for a 15’ field; Pokorny et al., 1976). Note that the LWS-cone sensitivity is slightly higher than the MWS-cone sensitivity at their respective peaks.

DISCUSSION

L/M cone ratios

deVries (1947) first suggested that individual differences in the ratio of heterochromatic flicker sensitivity for “red” and “green” lights might reflect differences in the proportion of

cones containing L and M photopi~ents. Qualitative support came from Rushton and

Fovea1 cone thresholds

i : : : :

i :

. i I

i : r i

450 500 550 600 650 700

~RV~ENGTH INMI

75

Fig. 9. The spectral sensitivity of the t cone for observers RP (left panel) and RV (right panel). The solid and the dashed lines represent LWS (I,) and MWS (M) fundamentals respectively for IS’ stimuli derived from Smith-Pokorny (SP) fundamentais for 2” data. The solid circles represent LWS-cone sensitivity

derived from threshold data (equation 8).

Baker’s (1964) comparison of red/green flicker ratios and retinal densitomet~. Further, red/ green ratios from females heterozygotic for protan and deutan color vision defects strongly point to an association between HFP and L/M ratios. Crone (1959) and Adam (1969) report that protan heterozygotes tend to be “green” sensitive (this decreased sensitivity to long- wavelen~h light is known as Schmidt’s sign) and deutan hetero~gotes tend to be “red” sensitive. If we assume that the defective alleles are associated with low production of photopigment (Pokorny and Smith, 1987), then we may interpret flicker photometric spectral sensitivities as reflecting L/M cone ratios. While the evidence is convincing that L/M cone ratios are reflected in HFP spectral ~nsiti~~es, there are other biological variables such as possible differences in photopigment spectra among color normal observers (Smith et al., 1976; Alpem and Pugh, 1977; Eisner and MacLeod, 1981; MacLeod and Webster, 1983; Nietz and Jacobs, 1986), photopigment optical density (Smith et al., 1976; Burns and EIsner, 1985) and pre-receptoral filtering ~~nci~lly the lens, Pokomy et al., 1987) which could contribute to the measured spectral sensitivities. A direct way to evaluate the effect of these variables is to compare population variability of anomalo- sopic color matching data with the variability of flicker sensitivities to wavelengths similar to or

identical with the color matching primaries. The HFP loga~t~ic G/R flicker ratios have a standard deviation of 0.07-0.10 log unit (Rush- ton and Baker, 1964; Adam, 1969; Wallstein, 1981; Lutze, 1988), two to three times larger than the standard deviation of log G/R ratios for Rayleigh matches (Schmidt, 1955; Rushton and Baker, 1964; Adam, 1969; Helve, 1972; Wallstein, 1981; Mari-& and Marre, 1984; Lutze, 1988). These data place constraints on the con- tributions of variables other than the L/M ratio to measured HFP spectral sensitivities. Analysis shows the L/M ratio to be a major source of population variability in HFP spectral sensitivity (Pokorny et al., 1988).

It is of note that these biological variables cont~bute in a rather di~erent way to the interpretation of the threshold detection data. The model developed in this paper uses only the ratio of the LWS and MWS spectral sensitivities. Given the possible range of biological variation in the color normal population (references cited above), the exact form of the fundamentals is not essential for the analysis.

The two paradi~ employed in the present study each yield an estimate of an observer’s L/M cone ratio. Though both the flicker photometric and threshold detection paradigms suggest that the L/M ratios of our two observers are very different, the two paradigms yielded similar estimates for a given observer. For RP,

the L/M ratio estimated from flicker photometry was 1. I compared to a value of I .6 from the analysis of detection measurements. For observer RV, the two estimates were 3.4 (flicker) and 4.0 (detection). The agreement of the estimates from two distinct methods suggests strongly that both flicker photometric spectral sensitivity at moderately low photopic lumi- nances and the analysis of threshold detection data reflect the relative proportion of L to M cones.

