compared to electrophysiological studies on X (sustained) and Y (transient) flickering stimuli (lines and gratings) on the contrast threshold

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1 J. Phyeiol. (1975), 249, pp With 9 text-ftgure8 Printed in Great Britain PATTERN AND FLICKER DETECTION ANALYSED BY SUBTHRESHOLD SUMMATION By P. E. KING-SMITH AND J. J. KULIKOWSKI From the Ophthalmic Optics Department, U.MI.LS.T., P.O. Box 88, Manchester M60 1QD (Received 18 November 1974) SUMMARY 1. We confirm Keesey's (1972) observation that, when a flickering line is viewed, there are distinct thresholds for detecting flicker (or movement) and for detecting a well localized line (pattern detection). Our measurements ofthe temporal sensitivity of these two mechanisms are similar to Keesey's. 2. The flicker and pattern detection mechanisms have been analysed using subthreshold summation, i.e. by observing the effect of subthreshold flickering stimuli (lines and gratings) on the contrast threshold for a flickering test line. 3. The pattern detector shows linear spatial summation of contrast while the flicker detector is non-linear in this respect. 4. The receptive field of the (most sensitive) flicker detector is about two to four times broader than that of the pattern detector. 5. The flicker detector has relatively weak surround inhibition and so, unlike the pattern detector, it is sensitive to a uniform flickering field. 6. The spatial arrangement of the pattern detector is the same at all temporal frequencies (including steady presentation); for flicker detection, the width of the receptive field increases with temporal frequency and the strength of lateral inhibition decreases at high frequencies. 7. Flicker detectors of various widths were demonstrated by using different test stimuli (for 12 Hz modulation); surround inhibition was relatively weak for the broadest detector. 8. There is a delay of surround inhibition of about 3 ms for both flicker and pattern detection. 9. By using a broad test stimulus modulated at a high frequency, a detector can be found with no significant surround inhibition. At threshold, this stimulus produces a sensation of flicker without the appearance of lateral motion observed for finer test lines at lower frequencies. 10. The characteristics of pattern and flicker (movement) detection are compared to electrophysiological studies on X (sustained) and Y (transient)

2 520 P. E. KING-SMITH AND J. J. KULIKOWSKI neurones respectively, and correlations are described for studies of temporal frequency response, non-linearity, width of receptive field, strength of the inhibitory surround and motion sensitivity. INTRODUCTION An important underlying principle of visual processing is that separate and parallel visual mechanisms may be involved in the analysis of different aspects of a visual scene (e.g. size, orientation, colour and stereoscopic information). Recently there has been considerable interest in the idea of discrete mechanisms for the processing of pattern information on the one hand and movement and flicker information on the other. Van Nes, Koenderink, Nas & Bouman (1967) observed that there are two distinct contrast thresholds for a moving sinusoidal grating; the lower threshold generally corresponds to the perception of flicker or brightness changes in the visual field while the contrast must be increased before a grating as such can be perceived. This observation may be interpreted in terms of separate mechanisms for the analysis of the spatial and temporal aspects of the stimulus (Rashbass, 1968). Kulikowski (1971) described a phenomenon which is roughly the inverse of the observation of Van Nes et al. (1967), namely that high spatial frequency gratings, alternated in phase by 1800 (i.e. reversed in contrast) appear stationary at their contrast threshold and that their contrast must be increased above threshold before the temporal changes (movement) can be observed. Separate contrast sensitivity functions were derived for the detection of pattern and the detection of movement. Ikeda & Wright (1972b), from their findings on single cells in the retina, suggested that 'X' (Enroth-Cugell & Robson, 1966) or 'sustained' cells (Cleland, Dubin & Levick, 1971) subserve spatial discrimination (the basis of visual acuity), whereas 'Y' or 'transient' cells subserve temporal discrimination or movement analysis the basis for the visual fixation reflex. Similarly, Tolhurst (1973), on the basis of pattern adaptation experiments showing differential effects to stationary and moving gratings, proposed separate systems for the analysis of pattern and movement which he suggested might correspond respectively to the X and Y cells of Enroth-Cugell & Robson (1966). Kulikowski & Tolhurst (1973) analysed the visual sensitivity for flicker/movement detection and for pattern detection using temporally modulated sinusoidal gratings. The flicker detection system was found to be most sensitive for intermediate temporal frequencies (about 5 Hz) and relatively low spatial frequencies (about 1P5 c/deg). Conversely, the pattern detection system was most sensitive to intermediate spatial frequency (about 3.5 c/deg) and to very low or zero temporal

3 PATTERN AND FLICKER DETECTION 521 frequency, i.e. steady presentation (similar temporal properties of the two detection systems had earlier been reported by Keesey (1972); see below). The above results all refer to the detection of sinusoidal gratings. However, Keesey (1972) has shown a similar dichotomy in the detection of a flickering line stimulus; the luminance of a 4' wide vertical line was modulated about the mean luminance level of the surrounding field of 10 diameter. At the visual contrast threshold only a diffuse flickering sensation was generally observed sometimes occupying the whole stimulus field; a higher contrast was needed for the perception of a well localized flickering line, i.e. pattern perception. A significant observation was that similar thresholds were found for the two systems for normal and stabilized viewing conditions; thus the separate flicker and pattern thresholds were not an artifact of eye movements. The spatial properties of line detection may be analysed using the subthreshold summation technique developed by Fiorentini (1968) and Kulikowski (1969). Using this technique, the 'detector' for a steadily presented line has been investigated by observing how the contrast threshold for a 'test' line is affected by different subthreshold 'background' stimuli; if the background stimulus tends to excite the detector, the contrast threshold for the test stimulus will be lowered while an inhibitory background stimulus will raise the test threshold. In this way it may be shown, for example, that the line detector has a 'receptive field' having an excitatory centre 6' wide with inhibitory regions on either side and that its sensitivity to sinusoidal gratings peaks at 5 c/deg (Kulikowski & King-Smith, 1973). These results refer to properties of the pattern recognition system for a steady line; here we apply the subthreshold summation technique to tackle a number of questions related to the detection of a flickering line. For example, do the spatial arrangements of the flicker and pattern detectors differ and do they vary with the temporal frequency of modulation? Does the flicker detection system respond to a linear summation of the contrasts of component stimuli as is found for the pattern system (Kulikowski & King-Smith, 1973)? Is there a delay in the signal from the inhibitory surrounds of the receptive field? Can detectors be found with no inhibitory surround? We have been particularly concerned to provide data which may be compared with electrophysiological studies on the X and Y cells discovered by Enroth-Cugell & Robson (1966). METHODS The experimental arrangement was similar to that used by Kulikowski & King- Smith (1973). Patterns were generated on a Solartron CD 1400 oscilloscope using a television technique based on that of Schade (1956) and Campbell & Green (1965). The lines and gratings used were all vertical. In most experiments the circular

