sity, " Behav. Res. Meth. Instr. 2, 297-300 (1970).°0H. K. 11artline and P. R. McDonald, "Light and dark adapta-tion of single photoreceptor elements in the eye of Lirnulus,"J. Cell. Comp. Physiol. 30, 225-254 (1947).

"G. Westheimer, "The maxwellian view," Vision Res. 6, 669-682 (1966).

12E. N. Willmer and W. D. Wright, "Colour sensitivity of thefovea centralis, " Nature 156, 119-121 (1945).

13G. Wald, "Blue-blindness in the normal fovea, "t J. Opt. Soc.Am. 57, 1289-1301 (1967).

14M. Aguilar and W. S. Stiles, "Saturation of the rod mecha-nism of the retina at high levels of stimulation, " Opt. Acta1, 59-65 (1954).

1 5L. A. Riggs, R. N. Berry, and M. Wayner, "A comparisonof electrical and psychophysical determinations of the spec-tral sensitivity of the human eye, " J. Opt. Soc. Am. 39,427-436 (1949).

16G. Wagner and R. M. Boynton, "Comparison of four meth-ods of heterochromatic photometry, " J. Opt. Soc. Am. 62,1508-1515 (1972).

Color vision in the peripheral retina. II. Hue and saturation*James Gordon

Hunter College, City University of New York, New York, New York 10021and The Rockefeller University, New York, New York, 10021

Israel AbramovtBrooklyn College, City University of New York, Brooklyn, New York 11210

and The Rockefeller University, New York, New York 10021(Received 9 April 1976)

Hue and saturation of spectral lights were measured (direct scaling) in the fovea and at 45' in the periphery;all lights were of equal photopic retinal illuminance (1200 trolands). At each retinal location both large andsmall targets were used. As shown by previous studies, small peripheral targets appear desaturated and ofuncertain hue, except long wavelengths which appear red. However, if target size is increased, saturationincreases and a full range of hues is seen; the hue functions for large peripheral targets are comparable tofoveal ones for very small targets. From a modified form of color matching, it was concluded that the colordeficiency in the periphery is more tritanlike than deutanlike; this is strengthened by the observation that, forsmall peripheral targets, hues are generally apportioned between two hue categories and the change from oneto the other is at about 580 nm.

INTRODUCTION

It is commonly accepted that color vision deterioratesprogressively as the stimulus is moved away from thefovea, and this is true even for intensities well abovephotopic thresholds. 1,2 The more recent quantitativemeasures have included color-matching functions ateccentricities up to 50° from the fovea, 3 color namingof monochromatic lights out to 400 in the periphery, 4

and measurement of the photochromatic interval out to720. 5 At these eccentricities, color-matching functionsare grossly different from foveal ones, and lights, es-pecially from the middle of the spectrum, appear de-saturated and of uncertain hue. The major problemswith these studies are that they used relatively smallstimuli and these were usually equated for photopicluminosity using the standard foveal function.

We have argued that the foveal luminosity curve isnot appropriate for the peripheral retina, which isrelatively much more sensitive to short wavelengths. 6

Size of stimulus may also be an important variable: inthe fovea and near periphery, any degradation of thestimulus (as from using a very small, or dim, orbrief stimulus) produces color vision with a tritan-like defect. 710 Previous studies in the far peri-phery did not use stimuli greater than 30 (often muchsmaller); while such stimuli may be "large" at thefovea, they may be "small" at retinal eccentricities

202 J. Opt. Soc. Am., Vol. 67, No. 2, February 1977

of 40Q-707

It is sometimes suggested that since the peripheralretina has abnormal color vision, it can be used tostudy mechanisms of color defect, with the fovea pro-viding the normal control. 11 It is therefore necessaryto know precisely the nature of the defect in the periph-ery and whether the defect exists under all conditions.Moreland concluded, from the confusion loci in colormatching functions, that the system in the peripheralretina tends towards deuteranopia. 311 Boynton and hiscolleagues reached a similar conclusion from color-naming experiments; they found that, in the periphery,hues of spectral lights tended to be either yellow orblue and the middle wavelengths were generally con-fused with each other. 4

