Simple-opponent receptive fields are asymmetrical: G-conecenters predominate
Carl R. Ingling, Jr., and Eugenio Martinez-Uriegas*
Division of Sensory Biophysics and Institute for Research in Vision, The Ohio State University, Columbus, Ohio43212
Received November 26, 1982; revised manuscript received June 9, 1983
For quantitative models of color vision, the R-cone contribution to the r-g channel is less than half of the R-conecontribution to the Vx channel. There is currently no explanation of how this different contribution of R conesto the two channels comes about. We propose an asymmetrical receptive-field arrangement to explain the differ-ence in weighting. Because cones in receptive-field surrounds are weighted less than cones in centers, placing Rcones predominantly in surrounds and G cones in centers provides a simple differential weighting mechanism.Electrophysiological and psychophysical evidence substantiates such an asymmetry of simple-opponent fields.
INTRODUCTION
The ProblemZone models of color vision transform the outputs of threecones, R, G, and B, to two chromatic or differencing channels(r-g, y-b) and one achromatic or summing channel (Vx). Theprincipal inputs to the r-g and Vx channels are the R and Gcones. Most quantitative models of color vision require thatthe R-cone input to the Vx channel be greater by approxi-mately a factor of 2 than the R-cone input to the r-g channel.Observations cited below suggest a theory of receptive-fieldorganization that accounts for the difference in the transfor-mation coefficients for the r-g and Vx channels.
Cone-to-Channel TransformationsThe heart of opponent theories of color vision is the threeequations that transform cone outputs to channel sensitivities.For a classic summary, see Ref. 1. More-recent theories haveprofited from an enlargement of the data base. In particular,a consensus has emerged concerning the spectral sensitivitiesof the three cone types that form the first stage.2 -4 Knowl-edge of the cone sensitivities now makes it possible to deter-mine the exact relationship between cone sensitivities andchannel sensitivities. This was not possible for earlier theoriesbased on transformations of color-matching functions.
Although different authors use slightly different sets ofR,G,B-cone sensitivities and derive their transformationequations from different principles, estimates of relative coneinputs to the V, and r-g channel closely agree. To comparethe different estimates requires a common normalizing con-vention. We adopt the convention used by Guth et al.5 andby Ingling and Tsou6: Normalize the R,G,B-cone sensitivitiesto 1.0 at Xmax. All coefficients then appearing in various termsof the theories refer to this normalization. We compare es-timates of the cone inputs for the VA and r-g channels fromfour sources: Guth et al.,5 Ingling and Tsou,6 Walraven, 3 andSmith and Pokorny.4 To simplify the comparisons, thecoefficients in each case are multiplied by a constant to makethe G coefficient 4.0. Because most opponent theories, in
addition to summing cone outputs to give a luminance (VA)channel, also difference the long-wavelength cones to producea neutral point (unique yellow) near 575 nm (see Guth et al.5),estimates for the R- and G-cone inputs for the r-g transfor-mation can be calculated for the data of Walraven and ofSmith and Pokorny. In summary, the four sets of cone-to-channel transformations are reduced to a common basis bythe following treatments: For the work of Guth et al.5 andIngling and Tsou,6 we use the transformation equations andthe R,G-cone normalizations as given in these papers. (Al-though both groups use cone sensitivities originating withSmith and Pokorny,4 they are not the same set.) The trans-formations both of Smith and Pokorny and of Walraven 3 fromcone sensitivites are renormalized (setting sensitivity = 1.0at Xmax) to give comparable coefficients. For both Ref. 3 andRef. 4, the r-g coefficients are calculated using a 575-nmunique yellow:
Guth et al.5 (VA = A, r-g = T for this work only):
So, roughly, when cone sensitivities are normalized to acommon Smax, then the input to the r-g channel is in the ratioof 3R to 4G, and the input to the VA channel is 6.5R to 4G.Thus the R-cone input to VA is more than double the R-coneinput to r-g. (The bottom part of Fig. 1 shows the relative R-
1528 J. Opt. Soc. Am./Vol. 73, No. 11/November 1983
HETEROCHROMATIC FLICKER PHOTOMETRY
2 degIBa S G R
5 deg
|B | S | G | R I
10
oL10-
0-
1.0 Td'
6.2Td
2!,
RR
400 490 700 400 580 700X (nm)
Fig. 1. Simple-opponent r-g-channel receptive fields of a hypo-thetical 16-receptor retina. The receptors also form achromatic re-ceptive fields (not shown) whose spectral sensitivity is proportionalto the receptors present, i.e., VA i (5R + 3G). Because surroundcones are weighted less than center cones, by putting R cones pre-dominantly in surrounds this retina also satisfies the r-g-channelnormalization, (r-g)5s0 = 0. The spectral sensitivity curves show theR,G normalizations for the VA and r-g channels.
