Pergamon 0042-6989(94)00116-2

Vision Res. Vol. 34, No. 24, pp. 3253-3263, 1994 Copyright 0 1994 Elsevier Science Ltd

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Illusory Perception of Gratings Stimulating a Small Number of Neurones VEIJO VIRSU,*t JYRKI ROVAMO,$ PENTTI LAURINENT

Received 8 April 1993; in revised form 22 December 1993; in final form 6 May 1994

We studied pattern perceptions caused by drifting gratings presented monocularly in the nasal and temporal visual fields at various suprathreshold contrasts. The grating and its surround and background were matched in lmninaoce. Small gratings produced illusions and reduced perceptions. When grating area or contrast increased from a subthreshold value, the gratings were Urst seen as mere flashes. Then each grating was sometimes perceived as a single small bright spot or point. Next each grating was seen as a single dark or bright line. Finally the stimuli were perceived as gratings consisting of several bars. Orientation or direction of movement were perceived correctly, but velocity, colour and number of bars were often perceived as illusions. Thus, in spite of the illusions, some features of the stimuli could have allowed correct discriminations. The area and contrast limits of illusory perception depended on eccentricity. Irrespective of retinal size, the stimuli were not perceived correctly as gratings at any eccentricities when the gratings were smaller than about 1 x 1 mm in their calculated cortical area and stimulated a small constant number of retinal ganglion cells. Relations between the results and retinal aliasing, cortical columns and phase locking of neurooal oscillations are discussed.

Gratings Illusions Peripheral vision Cortical magnification M-scaling

INTRODUCTION

The ocular dominance columns of the human striate cortex are 0.5-l mm wide (Hitchcock & Hickey, 1980; Horton & Hedley-Whyte, 1984; Horton, Dagi, McCrane & de Monasterio, 1990; Wong-Riley, Hevner, Cutlan, Earnest, Egan, Frost & Nguyen, 1993). From calculations of human cortical magnification factor it is found that human subjects can resolve dot separations and displacements smaller than 0.03 mm on the surface of the striate cortex in hyperacuity tasks in peripheral vision (Virsu, NHsPnen & Osmoviita, 1987b). On the other hand, gratings of 3-6 c/mm in calculated cortical spatial frequency can be resolved in discrimi- nation tasks in the periphery, depending on subject, task and eccentricity (Virsu & Rovamo, 1979). The period length of a monocularly resolvable grating or dot separation in hyperacuity tasks may evidently be much smaller than the average width of the ocular dominance column.

Thus, it seems that details can be perceived in peripherally presented gratings at suprathreshold con- trasts when the dimensions of gratings are much smaller than the width of the ocular dominance columns. How do

*To whom all correspondence should be addressed. TDepartment of Psychology, P.O. Box 11 (Ritarikatu 5), University of

Helsinki, Helsinki SF-00014, Finland. IDepartment of Vision Sciences, Aston University, Aston Triangle,

Birmingham B4 7ET, England.

the details actually appear when the gratings are made as small as possible in calculated cortical terms? Our experiments indicate that although some features, such as the orientation of grating bars, can be resolved correctly, other features of the same details, such as the colour or number of grating bars, are not necessarily perceived correctly when the calculated size of the grating stimuli is smaller than the width of the columns.

In this report, percept and perception refer to the conscious representation of a stimulus and its features such as colour and velocity. Feature is a perceived attribute of the stimulus, a variable that can have a value. The visual perception of a dark line and all its perceived properties, for example, is a percept but the apparent velocity and direction of movement of the line are features of this percept. Percept class is a set of similar percepts, such as single lines: the members of this class can be dark or bright, moving or stationary, flickering, and so on. Veridicality refers here to a similarity with fovea1 perception: for the extrafoveal stimuli used in the present study, the fovea1 percepts of the same gratings are regarded as veridical standards. Illusory perception refers to cases in which a percept is wrong or reduced in comparison to a veridical percept. Reduced perception refers to percepts that contain fewer values of features than the same stimuli would contain in central viewing. If a perception consists of only a report of flash or some other detection threshold event, it is considered maximally reduced and it is called unidentz@ed.

“R 34/2&b 3253

3254 VEIJO VlRSU et al

Complexity of a percept increases when the number of its potentially perceived attribute values grows. A percept is considered to be more complex or more veridical if it is less reduced and resembles its fovea1 representation more closely.

METHODS

Apparatus and stimuli

Drifting vertical or horizontal sinusoidal gratings were generated on a white (P4) cathode-ray screen under computer control (Virsu & Rovamo, 1979). The whole screen area was 20 x 25 cm’. An electronically generated rectangular window controlled the size of the stimulus area in the centre of the screen: the window generator set the contrast of the grating abruptly to zero outside the desired boundaries. The window was invisible when the contrast of the grating was subthreshold. The grating within the window and the rest of the screen always had the same average luminance of 10 cd/m’. A white surround field was created by an illuminated mask that extended from the screen to 40 x 40 deg2 for the viewing distance of 115 cm used. The luminance of the surround was also IO cd/m’.

