Spatial frequency doubling: Retinal or central?

WsitmRas.Vol. 13, pp. 212S2137.F~gunon fmsa 1973.Printedin Great Britain.

SPATIAL

FREQUENCY DOUBLING: OR CENTRAL?

WHITMAN RICHARDS~ Massachusetts

RETINAL

and THOMAS B. FELTON

Institute of Technology, Department of Psychology, Cambridge, Massachusetts 02139, U.S.A.

(Received 5 November 1972; in revisedform

1 I April 1973)

INTRORUCTION

1966, Kelly described an unexpected visual illusion (KELLY, 1966). Rather than studying sinusoidal waveforms that vary solely in time (flicker} or in space (gratings), Kelly combined these spatial and temporal parameters to generate a stimulus that was sinusoidally modulated in both time and space simultaneously. In this manner, spatial-temporal interactions in the visual system were explored. One striking property of such a stimulus is the appearance of a spatial second-harmonic response at high flicker rates. For photopic stimuli, if the temporal frequency is greater than about 10 Hz and the spatial frequency is less than 2 c/deg, then the displayed pattern appears to have twice the spatial frequency of the stimulus”. This phenomenon persists as the stimulus modulation is decreased right down to threshold. Kelly interprets spatial frequency doubling as due to a temporal integrator or Low-pass filter that follows sup~threshold non-linearities in the visual pathway. Evidence for nonlinearities is considerable (CORNSWEET, 1970), and includes distortions in sine-wave gratings whereby the dark and light portions do not appear to have equal width3. The effect of adding a temporal integrator is to average all these suprathreshoid, non-linear outputs. In this case, providing integration occurs over several cycles, the fundamental and all odd harmonics of the stimulus will vanish, leaving only a doubled-frequency component as the dominant output (see derivation by KELLY, 1966). In the case where temporal integration occurs only over a few modulation cycles, such as at low flicker rates, the spatial frequency of the pattern will appear to lie somewhere between its true spatial frequency and twice this frequency. For a suprathreshold grating of 1 c/deg, the approximate relation between flicker rate and apparent spatial frequency is shown in Fig. 1. (This figure will be described more fully later.) At present, Fig. 1 may be considered as an indication of the temporal frequency response of the integrator proposed by Kelly. IN

’ Supported by the AFOSR under contract F44620-69-C-0108, with supplementary funding from NASA. ‘IF was supported by NIH training grant 5-TOI-GM01064-01. ’ KELLY (1966) suggests that the effect lies in a region where the temporal frequency exceeds the peak sensitivity of the observer, while the spatial frequency should be less than his optimum. In this regard, see comment by MARIMONT. (1967). 3 Whether the darker or the lighter portions of a sine-wave grating will appear wider depends upon several factors. Our observations indicate that for high frequency patterns greater than 5 c/deg the light portion may appear slightly wider than the darker portion, whereas the opposite may be true for low frequency gratings viewed under appropriate conditions. Particularly impressive is the expansion of the dark areas of a low-frequency grating as the light level is reduced. Such observations suggest that the nature of the brightness non-linearity depends upon the frequency of the grating, the contrast, and whether steady state or transient changes in iIlumination are being considered (See also MAWONT, 1962). The introduction of flicker further complicates the subjective impressions (BROW, 1965). All of these complexities, including the nature of the non-linearity does not affect the arguments and conclusions reached in our study, however. 2129

2f30

WRITMAN RICHARDSand THONG 3. FELTON

o-25

05

f

2

Modulation

4

8

16

m%8,

32

64

Hz

FIG. 1. Apparent spatial frequency of a sine-wave grating as the modulation rate is increased from Q to 30 Hz. Standard deviations showing the range of judgements for the three observers are shown above and below the means (circles). The arrow indicates the region where the display takes on a square-wave appearance prior to “doubling”.