The analysis suggests that only two cones are active at fovea1 cone threshold. This may seem

odd given the number of cones illuminated under the image spread function for a 1’ dia. stimulus on the retina. A moment of reflection may convince the reader that this is a plausible result. With the assumption that thresholds are governed only by those cones which receive a

sufficient number of quanta to signal that they have been illuminator the distribution of the cones receiving “C or more quanta” is the spatial dete~inant for threshold rather than the retinal light profile. The threshold measurements indicate the minimum number of quanta absorbed per cone for detection, C, is 5-7. One consequence of the requirement of multiple quanta per cone at threshold is a significant nonlinearity in the spatial representation of a stimulus. We use the term *‘effective spread function” to refer to the spatial distribution of activity fo~owing this nonlinearity.

The “eflbctive spread function” for a 1’ stimulus detected by cones is substa~tiaily narrower than would be expected from the spread function of light on the retina computed for illumination by the stimulus. Near threshold, the point spread function is a probabilistic function for quanta1 absorption. If we assume that the center of an image of a point source falls exactly on the center of one receptor in a reti.nat mosaic and that the probability of that receptor catch- ing C quanta is 1.0, then the ‘“effective spread function” may be computed from the light distribution on the retina and the number of quanta required at threshold, C, If a receptor away from the peak of the light distribution has a 50% chance of absorbing one quantum, it has only a 25% chance of absorbing 2 quanta (SOOJO for the first, and 50% for the second: OS2 = 0.25). When C = 5, the probability of the same receptor absorbing a sufficient number of quanta for threshold (0.5’) would be only 0.03125. More generally, to obtain an estimate of the spatial nonlinea~ty a~omp~ying the

RETINRL DISTFINCE Imin of arc1

Fig. 10. The effective paint spread function based on Westheimer’s (1986) point spread function (solid line) for a minimum number of quanta per cone, C, of 6. The effective spread function (dotted line) is much narrower than the

point spread function.

threshold requirement of N or more quanta per receptor, we start with a point spread function, H(r), and raise it to the power C (the number of quanta needed for detection) to obtain the amplitude of the ‘“effective spread function”, E(r):

W) = CW)3” (9)

In Fig. 10 we show the “effective spread function” based on Westheimer~s (1986) point spread function, The “‘ef%ctive spread function” (dotted lines) is much narrower than the point spread function” If we assume a hexagonal lattice with cone to cone separation of 0.6’ (e.g, Geisler, 1984), then an estimated value of 2 for the total number of cones receiving on average 5-7 quanta for a 1’ stimulus seems reasonable.

SUMMARY

The ratio of the number of long wavelength sensitive cones to middle wavelength sensitive cones, that is, the L/M ratio, for observer RP was 1.6 from the threshold experiment and 1.X from the HFP experiment. For observer RV it was 4.0 and 3.4 respectively. Thus though our two observers appear to have disparate L/M cone ratios, the ratio estimated from the threshold experiment is in good agreement with that estimated from the HFP experiment for each observer. The minimum number of quanta absorbed per cone for detection was 7 for observer RP and 5 for observer RV. One impli-

Fovea1 cone thresholds

cation of this analysis is that under threshold conditions there is a spatial sharpening of the effective image. Therefore, the number of recep tors m~iating threshold detection should not be as large as that estimated from the stimulus illumination spread function, This analysis is consistent with the model estimate of 2 as the total effective number of illuminated cones for both observers.

Geisler W. S. (1984) Physical limits of acuity and hyper- acuity. J. opt. Sac. Am. A 1, 775-782.

Graham C. H., Brown R. H. and Mote F. A. Jr (1939) The relation of size of stimulus and intensity in the human eye: I. Intensity threshotds for white fight. J. exp. PsycItoI. 24, 555-573.

Helve J. (1972) A comparative study of several diagnostic tests of colour vision used for measuring types and degrees of congenital red-green defects. Acta Ophthal. (Suppl.) 115, l-64.

Hilhnann B. M. (1958) Relationship between stimuhts size and threshold intensity in the fovea measured at four exposure times. J. opt. Sot. Am. 48,422-428.