In this paper we examine in detail the color vision ofthe peripheral retina at high photopic levels. Spectralhue and saturation functions are presented for the nasalretina at 45° from the fovea, and at the fovea (using thelatter as a "normal" control). Stimuli were mono-chromatic lights, appropriately equated for luminosity,using previously determined curves, 6 and presented inMaxwellian view. Both large and small targets wereused in the fovea (1. 50 and 5') and in the periphery(6. 50 and 1. 50) Finally, to specify the nature of anycolor defect in the periphery, we used a modified formof anomaloscope match.

Copyright i 1977 by the Optical Society of America 202

80

60

40

20

Ia

(O) Red

-5° fo5eo-, 5, fovea

6 5° 45° from fovea- -- 1 5°, 45° from fovea

If

2",

500

®(a Yellow

500

- Green

600

600

600

; + -+

. . . . . . . . .II450 500 550

Wavelength ( nm)

600 650

FIG. 1. Percentages of red, yellow, green, andblue perceivedin monochromatic stimuli of equal retinal illuminance (1200 td).Each curve is the mean from six subjects. Two targets (1. 5°and 5') were viewed foveally, and two (6. 5° and 1.5°) wereviewed peripherally at 45° from the fovea. The particularsymbols and curves associated with each target are shown in(A). The appropriate luminosity functions for each target werepreviously obtained by Abramov and Gordon (Ref. 6).

METHODS

Subjects and apparatus

The six subjects and the apparatus were the same asin the previous paper. 6 The fields were the same as inthe previous study in which each subject's photopicluminosity function was determined for each field. Inthat study it was found that the foveal and peripheral

203 J. Opt. Soc. Am., Vol. 67, No. 2, February 1977

luminosity functions (from heterochromatic flickerphotometry) were drastically dissimilar. For thisstudy, the previous data were used to adjust the inten-sities of the monochromatic lights so that for each sub-ject and for each field they all matched the retinal il-luminance (1200 trolands) of a standard field.

Procedures

Spectral hue and saturation functions were obtainedfrom each subject for each of the four fields. Stimuliwere presented for 0. 5 s with 14. 5 s of darkness be-tween flashes; 1. 0 s before each flash a 0. 5 s warningtone alerted the subject. The test wavelengths rangedfrom 450 to 660 nm in 10 nm steps; order was random.

After each flash the subject rated its appearance us-ing a continuous scale ranging from zero to one hun-dred. A subject first decided how much of the scaleto use to describe the achromatic component of his sen-sation; the remainder was apportioned among the pri-mary hue categories of red, yellow, green, and blue.The sum of all components had to equal one hundred.For example, after presentation of a 520 nm light asubject might report that the achromatic portion was20 and the chromatic part was composed of 20 units ofyellow and 60 of green. No other restrictions wereplaced on the subject, nor were any defining examplesof the hue categories given; a subject was free to useany or all of the categories to describe each stimulus.

At the start of each experimental session a subjectwas dark adapted for 10 min. and then given a practicerun through the spectrum both to stabilize level ofadaptation and to familiarize him with the range ofstimuli. On the first session half the subjects beganwith the 1. 50 field and half with the 5' field; in eithercase the targets were imaged on the fovea. After com-pleting a single run through the spectrum with one tar-get, it was replaced by the other and the proceduresrepeated using a new random order; this was continuedthrough the first two sessions until the spectrum hadbeen presented a total of five times for each target.Additional practice trials were given each time thefield was changed. The next two sessions followed thesame routine except that the targets were the 1. 5° and6. 5° fields viewed peripherally. A final session wasused for a modified form of color matching experiment;the specific procedures are described later. Experi-mental sessions were separated, typically, by one ortwo days.

