THE STILES-CRAWFORD EFFECT: TWO MODELS EVALUATED’

RICHARD SANSBURY,’ JAMES ZAC& and JACOB NACHMIAS

Department of Psychology. University of Pennsylvania. Philadelphia. Pennsylvania 19174. U.S.A.

(Received 12 November 1973)

Abstract-Models explaining the Stiles-Crawford Effect typically characterize individual receptors as either narrowly or broadly “tuned” (i.e. reactive to light incident through a narrow or broad angle. respec- tively). Makous (1968) has shown that he retina contains narrowly-tuned channels. but his data do not require channels that are tuned differently to reside in different cones. In the present study we (1) bolster the evidence for narrowly-tuned channels by performing a replication of the Makous (1968) experiment using narrow-band stimuli. (2) show that increment threshold limiting factors operate only after the separ- ate channel outputs have been combined and (3) on the basis of data from a brightness-matching exper- iment argue that channel input-output functions and channel output combinations are linear. If cone in- put-output functions are sufficiently non-linear. the demonstrated linear combination of channel outputs suggests that narrowly-tuned channels co-exist within broadly-tuned cones.

INTRODUCIION

The Stiles-Crawford Effect of the first kind (Stiles and Crawford, 1933) is a manifestation of the directional sensitivity of the retina. As yet, however, the properties of the retina that cause it to be differentially sensitive to light incident at different angles are still uncertain. Many of the models that could explain this directional sensitivity can be thought of as compromises between two extreme positions.

According to the first of these positions the receptors in any local region of retina are approximately parallel in orientation. Each receptor responds to light coming through at least a significant portion of the pupil. although light rays striking a receptor at different angles are not equally effective in eliciting a response. Rather, the receptors are directionally “tuned”. That is, for each receptor there exists a maximally efficient angle of incidence of light (e.g. O’Brien. 1951). Because the receptors are similarly oriented. the sum of the indi- vidual receptor responses decreases in magnitude as the angle at which light is incident on the retina is deviated from the maximally efficient angle. The psy- chophysically measured Stiles-Crawford Effect reflects the summation of responses from many of these broadly tuned receptors.

The other extreme position (e.g. Safir and Hydms. 1969) is that each individual receptor is sensitive to light incident within only a very restricted range of

’ This work was supported h\ National Science Founda- tion Grant GB 16051-01 IO Dr. James Zacks and National Science Foundation Grant GB 24100X1 to Dr. Jacob Nach- mias.

’ Present address: Department of Psychology. Trinity College, Washington. D.C. 2000 7.

’ Present address: Department of Psychology. Michigan State University. East Lansing. Michigan 48824.

angles. According to this hypothesis. the relative effi- ciency of light entering the pupil at any particular po- sition reflects the relative number of receptors func- tionally oriented towards that position. Because Safir and Hyams (1969) found the Stiles-Crawford Effect to be well described by a Gaussian function they argued that there might be a population of such receptors whose axes of maximum sensitivity are normally distri- buted.

The Transient Stiles-Crawford Effect

The most compelling evidence supporting the exist- ence of receptors with very narrow acceptance angles comes from an experiment reported by Makous (1968). Makous changed the pupil entry position of a 10 background in such a way as to produce a change in the angle at which light was incident on the retina but not in the locus of its retinal image. While holding the pupil entry position (and hence angle of incidence on the retina) of a flashing test spot constant. transient ele- vations in the luminance increment threshold against these backgrounds were repeatedly generated (once each minute) simply by shifting the pupil entry pos- ition of the background. These transients occurred even though the intensity of the background in the two different pupil entry positions had been corrected for the steady-state Stiles-Crawford Effect. That is. the in- tensity of the background was adjusted to produce the same increment threshold (at the end of I min) for each of the two pupil entry positions. Thus. the transients were not due to steady-state differences in the effects of the backgrounds. Makous named this phenomenon the Transient Stiles-Crawford Effect.

The existence of the Transient Stiles-Crawford Effect seems to require that there be more than one dir- ectionally tuned “channel” in the retina. It does not

803

require. however that different channels reside in dif- ferent receptors: the channels could co-exist within receptors. Furthermore. although the phenomenon is not sufficient evidence to decide whether there is par- tial overlap in the directional sensitivities of the chan- nels. it does indicate that there is not complete overlap. The Transient Stiles-Crawford Effect also implies that each channel must contain its own mechanism for gene- ratins a transient response“ to a sudden increase in effective luminance (effective luminance = luminance x relative sensitivity of the channel to energy from the pupil entry position at which the incident light enters the eye). Finally, like Makous we assume that each channel has a steady-state response. Thus. a sudden increase in the effective luminance seen by a channel produces a transient increase in activity in that channel which slowly decays to a level higher than before the increase in effective luminance.

In view of these considerations, perhaps the simplest explanation of the Transient Stiles-Crawford Effect (an explanation slightly different from the one Makous proposed) would be as follows: When the pupil entry position of the background is changed from A to B. the effective luminance seen by the former channel (call it Channel A after the pupil entry position to which it is maximally sensitive) decreases substantially while that seen by a new channel (call it B) undergoes a sudden increase. As a result Channel Bis transiently respond- ing to the increase in its effective luminance, while Channel A is allowed to dark-adapt. Thus. when the pupil entry position is changed from B back to pos- ition A. Channel A is now dark-adapted somewhat and goes through a transient response to the sudden in- crease in effective luminance. This process could simply repeat itself with each complete cycle of the stimulus.