and G-cone sensitivities for the two transformations.) Infurther support of this conclusion, Fig. 2 shows an analysis ofdata taken from Burns 7 for one of his observers. For a rangeof intensities and field sizes, and for both heterochromaticflicker photometry and a minimum-border criterion, the R-cone input to the channel that mediates flicker and minimizesedge contrast is roughly twice that of G, in agreement with theabove estimates.
Cone-Normalization ProblemIt is not known what aspect of structure makes one class ofcone appear more sensitive than another. Possibilities arean inherent difference in the photosensitivity of the pigments,the length or size of the receptor, density of pigment withinthe receptor, the relative number of cones, and synaptic orneural effects. Further discussion will be simplified by as-suming that there is little if any difference in the sensitivityof individual R and G cones that is due to the first three ofthese factors. Primate single-cone microspectrophotometryshows no recognizable morphological differences betweencones identified by their spectra as R or G cones, and suchcones have comparable Xmax absorptions. 8 In the absence ofsuch differences, the aspect of structure most simply associ-ated with differential sensitivity between cone classes is thenumber of cones. In other words, if all other things are equal,we expect that a retina with 2R cones for every G cone will
:LW10-
28.0Td
IOL100.0 Td
MINIMALLY DISTINCT BORDER
1 deg 2 deg 5 degaB I S I G I R B SI B a S I G R
00
n X nLWII
:0L0-Lt
0.6 Td
1.0 Td
6.2 Td
28.0 Td
I0-
90.O Td
0-Fig. 2. Histograms showing the relative magnitude of the coefficientsthat are required to fit spectral sensitivity curves measured by het-erochromatic flicker photometry and minimum border for variousfield sizes and intensities. R, G, B, and S (rod) were normalized to1.0 peak sensitivity for the fit. For only one of the fourteen conditionsis the G/R ratio greater than 3/5 (V,, - 5R + 3G). The data analyzedhere are from Ref. 7.
C. R. Ingling, Jr., and E. Martinez-Uriegas
- -J
C. R. Ingling, Jr., and E. Martinez-Uriegas
exhibit a spectral-sensitivity function that, to a first approx-imation, will be fitted by using a 2:1 ratio of the R:G coeffi-cients in the VA transformation when the cones are normalizedto have the same Smax-
The above assumption is made in order to continue with thetheory, but it is not crucial. Because what is to be explainedis the apparently different R-cone sensitivity of two channels,if it is later discovered that some feature of cone structureother than numerosity must be factored in, then adjustmentscan be made without altering the basic idea. This will be trueif the feature is such that it affects cone sensitivities for bothchannels and cannot itself explain the differential r-g and VAinputs.
Interpretation of the Transformation Coefficients for VIGiven (1) the spectral sensitivities of the R,G cones, (2) achannel that sums R,G-cone outputs, (3) a method for iso-lating this channel, and (4) the correct relative normalizationof the R,G cones, it follows that a straightforward measure ofspectral sensitivity suffices to determine the cone ratios. Inother words, flicker photometry counts cone ratios. If it takesR and G cones in the ratio of 6.5/4 to fit the average luminositycurve for normal observers, then because the luminositychannel sums the outputs of cones the retina must containcones in the ratio NR/NG = 6.5/4 = 1.6/1.