RESULTS

Hue and saturation

The major findings deal with changes in the apparentcolor of spectral lights as a function of stimulus sizeand retinal location. The results for hue are shown inFig. 1, in which the perceived proportions of the fourprimary hues are plotted separately. Thus Fig. 1(a)shows the proportion of "red" seen at each wavelengthfor each of the four targets. Each point on a graph isthe mean from all six subjects (five presentations perstimulus per subject). The apparent saturation of the

J. Gordon and I. Abramov 203

80e

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(a)

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(b)

60F

40F

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/ +

I-

/ P-a. -d

*..+... -I

450 500 550 600 650

Wavelength (nm)

Percentage of saturation perceived in monochromaticGeneral conventions as in Fig. 1. (a) Foveally viewed(b) Peripherally viewed targets.

various stimuli is given in Fig. 2; saturation was de-fined as 100 minus the perceived achromatic componentfor any stimulus. The results for foveally viewed tar-gets are in Fig. 2(a) and peripheral ones are in Fig.2(b). As in Fig. 1, each point is the mean from allsubjects. It is worth noting that subjects generallyused two of the four hues, together with the achro-matic category, to describe any light. Virtually nolight was seen as totally saturated or of unique hue;red and green were never seen simultaneously; veryrarely (one subject) blue, green, and yellow were usedtogether.

One of the striking findings about hue is that thespectral curve for red is virtually the same for all tar-get sizes and locations [Fig. 1(a)]. Subjects often com-mented that, in the periphery, hues were often some-what uncertain; the exception was red: whenever anyred appeared in a stimulus, subjects had much moreconfidence in their judgements. Furthermore, the ap-parent saturation of long wavelengths did not changedrastically with stimulus size and position (Fig. 2).

The major changes in color are seen in the short andmiddle wavelengths. In the fovea the small target ap-pears more desaturated [Fig. 2(a)] and the biggestchange in hue is in the green category, which is con-

204 J. Opt. Soc. Am., Vol. 67, No. 2, February 1977

02

0If)3

J. Gordon and I. Abramov 204

siderably reduced [Fig. l(c)]. In the periphery thechanges are more extreme, especially if we considerthe smaller (1. 50) of the two targets. This entire re-gion of the spectrum appears quite desaturated [Fig.2(b)]. For hue, the green and blue categories differedthe most from the foveal levels. Green was drastical-ly reduced but its spectral extent was largely unaf-fected. Blue, however, was both reduced and spreadtowards longer wavelengths; the 1. 50 target at 450still appeared appreciably blue at 570 nm.

The data in Figs. 1 and 2 can be considered inanother way, a way that was clearly apparent to all sub-jects: in the periphery the small (1. 50) target was gen-erally achromatic and of uncertain hue. But increas-ing target size to 6. 50 made all wavelengths appearquite well saturated and increased subjects' confidencein their hue judgements. The larger target appeared tohave color comparable to that seen in the fovea. If thefunctions are examined in detail it seems that thecurves for the 6. 5° field at 450 are very similar tothose with a 5' field at the fovea. Thus the peripheralretina is "color blind" only for small targets, in muchthe same way as is the fovea.

The above results were found with all subjects, butthere were considerable individual differences in themagnitudes of the various effects. To illustrate someof this, we show in Fig. 3 separate sets of data fromsubjects JG and JT; for each subject we show thehue scaling curves for the 1. 50 target in the fovea andthe 6. 50 and 1, 50 targets at 450, These subjects werechosen because each displayed an extreme form of thegeneral tendencies. They had essentially similarcurves for the fovea. In the periphery both subjectsshowed large reductions in green and yellow; this wasmore pronounced for J. G., for whom no green wasever apparent in the smaller field. For both subjectsthe spectral extent of blue was greater in the periphery,especially with the 1. 50 field; for JT the blue wasrelatively saturated but for JG all lights appearedvery desaturated. It is interesting to note that with the1, 50 field both subjects tended to divide the spectrumbetween blue and red, with the dividing point in thevicinity of 580 nm. The mean data in Fig, 1 show aless pronounced but similar effect. The possible sig-nificance of this will be discussed when we considerthe nature of the peripheral color deficiency.