Since it is quite possible that this transient is caused by the same mechanisms that generate the early light and dark adaptation transients seen in increment threshold studies (e.g. Baker, 1963) there may also be a small “off’ transient for each channel. Thus under the conditions of the Makous experiment. the “on” tran- sient of one channel may be augmented somewhat bq a simultaneous “off” transient of the other channel.

The results of Makous’ experiment. then. seem to require the existence of separate directionally sensitive channels. each capable of generating its own temporal transient. Our experiments attempt to (I) support the hypothesis of the existence of such channels by per- forming a control experiment which further substan- tiates the original report by Makous (1968) and (2) in- vestigate further the properties of channels in the hope

’ K~~~~ww will br used. for ease of exposition. m the course of this paper to refer to the activity presumed to un- derlie the psychophysical effects which we actually mea- surcd

that these properties will enable us to infer their anato- mica1 locus.

GENERAL METHOD

In two of the experiments. increment threshold!, were determined for a 5.5’ arc test spot centered on a 44’ arc back- ground in an otherwise dark field (see inset of Fig. It. Two emmetropic observers. RS. one of the authors and SK. a paid observer. participated. Since the observer was m- strutted to fixate the center of the background. threshold judgments were made while looking directly at the positIon where the test spot appeared for 1 4sec. A small hack- ground was employed for two reasons: First. it has been shown (Steinman. 1965) that observers can fixate the center of such targets very well (SD. of distribution of eye positton < I@ arc). and second, even if a large eye movement did occur it could not produce a large shift (i.e.. of I“ or morel in the angle of incidence of light in the region of the mean target image position on the retina.

All stimuli were presented monocularly in Maxwellian view to the observer’s right eye. the filament images in the plane of the pupil measuring 1 mm dia. The observer’s right eye was dilated by I”,, Mydriacyl (tropicamide I.0 per cent) 15 min before the beginning of each session. During a ses- sion. head position was stabilized by the use of an acrylic bite bar.

The optical apparatus shown schematically in Fig. 1 is a three-channel Maxwellian view system. The general design of the system will be described here. The specific modifica- tions for each separate experiment will be outlined as each experiment is reported.

All paths derived light from a single. tungsten filament source (S) (G.E. Bulb 1183) operated at 6 A. Early in each path. the light was focused through a filament image stop (FISI located in the plane conjugate with the plane of the observer’s pupil. The size of these stops was adjusted so that

B oikground 9 Eye

Fig. 1. A schematic diagram ofthe three channel Maxwellian optical system and insert showing the stimulus fields. S-tungsten Nament source, FIS,--filament image stop, MFL-movable focusing lens, RM-rotatable mirror, FS- field stop. F,_,-neutral density filters, W,_,-neutral density wedges, C-chopper, SH,_,-shutters, P-pellicle,

DC&-diffusing glass, IF-interference filter.

The Stiks-Crawford Effect 805

the filament image at the pupil had a diameter of 1 mm. Movement of the filament images in paths X and 2 was accompli&d by the transverse motion of the movable focusing Iens (MFL) and the rotation of iirst surface mirror (RM). respectively. The size of the visual fields was limited by flefd stops (FS). The general level of light intensity was adjusted by neutral density filters (F,_,). Stepwise adjust- ments of O-1 log units were possible by rotation of the 2 log unit wedge(W,). while the other neutral density wedge (W,) was continuously adjustable. by the observer, over its 2 log unit range. Retina1 illuminances were cafculated from measurements with an SE1 photometer after a method de- scribed by Westheimer (1966). At the diffusing glass (DG) the experimenter couid monitor the separatian between the filament images. In all experiments the filament images were either coincident or set 5 mm apart. The focal length of the Maxwellian lens was 24.6 cm. The observer was aligned so that the fiIament image fell within the plane of his pupil and the distance between FS (see befow) and the Maxwellian iens was ad&ted slightly for maximum sharpness of the stop.

EXPERIMENT I

A significant proportion of the Transient Stiles- Crawford Effect could resuIt from differentia1 effects the ocular media exert on light passing through differ- ent portions of the eye. That is. when the background enters the pupil at position A, the chromatic aberrations and absorptions it undergoes on its way to the retina may be different from those it undergoes when it enters at pupil position B. Thus a sudden change in pupil entry position could result not only in a change of the angle of incidence on the retina, but also in a change in the wavetengh composition of the retinal image. If this did occur it would not be too sur- prising to find transient elevations of increment thres- hold. If instead of using white light (as Makous did ori- ginally) a narrow-band stimuhrs is used, then the con- sequences of these differential effects on wavelength composition and distribution in the retinal image will be much reduced. To the extent that the Transient Stiles-Crawford Effect results from these effects, the use of narrow-band light should reduce its magnitude, Therefore, if we can find no difference between the use of narrow- and broad-band stimuii on the magnitude of the Transient Stiles-Crawford Effect. we can rule out dif%rences in the wavelength composition of the retinal images of the two backgrounds as its major cause.