4 522 P. E. KING-SMITH AND J. J. KULIKOWSKI display region was viewed from 114 cm and subtended 2.50, surrounded by a uniform 6 square screen with approximately the same luminance (5 cd/m2) and colour. In the experiment of Fig. 8 the screen was viewed from 76 cm and subtended in a 90 square surround. The results reported here refer to subject J.J.K. (38 yr, corrected myope); binocular foveal viewing with natural pupils was used throughout. Test and background stimuli In most experiments the subject used a potentiometer to adjust the contrast of a test stimulus to threshold in the presence of a subthreshold background stimulus. The luminance of both test and background stimuli were modulated about the mean luminance of the screen by using electronic multipliers. In a typical series of measurements, a PDP-12 computer was used to set the background contrast and phase at random to one out of a number of prespecified values; each test contrast threshold was recorded by the computer using a ganged potentiometer and analogue to digital converter. A typical series consisted of five or ten threshold determinations for each of three to seven subthreshold background levels; at the end of each series the computer printed means and standard errors of test contrast threshold for each background level. Plotted points often correspond to weighted means derived from two or more series. Contrast In this paper we have defined the contrast of an unmodulated display by C = (L'a-L )ILO where Lpk is the peak luminance and Lo is the average luminance of the stimulus (see Fig. 2 a). Thus at the position of the peak, the luminance is modulated according to L = Lo (1 +C cos 2nrft), where f is the modulation frequency and t is time. It should be noted that this definition of contrast is that used by Keesey (1972), but, in the case of a line stimulus, contrast is twice that defined by Kulikowski & King-Smith (1973); for a grating (or edge) the present definition is equivalent to that used previously. RESULTS Temporal sensitivity offlicker and pattern detectors Our subjective impression of the flickering line stimulus at different contrast levels was similar to that described by Keesey (1972) with some differences in detail. For frequencies of 3 Hz and above, the detection threshold for the vertical flickering line corresponded to a poorly localized sensation of lateral movement; we will call this the movement of flicker detection threshold. The contrast had to be increased above this level before a sharply located stimulus could be observed, i.e. the pattern detection threshold was reached. At this point the sensation of diffuse movement was abolished and flicker appeared to be narrowly contained between two bright borders; these bright borders may correspond to the bright bars seen at the nodes of a standing wave pattern in the phenomenon of spatial frequency doubling (Kelly, 1966).

5 PATTERN AND FLICKER DETECTION 523 The contrast sensitivities (reciprocals of contrast thresholds) for flicker detection and pattern detection are represented in Fig. 1 as a function of modulation frequency. As reported by Keesey (1972) the sensitivity for pattern detection falls monotonically as a function of frequency while flicker detection has a peak sensitivity at about 5 Hz. In contrast to Keesey's results, a diffuse flickering sensation was not observed at 1 Hz so a flicker threshold could not be measured at this frequency. Kulikowski & King-Smith (1973) have shown that all lines less than 3' wide are detected by the same mechanism; it thus seems likely that the 1 2' test line used in Fig. 1 is a 'fine line' in this respect C 0.- U~~~~~~~ Temporal frequency (Hz) Fig. 1. Temporal frequency response of the flicker (motion) and pattern detection systems. The subject viewed a 1-2' wide line whose luminance was modulated sinusoidally about the mean luminance ofthe screen as in Fig. 2a; he adjusted the contrast of the line to its threshold either for seeing flicker (or lateral motion - circles) or for seeing a sharply-localized line (squares). Contrast sensitivity (reciprocal of contrast threshold) is plotted as a function of modulation frequency. One may ask how arbitrary is the pattern detection threshold when it is greater than the flicker threshold (for modulation frequencies of 3 Hz or more, Fig. 1). Some support for the validity of the pattern threshold in these conditions is provided by the accuracy of setting which may be obtained (a standard deviation of individual contrast thresholds of about 12 %, corresponding to a standard error of about 5 % for a mean of five settings; this is comparable to the accuracy obtained with steady presentation). A further check for the validity of pattern thresholds comes from Kulikowski & Tolhurst's (1973) demonstration that pattern thresholds depend only on stimulus contrast and not on the change in contrast during presentation. In correspondence with this we found that the pattern threshold for a line modulated in the normal manner (Fig. 2a) is equal to the pattern threshold when the line and the surrounding screen are modulated in antiphase about the 'middle luminance' (LO+ Lpk)/2 (see Fig. 2b).

6 524 P. E. KING-SMITH AND J. J. KULIKOWSKI Non-linearity in flicker detection It has been shown that the detection of a steady line may be considered to involve an initial linear stage in which signals from low contrast patterns in the vicinity of the line are added to the signal from the line. The evidence for this suggestion is that the contrast threshold for a test line varies linearly with the contrast of a subthreshold background pattern in its vicinity (Kulikowski & King-Smith, 1973) as would be expected if there is a linear response to test and background contrasts. It is supposed that the combined pattern is at threshold when the total response of this linear stage reaches a threshold value. A a b, Lpk 'E ] I. """A """ ;;} (LO+Lpk)12 Distance across screen Fig. 2. Two modes of stimulus modulation which yield similar thresholds for pattern vision. a, the luminance of the test line, Lpk, is modulated about the surrounding luminance, Lo. Continuous and dotted lines correspond to the maximum and minimum luminance of the test line during the modulation cycle. b, the luminance of the test line is modulated in antiphase to the luminance of the surround, i.e. both test line and surround are modulated about (Lo + Lpk)12 represented by the dashed line. Can a similar linearity be demonstrated for the detection of a flickering line? Fig. 3a shows how the pattern contrast threshold for a test line flickering at 1 Hz varies with the contrast of a subthreshold background of two lines spaced 6' on either side (also flickering at 1 Hz). The luminance of all three lines was modulated about the mean screen luminance. The width of test and background lines was 1-2' and the screen diameter Positive and negative background contrasts correspond respectively to in phase and out of phase background flicker; T and B represent corresponding luminance profiles for the test and background stimuli. It is seen that a linear relation is a good fit to the data. Corresponding data for the detection offlicker are represented in Fig. 3b to d. It is seen that the relation between test and background contrasts is curved downwards irrespective of whether the background lines have a generally excitatory effect (i.e. in phase background lines make the test

