628 J. Opt. Soc. Am. A/Vol. 17, No. 3 /March 2000 Volbrecht et al.

Effect of the short-wavelength-sensitive-cone mosaicand rods on the locus of unique green

Vicki J. Volbrecht, Janice L. Nerger, Sheila M. Imhoff, and Corey J. Ayde

Department of Psychology, Colorado State University, Fort Collins, Colorado 80523-1876

Received May 24, 1999; revised manuscript received September 8, 1999; accepted September 22, 1999

A primary goal of this study was to establish whether the magnitude of the short-wavelength-sensitive- (S-)cone signal into the yellow/blue (Y/B) mechanism was influenced by the absolute or the relative numbers of Scones. This was assessed by measuring the locus of unique green for various test sizes at four eccentric lo-cations chosen to exploit differences in the underlying mosaic of S cones. In general, the locus of unique greenwas unaffected by test size, retinal quadrant, or rod input but was influenced by retinal eccentricity. Thelocus of unique green shifted to shorter wavelengths as retinal eccentricity increased from 1° to 8°. The datado not support a model whereby the S-cone signal is determined by the absolute number of S cones, but a modelbased on the relative number of S cones cannot be eliminated. © 2000 Optical Society of America[S0740-3232(00)00901-7]

OCIS codes: 330.0330, 330.1720, 330.5510.

1. INTRODUCTIONPerceptually, unique green is defined as the wavelengthin the visible spectrum that appears pure green (i.e., nei-ther yellowish green nor bluish green). Previous findingsreveal that the locus of unique green is not necessarily in-variant with changes in stimulus intensity,1–4 stimulusduration,2,3 stimulus size,3,5–7 or retinal eccentricity.3,5,6

Furthermore, there is evidence that signals from rodsmay influence the locus of unique green.6,8

Nerger and colleagues6 found that at 20° temporal reti-nal eccentricity, the locus of unique green shifted tolonger wavelengths as the diameter of the stimulus in-creased from 0.125° to 8°. The authors proposed an in-crease in the neural weighting of the short-wavelength-sensitive (S) cones to explain this shift to longerwavelengths with increasing test size. They did not,however, specify what aspect of the retinal topographycould be responsible for this increase. A later study byNerger et al.9 investigated the potential influence of theretinal topography of S cones on the locus of unique blue.They found that the retinal topography of S cones predict-ably influenced the weighting of the S-cone signal into thered/green (R/G) opponent system; i.e., fewer S cones un-derlying the test stimulus reduced the neural weightingof the S cones and shifted the unique blue locus to shorterwavelengths. That study, however, did not examine theequilibrium points of the yellow/blue (Y/B) opponent sys-tem.

The retinal topography of S cones may also determinethe neural weighting of the S cones into the Y/B process.For example, as the absolute number of S cones changesacross the retina,10–12 the neural weighting of S conesmay also change. There are few, if any, S cones in thecenter of the foveola; the distribution of S cones peaks atapproximately 1.5° retinal eccentricity and then exponen-tially declines with eccentricity until approximately 7°–8°

0740-3232/2000/030628-07$15.00 ©

retinal eccentricity. In addition, the proportion of Scones to the total number of cones also changes witheccentricity.11,12 This change in relative numbers is dueto the difference between the distribution of the middle-(M) and long-wavelength-sensitive (L) cones and the dis-tribution of S cones. The peak density of the M and Lcones, as an aggregate, occurs in the fovea and then expo-nentially declines until approximately 7°–8° retinal ec-centricity. Thus the percentage of S cones is lowest inthe central fovea and greater in the periphery, with somestudies11 reporting the greatest percentage of S cones at1.5° eccentricity and others12 reporting the greatest per-centage at 8° and beyond. There is also evidence the dis-tribution of cones may differ among the four retinalquadrants.12,13

Another aspect of the retinal topography that may in-fluence the locus of unique green is the distribution ofrods. Nerger et al.6 reported that with smaller test sizesand under experimental conditions designed to maximizerod input, unique green loci measured at 20° in the tem-poral retina shifted to shorter wavelengths with decreas-ing test size. Even though the stimuli were equated at250 td in the Nerger et al.6 study, there still was an effectof rods. Others also report the effects of rods on hue per-ception at similar intensity levels and with small testsizes.14–16