One important feature of Kelly’s explanation for spatial frequency doubling is that the recognition of the grating frequency for pattern) foltows the temporal integrator. In order to retain delange’s simple model for fficker detection, which predicts a linear response for small signals, Kelly ptaces the temporal inte~ator after the site for the detection of flicker fusion. This solution is shown schematically in Fi,.* 3 _. However the deLange stages (indicated by the dashed line enctosure) could equally well be repfaced by Levinson’s mode for flicker fusion (LEVXNSON,1968). The critical point is that the temporal integrator must view a non-linear signal which is suprathreshold for the preceding flicker detector. The --

--

P -I t

-7

Linear

filter

i-__

_--.I 14(*,U

t-

Flickerthreshold

FOG. 2. Extension of the deLange model proposed by frequent-doubting.

fusion detector

KELLY

(1965) to account for spatiat

Spatial Frequency Doubling

213I

proposed sequence seems quite plausible, considering also the fact that as contrast is reduced, flicker is still observed after the grating has disappeared. U~o~unately the model schematized in Fig. 2 does not pinpoint the site of spatial frequency doubling in the visual pathway. To this end, it is helpful. to consider the question of whether spatial frequency doubling occurs before or after binocular interaction. Fortunately, this question may be answered by examining the relation between spatial frequency doubling and the processing of binocular disparities. The procedure will be to show that the disparity system is processing the fundamental spatial frequency and not the second harmonic. Thus, the appearance of the second harmonic must follow the site of disparity processing. METHOD In order to stimulate neural detectors of binocular disparity, a vertical sine-wave grating was presented 180” out-of-phase to each eye. Thus, if the light oortion of the grating auoeared at 1” from the fovea in one .. eye, then the dark portion of the grating would adpear at the same position in the opposite eye. The binocular effect of such a display is the appearance of a grating standing either in front or behind the plane of fixation. To accomplish this binocular effect simply, it is necessary only to present a single grating on a scope face, and then to provide a fixation target at the appropriate distance in front of the scope face. For our experiments, the optimal stimulus was a vertical grating of %c/deg which then required fixation at 15 cm in front of the scope screen in order to place the grating 180” out-of-phase to each eye. At the 100 cm observation distance, this fixation point corresponds to 0.65” disparity relative to the oscilloscope. The fixation point was a distinctive Q x t” spot on a dark wire protruding from the scope, and was located lo above the 3-5 x 4” display screen. When such a grating appears in depth off the plane of fixation, neural detectors of binocular disparity are activated. Strong evidence for disparity specific activation is the presence of a disparity specific adaptation effect that fohows extended viewing of a high-contrast grating seen in depth (FELTON,R~CKARDSand %ITH, 1972). Specifically, there is a marked elevation in threshold contrast for detecting the sinusoidal grating following a 3 min exposure to a high contrast grating of the same frequency. The threshold elevation is over twice as great for the disparate grating (adaptation condition) as for a grating seen in the plane of iixation. This disparity-specsc adaptation effect has been described more f&y elsewhere (FEL~ON er a(, 1972, BLAKEMORE and HAGUE, 1972 and FELTON,1972). It is truly disparity-sp~ific, for the phase reiation tcztween the gratings in each eye is important, with the effect disappearing when the gratings are in register in each eye. To elicit this disparity-specific adaptation effect, a sinusoidal vertical grating was displayed on the face of a Tektronix 535 oscilloscope using a modified television techniaue (BLAKEMORE and CAMPBELL.1969). To avoid the formation of conventional afterimages, the contrast ofthe‘grating was sinusoidally modulated in time at 2 Hz or greater (up to 20 Hz) using counterphase modulation. Such modulation merely exchanges the darker with the lighter regions of the grating. The critical experiment was performed with counzerphase modulation at 20 Hz, which should effectively eliminate any correlation between eye movements and the t” period of the grating.’ At the 1 m observation distance, the screen subtended 3.5 x 4”, with a mean grating luminance of 65 cd/m’. The modulation contrast of the grating could be adjusted remotely by the subject. The procedure was for the subject to begin by setting the modulation of the grating until the bars appeared at threshold. For each display condition studied, two initial (preadaptation) thresholds were obtained: (1) grating presented in the fixation plane and (2) with fixation in front of the grating. In the first case the subject fixated on the scope face; in the second, on the fixation point 15 cm in front of the display (eqtialent to O-65”of disparity). When the subject signalled that he had set his threshold, the r.m.s. value of the modulating voltage was recorded as his threshold reading. At least four such thresholds were taken, alternating the fixation conditions. Following the initial threshold determinations, the subject was then adapted to a high contrast grating of 5 c/deg (approximately 50 per cent contrast) modulated in antiphase at 20 Hz. Such a display exhibited spatial frequency doubling4 The adaptation period lasted 3 min, during which time the subject iixated 0.65” in front of the display. Thus, the adaptation condition was such that the grating was presented 180” out-of-phase to each eye. At the end of the adaptation period, the grating was instantly reduced in contrast, and the subject reset his threshold within 10 sec. In one case the threshold was taken for fixation in the pfane of the grating (no disparity): the next trial measured the threshold when fixating in front of the grating (same disparity as adaptation). Between threshold settings the subject was given 30 set of readaptation. 4 Scope nonlinearities were checked by raising the flicker rate to 60 Hz, above CFF. Upon close inspection at onequarter the observation distance, faint second harmonic distortions still occurred on the display. This artifact however, would go against the main experimental result.