The assumption that flicker photometry counts cones hasbeen tested by Rushton and Baker 9 (see also de Vries10).Observers vary in the amounts of, say, a green light that willbe required to match a standard red light by flicker photom-etry. Rushton and Baker used this fact to relate red-greenflicker-photometric ratios to retinal densitometric measure-ments made on the same observers and established that flickerphotometry indeed reflects pigment concentration. As-suming that the amount of pigment measured by retinaldensitometry in turn reflects cone populations, then the studyby Rushton and Baker further supports the psychophysicalassumption that the achromatic channel sums unweighted R-and G-cone responses.
Recent single-cone microspectrophotometry papers reportrecordings in sufficient numbers for estimates of relative conepopulations to provide evidence on this point. Queries elic-ited the opinion (from Bowmaker's group)8 that (of theirwork) the study most satisfactory in this regard is a recentreport by Dartnall et al. ,8 who found an NRJNG ratio of 69/49= 1.4/1 from measurements on seven human eyes. We takethis figure of 1.4/1 to be in agreement with the NRJNG = 1.6/1ratio established by flicker photometry. Should it turn outthat the 1.4/1 ratio is correct, it would mean that the nor-malization of the R and G cones to the same Smax should beadjusted slightly. R cones must be 15% more sensitive thanG cones for 1.4 R cones plus 1 G cone to sum to V,\. To makethis adjustment with confidence, it would have to be shownthat the microspectrophotometered cones were a represen-tative sample from a population having average flicker lumi-nosity. Given the wide interobserver variation in flicker lu-minosity and the sample size, it seems premature to make anadjustment.
Using a different argument, Walraven 3 derives a receptormosaic with the ratio R/G/B = 32/16/1. If Walraven's mosaicis correct, then R-cone sensitivity must be 20% less than G-
cone sensitivity for 2 R cones and 1 G cone (ignoring B cones)to sum to VX.
In summary, when R and G cones are normalized for thesame Xmax, 1.6 R cones to 1 G cone are required to fit thestandard luminosity curve VA. On what grounds do we nor-malize R and G cones to the same Xmax, and what does lumi-nosity have to do with cone numbers? There is no evidenceof a significant difference between R- and G-cone sensitivities,and Rushton and Baker9 have demonstrated the requiredrelationship between pigment concentration (numbers of Rand G cones) and sensitivity to red and green lights. Finally,cone counts from microspectrophotometry agree well (within15%) with the NRJNG cone ratio established by photometry,and an estimate by Walraven is not greatly discrepant.
THEORY
Asymmetry HypothesisGiven that the NR/NG cone ratio is about 1.6/1, which putsthe equal-sensitivity crosspoint at 490 nm (see Fig. 1), a hy-pothesis is required to explain how the r-g channel comes tohave a crosspoint near 575 (hereafter 580, for convenience ofcalculation). That is, the r-g channel seems to have only halfas many R cones contributing to it as does the Vx channel.Simply differencing the inherent R and G sensitivities pro-duces an r-g curve with a crosspoint at 490 nm. No observerperceives unique yellow at 490 nm.
The R-cone signals must be modified by neural mechanismsthat decrease their input by a factor of 0.5 to the r-g channel.The crosspoint must be moved from the natural R490 = G490to R580 = G580. A hypothesis for reducing the R-cone con-tribution to the r-g channel is this: There is an asymmetryin the simple-opponent receptive fields (X cells)1" that com-pute the r-g difference. Cones in the surround are less ef-fective than cones in the center. It takes several cones in thesurround to cancel one cone in the center of a receptive field.(Possible reasons for this-an extra neuron in the surroundpath, less direct access to the bipolar synapse, decrementalconduction from the surround periphery, etc.-are beyondthe scope of this discussion. We take it as given that sur-round-cone responses are attenuated relative to center-coneresponses.) By the introduction of an asymmetry of recep-tive-field types, R cones can be differentially weighted.Specifically, to shift the natural crosspoint to longer wave-lengths requires that the simple-opponent receptive fields thatcompute the r-g signal have more G centers-R surrounds thanR centers-G surrounds. If R cones lie predominantly in thesurrounds of simple-opponent fields, then they are weightedless in determining the balance point of the channel. Figure1 illustrates the asymmetry with a hypothetical retina com-posed of 10 R and 6 G cones. (With this cone population, theluminosity curve is approximately Vx. The receptive fieldsof a luminance channel for this retina, not shown in Fig. 1,would contain R and G cones in the ratio of 1.67/1.) For ther-g fields of this hypothetical retina, if the center cones areweighted 1.0, then surround cones have an average weight of0.274, the value of x in the equation 1 2
3(G 580 - x3R 5 80) + (R 5 80 - x3G5 8 0) = 0.