The movable end of an optical fibre emitting white light served as a fixation point. A mask in front of one eye allowed binocular fixation that was utilized to improve the stability of fixation but the extrafoveally presented grating stimuli were monocular. A bite board stabilized the head. No artificial pupils were used. The natural pupil was 5-7 mm in diameter. For a 6 mm pupil, our bluish-white screen produced about 300 phot td or 1100 scat td.

The area, dimensions, number of bars, orientation, spatial and temporal frequency, velocity, phase, drift rate (l-4 Hz), presentation time, and eccentricity of the gratings presented in the stationa~ window were varied. In the experiments reported in Figs 2-7, the window and stimulus grating had a square form, spatial frequency varied so that the width and height of the window were one cycle, and one cycle with a start phase of zero drifted at 1.56 Hz across the window during the presentation time of 640 msec. For these stimuli at least two bars, one light and one dark, appeared simultaneously. Slowly drifting gratings were used in all experiments because (i) they maximized peripheral acuity, (ii) did not tend to fade (the Troxler effect induced difficulties with stationary gratings) and (iii) these drift rates activate visual cells reliably (Lee, Elepfandt 8z Virsu, 1981; Virsu, Lee & Creutzfeldt, 1987a).

Procedures

When steadily fixating, the subject triggered the presentation of a drifting grating: the homogenous field within the electronic window was replaced by a grating for the presentation time (640,960 or 1300 msec were typical). A tone signalled the presence of the grating. The subject changed the contrast of the grating prior each presentation by 0 or 0.1 log units from 0.002 to 1 (or from

1 to 0.002 in the control experiments). He described what he saw by means of a code. Since the percept was usually similar for several consecutive contrast steps, it was sufficient to give a response only when a change in percept occurred.

In the initial series the phenomenon was established by means of open descriptive responses and procedures described here were developed. The modified forced- choice method could be used because the number of different perceptual reports was quite small and similar for different subjects.

The subject was provided with a list of 10 pre-defined response elements from which he could indicate any combination. That combination was the response describing the desired percept. The 10 response elements were “nothing seen, flash (something), stationary, moving, flickering, bright, dark, grating, line, and spot”. These elements were the same for all subjects. For example, when shown a stimulus grating, the subject could respond “line” and “bright” and “flickering”, which indicated that his percept was a single bright line flickering (two or more lines were a grating). Computer output indicated, in addition to stimulus data, which percept was reported and the contrast at which the percept started to occur. The subject could add free verbal descriptions to the computer lists when the response alternatives were not sufficient.

The subjective reports of various percepts and their properties were categorized into four percept classes for the analyses reported in Figs 2-7. The reports of agrating or several lines were taken to represent veridical percepts, reports of single fine (bright or dark, moving or stationary) and spot (single point or cloud) were taken to represent two kinds of reduced perceptions, and reports offlash and other non-patterned percepts were taken to represent unidentified threshold sensations. Only a few responses were discarded because they did not fall into these classes.

The procedure allowed simultaneous qualitative reporting of different percepts and quantitative esti- mations of perception thresholds because the lowest contrast of each single percept was recorded. When illusory percepts occurred, several percepts and thus several perception thresholds could result for the same grating at different contrasts. The conventional detection threshold, usually an unidentifiable flash sensation, occurred at the very lowest contrast and was preceded by responses “nothing seen”. At some higher contrast and in some threshold runs the next response could indicate, for example, that the observer saw a single bright line moving. This percept and its contrast was recorded. At still higher contrast, the percept of a grating could occur the first time. That contrast indicated the lowest contrast for the percept “grating”.

The threshold for each percept class was calculated as the average of the lowest contrasts at which any members of this class were first seen in successive repetitions where contrast was raised. The procedure allowed different percepts to occur in different orders with respect to contrast or be missing completely from some series of

ILLUSORY PERCEPTIONS OF SMALL GRATINGS 3255

rising contrasts, but transitivity was very seldom violated. The thresholds calculated represent the lowest thresholds of perception; high thresholds showing the upper limits of various illusory percepts are not considered here. This rough threshold estimation was sufficient for the present descriptive purposes.

For each area and spatiotemporal frequency, 10 repetitions with all contrasts were completed in the experiments. If more than one percept in each threshold run belonged to the same percept class, only the one with the lowest contrast was counted. If a percept class-a spot, for exampl&id not occur in some of the 10 runs through all contrasts, the threshold average was calculated only for the actual number of occurrence of the class.

Calculating cortical sizes of stimuli

The results were analysed in calculated cortical terms by using the values of the linear cortical magnification factor M estimated by Rovamo and Virsu (1979) for the human primary visual cortex. The values of the monocular M (mm/deg) along the temporal half-merid- ian of the visual field were obtained from

MT= 7.99/(1+0.29E+0.000012~),

and for the nasal half-meridian from

(1)

MN = 7.99/( 1+ 0.33E+0.00007E)),

where E is eccentricity in degrees.