2132

Wnrma

RICHARDSand THOMAS3. FELTON

DISPARITY-SPECIFIC

ADAPTATION

To

clarify what is meant by disparity-specific adaptation, an example may be helpful. FoIIowing adaptation to a 8 c/deg grating flickering in counterphase at 20 Hz, the subject’s thresholds will be raised. Two eIevations in threshold are of interest: (1) the elevation for the disparity condition (when he fixates in front of the scope face) and (2) the elevation when fixation is in the plane of the scope face (no stimulus disparity). For the average subject, the contrast threshold for the disparity condition is raised approximately fourfold following adaptation to the disparate grating. In addition, there is also an elevation of 1-9x in threshold when the subject tivates in the plane of the grating stimulus, even though adaptation occurred in the opposite (disparity) condition. Previous experiments have shown that this second elevation in threshold is customarily about half the elevation that occurs when the test and adaptation conditions are identical (FELTOE; er at, 1972). We interpret the second, lower threshold elevation as being not specific to disparity, for it is insensitive to the registration of the stimulus components in each eye. (In fact, this second threshoId elevation of 1.9 x is identical to the elevation obtained with monocular testing.) In order to obtain a disparity-specific adaptation effect, therefore, the four-fold elevation obtained with disparate adaptation and testing (fixation in front of the scope screen) is reduced by a factor of 1.9, yielding a disparity specific adaptation effect of 4/l-9 = 2.1. All subsequent values reported for disparity-specific adaptation are the reduced values, with the on-disparity component divided out. The reduced value of adaptation that measures the disparity specific rise in threshold appears truly specific to disparity and is not the result of local adaptation of each retina. Even though Iocal adaptation of each retina may occur (as indicated by the second threshold rise that is insensitive to the registration of the stimulus components in each eye), there is a further threshold elevation that must be sensitive to the spatial phase relations of the grating in each eye. In particular, the disparity-specific adaptation effect requires that a iight bar on one retinal region of one eye (say 0.6” from the fovea) be correlated with a light bar in a different retinal position on the other eye (say at 1.2” from the fovea) at the same instant in time. The correlation must occur almost simultaneously because at the 20 Hz rate of counterphase modulation, the dark and light portions of the grating will be reversed and the disparity-specific signal will be lost. Rather than proposing that individual neurons in separate retinae are time-locked to one another, the simpler alternative is to assume that one neuron at a higher level is responding to simultaneous input of the same kind from each eye. Such a neuron would be a disparity detector. In favor of this position are two other observations: (i) disparity-specify adaptation fails when the observer fails to see the grating in depth as the rate of counterphase modulation is increased; (ii) under appropriate conditions individuals with reduced stereo mechanisms fail to exhibit a disparity-specific adaptation effect (FELTON et al, 1972). RATIONALE