Psychophysical studies suggest the possible melding ofS-cone and rod signals (e.g., Refs. 17–19), which could po-tentially magnify the neural weighting of the S cones inthe Y/B opponent process. Anatomically and physiologi-cally this appears possible since the teledondria of the Scones directly contact rod spherules20 and signals fromrods are transmitted via rod amacrines to cone bipolarsand ganglion cells.21 Recent results from Lee andcolleagues22 indicate, however, that it may be only theparvocellular cells receiving antagonist input from the M

2000 Optical Society of America

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and L cones that are influenced by rod signals. Onemight expect, then, that since the R/G mechanism is as-sociated with parvocellular cells, the influence of rodswould be seen only in the R/G mechanism and not in theY/B mechanism.

The present study manipulated the relative and abso-lute number of S cones underlying our test stimuli to de-termine whether either of these factors contributed to theneural weighting of the S-cone input into the Y/B oppo-nent mechanism, as determined by changes in the locus ofunique green. Unique green measurements were ob-tained on both the cone and rod plateaus to assess rodcontribution.

2. METHODA. ObserversThree color-normal observers, one male (age 32) and twofemales (ages 30 and 38), participated in this experiment.Color vision was assessed by anomaloscopic matches(Neitz OT-II), three panel tests (Farnsworth-Munsell 100-Hue, D-15, Adams Desaturated D-15), and the F2 tritanplate. None of the observers received information re-garding their results until completion of all their experi-mental sessions.

B. ApparatusWe conducted the experiments utilizing three channels ofa standard four-channel Maxwellian-view optical system.A 300-W xenon arc lamp (Oriel) regulated at 290 W by adc power supply (Oriel) provided light for the optical sys-tem. Light exited the lamp housing via two ports andpassed through heat-absorbing filters and collimatinglenses. Beam splitters divided these two beams to createfour light paths. A series of collimating and focusinglenses imaged light from channel 1 onto the entrance slitof a grating monochromator (Instruments SA, Inc. H-20;4-nm half-amplitude bandpass) to define the spectralcomposition of the test stimulus. Channels 2 and 3 alsoconsisted of a series of collimating and focusing lensesthat produced the broadband (5500-K) bleaching field andfixation arrays, respectively. A neutral-density wedgeand neutral-density filters controlled the light intensity inchannel 1, while only neutral density filters were used inchannels 2 and 3. A potentiometer with a linear, digitalreadout system monitored the position of the neutral-density wedge. Shutter and shutter drivers (Uniblitz,model T132) placed at focal points in the optical systemcontrolled exposure durations for the test stimuli andbleaching field. Field stops located in collimated portionsof each channel defined the shape and size of the teststimuli, bleaching field, and fixation points. All lenseswere achromatic doublets, and all mirrors were front sur-faced. The final Maxwellian image was 2 mm as definedby an artificial pupil. The right eye of each observer wasaligned with respect to the optical axis of the Maxwellian-view system by use of a dental-impression bite-bar assem-bly.

C. StimuliTwo stimulus sizes were presented at four retinal loca-tions. Stimuli subtended 0.25° and 1.0° at 1° nasal and

superior eccentricities and 0.5° and 2.0° at 8° nasal andsuperior eccentricities. Estimates of the absolute andrelative numbers of S cones underlying the test stimuliwere achieved by assuming anatomical estimates fromCurcio et al.12,13 and an axial focal length23 of 16.667;these values are presented in Table 1. The test sizeswere selected so that the absolute number of S cones un-derlying the small stimuli were approximately the sameregardless of retinal position and the absolute numberunderlying the large stimuli were also approximatelyequated regardless of retinal position. Retinal positionswere selected to maximize the difference in the relativenumbers of S cones.

The fixation array for the nasal (superior) stimuli con-sisted of two vertically (horizontally) displaced pinhole-size points and one horizontally (vertically) displacedpinhole-size point, which formed the base and apex of atriangle. Observers fixated on the apical point while teststimuli were centered between the two points of the base.The subtense between the points of the triangle varied de-pending on the retinal eccentricity tested. Once fixated,observers initiated the presentation of the stimulus.