(2)

The topographical maps from the retina into the striate cortex and other parts of the visual system are distorted so that fovea1 stimuli activate neurones in much larger extents and numbers than the same stimuli in peripheral vision. The linear it4 indicates how many mm on the surface of the cortex correspond to 1 deg of visual angle at various locations of the visual field. It approximates the local average scale of mapping from the visual field into the striate cortex. Visual-field meridians and eccentricity specify location, and eccentricity refers to the angular deviation between the fixation point and the least peripheral edge of the stimulus.

We did not study foveally presented gratings because of the many uncertainties concerned with the cortical projections of very small gratings. The spread of light in the optical media of the eye (Campbell 8z Gubish, 1966) and the involuntary movements of the eye during visual fixation cause inaccuracies that are transferred into the cortical images in a direct proportion to M. If the value of the human M is 8 mm/deg at E= 0 deg as implied by equations (1) and (2), at an eccentricity of 37 deg in the nasal or 47 deg in the temporal visual field the value of M is 0.5 mm/deg. Hence, a retinal image subtending only 0.125 deg may stimulate 1 mm of the cortex in central vision, but in the periphery a retinal distance of 2 deg is required to stimulate this same cortical extent. In the latter case, optical spread and fixation movements of the eye are negligible as sources of variance for subjects who are experienced in fixation and have a good peripheral refraction.

The values of M are most uncertain for the fovea. Following Clark and LeGros, (1941) and Drasdo (1977; see also Wassle, Griinert, Riihrenbeck 8z Boycott, 1990), equations (1) and (2) assume that the cortical representation of the visual field in the striate cortex is proportional to the density distribution of retinal ganglion cell receptive fields per solid degree of the visual field. This assumption has been most controversial for the fovea. The recent results of Azzopardi and Cowey (1993) from the use of a retrograde transneuronal tracer indicate that much more cortical area has been reserved to central ganglion cells than to extrafoveal ones. Consequently, the fovea1 values of M should be much larger than those indicated in equations (1) and (2) in agreement with the fact that visual performance estimated with M-scaled stimuli is usually better in the fovea than periphery (Virsu & Rovamo, 1979). The estimates of equations (1) and (2) were used here for calculating the striate cortical sizes of retinal stimuli presented only at the extrafoveal eccentricities ranging from 8.01 to 72.5 deg.

The size measures of this report are given as linear dimensions in degrees or cortical millimetres because both the height and width of a grating and its spatial frequency are considered.

Subjects

Five subjects (PL, RN, JR, RV, W) served as observers. Four subjects were emmetropes and one was a corrected myope. Their fovea1 visual acuities measured with the Snellen E-chart were at least 1.4. No corrective lenses were used for peripheral viewing because their effects would have been small for our subjects (cf. Rempt, Hoogerheide & Hoogenboom, 1976). The peripheral refraction of one subject, PL, was examined in detail (Rovamo, Virsu, Laurinen & Hyvarinen, 1982). One experienced subject (RV) was not informed that only gratings were presented on the screen. Two subjects (PL and W), whose results are shown here, participated in almost all experiments. Eye movements recorded from the limbus showed that their maximum lateral eye movements remained smaller than 0.2 deg during 40 set fixations even when the subjects responded to large drifting gratings in a similar experiment.

RESULTS

Qualitative experiments

All subjects described similar reduced and illusory perceptions when small gratings were flashed on for OS-l.5 sec. At the eccentricities of 30-45 deg the most strikingly reduced perceptions were elicited by the vertical or horizontal gratings that subtended 0.75-2 deg along the bars and 0.25-0.5 deg across the bars, had spatial frequencies of l-3 c/deg and drift rates of l-4 Hz.

When the grating was very small, it was often perceived as a single, stationary, steady or flickering, bright spot. The spot percept evoked by a grating was often described

3256 VEIJO VIRSU et cd.

as a single point that was extremely small and bright, like the phosphenes that one may see after a blow to the head, but sometimes the spot had a cloud-like appearance. The spot occurred most consistently when the window was not larger than 0.25 deg wide and 0.75 deg long (bars parallel to the long side of the window). Seeing the spot, particularly as a point, required a steady fixation and good peripheral acuity. The spot was never dark or black and it would be improper to call it white: it represented a pure brightness sensation. It was bright without any colour. When flicker was seen it was much faster than that implied by the l-4 Hz temporal frequency of the drifting grating stimulus. The experienced subject, who did not know that gratings were only shown, was subjectively certain after the experiments that single points were actually used as stimuli, too.

At higher levels of contrast, or with larger stimulus windows, the dominant perceptions were well defined bright or dark lines. A few times a percept was reported to consist of a line and a spot. The perceived lines were narrow and their width was never reported too large as an illusion.

The following visual perceptions were described when the window was 0.5 x 0.75 deg, the width of the window was one full period of the drifting grating and the temporal eccentricity was 45 deg: single bright point or small cloud; single bright or white line stationa~, moving or flickering; single dark or black line stationary or moving; black line stationary and white line moving, or vice versa; and full grating stationary or moving. Only the perception of the drifting grating was veridical in the sense that its percept corresponded roughly to that of the same grating viewed centrally or to a much larger ~~pherally- viewed grating. In general, when either the contrast or area of the gratings increased, the percepts became more complex and veridical.