The rationale of our experiment should now be apparent. The subject adapted to a $ c/deg grating modulated at 20 Hz, fixating in front of the scope so that a disparity-specific adaptation effect would be elicited. Because of the high modulation rate the grating appeared to have twice the spatiaf frequency of the stimulus. If the modulation rate was lowered to 2 Hz, then the frequency doubling effect disappeared. Of interest is whether the disparity specific adaptation wifl occur at the apparent, doubled spatial frequency seen during adaptation, or at the actual stimulus frequency of 4 cfdeg. If disparity specific

Spatial Frequency

Doubling

2133

adaptation occurs at the apparent, doubled spatial frequency, then clearly the doubling occurred prior to the processing of disparity. On the other hand, if the disparity adaptation effect only occurs for the fundamental (t cidegf when modulated at Low rates (2 Hz), then the disparity mechanism must have adapted to the fundamental spatial frequency and not to the second harmonic seen by the observer. In this latter case, then, spatial frequency doubting must follow disparity processing, or at the very least occur in a separate pathway. (While recognizing the possibility of this latter alternative, we will at present consider only the heuristically more informative question of the sequential flow of information through a single pathway.) To determine whether spatial frequency doubling precedes or follows disparity processing, it is necessary to be sure that in the test conditions at the reduced flicker rate of 2 Hz, at least one spatial frequency matches that of the standard ($ c/deg) at 20 Hz. Each subject thus successively matched various spatial frequencies modulated at 2 Hz to the standard $ c/deg grating modulated at 20 Hz. On the average, such comparisons between the flickering gratings showed that the apparent spatial frequency at 20 Hz was onfy 1.6 times greater than the fundamental (see Table 1, last column). This result was not expected from Kelly’s original report, which implied a flicker boundary below which doubling did not occur. To clarify this difference, a 5 c/deg grating at 20 Hz was chosen as a standard spatial frequency. Three subjects then successively matched a variable spatial-frequency grating to this standard. The procedure was for the experimenter to choose a flicker rate from $ to 40 Hz. Gratings of different spatial frequency were then displayed at this flicker rate, and were judged by the subject to be coarser or finer than the standard grating of $ c/deg modulated at 20 Hz. The matches were made successively on the same scope face, with the standard and test gratings being exchanged roughly every 10-20 set until a judgement had been made. Measurements were taken both with fixation in front of the scope, and also in the plane of the scope. U~o~unately, as the fiicker rate of the test grating was increased from &Hz, there was aLo a change in the apparent structure of the grating. Between 7 and 12 Hz, the waveform appeared to be so altered that the original sine-wave pattern now seemed to approach a flickering square-wave, and judgements of spatial frequency became difficult. In this region, indicated by the arrow in Fig. 1, the variance was quite high, and partly because of this high variance, there were no significant differences between observers and fixation conditions. For simplicity, therefore, the results of all the matches were averaged and then normalized to 1 c/deg at the lowest modulation rate. Fig. I thus crudely characterizes the increase in apparent spatial frequency as counterphase flicker is increased. Presumably the inverse of this curve is related to the attenuation characteristics of Kelly’s temporal integrator shown in Fig. 2. The relation between apparent spatial frequency and flicker rate given in Fig. 1 requires that four test frequencies be examined following disparity adaptation to spatial frequency doubling: first, the fundamental seen at 20 Hz (adaptation condition, showing largest effect expected); second, the fundamental (Q c/deg) seen at 2 Hz; third, 1.7 times the fundamental at 2 Hz (corresponding to the apparent spatial frequency of the fundamental seen at 20 H@ and; fourth, the second harmonic at 2 Hz. For six observers, the disparity-specific adaptation effect was measured at each of those four conditions. 5 This factor of 1.7was chosen in advance for all observers before the average of 1.6 was obtained. We felt any slight departure from the observer’s own match to apparent spatial frequency should be toward the second harmonic, rather than the fundamental.