Test stimuli were equated at 250 td and presented for1 s with a 7-s interstimulus interval. In those conditionsrequiring a rod bleach, a 10°, 6.6-log-scot-td broadband(5500-K) bleaching field, centered over the test eccentric-ity, was presented for 10 s. This field bleached approxi-mately 98–99% of the rod photopigment.24,25 A previouscontrol study6 conducted in the fovea demonstrated thatthis bleaching field did not differentially adapt the threecone mechanisms since unique hue loci obtained bothwith and without a bleaching field were the same.

D. CalibrationRadiometric measures were obtained with an EG&GGamma Scientific radiometer (DR-1500A). Photometricmeasures for the bleaching field and at 550 nm weremade with a Minolta Chroma Meter (CS-100). Retinal il-luminances were computed with Westheimer’s26 method.The neutral-density wedge and filters were calibratedfrom 400 to 700 nm in 10-nm steps. A He–Ne laser(Spectra-Physics; 632.8 nm) was used to calibrate themonochromator.

Table 1. Estimates of Relative and AbsoluteNumber of S Cones and Total Cones

Quadrant

RetinalEccentricity

(deg)

TestSize(deg)

TotalCones

AbsoluteNumber of

S Cones

RelativeNumber of

S Cones (%)

Nasal 1 0.25 226 6 2.8Retina 1.00 3571 100 2.8

8 0.50 170 9 5.32.00 2713 144 5.3

Superior 1 0.25 194 8 3.9Retina 1.00 3079 120 3.9

8 0.50 147 9 6.42.00 2341 149 6.4

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E. ProcedureHue judgments were made under two adaptation condi-tions: without a rod bleach and with a rod bleach. Ob-servers dark adapted for 30 min before stimulus presen-tation to ensure maximum rod sensitivity in the no-bleachcondition. In the rod-bleach condition, observers darkadapted for 10 min, viewed the bleaching field for 10 s,dark adapted for another 4.5 min, and then made uniquegreen judgments for 4–5 min. This sequence of eventsensured recovery of cone sensitivity before unique greenjudgments were obtained and termination of measure-ments before the cone–rod break of the dark adaptationfunction.

Each stimulus presentation required a binary hue de-cision of blue or yellow by the observer. A response ofyellow indicated that the stimulus appeared yellowishgreen, and a response of blue implied that the stimulusappeared bluish green. The wavelength of the teststimulus was varied according to two randomly inter-leaved staircases. The experimenter set the initial twowavelengths of each staircase so that the observer clearlyperceived the two response hues. After the initial re-sponse reversal in each staircase, the wavelength stepsize was gradually reduced until 2 nm was reached.Reaching the criterion of at least four response reversalsat the smallest step size (i.e., 2 nm) terminated each stair-case. The mean of the last four reversals from each stair-case and across 2–4 experimental sessions defined theunique green locus.

Stimulus size, eccentricity, and retinal quadrant wererandomly selected for each test session. In each case theno-bleach conditions preceded the rod-bleach conditionsso that the appropriate cone and rod adaptation levelswere maintained. Each experimental session lasted ap-proximately 1.5 h.

F. ModelingThe primary objective of this experiment was to deter-mine whether known variations in the S-cone topographyinfluence unique green loci in the peripheral retina. As astarting point, we assume a linear model for the Y/B op-ponent code in the peripheral retina, similar to the fovealmodel proposed by Hurvich and Jameson.27 The locus ofunique green is predicted to occur when the Y/B opponent

Fig. 1. Predicted patterns of the locus of unique green for theabsolute (panel A) and relative (panel B) S-cone models (see textfor details).

process is at equilibrium (i.e., 50). The following equa-tion mathematically represents this model of uniquegreen:

k1S~l! 2 k2M~l! 2 k3L~l! 5 0. (1)

In the above equation, S, M, and L denote the S-, M-,and L-cone spectral sensitivity functions and k1 , k2 , andk3 represent the neural weighting factors associated witheach cone type. On the basis of previous research fromour laboratory,6 and according to Eq. (1), we know that anincrease in k1 increases the blueness signal, and conse-quently the locus of unique green shifts to longer wave-lengths. Although the manipulations of test size andretinal eccentricity also affect the absolute number of Mand L cones, it is assumed for this initial analysis that k2and k3 are determined by the relative number of L to Mcones. Recent psychophysical28–30 and genetic31,32 evi-dence indicates the ratio of L to M cones remains constantfor the range of eccentricities used in this study; thereforek2 and k3 are invariant for our experimental conditions.