This equation gives a slightly different crosspoint for the
1530 J. Opt. Soc. Am./Vol. 73, No. 11/November 1983
G-center fields than for the R-center field, which, when av-eraged, produce the 580-nm crosspoint.
In summary, the above equation illustrates the features ofthe asymmetry hypothesis: (1) the cones in receptive-fieldsurrounds count less by the factor X than cones in centers, and(2) an asymmetrical population of center types requires alarger population of those cones that lie in the surround of thepreferred center type.
OBSERVATIONS AND EXPERIMENTS
Electrophysiological Evidence for AsymmetryDe Monasterio and Gouras'3 (see their Table 1) tabulate thecenter and surround sensitivities as a function of retinal ec-centricity for 280 simple-opponent cells (which they callcolor-opponent concentric) from the Rhesus monkey retina.Of the tabulated cells, 229 are R-center/G-surround or G-center/R-surround cells. For cells within the central 10, theG-center/R-center ratio is 27/11; some 70% of the foveal cellsthat have R- and G-cone inputs have G-cone centers. (Thisratio becomes more symmetrical with eccentricity and is 1.0outside the central 40 of this sample.)
It is of interest to compare the foveas of the monkeysstudied by De Monasterio and Gouras with the schematicretina of Fig. 1. Assume for disussion an average receptivefield, i.e., all receptive fields have the same size. De Mo-nasterio and Gouras find 27 G centers and 11 R centers in thefovea. How many R and G cones must be added to the sur-rounds of each of these 27 G and 11 R centers, respectively,for the monkeys to have a Vx luminosity curve if all the R andG cones are summed? The answer is four. Thus there are27 G-center receptive fields with n G cones in the center and4 n R cones in the surround, and there are 11 R center recep-tive fields with n R cones in the center and 4 n G cones in thesurround. The fovea contains 190 n cones distributed in (11+ 27 = 38)h receptive fields for which R/G = 1.67/1.
We emphasize that this deduction about the averagechromatically opponent receptive field depends only on rel-ative luminosity or spectral sensitivity. It does not dependon any color-vision measurement or any measurement ofchromatically opponent fields save that of the 27/11 G-cone/R-cone asymmetry. The data that go into the determinationthat four surround cones must balance one center cone are (1)the spectral sensitivities of the R and G cones, (2) the ratio ofthe radiances required for a red light to match a green light,and (3) the 27/11 G-center/R-center asymmetry. These dataare sufficient to determine the center-surround populationsfor the average r-g simple-opponent cell.
Given the 4/1 surround/center ratio, the surrounds mustbe attenuated by a factor of 0.21, the value of x in the equa-tion
27(G 5 80 - x4R580) + 11(R 5 80 - x4G580) = 0.
These values are comparable with those used for the schematicretina of Fig. 1, for which the attenuation was 0.274 and thesurround/center population ratio was 3. Because the mon-keys studied by De Monasterio and Gouras (for the central10) have more cones in the surround than our arbitrary Fig.1 model (four versus three), they must correspondingly at-tenuate the surround responses more.
C. R. Ingling, Jr., and E. Martinez-Uriegas
Psychophysical Evidence for AsymmetryThe psychophysical evidence for the asymmetry hypothesisdraws on an earlier electrophysiological experiment by Gourasand Zrenner,1 4 who report that simple-opponent fields losecenter/surround antagonism for flickering stimuli. Withincreasing flicker rate, surrounds begin to add to centers.Gouras and Zrenner report that midspectral lights near theneutral point wavelength, which are poor stimuli at lowfrequencies, become effective stimuli at high frequencies.Given a delay between the center and surround responses ofa simple-opponent cell, the result of Gouras and Zrenner isexpected. That is, it can be shown that for high temporalfrequencies the spectral sensitivity of a simple-opponent cellis (R + G), whereas for low temporal frequencies it is (R - G).Figure 3 shows the responses of the center and the surroundof a simple-opponent receptive field to an impulse. Nor-malized or unit impulse-response functions are shown. Theseunit functions are multiplied by wavelength-dependentfunctions, i.e., the cone spectral sensitivities R and G, to obtainthe response at a given wavelength. Thus the first-order re-sponse of such a receptive field is given by R X f(center) + GX f(surround), where f(c) and f(s) are the temporal impulse-response functions for the center and surround, and R and Gthe cone sensitivities. Rewriting this expression for the re-ceptive field gives
R X f(c) + G X f(s) = '/2(R + G)]f(c) + f(s)]+ 1/2(R - G)f(c) - f(s)1.