7 PATTERN AND FLICKER DETECTION 525 line easier to see, Fig. 3b) or an inhibitory effect (Fig. 3c); the corresponding spacings between test and background lines were 6' (Fig. 3b), and 18' (Fig. 3c) and the modulation frequency was 16 Hz. A similar curved relation between test and background contrasts was also found when the background lines were modulated 900 out of phase with the test line (Fig. 3d, 6' spacing, 16 Hz). In all cases, the data for flicker detection (Fig. 3b to d) can be well fitted by parabolae (continuous curves). 1-5 a b c d -0.5 o OS Background contrast Fig. 3. The relation between test contrast threshold and background contrast for pattern and flicker detection. In each case the I -2' test line was flanked by two 1-2' background lines (luminance profiles represented by T and B. inset to Fig. 3a). Test and background contrasts are expressed as fractions of the contrast threshold for the test stimulus on its own. The continuous curves correspond to the best-fitting parabolas. Vertical bars in this and subsequent Figures correspond to ± 2 s.e. of the mean. The stimulus parameters were: a, pattern detection, I Hz modulation, 6' spacing between test and background lines, background phase. b flicker. detection, 16 Hz, 6', c, flicker detection, 16 Hz, 18', 0-180'. d, flicker detection, 16 Hz, 6', The curvature of the relation between test contrast threshold and background contrast is considered further in Fig. 9 where a normalized index of curvature (see Discussion, eqn. (7)) is plotted as a function of the spacing between test and background fines. Fig. 9a and b refer to pattern detection while Fig. 9c and d refer to flicker detection; Fig.- 9a and c correspond to in-phase backgrounds while Fig. 9b and d correspond to a 90 phase angle between test and background modulation. Positive values of the ordinate correspond to downward curvature of the contrast interrelation, as in Fig. 3b to d. The results indicate that, for flicker detection, there is significant downwards curvature in the contrast interrelation at spacings of up to about 20', both for in phase and 900 phase modulation of the background lines. Of the forty-two measurements of curvature for flicker detection, thirty-nine have downward curvature compared with eight out of eighteen for the pattern detection task. The origin of this curvature will be considered in the Discussion section.

8 526 P. E. KING-SMITH AND J. J. KULIKOWSKI For the present, it may be noted that, for flicker detection, the effect of the background may be separated into a linear component (i.e. general excitation or inhibition proportional to background contrast) and a quadratic component (effect proportional to the square of background contrast). Only the linear component is significant for pattern detection and its slope has been used to express the sensitivity of the detector to the particular background configuration (Kulikowski & King-Smith, 1973); this measure of sensitivity may be justified by its predictive power, e.g. the sensitivity to background lines could be derived, by linear analysis, from the sensitivity to sinusoidal gratings. For flicker detection, the sensitivity of the detector for the background lines may similarly be defined in terms of the linear component of the background effect; however, in view of the non-linearity observed in Fig. 3, it is necessary to check whether linear analysis may still be used to predict sensitivity to new background stimuli and this point will be considered later in the next section. The spatial arrangement of pattern and flicker detection for a flickering line In accordance with the above discussion, the sensitivity of a detector for a background stimulus will be defined to be proportional to the negative slope of the contrast interrelation plots (Fig. 3) at zero background contrast. Because the contrast interrelation is well fitted by either a straight line (Fig. 3a) or a parabola (Fig. 3b to d), this slope will be the same as the slope of the chord joining points of equal and opposite background contrast (e.g. dashed line, Fig. 3b). Thus the required negative slope is given by C_- 2C C+ B(1) where C+ and C_ are the test contrast thresholds for background contrasts +CB and -CB respectively; this slope is a measure of the relative sensitivity to the background compared to the test stimulus. The absolute sensitivity of the detector to the background may then be determined by multiplying by the contrast sensitivity to the test stimulus, i.e. 1/Co where Co is the contrast threshold for the test stimulus alone; thus C_-C 2B- CO BeC! (2) When the background contains two lines, equally spaced on either side of the test line (Fig. 3), the sensitivity to one background line is derived by halving the above expression; finally the sensitivity may be made independent of line width by dividing by the width of the background lines. The sensitivity to a background line for a test line modulated at 12 Hz is shown in Fig. 4a; circles correspond to flicker detection and squares to

9 PATTERN AND FLICKER DETECTION 527 pattern detection. Four significant points may be made about these 'line sensitivity' functions. 1. The points for zero background distance correspond simply to physical addition of equivalent test and background stimuli and thus represent the sensitivity to the test stimulus alone. The greater sensitivity for flicker detection thus corresponds to the contrast sensitivity data of Fig. 1 at 12 Hz. ~~ u * * u * * ~~~~~~40 4 a Iilb ~~~~~~~~~~~~~~0 B~~~~~~~~~~~~~~~~~~~~~~~~~~3 I 5AL~~~~~~Us I 0 0~~ Fi.) 4.Sail4.'mn 10 f 0h 1020lce n 0 atr dtcosfrafikr 5 ~~~~~~10-1 J L.T 0 ~~~~~B _J I.1k Ia t I -L Distance from centre (min) Spatial frequency (c/deg) Fig. 4. Spatial arangement of the flicker and pattern detectors for a flicker. ing line. The sensitivity of the detectors to different stimuli (lines and gratings) was determined by subthreshold summation, i.e. the effect of subthreshold background stimuli on the contrast threshold for a flickering 1-2' test line (see text). T and B represent luminance profiles of test and background stimuli which were modulated about the mean luminance at 12 Hz. a, line contrast sensitivity for flicker detection (@, dashed curve) and pattern detection (-, continuous curve). The width of the background lines was 1-2' b, grating contrast sensitivity for flicker detection (0) and pattern detection (EO). The dashed and continuous curves have been derived from the corresponding curves in (a) using Fourier analysis. 2. The line sensitivity function for pattern detection (squares) is similar in form to that for the detection of a steady line (Kulikowski & King-Smith, 1973). Thus, in both cases, the half width of the central excitatory region is about 3' and peak inhibition occurs at 5-6' and corresponds to % of peak excitation. It is tempting to speculate that the same mechanism is involved in both cases. '