Color matching

Previous investigators had concluded that the periph-eral retina is at least deuteranomalous. 3,4,11 However,to us it seemed that, for spectral lights, the deficiencyis more akin to a tritan type of defect. We based ourinitial conclusions on the hue scaling data: a completedeuteranope would be expected to divide the spectrumsomewhere about 500 nm while a tritan would divide itat about 580 nm. We do not know what hues a tritanwould see, but we note that our subjects, and those ofBoynton et al., 4 tended to change from one major huecategory to another at about 580 nm.

To investigate this further we used a modified anom-aloscope procedure. In one situation a series of mix-

FIG. 2.stimuli:targets.

. . . . .

- Red '--'Yellow +--+ Green '---'Blue

100 -T : 15', fovea

80 -

60 e / +,'9

40 -

20 ,,,.}t4 U l Bo,,

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60 -

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60 -

40 -

20 -.

0450 500 550 600 650

J G. 1 5',fovea

J.G.: 1.5, 45' from fovea

450 500 550 600 650

Wavelength (nm)

FIG. 3. Percentages of red, yellow, green, and blue per-ceived in monochromatic stimuli by subjects JT and JG.These data were included in the means shown in Fig. 1. Asmarked on the graphs, each row shows data for one size andlocation of target. Symbols and curves identified at top offigure.

tures of 560 and 620 nm was compared with a standard

of 590 nm; all three of these lights lie on a confusionlocus for a deuteranope. In the other situation, mix-tures of 480 and 540 nm were compared with a 510 nmstandard; all of these lights are approximately on atritan's confusion locus. It is clear, from the hue datain Fig. 1, that under no conditions were our subjectstrue dichromats. However, we might expect that, in so

far as the defect resembles deuteranopia, all mixturesof 560 and 620 nm would be similar in appearance to

590 nm, but in the other situation (480+ 540 nm vs 510nm) only some mixtures should appear similar, andvice versa for tritanopia.

All six subjects were used and data obtained for allfour targets for each of the two comparisons just de-scribed; half the subjects started with the one com-parison and half with the other. For those beginningwith the 590 nm standard, the procedure was as follows:on each trial the standard appeared for 0. 5 s, followed5. 5 s later by the mixture; the mixture, randomlychosen, was one of six possible combinations of 560 and620 nm in which the proportion of 620 nm could vary from0% to 100% in 20% steps. After seeing the mixture thesubject rated its similarity to the standard, using acontinuous scale from 0 to 100, where "100" signifies

205 J. Opt. Soc. Am., Vol. 67, No. 2, February 1977

identity. Each possible mixture was rated a total offour times. Intertrial interval was 5. 5 s. The sameprocedures were used with the 510 nm standard and themixtures of 480 and 540 nm. Intensities of all stimuliwere always adjusted according to the previously deter-mined luminosity functions for each subject. 6

The mean results for all subjects are shown in Fig.4. In each graph we show two curves; each gives thedegree of similarity between one of the standards andits appropriate set of mixtures; thus, depending on the

particular curve, the abscissa is percentage of either620 or 540 nm in the mixture. Any curve that has onehigh value indicates that a specific mixture was seenas similar to the standard, while others were clearlydifferent. In general this was true. But for the 1. 5°field at 450 one of the curves is uniformly high; thiswas for mixtures of 480 and 540 nm and a standard of510 nm. This confusion would seem akin to tritanopia.A similar tendency appears for the 5' foveal target[Fig. 4(b)]; all mixtures of the 480 and 540 nm lightsare more similar to the standard than is the case forthe 1. 50 foveal field [Fig. 4(a)]. It should also benoted, however, that for both peripheral targets [Figs.4(c), (d)] the curves for the 590 nm standard have someslight indication of deuteranomaly: in each case more560 nm light (by comparison to fovea) isneeded in themixture for maximal similarity.