Figure 1 presents the predicted pattern of results forunique green loci in both the nasal and the superior reti-nal quadrants. The predictions are based on Eq. (1) andour estimates of the absolute and relative numbers of Scones underlying our test stimuli (see Table 1). Further-more, we assume that an increase (decrease) in either theabsolute or the relative numbers of S cones results in anincrease (decrease) in the value of k1 [see Eq. (1)]. Thetop panel shows the pattern of results expected if the ab-solute number of S cones influences the neural weightingof k1 . As test size increases within a retinal eccentricity,the absolute number of S cones increases, and the locus ofunique green shifts to longer wavelengths. In thismodel, unique green is unaffected by retinal location sincethe absolute numbers of S cones at each retinal locationhave been equated by manipulating test size. As the bot-tom panel of Fig. 1 illustrates, a different pattern of re-sults is expected if the relative number of S cones affectsthe neural weighting of k1 . The locus of unique green islonger at 8° retinal eccentricity than at 1° retinal eccen-tricity since the proportion of S cones to total cones isgreater at 8° (see Table 1). In this model, unique greenremains invariant within an eccentricity since the rela-tive number of S cones is the same regardless of test size.

3. RESULTSA difference of at least 3 nm and nonoverlapping standarderrors of the mean (SEM’s) defined the criterion for a shiftor change in a unique green locus and a means by whichto interpret the results of this study. The basis for thesecriteria was results from wavelength discrimination func-tions of the fovea and peripheral retina,33 between-session variability of unique hue loci, and previous re-search from our laboratory.9

A. Absolute Numbers: Test SizeAn absolute model of S-cone input into the Y/B opponentsystem predicts longer unique green loci for the largertest stimuli compared with the smaller stimuli. Figure 2presents the results of this manipulation at 1° and 8° na-sal and superior retinal eccentricities. All data were ob-

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Fig. 2. Unique green loci plotted as a function of stimulus size for 1° and 8° nasal and superior retinal eccentricities. Different symbolsdenote different observers; error bars represent 61 SEM based on between-session variability.

tained following a rod bleach and on the cone plateau.Different symbols denote the different observers; errorbars specify 61 SEM based on between-session variabil-ity. On the basis of our shift criterion, except for one ob-server at 1° retinal eccentricity and a different observerat 8° retinal eccentricity, there was no effect of test sizeon the locus of unique green.

B. Relative Numbers: Retinal QuadrantAccording to Curcio et al.,12 there are approximately 1.1%more S cones in the superior retina than in the nasalretina at comparable eccentricities (see Table 1). If a1.1% difference is great enough to affect the locus ofunique green, then the relative model of S cones predictsthe locus of unique green to be at longer wavelengths inthe superior retina than in the nasal retina for compa-rable experimental conditions. Figure 3 comparesunique green loci obtained in the superior retina withunique green loci from the nasal retina for both periph-eral retinal eccentricities and their corresponding testsizes. The solid diagonal line represents the conditionsin which the same retinal eccentricity and test size re-sulted in identical unique green loci in the superior andnasal retinas. The dashed lines specify the 63-nm crite-rion. Error bars denote 61 SEM. Only one data pointfalls outside the criterion area, and its direction is con-trary to the predictions based on the relative model.

C. Relative Numbers: Retinal EccentricityAnother way to assess the effect of the relative number ofS cones on the locus of unique green is to examine the dif-ference between the unique green locus at 1° eccentricitywith that obtained at 8° eccentricity. According to Cur-cio et al.,12 there are approximately 2.5% more S cones at8° retinal eccentricity than at 1° retinal eccentricity (seeTable 1). Thus the unique green loci for the 8° retinal ec-centricities should be at longer wavelengths than the lociat 1° retinal eccentricities for comparable test sizes and

retinal quadrants. A comparison between the loci atthese two eccentricities is shown in Fig. 4. Data are plot-ted in the same manner as in Fig. 3. Eight points fall be-low the dashed line, indicating that the locus of uniquegreen at 1° is longer than at 8° for comparable stimulusconditions. This finding is opposite to the predictionsbased on the relative S-cone model.