WHITXAX RICHARDSand THOMAS3. FELTON

2134

RESULTS

Table 1 summarizes the main result for the six subjects. The first data column gives the disparity-s~cifi& elevations in contrast threshold when the test and adaptation conditions are identical, namely a 8 c/deg grating moduIated at 20 Hz and viewed by fixating 0.65” in front of the scope face. The mean disparity specific adaptation effect when the test and adaptation conditions are identical is therefore 2.1. This is the reduced value, with the non-disparity specitic adaptation effect divided out. (These non-specific threshold elevations are given in TabIe 2 and represent the rise in thresholds primarily attributable to monocular mechanisms.) TABLE 1. DISPARITY-SPECIFIC ADAPTATION

Flicker rate (Hz) Harmonic (re d c/deg)

i-7

2 2

Matched spatial frequency rati% 20-2 Hz

2.1 1.9

0.96 1.0

0.98 1.o

1.6 1.7

I.5 I8 2-2 t-8 2.0

1.2 0.94 I.02 i .5 1.1

0.88 1.15 1.04 I.3 i.1

I.5 1.7 I.7 I.5 I.6

20

2

_)

1

1

Subject $J*

1.8 I.1

TF MK WR’ RS Means

2.0 1.4 I.7 4.5 2.1

* Subject used in constructing

Fig. 1. TABLE 2. NOWSPEC~FICADAPTATZON

Flicker rate (Hz) Harmonic (re 9 c/deg)

20 1

2

1

2 l-7

7 2

2 3

Subject IB RD TF MK

2-3 1-6 i-6 2.5

1.4 i.3 2.4 2.05

2.1 1.1 i,9 1.7

1.3 I.1 l-8 1-6

(1.3) (1.3) * *

RS WR Means

0.97 1.7 1.9

1.4 1.0 1.6

1.4 I.2 16

1-2 1.3

1.4

(1Y2) (1.3)

+ Third harmonic not measured on these subjects.

In the second data column of Table 1 the test condition has the same grating frequency as the adaptation condition, but it is modulated at a reduced flicker rate of 2 Hz and hence does not appear doubled. We find, nevertheless, that the disparity-specific adaptation is essentially identical, on the average, to the frequency doubled pattern (compare first two data columns). This result suggests that the disparity mechanism has adapted to the fundamentaf grating frequency, and not to the apparent second harmonic?. This conclusion is reinforced in the third and fourth data columns, which show no disparity adaptation for 6 Note once again that even if a second harmonic component were present as an artifact in our display, this result shows that the visual system failed to respond to this higher frequency component.