Mrxhod

The background was presented either by path Y or Z (as shown in Fig. I ). The apparatus was aligned so that an aher- nation between the two tight paths resulted in a 5 mm hori- zontai shift in the pupil entry position of the background. This shift occurred once each minute. The shutter {SH,) was constructed so that as it moved horizontally one path was uncovered at the same time the other was covered. The sep- aration between the two paths at the shutter was such that if SkiI was hatted in mid-course. a thin dark bar (-z 10’ arc width) was visible between the haives produced by the dif- ferent tight paths ‘Se switch between beams norm&r required a smaE fraction of a second { c 114 seci for cornpie-

tion. fhe effect on thresh6ld of the traverse of the dark bar was not by itself significant. since realigning the two beams to eliminate the difference in filament image locations in the pupil eliminated the Transient Stiles-Crawford Effect. The test spot delivered via path X, entered the observer‘s pupil near its temporat edge at a constant position in this expcr- iment. The chopper (C) allowed light to pass for 1/4sec every second. An interference filter [(Lf.): Balzers half-peak bandwidth <30nm with peak transmittance at 551 nm] controlled the spectral composition of the background and test beams. The dependent variable recorded was the time from the last change af background to the first seen tlash of the increment.

At the beginning of a session the intensities of the two backgrounds were adjusted until their corresponding increm ment thresholds, sampled after a minute or more of viewing, differed by no more than 6 I log unit. A session consisted of six blocks of trials. each block separated by a I-min inter- vaf without test flashes. A btock of trials consisted of two ~asure~nts of the time to see the flash for each of the two backgrounds. Within a block the intensity of the increment was held constant. For any particular block the increment intensity was selected in a random fashion from a set of six 01 log unit intensity steps ranging upward from the “steady state” increment threshold determined at the onset of the session. For observer RS, the backgrounds IA and I* had retinal ~l~uminan~s of 3-46 and 3 18 fag td. respectively. For SK the backgrounds were 3-t% and 267 tog td respe&vely.

Rasults

In Fig. 2 the data shown for each observer were all collected on the same day. The ifluminance of the in- crement relative to the estimated increment threshold after a minute or more of viewing a steady background is plotted as a function of the median time to the first seen flash. To facilitate a comparison with the results of the experiment by Makous (196Q the dependent variable has been plotted along the abscissa. Filled symbols show the effects of changing to one of the two backgrounds, empty symbols the other. Each da% point represents the median of 10 measurements. The error bars asso&ated with each pair of data points show the greatest extent of the interquartile ranges of the two points. If no bars are shown the inter-quartile range was smaller than the data symbol. Arrows next to the symbols for the lowest values of AI/Al,,,, indi- cate medians greater than fro sec. A comparison of the transients shown in Fig. 2 with those reported by Makous (19681 reveals that the magnitudes and time courses of both areevery similar. The transients gener- ated by the narrow-band stimuli may be slightly smaller (10.1 log unit) than their wide-band stimuli counterparts but it is clear that the trnnsients do not depend crucially on the use of wide-band stimuli. Our rest&s are simiIar to Makous’ in another respect. The observers in this experiment also reported that the background transiently increased in brightness follow- ing the change in its angle of incidence on the retina.

Coftcficsions

These rewfts show that the Transient Stile*Crraiw- ford ERect does not depend primarily on artifact&

X06 RICIIAKU SANSRIIKI. JAMES ZACKS and JACOB NACHMIAS

-a

0.4 --*)I

Observer RS

t I

= I OOI

Time, set Fig. 2. The Transient Stiles-Crawford Effect for narrow- band stimuli. The difference between log illuminance of the transient increment threshold (AI) and the log illuminance of the steady-state increment threshold (Al,,) is plotted as a function of the median time (set) from the change of background to the first seen flash. Whange to backpound I, ; O--change to background I,. Test spot incident at the same angle as I,. Arrows (+) indicate that the median time

was greater than 60 sec.

changes in the wavelength composition of the retinal image.

EXPERIMENT 2

The original demonstration of the Transient Stiles- Crawford Effect, bolstered by the results of our ad- ditional control experiment strongly supports the con- clusion that directionally-sensitive “channels” exist in the retina. This clear evidence for the existence of chan- nels led us to consider whether the threshold-elevating effect of a background is exerted separately within each channel, or rather if this effect is exerted only after the outputs of the separate channels are combined in some way. Consideration of the Transient Stiles-Crawford Effect is revealing in this regard. Recall first the conclu- sion that different angles of incidence of a stimulus on the retina favor channels having diRerent directional sensitivity functions. If there were no overlap between the directional sensitivities of the channels, and if the threshold-elevating effect of a background is exerted within a channel, then, when the test flash is incident at the same angle as one of the two backgrounds only that background should have an effect on the thres- hold for the test flash. But this is not the observed

result. Both backgrounds transiently elevated thres- hold. Therefore. either there is some overlap in the di- rections from which the channels may be stimulated 01 threshold limiting factors do not operate exclusivcl! within separate channels. or both.