Krauskopf J. (1964) Color appearance of small stimuli and the spatial dist~bution of color receptors. J. opt. Sot. Am. 54, 1171.

Acknowledgements-This research was supported in part by NE1 grants EY00901 and EYO?OlO (Pokoruy) and EYO4802 (Shevell).

REFERENCES

Adam A. (1969) Fovea1 red-green ratios of normals, color- blinds and heterozygotes. Proc. Tel-Hashomer Hosp. Tei- Aviv 8, 2-6.

Alpern M. and Pugh E. N. (1977) Variation in the action spectrum of erythrolabe among deuteranopes. J. Physiol. Land. 266, 613446.

Bouman M. A. and van der Velden H. A. (1948) The two-quanta hypothesis as a general explanation of the behavior of threshold values and visual acuity for the several receptors of the human eye. J. opt. Sot. Am. 38, 570-581.

Bouman M. A. and Walraven P. L. (1957) Some color naming experiments for red and green monochromatic lights. $. opt. Sot. Am. 47, 834-839.

Brindley G. S. (1954) The order of coincidence required for visual threshold. Proc. Phys. Sot. Lond. 3 67, 613-676.

Brindley G. S. (1963) The relation of frequency of detection to intensity of stimulus for a system of many independent detectors each of which is stimulated by a mquantum

coincidence. J. Physiol., Land. 169, 412-415, Burns S. A. and Elsner A. F. (1985) Color matching at high

illuminances: the color-match-area-effect and photopigment bleaching. J. opt. Soe. Am. A 2, 698-704.

Chandler J. P. (1976) STEPT: direct search optimization solution of least-squares problems. QCPE 11, 307.

Cicerone C. M. and Nerger J. L. (1985) The ratio of long-wavelength-~nsitive to addle-wave~ngth-motive cones in the human fovea. invest. Uphthal. visual Sci.

(Suppl.) 26(3), 11. Crone R. A. (1959) Spectral sensitivity in color-defective

subjects and hetero~gous carriers. Am. J. Ophthai. 48, 231-238.

Dartnail H. J. A. (1972) Photosensitivity. In Photochemistry of Vision. ~~d~ook of Sensory Psychology, Vol. VII/l (Edited by Dartnall H. J. A.), pp. 122-145. Springer, Berlin.

DeMonasterio F. M., Schein S. J. and McCrane E. P. (1981) Staining of blue-sensitive cones of Macaque retina by a fluorescent dye. Science, N.Y. 213, 1278-1281.

DeMonasterio F. M., McCrane E. P., Newlander J. K. and Schein S. J. (1985) Density profile of blue-sensitive cones along the horizontal meridian of macaque retina. Invest. Ophthal. visual SA. 26, 289-302.

Eisner A. and MacLeod D. 1. A. (1981) Flicker photometric study of chromatic adaptation: selective suppression of cone inputs by colored backgrounds. J. opt. Sac. Am. 71, 705-718.

77

Krauskopf J. (1978) On identifying detectors. In Visual Psychophysics and Physiology (Edited by Armington J. C., Krauskopf J. and Wooten 3. R.), pp. 283-295. Academic Press, New York.

Krauskopf J. and Srebro R. (1965) Spectral sensitivity of color mechanisms: derivation from fluctuations of color appearance near threshold. Science N. Y. 150, 1477-1479.

LeGrand Y. (1957) Lighr, Colour and Vision. Wiley, New York.

Lutze M. (1988) Genetics of fovea1 cone photopigtnent sensitivities and receptor populations. Doctoral dissertation, University of Chicago.

Lutze M., Pokomy J. and Smith V. C. (198’7) Improved clinical technique for Wald-Marre functions. Documenta ophth. Proc. Ser. 46, 259-265.

MacLeod D, I. A. and Webster M. A. (1983) Factors influencing the color matches of normal observers. In Colour Vision (Edited by Mollen J. D. and Sharpe L. T.), pp. 81-92. Academic press, London.