10 528528P. E. KING-SMITH AND J. J. KULIKOWSKI 3. The width of the curve for flicker detection is considerably broader than that for pattern detection, the half width of the central region being 7-5' and peak antagonism occurring at 12' from the test line. 4. The antagonistic surround for flicker detection is relatively weak; peak inhibition is only about 15 % of peak excitation. By using flickering sinusoidal gratings as subthreshold backgrounds, the 'grating sensitivity' of the line detectors may be determined as a function of spatial frequency (Fig. 4b); circles and crosses, as before, refer to flicker and pattern detection respectively. Again, four corresponding points can be made. 1. The flicker detection system is generally more sensitive than the pattern detection system at 12 Hz, except at high spatial frequencies. 2. The grating sensitivity for pattern detection is similar to that found for detection of a steady line (Kulikowski & King-Smith, 1973); thus, in both cases, peak sensitivity is near 5 cfdeg and falls rapidly towards zero and 10 c/deg. 3. In contrast, the flicker detector is relatively more sensitive at low spatial frequencies, peaking at about 1.5 c/deg. This is consistent with the broader receptive field shown in Fig. 4a. 4. The flicker detector, unlike the pattern detector, is sensitive to zero spatial frequency, i.e. to a uniform flickering screen. This presumably reflects the relatively weak surround inhibition for flicker detection (Fig. 4a); thus the central excitatory response to the uniform flicker is stronger than the antagonistic surround response. For pattern detection, however, excitation and inhibition due to a uniform flickering screen are equal and opposite, yielding no net effect. We must now consider the value of these sensitivity determinations as a general description of the spatial properties, particularly of the flicker detection mechanism where a non-linear interaction between test and background stimuli occurs (Fig. 3b-d). Can the line sensitivity data of Fig. 4a be used to predict the sensitivity to other background patterns using a simple linear analysis? We have checked this by applying the Fourier transform technique of Kulikowski & King-Smith (1973, Appendix 1) to the line sensitivity data of Fig. 4a, to predict the corresponding grating sensitivity data of Fig. 4b; thus, for flicker detection, the dashed curve in Fig. 4b has been derived from the dashed curve in Fig. 4a while the continuous curves correspond to pattern detection (this procedure is, in fact, the reverse of that used by Kulikowski & King-Smith (1973) where grating sensitivity data were used to predict line sensitivities). Neither curve in Fig. 4b has been scaled on either axis and both curves are seen to be in good agreement with the experimental data; we may therefore conclude that the sensitivity data for both flicker and pattern

11 PA14TTERN AND FLICKER DETECTION detection have a general validity in that they may be used to predict the sensitivity to other subthreshold background patterns using linear analysis. Th~e spatial arrangement of th~e line detectors at different temporal frequencies. In this section, we study how varying the temporal frequency of modulation of test and background lines affects the spatial arrangement of excitation and inhibition for pattern and flicker detection. The general a + apattern Flicker +1 b.5 ~~~~~~~12 ~16 4J ~ ~ ~~~v24 U - 0 -~A -0.5 o Distance from centre (min) Fig. 5. The effect of modulation frequency on the spatial arrangement of pattern and flicker detectors. Test and background lines were 1-2' wide in all cases except for the test line used at 24 Hz which was 5' wide. Modulation frequencies were: + steady presentation, U 1 Hz, * 3 Hz, A 5 Hz, fl1 8 Hz, 0 12 Hz, A 16 Hz,K>24Hz. a, relative line contrast sensitivity for pattern detection. The continuous curve has been fitted to the data for steady presentation while the dashed curve has been fitted to all the data for modulation (see text). b, relative line contrast sensitivity for flicker detection. Five curves have been fitted to the results for different frequencies as described in the text. variation in sensitivity to a flickering test line has already been described (Fig. 1) so, for ease of comparison of results at different frequencies, the results will be expressed in terms of relative sensitivity, i.e. with peak sensitivity scaled to unity for each frequency. Fig. 5a represents line sensitivity data for pattern detection, plotted in this way, for temporal frequencies from 1 to 12 Hz. In addition, crosses correspond to the results for steady presentation of test and background lines from Kulikowski & King-Smith (1973). As already noted, the spatial 20 PHY 249

12 530530P. B. KING-SMITH AND J. J. KULIKOSWKI arrangement is seen to be very similar for detection of a steady line and for pattern detection of a flickering line; alteration of the temporal frequency of modulation causes no systematic change in the spatial arrangement of the pattern detection mechanism. These observations may be further illustrated by fitting the data of Fig. 5a by expressions of the form S = (1 + a) e X212b2 -a e7x122c2, (3) where S corresponds to sensitivity at distance x, and the parameters a, b and c are adjusted to provide the best fit to the data using a least-squares method (it should be noted that eqn. (3) was used merely because it provided a good fit to the data; its use does not imply that the underlying neural sub-units responsible for the detection process may also be described in these terms; indeed, probability summation between sub-units may cause a significant difference between the spatial arrangement of the sub-units and the over-all detection mechanism; King-Smith & Kulikowski, 1975). The continuous line in Fig. 5a is the best fit to the data for steady presentation (crosses); the dashed curve is the corresponding best fit for pattern detection obtained by pooling the results for all temporal frequencies (1-12 Hz). Again, close agreement is found between the detection of a steady line and the pattern detection of a flickering line; in both cases, peak inhibition is between 30 and 35 % of excitation. Corresponding data for flicker detection are represented in Fig. 5b. Best-fitting curves (eqn. (3)) are shown for 3, 8, 12, 16 and 24 Hz. The most striking observation is that the curves become systematically broader with increasing temporal frequency. Thus, the crossover between excitation and inhibition occurs at distances from the centre of 5', 6',) 7-5' 8' and 12' for modulation frequencies of 3 Hz, 8 Hz, 12 Hz, 16 Hz and 24 Hz respectively. This correlation between spatial extent and temporal frequency is in contrast to the independence of the effect of temporal frequency seen in Fig. 5a. Peak inhibition at 8, 12 and 16 Hz is seen to be about 15 % of peak excitation. At 3 Hz, peak inhibition seems rather less (10 %) but the significance of this reduction is uncertain as it is based on rather few observations. The reduction in peak inhibition to 6 % at 24 Hz is more likely to be significant; further evidence that inhibition is reduced at high temporal frequencies will be considered later. Broad and narrow mechanisms for flicker detection Up to this point, the mechanisms which respond at threshold to a narrow (1.2') flickering line have been studied. It should be emphasized that any of these detection mechanisms may be just one of a continuous spectrum of detectors of different widths. Kulikowski & King-Smith (1973)