In the original experiment (Makous, 1968) the test flash was incident at the same angle as one of the back- grounds, and the luminances of the two backgrounds were adjusted to produce the same steady-state thres- hold for that test flash. Assume that the threshold-ele- vating effects of a background were exerted separately within each channel. If so. then both backgrounds suc- ceeded in raising threshold for the test spot because the channel that was detecting the test spot had a non-zero sensitivity at both of the background angles of inci- dence. The fact that one of the backgrounds was more effective in raising threshold was compensated by an appropriate adjustment of the relative luminances. It follows from this state of affairs that the relative effec- tivenessofthe two different backgrounds in determining increment threshold should change whenever the angle of incidence of the test spot is altered sufficiently to change which of the channels is detecting the test spot. That is, there is an interaction between the angle at which the background is incident on the retina and the angle at which the spot is incident on the retina.

Alternatively it could be assumed that the threshold- elevating effects of a background are exerted only after the outputs of the separate channels are combined within some kind of summation pool (Rushton. 1965). By this assumption two backgrounds striking the retina at different angles of incidence will increase in- crement threshold equally when they both produce the same steady-state response at the pool. Changing the angle of incidence of the test flash need not necessarily affect the threshold raising capability of a background. From this point of view. once two backgrounds are equated for their threshold raising ability for any par- ticular angle of incidence of an increment they remain equated regardless of the angle at which the increment strikes the retina. (That is to say, there is no interaction between the angle at which the background is incident on the retina and the angle at which the test spot is in- cident on the retina.) The following experiment explores the effects of the relationship between the angles of incidence of the test and background stimuli in order to determine whether or not there is an inter- action between the angles of incidence of the back- ground and test stimuli.

.Method

In this experiment the backgrounds were presented con- tinuously via light paths Y and 2. while the superimposed test spot was delivered by light path X. The shutter (SH,) determined the l/4 set exposure of the test spot. F, deter- mined the upper bound of the test spot luminance% but the exact intensity. calibrated in 0.1 log unit steps, was set by wedge W,.

The position of wedge WI and hence the luminance of the test flash was determined by a double random staircase pro- cedure (Cornsweet, 1962). For every test flash not seen the

The Stiles-Crawford Effect 807

Iuminan~ of the test spot was incre&scd by @l log unit on the next trial of that staircase. An equal change in the oppo- site direction followed any two consecutively seen test spot flashes on the same staircase; otherwise test spot luminance remained constant. The starting point was chosen to be slightly above the expected threshold. A total of 60 trials were run for each double random staircase, the first 20 trials ~ingdi~r~d to minimize starting point bias. The mean of the remaining 40 trials was used as the estimate of the thre- hold. Increment threshold functions were measured for each of four conditions--all the possible combinations of two directions of incidence on the retina for both background and increment. If we indicate the angle of incidence on the retina by a subscript A or B the four functions were: Al, vs 1,. AI, vs ill, Ala vs 1, and Ala vs fa. Increment thre& hold was estimated at three different background illu- minances for each of the four combinations of backgrounds and increments. Retinal illuminances ranged from a low of 3.39 to a high of 5.23 log td. One staircase was run at each level of the background for oberver RS. For observer SK two staircases were run at each background level.

Results

The results for both observers are sho+m in Fig. 3. In this figure log increment threshold (log AZ) is plot- ted as a function of log background (log I) for each of the four combinations of test and background stimuli. The results show that there is no interaction between the angie at which the test spot is incident on the retina and the angle at which the back~ound is incident on

5 Observer RS

i 2, I I

Fig. 3. Increment threshold for a test spot striking the retina at the same. or at a ditTerent angle from the background. Abscissa: log illuminance (trolands) of background entering the pupil at position A (I,) or B (Is) as indicated by the subscripts. Ordinate: log illuminance (td) of the incremental test flash when at threshold. Data points for increments entering at position A (Al,) and B (A&+) are shown as circles, (o), or triangles (A), respectively. The filled symbols. (0, A), for SK represent a second set of threshold estimates. Halved symbols (e) indicate that the two estimates differed by no more than @03 log unit. The dotted lines and x’s represent

an analysis described in the text.

the retina. This can be demons~ated graphically. If there is no interaction then every pair of backgrounds log Z* and log Za, for which log AZ,, is the same should also require the same log AZ,. That is if two back- grounds are equally effective in setting the threshold for test beam A. they should also be equally effective in their influence on the threshold for test beam B. To see if this occurs pick a background illuminan~ log ZA and determine the thresholds for the two test beams log AZ, and log AZs. Graphically. this simply means to determine where a vertical line through some chosen value of log Z, intersects the log AZ, and log AZs vs log I, functions. Now, find the background log I, which is equally effective in elevating the threshold for test beam A. To do this extend a horizontal line (dashed line I in Fig. 3) to interesect the log AZ,, vs log Z, function. and then extend a vertical line (2) through the point of intersection to the abscissa, where the illu- minances of background B, log le. can be read off. Finany, having thus far determined the illuminances of the two backgrounds log Z,, and log Z, which are equally effective in raising the threshold for test beam A, we want to know if they are equally effective in rais- ing the threshold for test beam B. To do this graphi- cally, extend a horizontal line (3) through the value of log AZ, intersected by the vertical through log Z,. Where this horizontal intersects the log AZ, vs log Z, function should be the same place the previously con- structed vertical through log Za intersects this function, As can be seen by the examples of this graphic analysis shownin Fig. 3, the prediction based on the assump tion of independence of the angles of incidence of test and background beams are in very good agreement with the data. The x ‘s indicate predictions made by an analytic analysis equivalent to the graphic analysis de- scribed.