Several descriptions were usually given during one series of contrast increments or decrements and they followed roughly the order of the list above. Whenever lines were seen, their orientation was veridical regarding the horizontal or vertical so that the orientation of the grating presented could have been judged correctly regarding these alternatives. Multiple lines and other illusions were sometimes also described. Spot and bright line percepts dominated when the window was narrow. The length of the bright line appeared sometimes clearly excessive. If the window was wider and allowed several periods of the grating to appear simultaneously, a single line or multiple bright (white) or dark (black) lines could be seen in various combinations. However, enlarging the width over 2 deg at E=45 deg deleted most illusory perceptions. Extending the length of the bars removed all spot percepts, but some illusory line percepts could occur even when the window was several degrees long. Most percepts were subjectiveIy clear-cut and suprathreshold, not at all comparable to the fleeting threshold sensations (called unidentified here).

The colourless character of the spot percepts was confirmed in experiments in which saturated colour filters (Kodak Wratten Gelatin 29-red, 61-green and 473-blue)

were inserted in front of the eye for the duration of grating presentation with a solenoid under computer control. The perceived hue of the bright spot and also of many bright line percepts was not affected by the filters even though the homogeneous field and the luminous bars of larger gratings viewed under the same conditions adopted the filter colours.

Figure 1 illustrates how the thresholds of the various percepts varied as a function of retinal location: at the ho~zont~l temporal ~entricity of 4.5 deg, the retina1 position of the stimulus was changed vertically from the lowest to the highest position by moving the fixation point manually. Particular percepts tended to dominate within each small retinal region that was “blind” to other percepts at least in a single experiment. It seemed that the capacity to signal a particular feature or its values

C!ortkal displacement (mm~ I 2 3 4 5

1

B 0.5 x 0.75 deg f “‘i’rrit‘

-5 -4 -3 -2 -1 0 1 2 3 4 5 Retinal displacement (degrees)

FIGURE I. Threshold contrasts of various visual percepts for two areas of horizontal gratings at different retinal locations. The displacement was varied vertically across the temporal half-rne~~an at the eccentricity of 45 deg. It is shown in retinal terms on the lower abscissa and in calculated cortical terms on the upper abscissa. The gratings subtended 0.25 x 0.75 deg* in (A) and 0.5 x 0.75 deg’ in (B) (longer side ho~~ont~). The spatial frequency of the gratings was 2 c$deg and the drift rate of movement 1.56 Hz. Presentation time here was 0.7 sec. which allowed slightly more than one grating period to drift across the window during each p~~nta~on. The data inch&e all the percepts that were described by subject PL in 11 series when contrast always rose in 0.1 log unit steps from 0.05 to 1. Each series concerned another retinal location; the ordinate indicates the contrast at which each new appearance was reported (single cases, not averaged here). The same percept occurred usually at several consecutive contrasts, and therefore, only its first and lowest contrast was recorded. The window was displaced vertically on either side of the horizontal meridian of the visual field for each threshold run as shown on the abscissa; the corresponding cortical displacements were calculated from a value of 0.52 mm/deg for the cortical magnification factor (temporal eccentricity E = 45 deg). The percepts for this figure have been grouped in the following way: 0 single bright spot steady or flickering; a single bright or white line stationary; 0 single bright or white line moving; R single dark or black line s~tiona~; + single dark or black line moving; A at least two lines (dark moving, bright stationary; bright moving, dark stationary; grating stationary or moving). The threshold values of the related appearances in the neighbouring regions marked with similar symbols have been connected with lines. For example, the subject reported single dark lines

only in one region about 2 deg wide (+) in (B).

ILLUSORY PERCEPTIONS OF SMALL GRATINGS 3251

required that the stimulus covered some specific retinal locations. The spatial distribution of overall sensitivity was relatively even and no absolutely blind microregions were found.

Percepts caused by a grating became more complex when its contrast or area was increased [area doubles from Fig. l(A) to Fig. l(B)]: when either one grew, unidentified sensations preceded spots, spots preceded lines and lines preceded gratings, if none of these percepts were missing. Expanding the width of the grating clearly over 1 mm in calculated cortical terms deleted most illusory percep- tions, however, no matter how much the constant spatial frequency was below the resolution threshold.

The direction of perceived movement never changed during the presentation although it lasted up to 1.5 sec. In fact, the perceived direction of movement was probably always veridical: an illusory direction of movement was never reported by the subjects who knew the stimuli and reported various kinds of illusory perceptions concerning the apparent speed or lack of movement. The illusions were similar in horizontal and vertical gratings.