Center and surround unit responses
fc+fs fc-f s
t
Rfc+Gfs= 2 R+G) (fc+fs)
= I f(R+G)rKj+(I
t
+ (R-G)(fc-fs) =
}Fig. 3. (Top) Hypothetical impulse responses for a simple-opponentcell. The surround response is delayed with respect to the centerresponse. (Bottom) The cell response is identically equal to the sumof an achromatic (R + G) high-frequency term and a spectrally op-ponent (R - G) low-frequency term. Thus at high temporalfrequencies (R - G) is attenuated and the spectral sensitivity of thecell becomes R + G. The converse occurs at low frequencies.
R-G) lj"""�-I
C. R. Ingling, Jr., and E. Martinez-Uriegas
As is shown in Fig. 3, V1(c) + f (s)] is a bandpass filter and V1(c)- f (s)] is a low-pass filter. The filters act as weighting func-tions for the difference and sum spectral sensitivities. Thelow-pass temporal filter passes (R - G) at low flicker rates,and the bandpass filter passes (R + G) at high flicker rates.
This result, that surrounds add to centers for high flickerrates, has implications for the asymmetry hypothesis. If thereis an asymmetry of receptive-field types on the retina, flick-ering a stimulus will cause the hue to change. Suppose thatfor a given yellow light all surround responses have canceledthe center responses. The R-cone surrounds of G centers stopthe G centers from signaling greenness; likewise, the G sur-rounds of R-cone centers stop the R centers from signalingredness. With reference to the above equation, the (R - G)difference term is zero for a steady yellow background becauseR - G = 0, and the (R + G) term is zero because the V1(c) +f(s)] filter has zero sensitivity for temporal frequency co = 0.Flicker causes the surrounds to add to centers instead of in-hibiting them; with increasing temporal frequency, the 11(c)- f(s)] term goes to zero and the sum term dominates. Thusas X increases, the receptive-field centers are no longer in-hibited and begin to signal as Gouras and Zrenner1 4 demon-strated. The net r-g signal from the retina will be zero onlyif R and G centers are of equal number, i.e., if as many centerssignal greenness as signal redness. Specifically, if there aremore G-cone centers than R-cone centers, then flickeringyellow will make it appear greener; conversely, if there aremore R-cone centers than G-cone centers, flickering yellowwill make it appear redder. If there is no asymmetry, flickerwill have no effect.
Piantanida and Hammon15 have measured hue shifts forunique hues. For all their observers, flickering a uniqueyellow caused it to appear greener.