Spatial

Frequency Doubling

2135

either the second harmonic or for the spatial frequency at 2 Hz, which matches the apparently doubled fundamental at 20 Hz. Thus, because the disparity mechanism ignored the second harmonic component, we must conclude either (1) spatial frequency doubling occurs after the adaptation of disparity mechanism, or (2) is independent of the disparity adaptation effect. This conclusion may also be reached by a less formal, subjective observation: During adaptation to the fundamental modulated in counterphase at 20 Hz the pattern is seen as doubled, but yet the location of the pattern does not coincide with the plane of fixation. Consider that when the subject fixates 0.65” in front of the scope, then the bars are binocularly 180” out-of-phase in one eye as compared with the other. Thus, at any instant in time, the dark bars in one eye lie at retinal positions corresponding to the light bars in the opposite eye. If now the stimulus frequency is doubled, the gratings would then be in exact register in each eye and hence the grating would appear to be in the plane of fixation regardless whether fixation was on or O-65”in front of the scope screen. The fact that the illusory frequency doubled pattern does not lie in the plane of fixation shows that the disparity mechanism was not responding to the doubled frequency component. Instead, the magnitude of the displacement of the grating in depth from the fixation point suggests that the fundamental frequency provided the principal stimulus for the disparity mechanism. DISCUSSION Even though the most straightforward explanation of disparity adaptation to the fundamental and not to the apparent second harmonic is that spatial frequency doubling occurs after disparity processing, there is an alternate possibility. Consider the case where the disparity mechanism itself is a low-pass spatial and temporal filter. Then it is possible that when presented with a high spatial frequency above threshold, only a sub-harmonic component will be passed by the filter. Even though the non-linearities presumed by such an alternative seem implausible, this possible explanation for our result may be excluded by determining whether disparity specific adaptation is present at spatial frequencies above Q c/deg. Unfortunately, as the spatial frequency is increased, both the disparity specific adaptation and also the frequency-doubling effect have been shown to decrease (KELLY, 1966; FELTON ef al. 1972). Yet in spite of this reduction, we still obtained a disparity specific adaptation effect of 1.2 on two observers following adaptation to a $ c/deg pattern (3rd harmonic of original spatial frequency) modulated at 20 and 2 Hz. Furthermore, under the same adaptation conditions, there was no disparity-specific adaptation effect at the original fundamental of 8 c/deg (average of 0.97 for the two observers). Hence we may conclude that the disparity mechanism is capable of being adapted to a real stimulus corresponding to the second harmonic of Table 1 (See also FELTON,1972). The reason the disparity mechanism did not adapt to the apparent doubled frequency is that the doubling occurred after or independent of disparity processing. Our result suggests that spatial frequency doubling should also follow sites of adaptation effects that precede disparity encoding. One such phenomenon may be the original grating adaptation effect reported by BLAKEMORE and CAMPBELL(1969). Following exposure to a high contrast grating, the threshold for gratings of the same or neighboring frequencies are elevated. Only half of this adaptation effect will transfer from one eye to the other, so a significant portion of this effect precedes or is independent of binocular interaction. Our non-disparity specific adaptation component probably corresponds to this non-binocular component (FELTONet al., 1972). The values for non-specific adaptation obtained in the

WH~~SSAN RICKAR~Sand THOMASB. FELTON

2136 present experiment to the apparent

are shown in Table 2. Even though one observer

spatial frequency

(data column

ential effect of spatiai frequency. the thresholds

Following

slight decrease

as the test frequency

spatial half-width

of the adaptation

BLAKEMORE and CAMPBELL (1969) firm conclusion or precedes

adaptation

regarding

increases.

This decrease,

effect that is considerably at higher adapting

provide

and spatial

c/deg do not exhibit

however,

grating

a stronger

frequencies.

Thus,

specific adaptation

frequency

doubling.

pronounced

results,

test of the relation

spatial

But spatial frequency

TR our study using disparity-specific

frequency

generating

and disparity

yielding

the best spatial frequency

disparity-specific

adaptation

frequency

doubling

temporal

integrator

a grating

between

be a component

a by

we can reach no is independent

of

doubling

doubling.

greater

(KELLY,

the temporal

also may peak near the appropriate these correlations,

by Kelly to account

of the disparity

mechanism

effect flicker

grating

than

1966).

1 or 2

The

most

grating adapta-

we are fortunate

adaptation

Furthermore,

of higher spatial

non-disparity

frequencies

adaptation,

the greatest

(FELTON, 1972). Considering proposed

would suggest

broader than that reported

effective display is one near 0.5 cfdeg, which does not yield a sharply-tuned tion-effect.

pattern,

with a possible

doubting.

to the BLAKEMORE and CAMPBELL (1969)

should

to the frequen~y~oubled

are roughly equafly elevated,

whether or not non-disparity

spatial frequency

According frequency

adaptation

for all higher spatial frequencies

(IB) shows adaptation

31, on the average there is no clear differ-

in that the

is close

to that

response

of the

rates for spatial

we wonder whether the

for spatial frequency

doubling

might not

itself.