DISCUSSION

Our major conclusion is that it is misleading to termthe peripheral retina color blind, or even "color de-ficient. " The quality of color vision in the periphery

B 5', fovea

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UE

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Percent 620nm, or 540 nmx-'590nm vs.(560 +620)nm -- 51-0nm vs.(480 +540)nm

FIG. 4. Perceived similarity between a standard wavelengthand a mixture of two other wavelengths. Solid curves are fora 590 nm standard compared with mixtures of 560 and 620 am;the abscissa shows percentage of 620 nm in the mixture.Dashed curves are for a 510 nm standard compared with mix-tures of 480 and 540 nm; the abscissa shows percentage of 540nm in mixture. Each symbol is the mean from six subjects.

J. Gordon and I. Abramov 205

I

depends crucially on stimulus size. If the stimulus issufficiently large, subjects see a full range of wellsaturated hues. But this principle holds also for thefovea, The results in Fig. 1 suggest quite stronglythat small colored stimuli anywhere on the retina willbe perceived in much the same way. The peripheraleffects are more obvious mainly since even fairly largetargets fall below the critical size.

The above conclusions agree with the psychophysicalfindings that all three primary cone-related mecha-nisms are present throughout the retina and that theirspectra are essentially as in the fovea. 12 Presumably,though, the peripheral cones are so sparse that largerstimuli are needed to stimulate adequately all the colormechanisms. Indeed, this is what would be expectedfrom the many observations that sizes of receptivefields increase with retinal eccentricity. However, thepresent study also suggests that the channels subserv-ing the various primary hues do not all have the samespatial "tuning. " As stimulus size is reduced greenis the first hue to disappear, and then yellow. This, ofcourse, is the basis of the "color zones" mapped inperimetric studies in which color disappears as a smalltarget is moved from the fovea towards the periphery.

So far we have emphasized the qualitative similari-ties between foveal and peripheral color vision. Thereare, however, some real differences. The clearestone is the spectral extent of blue. In Figs. 1 and 3 wesee that for both targets blue is still perceived at wave-lengths much longer than in the fovea, and for smalltargets blue may be one of the dominant hues. This isa little difficult to understand if blue is determinedsolely by the short-wavelength cone system since ithas the same spectral sensitivity as in the fovea butmay be depressed in absolute sensitivity in the periph-ery. 12 A possibility which we cannot rule out is thatrods may contribute both to the channel signaling blueand to the general desaturation of much of the spectrumin the periphery. 5,13 The suggestion is attractive sincethe short-wavelength cones cannot by themselves con-tribute to the perception of blue at wavelengths longerthan about 530 nm. However, if rods are involved(even at the present high levels of illuminance) onemight expect an increase in target size to magnify the"rod" contribution; the opposite was the case in ourdata.

We must now say something more about the possiblenature of the color deficiency observed in the peripheryfor small targets. In our modified color matching ex-periments we found that the largest hue confusionswere not in the vicinity of 500 nm, where we would ex-pect them to be for deutanlike defects. Added to thisis the observation that for most subjects two hue names(blue and red) were largely sufficient for describingmost small, peripheral stimuli; subjects changed huecategories in the vicinity of 580 nm. Taken together,the results suggest a tritanlike defect. But as alreadynoted, there were some indications also of a deutanlikedefect; "small-field tritanopia" may in fact includeboth aspects. 14 This of course raises the essentiallyunresolvable problem of categorizing a defect in color

206 J. Opt. Soc. Am., Vol. 67, No. 2, February 1977

vision that is not complete dichromacy. However, weargue that the spectral locus of change from one majorhue category to another is the more important cri-terion. In this connection we note that in Boynton etal. 's study4 they concluded that the deficiency was deu-tanlike and yet all their subjects also changed hue cate-gories at 580 nm, rather than 500 nm as might havebeen expected.