Discussion

It seems clear, from Fig. 3, that once the two back- grounds are adjusted so as to produce the same incre- ment threshold when the test flash is incident on the retina through pupil entry position A, they will also produce equal thresholds when the pupil entry pos- ition of the test flash is changed. by 5 mm, to B. This is not to say that the actual value of the increment threshold would remain the same when the pupil entry position of the test flash is changed-we know that it does change (Stiles-Crawford Effect). Even though the actual value of the increment threshold changes, the important fact remains: The relative threshold-raising effectiveness of the two backgrounds remains matched independent of the angle of incidence of the test flash on the retina.

Recall the initial reasons for undertaking this exper- iment. If t~eshold-raising effects accrued separately within each channeI, then changing the channef that detected the test flash would necessitate a readjustment of the relative illuminance of the two backgrounds. This was not the observed result. If. on the other hand, an adjustment of the relative illuminance in the two

x0x RICHAKI) SANSH~ ~1. .Lwrs ZACKS and JACOH ~ACHMIAS

backgrounds equates them for their effect on some kind of “pool” (Rushton. 1965). then changing the angle of incidence of the test flash need not unbalance this equivalence. Our results, therefore, indicate that the effect of a background in elevating threshold is not exerted separately within each channel. but rather at some stage by which the responses of the channels have been combined.

Our results also indicate that a channel’s response to the test flash must be independent of the magnitude of its ongoing response to the background. If this were not the case. then the response to the test flash at the pool would depend on whether or not the simul- taneously present background was coincident with the test flash. Thus changing the incidence of a test flash would change which of the two backgrounds causes the test flash to produce a larger response at the pool. As a result, the ability of the backgrounds to raise threshold would not be independent of the test flash.

It is possible, though not necessary, that the inde- pendence of the channel’s response to the test flash is due to the fact that the channels and the summation pools to which they contribute are linear in the follow- ing sense: The output of each channel is proportional to the rotal effective input to that channel, and the out- put of the summation pool is a function of a linear combination of the channels’ outputs. On those assumptions. the pool’s output would be the same re- gardless of whether the test flash and background sti- mulate the same or different channels. In the next exper- iment we investigate the question of linearity more di- rectly.

EXPERIMENT 3

The results of the previous experiment are consistent with the hypothesis that both the input-output func- tions of the channels and the combinations of these outputs in the summation pool are linear processes. Experiment 3 was designed as a further test of this hypothesis. Whereas the previous experiment consi- dered the effects of the angle at which light strikes the retina on threshold, the present experiment was designed to reveal the manner in which the responses to rays striking the retina at different angles were com- bined to determine the brightness of suprathreshold stimuli. The form of the experiment was to fix the ratio of the illuminances of two beams striking the same place on the retina but at different angles, and then to find the pair of intensities in that ratio which produced a brightness which matched that of a standard stimu- lus. This was repeated for several different ratios.

Mt,thod

The standard half of a 44’ arc dia bipartite field was deli- vered via light path Z while the comparison half-field was delivered via paths X and Y (Fig. 1). The half-fields were separated by a narrow black bar (width -z 10’ arc). Care was taken to insure that the half-field contours were not changed by the manipulations of the optical systemduring the exper- iment. Light delivered via path X struck the retina at a dif-

ferent angle from light delivered via path l’. Pup11 cntrj positions for the two paths differed by 5 mm.

The locations of neutral density wedge W, and tilamcnt image stop FIS, were interchanged with respect to those shown in Fig. 1. and an additional filament image stop (not shown in rhe diagram) was added to parh X so that its fila- ment image in the plane of the observer‘s pupil measured I mm dta. W,. which controlled the intensity of the beam that subsequenti! bifurcated into the two hght paths X and Y, was positioned bq a reversible -l re\ min motor con- trolled by the observer.

The observer adjusted wedge W, until the comparison field matched the standard field in brightness. The position of W? determined the illuminances contributed b! hght paths X and Y to the retinal image of the comparison field without changing the ratio of these illuminancrs. The valur of the ratio depended upon the transmittances of neutral density filters F, and F3 located in the two light paths. At the outset ofeach session determinations were made of the matching illuminances from light path X alone. and from light path Y alone. Taking these illuminances as unirs of illuminance from each light path. values of F, and F3 were chosen which produced illuminance ratios of approximatel) l/2. 1 and 2. In the main part of each experimental session the observer made matches with each of these ratios as well as with each light path by itself-five conditions in all. Each session consisted of 10 blocks of trials. each block contain- ing one match at each of the five conditions. Within a block the five conditions were presented in a random order.

The same interference filter that was used in the Transient Stiles-Crawford Effect experiment was also used in the pres- ent experiment. Furthermore. the illuminances of the stan- dards (2.67 log td for SK and 3.18 log td for RS) were the same as those used for two of the backgrounds in the Tran- sient Stiles-Crawford Et&ect experiment.

After the apparatus was set for a selected comhinatlon the observer was instructed to “make a match”. At this point the observer opened his right eye (which was closed during set- up time) and maintamed fixation on the narrow black bar while adjusting W1 until the comparison equalled the stan- dard in brightness. Each match required IO 15 sec. and set- up time required another IOsec. Each trial was, therefore, about 25 set long. Once a match had been made the observer again closed his eye. All the data for each observer were collected on the same day. thrre sessions for RS. four for SK. The mean intensity of each combination to match the standard is. therefore. based on 30 trials for RS and 40 trials for SK.