Marc R. E. and Sperhng H. G. (1977) Chromatic or- ganization of primate cones. Science IV. Y. 143,454X%.

Ma& M. and Mar& E. (1984) Rayleigh equation in acquired color vision defects. Doc~e~ta ophth. Proc. Ser. 39, 165-170.

Marriott F. H. C. (1963) The fovea1 absolute visual threshold for short flashes and small fields. f. Physiaf. Land. 169,416-423.

Neitz J. and Jacobs G. H. (1986) Polymorphism of the long-wavelength cone in normal human colour vision. Nature, Loti. 323% 623-625.

O’Brien B. (19.51) Vision and resolution in the central retina. J. opt. Sot. Am. 41, 882-894.

Pokomy J. and Smith V. C. (1987) The functional nature of poIymo~hism of human coior vision. in Frontiers of Visual Science: Proc. I985 Symp., pp. 150-159. National Academy Press, Washington DC.

Pokomy 3. and Smith V. C. (1989) L/M Cone ratios and the null point of the perceptual red/green opponent system. In Proc. AIC Wyszecki and Stiles Memorial Symp. on Color Vision ~~eIs (In press).

Pokomy J., Smith V. C. and Starr S. (1976) Variability of color mixture data. II. The effect of viewing field size on the unit coordinates. Vision Res. 16, 1095-1098.

Pokomy J., Smith V. C. and Lutze M. (1987) Aging of the human lens. Appt. Opt. 26, 1437-1440.

Pokomy J., Smith V. C. and Lutze M. (1988) Sources of shared variance in Rayleigh and photometric matches. J. opt. sot. Am. A A&r. 5, (In press).

Rushton W. A. H. and Baker H. D. (tQ64) Red&men sensitivity in normal vision. Vision Res. 4, 75-85.


Schmidt I. (1955) Some problems related to testing color vision with the Nagel anomaloscope. J. Opt. Sot. Am. 45, 514-522.

Smith V. C. and Pokorny J. (1975) Spectral sensitivity of the fovea1 cone photopigments between 400 and 5OOnm. V&WI Rex 15, 161-171.

Smith V. C., Pokomy J. and Starr S, J. (1976) Variability of color mixture data-I. Interobserver variability in the unit coordinates. l’&ion Res. 16, 1087-1094.

Stiles W. S. (1949) Increment thresholds and the mechanisms of colour vision. Documenta ophth. 3, 138-163.

Vos J. J. and Walraven P. L. (1971) On the derivation of tbe fovea1 receptor primaries. Vision Res. 11, 799-818.

devries H. L. (1947) The heredity of the relative nears of red and green receptors in the human eye. Genetica 24, 199-212.

Wald G. (1967) Blue-blindness in the human fovea. J. opt. Sot. Am. 57, 1289-1301.

Wallstein R. (1981) Photopi~ent variation and the percep-

tion of equilibrium yellow. Doctoral dissertation, Univer- sity of Chicago.

Walraven P. L. (1974) A closer look at the tritanopic convergence point. Vision Res. 14, 1339-1343.

Westheimer G. (1986) The eye as an optical instrument. Handbook of Perception and Human Performarxe, Vol I: Sensory Processes and Perception (Edited by BotT K. R., Kaufman L. and Thomas J. P.), pp. 4-1-4-20. Wiley, New York.

Williams D. R., MacLeod D. I. A. and Hayhoe M. M. (198Ia) Fovea1 Tritanopia. Vision Res. 21, 1341-1356.

Williams D. R., MacLeod D. I. A. and Hayhoe M. (1981b) Punctate sensitivity of the blue-sensitive mechanism. Vision Res. 21, 1357-1375,

Willmer E. N. (1950) The relationship between area and threshold in the central fovea for lights of different colours. Q. J. exp. Psychol. 2, 53-59.

Wyszecki G. and Stiles S. (1982) Color Science, pp* 515-519. Wiley, New York.

foveal cone thresholds

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