Piantanida and Hammon used a square-wave flicker forwhich the on-and-off cycles were equal. An impulse at thebeginning of the cycle should be a better stimulus for dem-onstrating the effect. After the impulse, the center and sur-round responses should run their courses with less responseoverlap. We set up a bipartite field with 580 nm on each sideand tested a few flicker parameters. Using a 5-msec spike forboth 10- and 20-Hz flicker produed striking shifts towardgreen in the flickering half of the field, which appeared muchmore noticeable and larger than could be obtained withsquare-wave flicker. Appropriate intensity adjustments weremade to keep the same average intensity on both sides of thefield. These observations confirm the results of Piantanidaand Hammon.16
DISCUSSION AND CONCLUSIONS
Interdependence of the R-Cone/G-Cone Ratio and theDegree of AsymmetryAs was noted above, Rushton and Baker 9 showed that ob-servers vary widely in the relative numbers of R and G coneson their retinas. Some observers are rich in R cones, some inG cones. This means that the equal-sensitivity point orcrosspoint for the achromatic channel varies from observerto observer. If the crosspoint of the (r-g) channel were sim-ilarly at the mercy of R- and G-cone proportions, then thedistribution of unique yellows would occupy two thirds of thespectrum, given the range of R/G ratios reported by Rushton
and Baker.9 In fact, the crosspoint of the (r-g) channel isindependent of the crosspoint of the (R + G) channel. Whilethe (R + G) channel crosspoint varies greatly, the (r-g) cross-point varies hardly at all, despite its dependence on the samecone types. For different observers, red/green-flicker matchratios are uncorrelated with the spectral position of uniqueyellow.17 Therefore, if the asymmetry hypothesis is the cor-rect explanation of the way in which the Vx and r-g-conenormalizations are achieved, we expect R-cone-rich observersto have a greater asymmetry than G-cone-rich observers, otherthings being equal, because they have more R cones to bediscounted. In some way, a single genetic mechanism mustsimultaneously specify the R/G-cone proportion and also theR-center/G-center asymmetry in order to keep the r-g cross-point invariant across observers. In other words, to keep ther-g crosspoint fixed at 575 while the R/G-cone ratio varies,observers rich in R cones must have relatively more G-conecenters (or more R cones packed into the surround). R/G-cone ratios and R-cone-center/G-cone-center ratios cannotvary independently. Although speculation about the vari-ables that control the center-surround structure is notworthwhile, the interdependence of R/G-cone ratios andR/G-center ratios restricts the possibilities.
ConclusionsPsychophysical data by themselves cannot determine therelative numbers of cones on the retina unless assumptionsare made about cone size, density, photosensitivity, synapticefficiency, etc. Nonetheless, the transformation equationsof opponent theory have a meaning under any set of as-sumptions because they are relative and hence immune tocertain normalizing and scaling operations. The aspect of thetransformation focused on here, namely, a difference inchannel inputs, is a particularly useful datum. Because bothcones appear in both transformations, the possibilities forexplaining such a difference are restricted. The differencecannot be explained by using a particular normalization ofcone sensitivities. This degree of freedom can be used toaccount for either the VA normalization or the r-g normali-zation but not both. Relative cone sensitivity and conenumerosity, although conceptually different, are inter-changeable in this regard and do not provide additional lati-tude for satisfying the transformation equations. Hence itappears that, when one uses the single degree of freedomprovided by inherent cone sensitivity or cone numbers to ex-plain one of the sets of coefficients (either Vi or r-g), it isnecessary to invoke a neural explanation for the other. Thehypothesis offered explains both the transformation coeffi-cients and the hue change with flicker as a consequence ofreceptive-field asymmetry.
Finally, it is surprising that the reported asymmetry ofcenter-surround receptive fields does not have some strikingconsequence already reflected in the psychophysical litera-ture. To our knowledge, this report is the first in which psy-chophysical data have been attributed to an asymmetry ofphysiological receptive fields.
SUMMARY
1. Estimates from single-cone microspectrophotometryare consistent with psychophysical estimates that the humanretina contains about 1.6 R cones for every G cone. If so, then
1532 J. Opt. Soc. Am./Vol. 73, No. 11/November 1983
R and G cones contribute proportionally to the spectral sen-sitivity of the achromatic channel when measured by het-erochromatic flicker photometry: VX = k1 (6.5 R + 4 G).
2. The r-g channel differences R and G cones to computethe r-g signal. The R cones are discounted by a large factorwhen this difference is taken; r-g = h2 (3 R - 4 G).
3. A receptive-field structure that decreases the weightingof R cones in the r-g channel is proposed. Because manycones in the surround are required to balance a few cones in
the center, R-cone signals can be weighted less by putting R
cones predominantly in surrounds and G cones in centers.4. Because of the latency difference between center and
surround, the asymmetry may cause a hue shift when stimuli
are flickered. Piantanida and Hammon15 find a hue shift inthe predicted direction, which we have confirmed.
De Monasterio and Gouras'3 have reported that the ratioof R-cone centers to G-cone centers is asymmetrical; G-cone
centers indeed predominate, in agreement with the predic-tion.