Quantitative experiments

The main finding of the qualitative experiments was that small drifting gratings cause various illusory perceptions many of which are similar to normal suprathreshold perceptions: percepts could look normal and veridical although they were illusory. In many instances the illusory perceptions would have allowed correct discrimination of some attributes of stimuli. For example, the orientation or direction of movement would

have been judged veridically although the number of bars in a grating or the velocity of movement was perceived incorrectly. The veridicality of percepts improved if the grating contrast or area increased.

The area of the grating was varied in the qualitative experiments so that spatial frequency, temporal fre- quency and translation velocity were independent of area. Then the number of spatial periods increased and bandwidth of the gratings became narrower when the area of the grating increased. Increasing grating area led to more complex and veridical percepts, but this could have followed from the fact that the stimulus also became more complex in the sense that it contained more spatial periods. Therefore, in the following experiments, the size of the grating was varied by enlarging a constant stimulus in the same manner as its retinal size grows when an observer gets nearer to the stimulus: the change of size was a change of the scale of the frequency axes in the two-dimensional spatial frequency spectrum of stimulus grating, and the structure of the stimulus did not change when its size varied.

The gratings limited by the electronic window were vertical and each side of the grating was equal to one spatial period in the experiments of Figs 2-7. The initial phase was zero at the edge of the electronic window and one spatial period always drifted to the right across the window at 1.56 Hz during the grating exposure of 640 msec. Therefore, the average luminance integrated over time and space during the presentation time was constant for the whole 40 x 40 deg2. The spatial and temporal structure of the stimulus pattern was independent of size, because one cycle of the grating drifted across the window

Cortical size (mm) 0.125 0.25 0.5 1 2 0.125 0.25 0.5 1 2

0.25 0.5 1 2 4 0.25 0.5 1 2 4 Lethal size (degrees)

FIGURE 2. Frequency of occurrence of various percept classes as a function of the retinal size of vertical grating at a constant horizontal eccentricity of 39.8 deg in the temporal visual field for subject W and 37.5 deg in the nasal visual field for subject PL. Calculated cortical size in mm [retinal size in deg multiplied by M mm/deg (Rovamo & Virsu, 197911 varied as shown on the upper abscissae. In this case, size refers to the length of one side of the square-shaped drifting gratings. Spatial frequency in c/deg and c/mm is the inverse of the sizes indicated. The symbols corresponding to the different percept classes in subjects’ reports are indicated in the figures: each symbol refers to the total number of percepts in 10 runs at a constant size. For each size contrast increased in 0.1 log unit steps through all values from 0.002 to 1. Frequency of occurrence of each percept class varies between 0 and 100% in 10% steps but since some percept classes were not reported at all in some threshold runs, occurrences for many classes do not reach 100% at certain sizes. For the size of 1 deg, for example, W reported in 10 runs through all contrasts

a percept that was classified as spot percept in 4 runs, single line percept in 8 runs and grating percept in all 10 runs.

3258 VEIJO VIRSU ef al

in the same constant time. Depending on the phase, two or three bars were present at the same time. Since the percepts and their thresholds depended on the precise retinal location of stimulation (Fig. 1), we recorded the responses at different locations within a 5 deg vertical strip by shifting the gratings systematically for consecutive threshold runs.

Percepts and illusions behaved in the same manner in these experiments as those reported in the qualitative experiments. When eccentricity was constant in the temporal or nasal visual field but the size of the retinal area stimulated by the grating was varied, various percepts occurred as in Fig. 2. Since only the frequency of occurrence is considered, no attention is paid to contrast and it varies freely in this figure. When size grew and retinal image area increased, illusory and reduced perceptions, classified as single lines (diamonds) or spots (circles in Fig. 2), became first more and then less frequent. Only when the gratings were larger than about 2 x 2 deg2, percepts became veridical, that is, grating or several lines were seen (squares). In terms of calculated cortical projection sizes, most illusory perceptions occurred when grating size was less than 1 x 1 mm’, and a consistently veridical perception required calculated cortical projection images that were at least 2 x 2 mm’ in size.

As Fig. 3 shows, the contrast thresholds of all percepts decreased with increasing grating size. Detection thresholds indicated by the solid triangles were lowest. For small gratings more complex percepts had higher thresholds than simpler percepts. For each grating size, flashes or other unidenti~ed visual sensations occurred at the lowest contrasts, spots were seen at somewhat higher contrasts, single lines at still higher contrasts, and multiple lines or gratings at the highest contrasts. This order was seldom violated in single runs. Sizes smaller than I x I mm2 in calculated cortical terms produced high

contrast thresholds. Thus, the results correspond to those of Fig. 2: contrast thresholds were high at the same sizes that produced illusory perceptions. Since nominal spatial frequency is the inverse of grating size, it can be seen from Figs 2 and 3 that the resolution threshold for the smallest grating stimuli was 2-4 c/deg. This frequency was 4-X times higher than the highest spatial frequencies at which the illusions were not observed any more.

Ex~riments reported in Figs 4 and 5 tested the hypothesis that the various illusory perceptions and their thresholds depended on the calculated cortical size in mm rather than retinal size in degrees of the visual field. The results of these experiments showed that the percepts and their thresholds were always consistently related to the calculated cortical size irrespective of retinal size or location.