13 PATTERN AND FLICKER DETECTION 531 demonstrated, for steady viewing conditions, detectors which were both narrower and broader than the detector for a fine line; it seems probable that a similar range of detectors would be found for the pattern detection of flickering lines, in view of the similarity of the two processes (Fig. 5a).._ 0._._ C0 Wc 0 0 C E X i Distance from centre (min) Fig. 6. Broad and narrow flicker detectors. The line contrast sensitivities were determined by subthreshold summation for a modulation frequency of 12 Hz; the insets indicate the luminance profiles of the test stimuli used. The upper inset corresponded to the 12' test line used in Figs. 4 and 5; the next stimulus corresponded to 1 cycle of a cosine grating of 45' period. The next two stimuli consisted of a 1*2' line superimposed on a 10' bar of opposite phase; in the upper of these two insets, the 10' bar had half the effective strength (width x luminance step) of the 1-2' line, while in the lower inset the 10' bar was equal to the 1X2' line in this respect. The curves have been fitted to the points as described in the text. Fig. 6 illustrates that a similar range of detectors may be observed for the detection of flicker in localized stimuli flickered at 12 Hz. The luminance profiles of the 4 test stimuli used are illustrated in the insets (1 2' background lines were used in every case); the open circles and continuous line represent the results already described for a narrow test line (Figs. 4a and 5b). The results are expressed in terms of absolute sensitivity to the background lines (eqn. (2)); the curves drawn through the points are the best-fitting difference of two Gaussian curves (cf. eqn. (3), but because the results are expressed here in terms of absolute sensitivity, the curves have 20-2

14 532532P. E. KING-SMITH AND J. J. KULIKOWSKI not, of course, been constrained to a maximum sensitivity of unity as in the relative sensitivity plots of Fig. 5). Three points may be noted about Fig The detector for the fine line (circles, continuous curve) has the highest sensitivity to a central line (as is to be expected, otherwise one of the other detectors would respond to a fine line at threshold). However, rather broader and narrower detectors have nearly as much sensitivity. 2. The narrowest detector studied (filled triangles, dotted line) has its crossover point between excitation and inhibition at about 3' from the centre and in this respect is similar to the pattern detector for a 12 Hz flickering line (Fig. 4a). However, the two detectors are quite distinct in that the peak sensitivity of the detector in Fig. 6 is about twice as much while its peak inhibition is relatively weak (about 20% of peak excitation compared with over 30 % for the pattern detection system). 3. There is some evidence that the relative strength of inhibition decreases with increasing width; peak inhibition falls from 20 % of peak excitation for the narrowest unit to about 12 % for the broadest unit. This observation may be related to the concurrent broadening of receptive fields and reduction of inhibition illustrated in Fig. 5b for flicker detection of a fine line. The latency of 'surround inhibition' The effect of a flickering background on the threshold for a flickering test stimulus depends on the relative temporal phase of the two stimuli. The results considered so far correspond to in phase (00 phase) and out of phase (1800 phase lead) background modulation. We might expect that, if there is a phase lead of a'0 in the response to the background (relative to the test stimulus), then the background modulation will have maximum effect when its phase is a'0 behind the test modulation (thus compensating for the phase lead). In practice, however, it is difficult to estimate a in this way, first because a number of background phases must be used and secondly because the position of a maximum in a curve is inherently difficult to determine accurately. In practice, we can take advantage of the observation that, as shown by the application of Fourier theory in Fig. 4b, it is possible to apply simple linear theory to sensitivities defined by eqn. (2). This implies that the sensitivity should be a sinusoidal function of background phase; if the background modulation is qs0 in advance of the test modulation, the background response will be (S ±+x)' in advance of the test response and the corresponding sensitivity will thus be 8(tb) = Smnax Cos (qs+cc)p

15 PATTERN AND FLICKER DETECTION 533 where Smax is the maximum sensitivity corresponding to a background phase lag of a'~. Thus for in phase (0S = 00) background modulation 5(0) = SM. Cos ax (4) while for a 900 phase lead S(90) = max COS(90+ a) = Smax sin a. (5) Thus the required phase lead of the background response, ac, may be derived by dividing eqn. (5) by eqn. (4); hence ac = tan-,(-s(90)/s(0)). (6) 5(0) corresponds to the sensitivity obtained from eqn. (2) using in phase and out of phase background modulation; S(90) may be derived similarly but using 900 phase lead and 900 phase lag for the background stimulu's. o a 0~~~~~~~~~~~~~~~~~~~~ b ~e C -o ~~~~~~~~~~~~~~~~~ o Pattern Flicker Li -0 C (U 0~~~~~~~ Distance from centre (min) Fig. 7. The latency of surround inhibition. The phase lead of the response to a pair of flanking lines is plotted as a function of the spacing between test and background lines (see text). Modulation frequencies: R 8 Hz, 0 12 Hz, A 16 Hz. a, pattern detection; b, flicker detection. The corresponding latency of inhibition, for 12 Hz modulation, is shown on the right-hand scale. The phase lead of the background response, determined in this way, is shown in Fig. 7a' and b for the cases of pattern detection and flicker detection respectively. It may seem surprising that the results may be expressed as a phase lead ofthe background response which varies from small angles within the excitatory central region to about o in the inhibitory surround region. However, the results seem more reasonable when it is remembered that a phase lead of, say, 1600 is equivalent to an inhibitory mechanism with a phase lag of 200, or a latency of 20f360f sec wheref is the temporal frequency (cf. right-hand scale in Fig. 7). Surround latencies have been derived in this way for all background line spacings which are well within the inhibitory region (thus avoiding significant

16 534 P. E. KING-SMITH AND J. J. KULIKOWSKI response from the central mechanism to the background lines) and weighted means are given in Table 1. The results are consistent with a fixed latency of surround inhibition (relative to the centre) of about 2*7 ms in the case of flicker detection; the delay is perhaps slightly longer for pattern detection (about 38 ms). The phase lead of the background response within the excitatory central region (e.g. for flicker detection at 7-5' line spacing, 12 and 16 Hz, Fig. 7b) may be explained in terms of the summed response from a central excitatory mechanism and a weaker surround mechanism providing delayed TABLE 1. Latency of surround inhibition Surround Detection mechanism Frequency (Hz) Line spacing (min) latency (Ms) Flicker 8 9 to to ± to to ±+19 Weighted mean Pattern 12 6 to inhibition (the reader may verify this statement by drawing the corresponding sinusoidal wave forms of excitation and delayed inhibition and constructing their algebraic sum). These observations thus support the idea of separate and overlapping central and surround mechanisms; it is not possible to say whether the surround mechanism extends to the centre of the receptive field. The results would be consistent with a constant latency within the central mechanism and within the surround mechanism; all observed phase shifts would then be attributable to a fixed delay of the surround inhibitory mechanism relative to the central mechanism, as though an additional synapse existed in the antagonistic surround (Maffei & Fiorentini 1972; see Discussion). Pure flicker detectors The results of Fig. 6 indicate that relatively broad mechanisms for flicker detection may have relatively weak surround inhibition. The results of Fig. 5b indicate that inhibition also becomes weaker for high modulation frequencies; this weakening may correspond partly to an attenuation of the inhibitory signal (relative to the excitation) at high frequencies which could be related to the increased latency of inhibition discussed above; it may also be related to the broadening of the receptive field with increasing frequency (Fig. 5b) which in turn could lead to reduced inhibition (cf. Fig. 6 again).