D. RodsIf the rods enhance the S-cone signal of Eq. (1), it is ex-pected that unique green loci will shift to longer wave-lengths with rod input (no-rod-bleach condition) whencompared with no rod input (rod-bleach condition). Fig-ure 5 compares the results of the no-bleach and rod-bleach conditions. Data are plotted as in the previousfigures. The solid diagonal line represents the condition

Fig. 3. Unique green loci measured in the nasal retina in com-parison with unique green loci measured in the superior retina.Different symbols specify different retinal eccentricities and testsizes; error bars represent 61 SEM based on between-sessionvariability. Dashed lines delimit the 63-nm-shift criterion.

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in which the locus of unique green is the same in thebleach and no-bleach conditions; dashed lines delimit the63-nm-shift criterion. Plotted in this manner, only twopoints fall outside the criterion area, and the direction isopposite to that predicted by the model. We concludethat for our stimulus conditions, the data demonstrate noeffect of rods on the locus of unique green.

4. DISCUSSIONFigure 6 summarizes the pattern of results from thisstudy. We have plotted the data in the same format as inFig. 1 in order to assess directly the predictions of the twoS-cone models. As Fig. 6 illustrates, the data from thisstudy do not follow the predictions of either the absoluteor the relative S-cone model. The absolute S-cone modelpredicts that the locus of unique green should vary withtest size. The data demonstrate, however, that there isno effect of test size and that the unique green loci for the

Fig. 4. Unique green loci measured at 1° retinal eccentricity incomparison with unique green loci obtained at 8° retinal eccen-tricity. Different symbols specify different retinal quadrantsand test sizes; error bars represent 61 SEM based on between-session variability. Dashed lines delimit the 63-nm-shift crite-rion.

Fig. 5. Unique green loci measured in the rod-bleach conditionin comparison with those from the no-bleach condition. Differ-ent symbols specify different retinal eccentricities and test sizes;error bars represent 61 SEM based on between-session variabil-ity. Dashed lines delimit the 63-nm-shift criterion.

1° retinal eccentricities at both test sizes are longer thanthose for the 8° retinal eccentricities at the two test sizes.Thus the data do not support a model whereby the abso-lute number of S cones determines the weight of theS-cone signal into the Y/B opponent code.

The relative S-cone model predicts that retinal eccen-tricity should influence the locus of unique green, but itpredicts a pattern that is opposite to the results of thisstudy; i.e., the locus of unique green at 1° retinal eccen-tricity was predicted to occur at a shorter wavelengththan that obtained at 8°. One explanation for this resultmay be that our calculations for the absolute and relativenumbers of S cones were based on the findings of Curcioet al.12,13 If we had used the S-cone values of Ahneltet al.,11 we would have predicted the same pattern of re-sults for the absolute S-cone model, but a different pat-tern of results would have been predicted for the relativeS-cone model. Both studies concur that the S cones rep-resent approximately 6–8% of the total cones at eccen-tricities beyond approximately 7°, but they differ in theirestimates of the relative number of S cones at 1° retinaleccentricity. Curcio et al.12 report that S cones represent3–4% of the total cones at 1° retinal eccentricity, whereasAhnelt et al.11 report a much higher number, 15%. If thepercent of S cones is higher at 1° than at 8°, then the pat-tern of results that we obtained follow the predictionsbased on a relative S-cone model.

Figure 6 also reveals that there is some individual vari-ability among the three observers: two of the three ob-servers show a similar pattern of results, while the thirdobserver’s (squares) pattern differs. One possibility forthe differences among the observers is the reported indi-vidual variability in the S-cone mosaic.12 Although ourS-cone estimates were based on mean data, it is possiblethat our observers are not representative of these meanvalues, and perhaps some of the observers represent indi-viduals with higher density values at 1° retinal eccentric-ity. This individual variability has been shown to bequite striking along the foveal slope, where there is arapid rate of change in cone densities.

Fig. 6. Unique green loci obtained in the nasal (upper panel)and superior (lower panel) retinal quadrants are plotted in themanner of Fig. 1. Different symbols denote the three observers.The solid line represents the mean of the three observers.