The cortical and retinal sizes were dissociated by varying eccentricity. In the experiments of Figs 4 and 5, the retinal size of the grating was always the same 1 x 1 deg’ and its spatial frequency was continually 1 c/deg, but the cortical size and spatial frequency varied because the same grating was viewed at different eccentricities. Eccentricities smaller than E = 8 deg were not used for the reasons explained in the methods. Eccentricities up to 72 deg were tested. The smallest cortical sizes (0.125 mm?) were not studied because of the border of the visual field. The results were similar to those of Figs 2 and 3, although the retinal size in degrees of the visual field did not vary in Figs 4 and 5. In all cases the gratings began to yield illusory perceptions when their calculated cortical size became smaller than about 1 x I mm2. At the same sizes, contrast thresholds of various percept classes began to increase steeply.

In the experiments reported in Figs 6 and 7, the retinal size in degrees of visual field was varied with eccentricity so that the estimated cortical representations of the gratings had a constant calculated cortical size of

Cortical size (mm) 0.125 0.25 0.5 1 2 0.125 0.25 0.5 1 2

0.25 0.5 1 2 4 0.25 0.5 1 2 4 Ret&ml size (degrees)

FIGURE 3. Threshold contrasts of the percept classes of Fig. 2 as a function of the retinal size of the grating at the constant horizontal eccentricities in the temporal and nasal visual fields. Contrast refers to the average contrast of those gratings that just-and-just started to evoke each percept class indicated in the figure in the 10 series ofcontrast increments at each retinal grating

size. Other details as in Fig. 2.

ILLUSORY PERCEPTIONS OF SMALL GRATINGS 3259

Eccentricity (degrees)

72.5 39.8 19.2 8.01 56.2 37.5 19.2 8.92

1 VV, temporal 1 x lo

/+

‘*. ‘\

0.125 0.25 0.5 1 2 0.125 0.25 0.5 1 2 Corticalsize

FIGURE 4. Frequency of occurrence of various percept classes as a function of calculated cortical size. Eccentricity varied along the temporal and nasal half-meridians of the visual field as shown on the upper abscissae. The retinal image size was a constant 1 x 1 deg2, for the same grating was viewed at different eccentricities. The variation of the cortical size follows from the variation

of eccentricity. The blind spot was bypassed from below. Other details as in Fig. 2.

0.6 x0.6 or 0.5 x 0.5 mm*. The retinal size was thus M-scaled (Virsu & Rovamo, 1979), i.e. it was kept as a constant multiple of the inverse of the cortical magnification irrespective of eccentricity. The variation of eccentricity and retinal size now had practically no effect: the constant cortical size produced similar frequencies of occurrence and thresholds for various percepts at all eccentricities. Although variation in these variables remained high, their values did not change systematicly as a function of eccentricity or retinal size after M-scaling. The thresholds were somewhat higher and percepts less veridical for the smaller calculated cortical image as shown in Fig. 7(B) than in Fig. 7(A).

DISCUSSION

Various clear-cut but strikingly illusory perceptions were reported when small grating stimuli were viewed in peripheral vision. Details were perceived so that correct discriminations between stimuli or their parts could have been made, but the appearance of the stimulus as a whole was wrong in many cases. The illusions were so varied that considerations of spatiotemporal frequency spectra of the stimuli do not explain them.

Although the variation of size was different in the qualitative and quantitative experiments, changing areas in the former and magnifying images in the latter, similar results were obtained. The complexity of stimuli was not

Eccentricity (degrees)

72.5 39.8 19.2 8.01 56.2 37.5 19.2 8.92

1

* 3 s

g s 0.5

2 B

g

0

0.125 0.25 0.5 1 2 cortical

l-

O- I I I I

0.125 0.25 0.5 1 2 size (mm)

FIGU RE 5. Threshold contrasts as a function of calculated cortical size. The same grating subtending 1 x 1 deg’ in its retinal image was viewed at different eccentricities. Other details as in Fig. 4.

3260 VW0 VIRSU er al

Eccentricity (degrees) 8.01 19.2 39.8 72.5 8.92 19.2 37.5 56.2

z !I : lines 0 50- *e

“0 0 uh 8

(./ ‘:*, .D*.Q

& -6,. Q”’ **.__

A W, temporal *.: 0.6xO.6mm b

I I i i

0.25 0.5 1 2 4 0.25 0.5 1 2 4 Retinal size (degrees)

FIGURE 6. Frequency of occurrence of various percept classes as a function of retinal grating size and eccentricity. Eccentricity varied as in Fig. 4, but the retinal size of the grating was adjusted (M-scaled) so that the calculated cortical size was a constant 0.6 x 0.6 mm2 for the temporal half-me~dian in (A) and 0.5 x 0.5 mm2 for the nasal half-me~dian in (B). The retinal image side length was thus 0.6 or 0.5 times the inverse of the linear human cortical ma~fication factor at each eccentricity. Other details

as in Fig. 4.

affected by the change of size obtained as magnification in the quantitative experiments. The determining factor in the occurrence of the illusory perceptions was thus the size of the stimulated area in the retina and cortex rather than the spatial and temporal frequency of stimulus gratings. Illusory perceptions occurred at nominal spatial frequencies that were much lower than the resolution limit observed for the same stimuli. The spatial cycle lengths had to be only short enough to make the gratings small, and drift rate or velocity of movement had to be low enough for the good visual resolution. Nothing was seen when the cycle length was shorter than that required by the resolution threshold or contrast lower than the observed contrast threshold.