Finally, there is the problem that in the Boyntonstudy the hues changed from blue to yellow 4 We find(Fig. 1) that the change is from blue to red, We do notknow how to reconcile the difference except to point outthe differences between the two studies. Their lumi-nances were equated according to a foveal photopicfunction. We argue that this is inappropriate and mightmake long wavelengths too dim6 ; if this also desatu-rated these stimuli, their findings could simply resultfrom the fact that desaturated reds are sometimesnamed yellow. 15 Their study also used a very limitedset of categories within any hue, whereas we alloweda continuous range of variation. But this seems some-what unlikely as the cause, since, for the fovea, bothtechniques give closely comparable results and one ofour subjects (JG) has served as a subject in the samesort of situation used by Boynton et al. , 16 and yet hetoo perceived that long wavelengths were always red.

ACKNOWLEDGMENTS

This work was supported, in part, by the following:Grant EY188 from the National Eye Institute; GrantBMS 72-02435 A02 from the National Science Founda-tion; Training Grant GM 1789 from the National In-stitute of General Medical Sciences, Computer timewas provided in part by the C. U. N. Y/University Com-puter Center. We thank Floyd Ratliff, Bruce W.Knight, Jane Imperato, John R. Tuttle, and Lee L.Rubin for the many hours they patiently spent as sub-jects.

*Some of these data were presented at the Spring Meeting ofthe Association for Research in Vision and Ophthalmology,Sarasota, Florida 1973.

tAddress correspondence to I. A. at The Rockefeller Uni-versity, New York, N. Y. 10021.

1R. W. Burnham, R. M. Hanes, C. J. Bartleson, Color:A Guide to Basic Facts and Principles (Wiley, New York,1963), pp. 54-65.

2J. Rainwater, Vision: How, Why, and What We See (Golden,New York, 1962), pp. 31-32.

3J. D. Moreland and A. C. Cruz, "Colour perception with theperipheral retina," Opt. Acta 6, 117-151 (1958).

4R. M. Boynton, W. Schafer, and M. A. Neun, "Hue-wave-length relation measured by color-naming method for threeretinal locations," Science 146, 666-668 (1964).

5B. A. Ambler, "Hue discrimination in peripheral vision un-der conditions of dark and light adaptation," Percept.Psychophys. 15, 586-590 (1974).

6I. Abramov and J. Gordon, "Color vision in the pheripheralretina. I. Photopic spectral sensitivity," J. Opt. Soc. Am.67, 195-202 (1977) (preceding article).

E. N. Willmer and W. D. Wright, "Colour sensitivity of thefovea centralis, " Nature 156, 119-121 (1945).

8C. R. Ingling, H. M. 0. Scheibner, and R. M. Boynton,"Color naming of small foveal fields," Vision Res. 10, 501-

J. Gordon and I. Abramov 206

511 (1970).9 D. 0. Weitzman and J. A. S. Kinney, "Effect of stimulus

size, duration, and retinal location upon the appearance ofcolor," J. Opt. Soc. Am. 59, 640-643 (1969).

'OM. M. Connors, "Luminance requirements for hue percep-tion in small targets," J. Opt. Soc. Am. 58, 258-263 (1968).

11J. D. Moreland, Handbook of Sensory Physiology, Vol. VII/4edited by D. Jameson & L. M.. Hurvich (Springer-Verlag,Berlin, 1972), Chap. 20.

1B. R. Wooten and G. Wald, "Color-vision mechanisms in theperipheral retinas of normal and dichromatic observers,"J. Gen. Physiol. 61, 125-145 (1973).

13 P. W. Trezona, "Rod participation in the 'blue' mechanismand its effect on colour matching," Vision Res. 10, 317-332(1970).