Volbrecht et al. Vol. 17, No. 3 /March 2000/J. Opt. Soc. Am. A 633

Another factor that may have contributed to the pat-tern of results in this study is a change in photopigmentdensity with eccentricity. For example, cone photopig-ment density decreases from the fovea to the peripheralretina.34,35 Retinal densitometry measurements haveshown that the greatest change in density occurs from thefovea to 2° retinal eccentricity with minimal, if any, de-crease from 2° to 4° retinal eccentricity.35,36 Unfortu-nately, these measurements have not been extended to 8°retinal eccentricity, but the retinal densitometry mea-surements made at 4° suggest that there may be rela-tively little if any decrease in photopigment density from4° to 8°. This decrease in photopigment density couldcontribute to a shift in the locus of unique green toshorter wavelengths at 8° retinal eccentricity comparedwith the locus of unique green at 1° retinal eccentricity;however, the expected shift is very small (,3 nm) andtherefore does not exceed our shift criterion.37

The relative number of M and L cones remained con-stant across the experimental conditions of thisstudy,28–30 but the absolute number of M and L cones didchange. If the absolute number of M and L cones influ-enced the locus of unique green, then we would expect tosee an effect of test size in our results. As Figs. 2 and 6illustrate, however, test size did not consistently influencethe locus of unique green. Thus the absolute numbers ofS, M, and L cones are not the primary components of theneural weighting factors for the cone input into the Y/Bmechanism [see Eq. (1)].

In this study we assumed a linear model in which theoutput of the S cones opposes the combined output of theM and L cones.27 Another linear model combines theoutput for the S and M cones to oppose the L cones (e.g.,Refs. 38 and 39). This model would ultimately predict agreater shift in unique green than the linear model in Eq.(1) since an increase in the neural weighting of S cones isfurther enhanced with the signal from the M cones. Thisstudy, however, cannot distinguish between the two mod-els, because both models predict that the locus of uniquegreen will shift in the same direction. Alternatively,other researchers1,40,41 have suggested that a nonlinearmodel may be a better descriptor of the Y/B opponent pro-cess.

A recent physiological study22 has suggested that rodinput at lower intensity levels does not affect the S-coneopponent ganglion cells but does influence the R/G gan-glion cells. If the S-cone opponent ganglion cells provideinput primarily to the Y/B opponent mechanism, then it ispossible that there would be no rod influence on uniquegreen loci; however, one might expect an influence onunique blue and unique yellow loci. Indeed, results fromthis study showed no effect of rods on the locus of uniquegreen, while previous research9 demonstrated an effect ofrods on the loci of unique blue and unique yellow.

In this study, the influence of rods on the locus ofunique green was minimal to nonexistent. While astimulus of 250 td, as used in this study, might not be ex-pected to elicit much rod activity, others have shown atsimilar and even higher intensities the influence of rodson hue perception (e.g., Refs. 6, 15, and 16). The resultsof this study are in apparent disagreement with the re-sults reported by Nerger et al.6 In that study, Nerger

et al. reported that signals from rods shifted the locus ofunique green at 20° in the temporal retina to shorterwavelengths. The shift occurred only for the smallesttest sizes, which were smaller than those used in thisstudy at 8° retinal eccentricity; however, when the testsize was increased, there was no effect of rods on the locusof unique green.

Not only are there differences in rod influence amongthe unique hue loci, but the unique green data from thisstudy differ from the findings on unique blue loci obtainedin the rod-bleach condition.9 Changes in test size, butnot in retinal eccentricity, influenced the locus of periph-eral unique blue, suggesting that an absolute rather thana relative model of S cones was a determinant of the neu-ral weighting of S cones in the R/G opponent mechanism.Taken together, this study and the previous study9 onunique blue indicate that the factors influencing the neu-ral weighting of the S cones into the two chromatic-opponent mechanisms may be different for the R/G sys-tem in comparison with the Y/B system.

ACKNOWLEDGMENTSThis research was supported by a National Science Foun-dation grant (IBN-9603613) to V. J. Volbrecht and J. L.Nerger.

V. J. Volbrecht’s e-mail address is vickiv@lamar.colostate.edu.

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