17 PATTERN AND FLICKER DETECTION 535 Is it possible to isolate a detector with no significant surround inhibition by using a sufficiently broad test stimulus modulated at a high frequency? The line sensitivity measurements of Fig. 8a show that such detectors exist; the modulation frequency was 24 Hz and the test stimulus was a 'cosine bar' and had half-width of 45' (see inset). The continuous line in Fig. 8a corresponds to the best fitting Gaussian curve; little improvement to the fit could be obtained by assuming an additional inhibitory Gaussian term (as in eqn. (3)). Corresponding grating sensitivity data are shown in Fig. 8b. It should be noted that there is no significant decrease in sensitivity towards low spatial frequencies (cf. the large decrease seen in both curves 0.3 b i 4J 4V 0.1 to co b 0 Th.0 ~ 12 Spatial frequency (cldeg) Distance from centre (min) Fig. 8. Spatial arrangement of a flicker detector with no significant lateral inhibition. The test stimulus corresponded to 1 cycle of a cosine grating of period 90' (see inset) and the stimuli were modulated at 24 Hz. The viewing distance was reduced to 76 cm for this experiment so that the screen diameter was a, line contrast sensitivity. The width of the background lines was 1-8'. The curve is the best fitting Gausian function. b, grating contrast sensitivity. The curve has been derived from the curve in a by Fourier analysis. of Fig. 4b); as a decrease in sensitivity towards low spatial frequencies is associated with the effects of surround inhibition (e.g. Enroth-Cugell & Robson, 1966) this is further evidence for the absence of significant inhibition. The continuous curve in Fig. 8b has been derived from the curve in Fig. 8a by applying the Fourier method (Kulikowski & King-Smith, 1973); the data fit this curve within experimental error (but there may have been a small systematic increase in sensitivity for the data of Fig. 8b) again indicating that linear analysis may be applied to the sensitivity data. The appearance of this test stimulus near threshold corresponded to a pure flicker sensation with no indication of the lateral movement sensation

18 536 P. E. KING-SMITH AND J. J. KULIKOWSKI observed for finer test targets and lower frequencies. It may thus be necessary to distinguish between 'pure flicker' detectors (Fig. 8) which have no significant surround inhibition and 'motion detectors' (Figs. 5b and 6) having surround inhibition; this would be in accordance with the model proposed by Foster (1971). Kelly (1972) has shown that, for low spatial frequency gratings modulated at high temporal frequencies, the contrast threshold is inversely proportional to mean luminance (i.e. the threshold is constant in terms of luminance modulation). We have checked that the same law applies for the pure flicker detector of Fig. 8 (but not for motion detectors) indicating that this sort of detector may be responding in the conditions described by Kelly. Plots of contrast threshold for the test stimulus of Fig. 8 as a function of the contrast of the flanking background lines show non-linearity of the type observed in Fig. 3b, c and d, but this effect has not been studied in detail. DISCUSSION Non-linearity in flicker detection A basic difference between the pattern and flicker detection systems described above would seem to be the non-linear summation of the effects of test and background contrast found for flicker detection (Fig. 3b, c and d) which contrasts with the linearity found for pattern detection (Fig. 3a). This difference is further illustrated in Fig. 9 where the normalized 'curvature index' Q = C0. (2CO-C+- )f2c2 (7) is plotted as a function of the spacing of the two background lines from the test line (Co is the contrast threshold for the test stimulus alone, while C+ and C_ are the contrast thresholds for background contrasts +CB and -CB respectively). Fig. 9a and b refer to pattern detection, Fig. 9c and b to flicker detection; Fig. 9a and c correspond to 00 and 1800 phase of the background modulation, Fig. 9b and d to 900 and 2700 phase. There is evidently a strong tendency for the curvature index to be positive for flicker detection (Fig. 9c and d) but not for pattern detection (Fig. 9a and b). Does the non-linearity observed for flicker detection really indicate some basic non-linearity in the neural sub-units? To answer this, we must consider two other factors which contribute to the curvature of contrast interrelation plots. 1. Curvature may be due to the activation of different detectors for different levels of background contrast (see discussion of Fig. 1 c, Kulikowski & King-Smith, 1973). Using the data for different detectors in

19 PATTERN AND FLICKER DETECTION 537 Fig. 6, the contribution of this factor to the curvature has been estimated (see Appendix 1) and is represented by the continuous curve in Fig. 9 for the case of 12 Hz flicker with O0 and 1800 background phase. Even allowing for a considerable uncertainty in the height of this curve, it would seem that the activation of different detectors can be only a partial explanation of the curvatures plotted in Fig. 9c, particularly for background lines at 10-20' from the test line. The corresponding contribution of the activation of different detectors for the case of background phase (Fig. 9d) may be shown to be relatively insignificant. a I > ;b' d 1 LC _ papattern Flicker Distance from centre (min) Fig. 9. Non-linear spatial summation of contrast. The curvature index, derived from the curvature of the relation between test and background contrast (Fig. 3) is plotted as a function of the spacing of the background lines from the test line. Modulation frequencies: * 1 Hz, * 3 Hz, O 8 Hz, 0 12 Hz, A 16 Hz. a, pattern detection, background phase 0 and 180. b, pattern detection, background phase 90 and 270. The dashed line is the prediction for a linear system (see Appendix 2). c, flicker detection, background phase 0 and The continuous line is the prediction for a range of detectors (as in Fig. 6) assuming that each detector summates contrast linearly (see Appendix 1). d, flicker detection, background phase 90 and The dashed line is the prediction for a linear system (see Appendix 2). 2. Even a perfectly linear system will give rise to a non-linear contrast interrelation for the case of ' background phase (Fig. 3d, 9b and d). The origin of this purely physical effect is discussed in Appendix 2 and its magnitude is represented by the dashed lines in Fig. 9b and d. In the case of flicker detection (Fig. 9d), there is again a significant amount of nonlinearity which cannot be explained in terms of this physical contribution. In conclusion, it may be seen that a considerable amount of the nonlinearity represented in Figs. 3 and 9 for the case of flicker detection