"P. L. Walraven and M. A. Bouman, "Fluctuation theory ofcolour discrimination of normal trichromats, " Vision Res.6, 567-586 (1966).

"5 D. 0. Smith, "Color naming and hue discrimination in con-genital tritanopia and tritanomaly, " Vision Res. 13, 209-218(1973).

16R. M. Boynton and J. Gordon, "Benzold-Briicke hue shiftmeasured by color naming technique," J. Opt. Soc. Am. 55,78-86 (1965).

Spatial frequency and light-spread descriptions of visual acuity andhyperacuity*

Gerald WestheimerDepartment of Physiology-Anatomy, University of California, Berkeley, California 94720

(Received 27 July 1976)

Resolution (visual acuity) and differential spatial localization (hyperacuity) targets were selected to allowrigorous psychophysical measurements as well as ready expression of both their spatial frequency spectrumand their retinal image light distribution. Thresholds were about 1 arcmin for acuity and 4-6 arcsec forhyperacuity. As is consistent with the reciprocal relationship between the space and spatial frequency domains,the small locally restricted spatial differences between just distinguishable patterns are represented in thefrequency domain by equally small differences, which are distributed over the entire spatial frequencyspectrum. While they occur in many test situations, phase variations of spatial frequency components are notnecessary for achieving optimum acuity and hyperacuity.

A visual acuity threshold is measured by varying thevisual angle of a small feature until a discriminationjust can or cannot be made.

Ordinarily one thinks of Snellen letters or LandoltC's as targets for visual acuity. They test what hasbeen called the minimum separable; being resolutiontasks in the full sense, they have a prominent basis inthe optical performance capabilities of the eye. Thresh-olds are of the order of an arc min, an appropriatevalue in view of the size of the eye's Airy disk.

There is another class of visual discriminations,where the variable is also visual angle, but where theperformance is much better: a few arc sec. Vernieracuity is one example. Since the performance is be-yond what the optical and anatomical parameters of theeye would lead one to suspect, the word hyperacuitylcan be applied to these capabilities. They must still becompatible with the physical and anatomical limitationsof the eye's optics and the retina, of course, but theirneural processing mechanisms have not yet been fullyoutlined.

A third kind of spatial discriminating ability, theminimum visible, is occasionally included as a specialcase of visual acuity. A dark line can be seen againsta uniform background when its visual angle subtendsless than even 1 arc sec. As startling as this perf or-mance appears, it is really, as was shown by Hechtand Mintz,-' based on simple luminance increment ordecrement thresholds for a constant minimum size ofretinal pattern. For all dark lines of width an arc min

207 J. Opt. Soc. Am., Vol. 67, No. 2, February 1977

or less, the shape of the dimple in the retinal light dis-tribution is the same, but its depth changes with line-width. Visibility then depends on detection of lumi-nance decrements, whose magnitude is a function oflinewidth. Because it is not a distance discrimination,the minimum visible need not be treated in detail whendiscussing visual acuity.

The Fourier analysis of light distributions has so farnot been applied to visual acuity. This is in part dueto difficulties in obtaining, and presumably interpret-ing, the spatial frequency spectrum of many of the tar-gets that are used to test visual acuity and hyperacuity,such as individual Snellen letters, a Landolt C, or avernier target at threshold. In this study, one exampleof a visual acuity task and two examples of hyperacuitywere subjected to analysis. They were selected to berepresentative of the task, yet amenable to straight-forward experimental measurement as well as to anunambiguous spatial frequency description.

I. METHODS

Experimental. Luminous patterns were created un-der computer control on a cathode-ray-tube with greenphosphor. The element of the display was a line, about12 arc sec wide at the observation distance of 6.8 m,whose length and position could be varied in modulesof 6 arc sec. Luminance of the pattern was measuredas follows: A part of the screen was uniformly coveredwith lines, and the luminance of the patch was deter-mined by an S. E. I. illuminometer. For dark line pat-

Copyright © 1977 by the Optical Society of America