Rrsults

Figure 4 shows the results of the summation exper- iment for both observers. In this figure we have plotted against each other the values of the illuminances from channels X and Y which when combined in the com- parison field match the standard field in brightness. The points at (LO) and (0.1) represent the matches obtained with channel X alone and with channel Y alone, respectively. The straight line drawn between (1,0) and (0,l) represents the expected results if the in- put-output functions of the channels and their com- bination are linear processes in the sense defined ear- lier. If. for example, one-half the total energy required from light path X alone to match the standard is added to one-half the total required from Y then their sum,

The Stiles-Crawford Effect 8oV

Normalized llluminance X

Fig. 4. Summation of the brightness producing effects of light striking the retina at different angles. Each data point represents a mean combination of i1luminance.s from paths X and Y which match the brightness of the standard: tobserver RS; @-observer SK. Error bars indicate + 3 S.E. of the mean. The data have been plotted on coordinates which normalize the illuminances in light paths X and Y. The normalization is such that for each angle of incidence (path), a value of I is the illuminance required of that path alone to match the standard brightness. The solid lines are predictions based on the two models discussed in the text,

in a perfectly linear system, would also match the stan- dard in brightness.

Predictions from an alternative model are also shown in Fig. 4. The curved line drawn between (1,0) and (0,l) is based on two assumptions. First it is assumed that each channel is sensitive to light striking the retina over such a narrow range of angles that the beam which stimulates one channel is completely inef- fective in stimulating the other channel, and vice versa. Second, we assume that the response of each channel is a compression function of stimulus intensity, and in particular, that compression function chosen by Boyn- ton and Whitten to describe the late receptor potential of the cynomolgus macaque monkey: namely. R = !“/(I” + K). where K = 831 td, n = 0.73 and I is

expressed in td. We chose this compression function because it seemed to us to be the best available esti- mate of the human cone response function.

The data points in Fig. 4 lie much closer to the straight line than to the curved one. The error bars about these points represent f 3 S.E. Although there appear to be small systematic deviations from perfect linear summation, these deviations are in opposite dir- ections for the two observers. It seems to us more likely that these deviations are due to some kind of artifact than to genuinely different r_~pes of non-linear channel response functions for the two observers. On the basis of these data, therefore, we do not feel that we can reject the linearity hypothesis. On the other hand, it

seems quite clear that the non-linearity hypothesis represented by the curved line can be rejected.

Experiment 3 bears directly on the form of the in- put-output function which describes the responses of the channels. In Fig. 4 we have contrasted the predic- tions of two specific models by way of illustration. The first model assumes (1) that the input-output functions are negatively accelerated functions of the type reported by Boynton and Whitten (1970) and (2) that the channels are so directionally selective that each channel is sensitive to light incident at the preferred di- rection and essentially insensitive to light incident along the preferred axis of the other channel. The second model for which predictions are shown requires no assumption about the extent of directional selecti- vity of the channels but assumes that the input-output function which describes the channels is linear. The data provide considerably stronger support for the second model.

The shape of the expected summation curve based on the non-linear channel hypothesis (first model) depends critically on the assumption that the maxi- mally efficient stimulus for one channel is an ineffective stimulus for the other. If this assumption were wrong, and there were no difference in the directional selectivi- ties of the two channels. then the predictions based on different input-output functions would all be identical to the predictions of the Iinear model. What. then. is the evidence that the directional selectivities of the channels are different and significantly non-overlap- ping? Makous’ (1968) demonstration of the Transient Stiles-Crawford Effect. Because of the importance of Makous’ results we replicated his experiment. The transients in increment sensitivity generated in our rep- lication were of the order of 05 log unit. The change in angle of incidence of the background must therefore have produced a change in the stimulation of a channel big enough to produce the transient threshold eleva- tion. Baker’s (1963) data on early light adaptation show that going from darkness to 2 or 3 log td pro- duces transients of the size measured by Makous and ourselves. Furthermore. Baker (1963) has shown that changing from a non-zero pre-adaptation luminance level is less effective in generating transient elevations of threshold. All of this suggests that the difference in directional sensitivity of the channels is considerable, and that our assumption is a reasonable approxima- tion.

Previous studies. If the Stiles-Crawford Eflect is known for every point in the pupil. and if the effects of light rays striking the retina at different angles are summed linearly. then it should be possible to predict the relative efficiency for a pupil of any size. A number of studies have attempted to verify this prediction. The results have been equivocal-some observers show linear summation, others non-linear. Enoch (1958) gives a brief summary of these results, and considers some possible sources of the discrepancies. Enoch

(1958) also reports some results of his own. Usmg a flicker photometrv technique. Enoch found one observer to show l&ear summation while two others showed slightfy better than linear summation. That is. as the area of the effective entrance pupil was in- creased. the efficiency for two of the observers grew at a rate greater than that predicted on the basis of linear summation and the estimated corrections for the Stiles-Crawford Effect. Two points should be men- tioned in regard to these results. First. the deviations from the expected summation curves are small i = 04% log unit) with no indication of variability being reported. Second, it seems that Enoch (1958) measured the Stiles-Crawford Etfect along the horizontal meri- dian and then assumed radial symmetry to calculate the expected summation curve. The assumption of radial symmetry is often only roughly correct (see. for example. Stiles and Crawford. 1933: ErcoIes_ Ronchi and Torafdo di Franc& 1956f. It is possible. therefore, that the small deviations are attributable to asymme- tries in the directional sensitivity of the retina.