20 538 P. E. KING-SMITH AND J. J. KULIKOWSKI represents an intrinsic non-linearity of the neural sub-units. Thus responses of these sub-units may be considered to have a linear component (which is sensitive to background phase) and a non-linear quadratic component (which is perhaps insensitive to the background phase). A basic observation of the present results is that, while the linear component changes from excitation to inhibition with increasing separation of the background lines from the test line (e.g. Figs. 3b, 3c and 4) the non-linear component is always excitatory (i.e. it always tends to produce a reduction in test contrast thresholds, Figs. 3b, c, d, 9c and 9d). This observation has the following important consequence. Suppose that the non-linearity is generated in localized elements at an early stage in the visual process, before the interaction of test and background stimuli (this would be in accordance with neurophysiological evidence e.g. Enroth-Cugell & Robson, 1966; see below). Then it can be shown that the non-linear elements contributing to the centre and the surround must be of different types, because, if they were all of the same type, we would expect a reversal of both the linear and the non-linear components as the background lines moved out into the inhibitory region of the receptive field. Relation to electrophysiological studies Tolhurst (1973) has pointed out the possible correlation between the movement and pattern detection systems observed psychophysically and two distinct classes of neurones described electrophysiologically. This distinction was first made by Enroth-Cugell & Robson (1966) who differentiated X cells showing linear summation of contrast from Y cells which were non-linear; this classification appears to be equivalent to many more recent classifications based on other properties (e.g. the sustained/transient classification of Cleland, Dubin & Levick, 1971). The following characteristics tend to distinguish X cells from Y cells (cf. the Summary of Ikeda & Wright, 1972b): linear spatial summation of contrast, sustained response to standing contrast, high spontaneous activity, small receptive field centres and surrounds, strong surround inhibition, poor response to rapid movement, relatively low conduction velocity of axon. Most studies have been based on retinal ganglion cells and lateral geniculate cells of the cat; however, there is some evidence that the classification may be extended to the cat cortex (Maffei & Fiorentini, 1973; Ikeda & Wright, 1974, 1975) and to the monkey (Gouras, 1968, 1969). We now consider how five different aspects of our observations on pattern and flicker (or movement) detection may be correlated with electrophysiological studies on X and Y cells respectively. The electrophysiological results refer to cat retinal ganglion cells unless otherwise indicated. 1. Temporal frequency response. The flicker detection system is more

21 PATTERN AND FLICKER DETECTION 539 sensitive than the pattern detection system at high temporal frequencies and less sensitive at low frequencies; also the sensitivity for the flicker detection system is maximal at an intermediate frequency while the sensitivity for pattern detection declines uniformly with increasing frequency (Keesey, 1972; Kulikowski & Tolhurst, 1973; Fig. 1, this paper). In electrical terminology, the flicker detection system is like a 'band pass'filter while the pattern detection system corresponds to a 'low pass' filter. Correspondingly, according to electrical filter theory, one would expect the response of the flicker system to a step-type input (e.g. light switched on) to show a considerable transient overshoot followed by a fall in response towards the original level; the pattern system should show little or no transient response but should have a much more prolonged response to the step. This distinction may be correlated with the two classes of nerve cells; X or 'sustained' cells show a well-maintained response over periods of about 1 sec while Y or 'transient' cells give a large transient response lasting about 50 ms which is followed by relatively weak activity (Enroth- Cugell & Robson, 1966; Fukada, 1971; Cleland, Levick & Sanderson, 1973). A more direct electrophysiological correlation is provided by the studies of Fukada & Saito (1971) who show that the mean discharge rate of 'Type I' (transient) cells may be greatly increased by a flickering stimulus, while 'Type II' (sustained) cells show little change in discharge rate. Transient cells are evidently better suited for the signalling of flicker information. 2. Non-linearity. Our results show a non-linearity occurring in the flicker detection system (Figs. 3b, c, d, 9c and d) which does not occur for pattern detection (Figs. 3a, 9a and b). This may be correlated with the non-linear summation of Y cells and the linear summation of X cells described by Enroth-Cugell & Robson (1966). Non-linear responses within the surround of transient (Y) cells have been described by Cleland et al. (1973) and Winters, Hickey & Skaer (1973), and a non-linear interaction between centre and surround mechanisms of transient cells has been described by Hickey, Winters & Pollack (1973). 3. Width qf receptive field. The results of Figs. 4a and 5 show that, for a flickering test line, the receptive field for flicker detection is about 2-4 times broader than the receptive field for pattern detection; consequently, the flicker detection system has peak sensitivity at a lower spatial frequency (Fig. 4b). In correspondence with this, there is much evidence that transient cells have larger receptive fields than sustained cells. Cleland et al. (1973) find 'effective centre diameters' for ganglion - cells have a mean of I 1 0 for transient and for sustained cells, a ratio of 2'5 to 1; Ikeda & Wright (1972b) give corresponding figures of 3.70 and using a different technique, but these figures may have been affected

22 540 P. E. KING-SMITH AND J. J. KULIKOWSKI by the different retinal areas sampled for the two types of cell. Cleland & Levick (1974), Hammond (1974) and Stone & Fukada (1974) have shown that, in all regions of the retina, the centre size of transient cells is at least twice that of sustained cells. Correspondingly, Maffei & Fiorentini (1973) have shown that Y cells are generally less sensitive than X cells to high frequency gratings. Boycott & Wassle (1974) have distinguished large (a) and small (fi) cells anatomically, which probably correspond to Y and X cells respectively. In the primate, Gouras (1968, 1969, 1971) notes that 'tonic' cells tend to yield small action potentials and have low conduction velocities, perhaps implying that they are small cells with small receptive field centres. Because the tonic cells are those with opponent colour properties, more direct evidence is provided by Wiesel & Hubel (1966) who show that, in the lateral geniculate nucleus, opponent colour cells tend to have the smallest receptive field centres. By studying cortical potentials evoked by grating stimuli in man, Kulikowski (1974, 1975) has demonstrated the presence of separate components related to pattern and movement (transient) information. At low spatial frequencies (e.g. 1 c/deg) only the movement component is observed, i.e. the evoked potential depends only on the transient change in contrast. At higher spatial frequencies another component may be observed which may be associated with pattern detection since its size can be reduced by adapting to a steady grating. 4. Strength of the inhibitory surround. The data of Figs. 4a and 5 illustrate that the inhibitory surround is weaker for flicker detection than for pattern detection; consequently the flicker detector (but not the pattern detector) for a fine line is sensitive to a uniform flickering field (zero spatial frequency, Fig. 4b). Correspondingly, there is evidence that the surround of transient or Y cells is relatively weak. Fukada (1971) has shown that type I (transient) but not type II (sustained) ganglion cells respond to a diffuse flash of light. The weakness of the surround in transient cells is also illustrated by the 'sensitivity profiles' of Ikeda & Wright (1972a, b) and the areathreshold measurements of Cleland et al. (1973). In some circumstances it may be impossible to evoke pure antagonistic responses from the surrounds of transient cells (Winters, Hickey & Pollack, 1973; Enroth-Cugell & Pinto, 1972); however, Hammond (1975) has shown that pure surround responses may be obtained at high adapting luminances. Hamasaki, Campbell, Zengel & Hazelton (1973) demonstrated that some cells (probably transient cells) do not exhibit any inhibition as a moving stimulus enters the periphery of the receptive field. Concordant results have been obtained by Maffei & Fiorentini (1973) who demonstrated that the fall-off in sensitivity at low spatial frequencies