ACKNOWLEDGMENTS
This research was supported in part by National Eye InstituteGrant EY 03236 to Carl R. Ingling, Jr.
The hypothesis that G-cone centers must predominate inthe human retina was deduced from the psychophysical evi-dence; we are grateful to F. M. De Monasterio for bringing to
our attention Table I of Ref. 13.We also thank T. Piantanida and R. Hammon for an early
report of their flicker hue-shift experiments.
* Current address, Instituto de Investigaciones Biomedicas,
Departamento de Biomatematicas, Apartado Postal 70-228,04510, Ciudad Universitaria, Mexico 20, D.F.
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C. R. Ingling, Jr., and E. Martinez-Uriegas
7. S. A. Burns, "Spectral sensitivity as determined by the minimallydistinct border criterion and heterochromatic flicker photometry,Ph.D. Thesis (Ohio State University, Columbus, Ohio, 1977).
8. H. J. A. Dartnall, J. K. Bowmaker, and J. D. Mollon, "Micro-spectrophotometry of human photoreceptors," presented atNATO Color Vision Conference, University of Cambridge,Cambridge, UK, 1982.
9. W. A. H. Rushton and H. D. Baker, "Red/green sensitivity innormal vision," Vision Res. 4, 75-85 (1964).
10. H. L. De Vries, "The luminosity curve of the eye as determinedby measurements with the flickerphotometer," Physica XIV,319-348 (1948).
11. P. Lennie, "Parallel visual pathways: a review," Vision Res. 20,561-594 (1980).
12. R- and G-cone sensitivities used for this calculation (V. Smithand J. Pokorny, Eye Research Laboratories, University of Chi-cago, Chicago, Illinois 60631; personal communication) are tab-ulated in Ref. 6, where they are called L and M.
13. F. M. De Monasterio and P. Gouras, "Functional properties ofganglion cells of the rhesus monkey retina," J. Physiol. 251,167-195 (1975).
14. P. Gouras and E. Zrenner, "Enhancement of luminance flickerby color-opponent mechanisms," Science 205, 587-589 (1979).
15. T. Piantanida and R. Hammon; SRI International, Menlo Park,California 94025 (personal communication) also report hue shiftsfor unique green in the opposite direction. This implies that they-b channel is constructed with an asymmetry favoring the +yprocess in the center and the -b process (probably B and G) conesin the surround. The direction of the unique-green hue shift andthe fact that it is greater for Class II than Class I [W. Richards,"Differences among color normals: classes I and II," J. Opt. Soc.Am. 57, 1047-1055 (1967)] observers confirms a proposal byIngling [C. R. Ingling, Jr., "The spectral sensitivity of the oppo-nent-color channels," Vision Res. 17,1083-1089 (1977)].
16. More systematic work is needed before the flicker hue shift canbe used to study receptive-field asymmetries. We attempted toverify the prediction that observers rich in R cones as determinedby flicker matches would have greater receptive-field asymmetriesand therefore show more pronounced hue shifts (see the sectionentitled Discussion and Conclusions), but our methods were notprecise enough even though an asymmetric duty cycle, insteadof square-wave flicker, amplified the hue shift. For example,adaptation to the flickering field depressed flicker sensitivity andmade the hue shift more apparent, but it also had a second-ordereffect on the hue itself, tending to make it greener. More seri-ously, the hue change across the flickering half of the bipartitefield is not uniform. Thus the magnitude of the hue shift dependson what the observer decides to notice about the field. To reducespatial contrast effects, the flickering and the reference fieldsshould probably be separated. Finally, the method of adjustmentdoes not allow good control over the adaptation. Taken together,these effects cause a response variability that makes it hard tomeasure small effects. For our 20-Hz condition (50-msec cycles:5-msec flash, 45-msec dark) with a 580-nm reference field, thesettings of our six observers ranged between 588 and 600 nm.
17. R. S. Wallstein, "Individual differences in equilibrium yellow,"Invest. Ophthalmol. Vis. Sci. Suppl. 22,18 (1982). We have alsoobtained the result that relative R,G-cone populations estimatedby flicker photometry for individual observers do not predict thespectral position of unique yellow.