Ercoles et al. (1956) report an experiment very simi- lar to our Experiment 3. If their data are plotted in a manner simiiar to our Fig. 4_ the observed deviations from linearity are about the same magnitude as those we report. The Ercoles et al. f 1956) data, however. tend to lie above the line representing the linearity hypoth- esis, in a direction away from the nonGnear summa- tion curve shown in our Fig. 4. Unfortunately. once again there is no indication of the amount of variabi- lity.

In conclusion. neither earlier data nor the results of our Experiment 3 provide clear evidence From which we can reject the linear summation hypothesis.

What can we conclude about the nature and loca- tion of the “‘channels’? The result of Experiment 2 can be explained if we assume that the magnitude of the re- sponse to the test flash is independent of its steady- state response to the background. and that the chan- nels’ outputs are combined linearly in or before the summation pool that determines the dependence of Af on f. Although this would be true if each channef’s in- put-output function were linear. it would be correct re- gardless of the form of the input-output function SO

long as the response to a brief increment is indepen- dent of its steady-state response to the background. Thus the results of Experiment 2 are compatible with a linear input-output function for the individual chan- nels., but do not force this upon us. The results of the brightness suinmation experiment (Experiment 3), however. provide strong support for the assumption that channel input-output functions are nearly linear and that channel outputs are added together in a linear fashian.

What does this imply about the anatomicat iocus of the channels+? This depends upon our evaluation of the available e~e~tropbysiologj~~ and anatomical evi-

dence. First. it could be argued that the local varlahl- lit? of the anatomical axes of human cones (Latics. tiebman and Campbell. 1968) is not as great as required bp the cone distribution hypothesis. kInfor- tunateiy thrs is nat a conclusive argument in itsetf. The functional optical axes of cones ma) vsr> even though the gross anatomical axes do not. Second, it could be argued that the most relevant ph>siulogical response available to date from the cones of higher mammals are the recordings of the late receptor potential b> Boynton and Whitten (1970). anti the> ctre s~gni~~ant~~ non-linear. However. this argument is also open to dis- pute. Interactions have been reported between recep- tors in turtle retina (see Fuortes. 1972). and Penn and Wagins (1972) have reported receptor response func- tions, in rat retina. that are neari! linear. It is conceiv- able therefore that the massed late receptor potential measured by Boynton and Whitten 11970) was in- fluenced by interactions between receptors and does not accurately reflect the individual receptor response, Thus a completely satisfactory description of the indi- vidual receptor response in the primate retina is. as yet, lacking. Nevertheless it seems that the Boynton and Whitten f1970) data currently provide the best avail- able indication of the primate receptor input-output function. Their results imply that the cone input-out- put functions are non-linear. This implication. taken in conjunction with the results of our brightness match- ing experiment. suggests that differerit channels co- exist within individual cones with their outputs being combined f~+or to the site of the cone non-linearit>,

Speculation concerning the features of ~ndjvidua~ receptors that permit muit~ple~hanne~s within the same receptor lead immediately to the notion of wave- guide modal patterns (Enoch. 1960: Enoch, 1961; Enoch, 1963; Snyder, 1969; Snyder and Pask. 1973). Enoch (1961) has observed such modal patterns in human receptors, Furthermore. some of these patterns changed with changes in the angle of the incident tight (Enoch. 1961). It seems plausible, therefore. that the “channels” we have been studying nrc different local regions of the receptor outer segment. Hence a large change in the angle of incidence of the light falling on the retina could produce a change in the energy distri- bution within the receptors thereby changing the maxi- mally excited channel. it shoufd be pointed out that if this hypothesis is to explain the fact of the Transient Stiles-Crawford Efkct. it must posit that smaller changes in the angle of incident light--such as those produced by microsrlccadrs during fixation-produce less significant changes in modal patterns than do larger changes in angle of incidence. The differences in the effects of large vs small changes could bc either qualitative or quantiwive. Although we have not offered a detailed model, we have tried to indicate that it is plausible for multiple-channels to co-exist within individual receptors.

In conclusion, it seems at the present time that the Stiles--Crawford EfGzct is best characterized as a mani- festation of a ~puiat~on of receptors or&ted in a

The Stiles-Crawford Effect 811

more or less parallel fashion but ~n~ining multipfe Ercoles A. M.. Ronchi L. and Totaido Di Francis G. (1956) receptor sites, each of which is sensitive to a limited The relation between pupil &ciencies for smalf and angle of incidence and each capable of generating a extended pupils of entry. Oprica Acta 3,&t-89.

transient response to a sudden increase of effective Fuortes M. G. F. (1972) Responses of cones and horizontal

luminance. This conclusion rests squarely on the cells in the retina of the turtle. Invest. Ophthal. 11, 275-

assumption that the input-output function for human 284.

cones is as non-linear as the function derived by Boyn- Laties A. M.. Liebman P. A. and Campbell C. E. M. (1968)

ton and Whitten (1970) for primate cones. The final Photoreceptor orientation in the primate eye. Narure. Land. 218 172- 173.

resolution of this issue can only come from direct elec- Makous W. L. (1968) A transient Stiles-Crawford Effect. I/‘i- trophysiological evidence showing the input-output sion Res. 8, 1271-1284. function of individual receptors. O’Brien B. (1951) Vision and resolution in the central retina.