The most elementary patterned visual perception,

obtained with the smallest gratings, was a stationary or flickering bright spot. A local stimulation of the human visual cortex seems to evoke similar spot perceptions (Brindley & Lewin, 1968; Dobelle & Mladejovsky, 1974). Electrical stimulation has been reported to evoke cloud-like perceptions, excessive numbers of spots, flickering spots, coloured phosphenes, and elongated spots or even lines. The percepts became more complex when stimulus size or contrast increased.

When any movement of lines or gratings was perceived, the direction of movement never changed during presentation time. The direction of movement was evidently always perceived veridically, whereas the perceived speed of movement was often illusory: sometimes the whole percept or its part was stationary

1

Eccentricity (degrees 8.01 19.2 39.8 72.5 8.92 19.2 37.5 56.2

f I I I r t

Cl Bating. lines 0 gingleline A ^_^C * I u ayul.

A unid.. flash

0.6 x 0.6 mm

k’ nasal x 0.5 mm

0.25 0.5 1 2 4 0.25 0.5 1 2 4

Retinal size (degrees)

FIGURE 7. Threshold contrasts for M-scaled gratings as a function of retinal grating size and eccentricity. Other details as in Fig. 6.

ILLUSORY PERCEPTIONS OF SMALL GRATINGS 3261

although drifting gratings served as stimuli, and sometimes the perceived velocity or flicker frequency was clearly excessive.

The main consequence of increasing stimulus area was to stimulate a larger amount of visual neurones. A higher contrast also led to a more veridical perception even when grating size (and area) remained constant. The effects of contrast were similar and probably at least partially secondary to the effects of size, however, because high contrast activates more visual neurones than low contrast. Also the effective spread of light is larger and the effects of stimulation diffuse farther in the neural network at higher contrasts.

Aliasing is one possible source of the illusions. If sampling density is lower than a limit determined by the Nyquist frequency, details requiring a correct represen- tation of frequencies higher than the limit cannot be transmitted (see Anderson & Hess, 1990). The coarseness of the retinal mosaic sets spatial limits particularly in peripheral vision and aliasing can occur there in normal viewing (Galvin & Williams, 1992). Stimulus edges do not produce aliasing, however (Galvin & Williams, 1992).

Large stationary high-contrast gratings produced directly on the retina as interference fringes (Thibos, Walsh & Cheney, 1987) and large drifting gratings (Campbell & Maffei, 1979; Coletta, Williams & Tiana, 1990) may cause various illusory perceptions, such as errors of perceived orientation, checkered appearance, shimmering, and stopped and reversed motion. Illusions observed in our experiments were not similar to these, however. Orientation or the direction of movement was not perceived erroneously, but instead, many other kinds of illusions occurred. The illusions occurred below, not above the observed resolution threshold.

Receptor spacing is irregular (Curcio & Sloan, 1992), but the illusory perceptions reported here occurred at spatial frequencies that were well resolved in the same gratings. Our gratings were thus well resolved also by retinal ganglion cells. A drifting grating subtending 0.5 deg2 at a temporal eccentricity of 40 deg may stimulate 30-50 retinal ganglion cells (Curcio & Allen, 1990; Rovamo & Virsu, 1979), which may give enough opportunity to perceive gratings and their movements veridically, but usually this size (0.7 x 0.7 deg*) led only to illusions even at the highest contrasts (see Fig. 3). The receptive field centre diametres of the retinal ganglion cells at this eccentricity in the macaque monkey subtend 0.2-l .O deg (De Monasterio & Gouras, 1975).

If aliasing is understood in the conventional way as a retinal undersampling, the irregularity of sampling notwithstanding, it must produce reverse motion and errors of orientation that were not observed in our experiments. Therefore, if aliasing is the explanation of the present findings, a new form of aliasing occurring only for small images and low contrasts must be assumed. The perceptual phenomena observed in the experiments were probably too complex to be caused by aliasing at the retinal level. YK 34iz4-X

The central outcome of the present studies was that suprathreshold stimulation must exceed a critical neural extent, which is approximately the same for different visual-field locations, before features can be linked so that a veridical composite percept can develop. If the neural extent is below this limit but something distinct is still perceived, illusions occur and percepts are reduced. The critical extent was calculated for the striate cortex by means of the cortical magnification factor estimated from the density of retinal ganglion cells (Rovamo & Virsu, 1979). On the other hand, various percepts and their contrast thresholds were approximately independent of eccentricity in the peripheral visual field when M-scaled grating stimuli were used. For small gratings, this result generalizes to suprathreshold contrasts our previous suggestions (Rovamo & Virsu, 1979; Virsu & Rovamo, 1979; Virsu, Rovamo, Laurinen & Nasanen, 1982) that contrast sensitivity measured with cortically equivalent (M-scaled) gratings is independent of eccentricity, and the result agrees with the cortical magnification theory (Virsu et al., 1987a, b; Strasburger, Rentschler & Harvey, 1994).