REFERENCES BLAKEMORE, C. and CAMPBELL, F. W. (1969). On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images. 1. Physiol., Land. 203.237-260. BLAKEMORE, C. and HAGUE,B. (1972). Evidence fordisparitydet~tin& neurones in the human visual system. f. Physioi,, Lmd. t25,437-455. BROW, J. L. (1965). Flicker and intermittent stimulation. pp. 251-320 (esp. p. 301). In: ViXon and V&af Perception (edited by C. H. GRAHAM)Wiley, New York. CORNSWEET, T. (1970). Visual Perception, p. 249, Academic Press, New York. FELTON,T. B. (1972). Temporal characteristics of a disparity-specific adaptation phenomenon. J. opt. Sot. Am. 62,7 15A-716A. FELTON,T. B., RICHARDS,W. and S;C~~TH, R. A. (1972). Disparity processing of spatial frequencies in man. J. Phydoi. 225, 349-362. KFALY,D. H. (1966). Frequency doubling in visual response. f. opr. Sot. Am. 56, 1628-1633. LEVINS&, J. 2: (1968). Flicker fusion phenomena. Science, N. Y. 160,21-28. MARIMONT, R. B. (1967). Frequency doubling. 1. opt. S’oc. Am. 57,968-969. MARIMONT, R. B. (1962). Model for visual response to contrast. J. opt. Sot. Am. 52,800-806. Abstract-When a wide field is sinusoidally modulated both in space and in time, the spatial frequency of the pattern wit1 appear doubled at high rates of modulation. KELLY (1966) proposes that this illusion is due to temporal integration of the nonlinear brightness response of the visual system. The anatomical locus of this temporal integrator is uncertain, however, and could be subcortical. Our results show that spatial frequency doubling follows binocular disparity detection and is thus a cortical phenomenon.

R&u&--Quand on module sinusoi~ement un grand champ a la fois en espace et en temps, la f&quence spatiale du test sembk doubi&e aux taux elev& de modulation. KELLY (1966) explique cette illusion par l’inttgration temporelle de ia r6ponse non Iin&aire du systeme visuel ii la luminositd. Le lieu anatomiquc de cette integration temporelle est cepeadant incertain et pourrait &e subcortical. Nos r&hats montrent que le doublage spatial de fr6quence suit la detection de la disparite binoculaire et est done un phenombne cortical.

2137

Spatial Frequency Doubling

Z~aasuag-Wiid

ein grosses Feld sinosfdrmig sowohl Crtlich als such zeitlich moduliert, so erscheint die Ortsfrequenz des Musters bei hohen Modulationsraten verdoppelt. KELLY (1966) schfug vat, dii Tauschung auf eine zeitliche Integration der nichtlinearen Helligkeitssantwort des visuellen Systems ~r~c~u~~en. Die anatomi~he~kalisierung dieseszeitiichen integrators ist unsicher, sie kannte subkortikal sein. Unsere Resultate zeigen. dass die Orts-

frequenzverdoppelung der Erkennung kortikales Phrinomen ist.

der

binokularen

Disparitat

folgt

und deshalb ein

Pe3ro~+Eum boJIbU!Oe none R3MeHReTCR B IIpOCTpaHCTBe R BpeMeHH no ~pH~~ny CiwyCOmbI, TO XpOCTpaHcTBeHHiur 5aCToTa Si306~xeHHR I(ilXeTC)I y2lr?OWIHO~, llpE BbiCoKSiX c~opocrrx ~onyn8uwH. KELLY (1966) npennonaraeT, 4T0 na wInI 303HmaeT B pe3ynbraTe speMeHHok smTerpamiH HeniiHegHofi ceernoTHoft peaKIwi 3pmenbwoU cwreMbl. OnHaKo noKa~~inaLwff YroroBpeMeHsoroHHTerpaToparortroHeycraHoanenanMorna6bI6bIKb Cy6KOpTHKWlbHOii. HaruH HCCJIeJlOBaHHIIllOKa3blBalOT, YTO ny6nHpoaaHHe IlpOCTpaHCTBeHHoiR YaffoTbI UreayeT 3a 06HapyncewiieM 6nHoKynxpnoR niicnapaTnoCM 39,TaIUiMo6pa30u, XBJI%?TCR KOpKOWlM@HOMeHOM.

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