J. opt. Sot. Am. 41, 882-894.

REFERENCES

Penn R. D. and Hagins W. A. (1972) Kinetics of the photo- current of retinal rods. ~jo~~~sic#l J. 12, 10731094.

Rushton W. A. H. (1965) The Ferrier Lecture. 1962: visual adaptation. Proc. R. Sot. Bt62, 20-46.

Baker H. D. (1963) Initial stages of dark and light Safir A. and Hyams L. (1969) Distribution of cone adaptation. J. opt. Sot. Am. 53,98-103. orientations as an explanation of the Stiles-Crawford

Boynton R. M. and Whitten D. N. (1970) Visual adaptation Effect. J. opt. Sot. Am. 59, 757-765. in monkey cones: recordings of late receptor potentials. Snyder A. W, (1969) Excitation and scattering of modes on Science. N.Y. 170, 14231426. a dielectric or optical fiber. IEEE Trans. Microwaw

Cornsweet T. N. (1962) The staircase method in psychophy- Theory and Techniques, MTT-17, 1138-l 144. sits. Alit. J. Psychof. 75, 485-491. Snyder A. W. and Pask C. (1973) The Stiles-Crawford Effect

Enoch J. M. (1958) Summated response of the retina to light entering different parts of the pupil. J. opr. Sot. Am. 4&

-explanation and consequences. vision Res. 13, 111 I- 1137.

392-405. Steinman R. M. (1965) Effect of target size. luminance, and Enoch J. M. (1960) Waveguide modes: are they present, and color on monocular fixation. J. opt. Sot. Am. 55, 1158-

what is their possible role in the visual mechanism? J. opt. 1165. Sot. Anr. 50. 1025-1026. Stiles W. S. and Crawford B. H. (1933) The luminance es-

Enoch J. M. (1961) Nature of the transmission of energy in the retinal receptors. J. opr. Sot. Am. 51. 1122-l 126.

ciency of rays entering the eye pupil at different points. Proc. R. Sot. B112.428-450.

Enoch J. M. (1983) Opticai properties of the retinal recep- Westheimer G. (1968) The Maxwellian view. Vision Res. 6, tots. J. opf. Sot. Am. 53, 71-85. 669-682.

R&m&--Les modtles de I’elTet Stiles-Crawford caracterisent typiquement ies rkcepteurs individuels comme “accordes” d’une facon soit Ctroite sait large. (c’est-i-dire rCagissant $ la lumikre incidente selon un angle respectivement petit ou grand). Makous (1968) a montre que la r&tine contient des canaux accordts Ctroitement, mais ses donnQs n’impliquent pas que les canaux diriremment accord&s resident dans des cdnes diffkents. Dans ia prksente etude on montre (1) une confirmation des canaux $ accord etroit en tecom~n~nt l’exp&ience de Makous (1968) avec des stimulus B bande etroite. (2) I’entrk en action des facteurs qui timitent te seuil diffetentiel seulement apr&s une combinaison des rkponses des canaux &pares et (3) sur la base des donnhs d’une exerience d’egalisation de luminositt un argument en faveur de la IinCariti des fonctions entrk-sortie des canaux et des combinaisons des sorties des canaux. Si les fonctions entrk-sortie des cbnes s’tcartent assez de la linearitt. la dtmonstration de la combinaison liniaire des riponses des canaux suggkre que des canaux ;I accord itroit coexistent avec des chnes g accord large.

Zusnmmenfassung-ModelIe zw ErkfPrung des Stiles Crawford Effek’ektes beschreiben die einzelnen Rezeptoren entweder als breit- oder engbandig (d.h. dass sie auf Licht reagieren, das unter einem kleinen oder grossen Winkel einftillt). Makous (1968) hat gezcigf dass die Retina engbandige Kaniile enthiilt. Es ist jedoch nach seinen Daten nicht notwendig, dass Kan;ile, die unterschiedlich abgestimmt sind, in vers- chiedenen Zapfen lokalisiert sind. In dieser Arbeit wiederholen wir (I) den Versuch von Makous (1968) mit engbandigen Reizen urn die Hypothese von engbandigen Kaniilen zu untermauern, und zeigen (2) dass die Begegrenzung der Unter~hied~hwellen east erfolgt, nachdem die Auger der einzelnen Kaniile kombiniert wurden und (3) aufgrund von~~eiligkei~~bgleichs~ssunge~ dass die Ein~ngs-Ausgangs- funktionen der einzelnen Kantile sowie die Uberlagerungen der verschiedenen Ausgiinge linear sind. Wenn die Eingangs-Ausgangsfunktionen der Zapfen hinreichend nichtlinear sind, weisen die gezeigten linearen Kombinationen der Kanalausgtinge darauf hin, dass engbandige Katile gleichzeitig mit breit abges- timmten Zapfen vorkommen.

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