The type of spatial integration recognized generally is the decrease of thresholds with growing stimulus size. Our results suggest that another type of spatial integration exists in which the complexity and veridicality of perception increase with stimulus size. The primary determinant of integration both for thresholds and percepts was the calculated cortical size of the stimuli. This suggests that an important variable in the integration is the number of visual cells properly stimulated: sensitivity improves and more complex ~rceptions become possible when the number of relevantly stimulated cortical and other visual neurones increases. This interpretation is supported by the result that the complexity and veridicality of perception increased also with contrast. The small stimuli causing illusions were insolent for satisfying the input requirements of cortical cells. In the macaque striate cortex the receptive field linear size at 40 deg eccentricity on the average is about 3 deg in the visual field (Hubel & Wiesel, 1974; Van Essen, Newsome & Maunsell, 1984), and the fields of later cortical areas are even larger. The percepts produced by gratings that were large enough to fill the striate receptive fields completely were veridical but they were able to activate many cells with related properties, too.

One phenomenon that we observed was that drifting gratings evoked only the perception of a bright spot when size and contrast were at a minimum needed for producing any suprathreshoid perceptions. The brain does not seem to interpret the activation of cortical cells in terms of the features that are useful for activating them. The number of brain cells involved even in the reduced perceptions is probably quite large, for in the human striate cortex alone a block of cortex 1 x 1 mm2 in surface area may contain 200,000 neurones (Blinkov & Glezer, 1968).

Distinct features were perceived even when stimuli were calculated to be smaller than the 0.5-l mm width of the human ocular dominance coIumns (Horton er nl., 1990).

3262 VEIJO VIRSU et a/

Percepts were not veridical in this case, however. If gratings extended less than about 1 mm in calculated striate cortical terms, they consistently produced illusory perceptions at all eccentricities. Due to the monocular presentation of stimuli, it is likely that these stimuli activated cells in one ocular dominance column only because each ocular dominance column contains projections from one eye and is flanked by projections from the other eye.

When the contrast or size of the grating was made smaller, the number of cells active above some threshold level became smaller and the activity became even more probably limited into one ocular dominance column. It is possible that the reduced perceptions occurred when the relevant stimulation was limited to one cortical module (Hubel & Wiesel, 1977) or its part. Although some features of stimuli may be distinguished veridically when an area estimated to be less than the size of a cortical module is stimulated, a veridical perception of the whole stimulus may require the activation of more than one module in the striate cortex as hypothesized by Hubel and Wiesel (1974). This suggestion agrees with the proposal that there exists a perceptive hypercolumn whose size is about the same as that of the anatomical module of the striate cortex. Levi, Klein and Aitsebaomo (1985) suggested the perceptive hypercolumn to explain their result that at all eccentricities vernier thresholds were elevated when interfering contours were present within 1 mm calculated for the surface of the striate cortex.

The complexity of perception grew and veridicality improved as a function of stimulus contrast and cortical area stimulated. In both cases the number of activated visual neurones and cortical modules increased, because the probability of activation in the non-optimally tuned cells grows with contrast and new cells are recruited with the expanding area of stimulation. Our results support the view that the veridical perception of patterns and simple features (e.g. colour and movement) requires integration of activity from many cells (Mitchison & Miall, 1990). A similar conclusion can be reached for the control of movements (Fetz, 1992).

The findings of the present experiments can be summarized so that the veridicality of visual perception requires exceeding a minimum size that is approximately constant as a calculated cortical distance. The existence of a critical neural extent for veridical perception agrees with the idea that normal perception requires selective phase locking (Engel, Kbnig, Kreiter, Schillen & Singer, 1992). Animal results indicate that there is a cortical separation, equal to the maximum distance between neurones that still have overlapping receptive fields, that must be exceeded before phase locking of single-unit neuronal responses becomes selective to stimulus parameters (Gray, Kbnig, Engel & Singer, 1989; Engel, Konig, Gray & Singer, 1990). If the separation is smaller, the receptive fields overlap and responses of single neurones become synchronized although their stimulus preferences are not met, provided that several distinctly different stimuli are not used in the same location (Engel, Konig & Singer,

199 1). When cell responses are phase locked for unusual and nonselective responses, their signals cannot have a veridical interpretation and illusions occur. Contrast can affect perception of small stimuli because increasing contrast widens the extent of responses due to point image spread (McIlwain, 1986): the ends of a stimulus can reach non-overlapping receptive fields at high but not at low contrasts.

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Acknowledgement-We thank Pekka K. Lehtiii for designing much of the equipment used in this study.