23 PATTERN AND FLICKER DETECTION 541 is relatively weak for Y cells in the retina and lateral geniculate nucleus (cf. Fig. 4b). These authors also find that complex cells in the visual cortex are like Y cells in this regard while simple cells have a considerable attenuation at low spatial frequencies like X cells; they therefore suggest that complex and simple cells may be continuations of the Y and X systems respectively (in line with the conduction velocity studies of Stone & Hoffman, 1971), but this view has recently been disputed (Ikeda & Wright, 1974, 1975). For simplicity, we have used the term 'surround inhibition' to describe the reduced visibility of a test line due to surrounding background lines; strictly speaking, the expression 'surround antagonism' may be preferable as the surround region can, of course, cause excitation of a cell. The complexities of inhibition in cortical neurones are considered by Bishop, Coombs & Henry (1973). 5. Motion sensitivity. A remarkable observation is that the vertical test line, when it is modulated at frequencies of 3 Hz or more, produces a strong sensation of lateral motion at threshold. A modulated grating may similarly produce a motion sensation (Kulikowski, 1971) and Sekuler & Levinson (1974) have provided more objective evidence that this stimulus can be detected by motion sensitive mechanisms. It thus seems likely that what we have called the flicker detection system is primarily concerned with the detection of motion. Again, the flicker detection system may be associated in this respect with the transient cells which have a much greater response to rapid movement than the sustained cells (Cleland et al. 1971); for lateral geniculate cells, see also Dreher & Sanderson (1973). In the cortex, Movshon (1974) has demonstrated that complex cells prefer more rapid motion than simple cells (in line with Maffei & Fiorentini's (1973) association of the complex cells with the transient system, see above); the existence of a specialized system for motion detection is emphasized by Zeki's (1974) demonstration of a visual area in the posterior bank of the monkey's superior temporal sulcus where stimulus motion is the important characteristic which is common to all cells. In conclusion there are many points of similarity between the flicker detection system and the Y (transient) system on the one hand and the pattern detection system and the X (sustained) system on the other hand. However some caution is required in considering the analogies for the following reasons. 1. Electrophysiological studies have been mainly concerned with the retina and lateral geniculate cells while the sustained/transient classification for cortical cells is at present more confused (see above). It seems reasonable that the psychophysical studies are most closely related to the properties of cortical cells; thus, for example, the surround inhibition

24 542 P. E. KING-SMITH AND J. J. KULIKOWSKI studied psychophysically may be only partially determined by the surround inhibition of ganglion cells (Maffei & Fiorentini, 1972; Fiorentini & Maffei, 1973; Hammond, 1973). 2. A psychophysical detector is unlikely to correspond to any single cell in the cortex but may be considered to be some sort of weighted mean derived from a number of 'sub-units' (perhaps cortical cells). These subunits may differ to a certain extent from the detector, e.g. some may have a region of disinhibition in their receptive fields (King-Smith & Kulikowski, 1975). 3. Most electrophysiological studies have used cats which differ from primates in a number of ways (e.g. absence of a fovea and poor colour vision); more detailed unit studies of the 'phasic' and 'tonic' systems in primates would be of great value. One surprising finding is that the tonic (pattern?) system has an opponent colour organization (Gouras, 1968, 1971) while the opponent colour system measured psychophysically seems to have poor acuity (van der Horst, de Weert & Bouman, 1967; Hilz & Cavonius, 1970); perhaps different types of opponent colour inputs to the cortex are combined to yield non-opponent responses signalling detailed pattern information (Gouras, 1971). The latency of surround inhibition The results of Fig. 7 indicate that the latency of the surround inhibitory response is 3 ms more than for the central response. What physiological processes underlie this delay? The delay of the surround in cat retinal ganglion cells is considerably greater than this (20 ms or more depending on temporal frequency; Maffei, Cervetto & Fiorentini, 1970); this would indicate that the inhibition measured psychophysically is generated at a later stage, e.g. through an additional inhibitory interneurone at the lateral geniculate nucleus (Maffei & Fiorentini, 1972; Hammond, 1973). It should, however, again be emphasized that psychophysical measurements in humans may not be quantitatively comparable to electrophysiological measurements in cats. Fiorentini & Maffei (1970) have described a related psychophysical experiment where the threshold modulation for a test spot is determined as a function of the phase of modulation of a surrounding annulus. In the range Hz, they find that the surround has a maximum effect on the spot threshold for a phase shift of around 450, which would correspond to about 10 ms delay. They also find that the inhibitory effect of the annulus is more rapidly attenuated at high temporal frequencies than in our results (Fig. 5). Perhaps the concentric arrangement of their stimuli tends to isolate the properties of ganglion and geniculate cells, whereas our linear arrangement may reflect the properties of cortical cells.

25 PATTERN AND -PLICKEI DETECTION 543 Relation to other studies Our results are consistent with the previous psychophysical studies mentioned in the introduction. Thus the results of Fig. 1 confirm the generally higher sensitivity of the flicker/motion system at high temporal frequencies and the pattern system at low temporal frequencies (Keesey, 1972; Kulikowski & Tolhurst, 1973). Fig. 4 emphasizes the tendency of pattern detectors to be more sensitive at high spatial frequencies and flicker/motion detectors to respond better at low spatial frequencies (Tolhurst, 1973; Kulikowski & Tolhurst, 1973). The non-linear spatial summation of contrast for flicker/motion detection (Figs. 3 and 9) may be tentatively related to a number of studies. The sensation of lateral motion evoked by a threshold flickering line (modulated at 5 Hz or more) indicates that the corresponding detector is primarily concerned with the analysis of motion; this suggestion is supported by the demonstration by Sekuler & Levinson (1974) that a modulated grating can be detected by direction-selective movement detectors. Pantle & Sekuler (1969) and Tolhurst (1973) have provided evidence for such direction-selective mechanisms in human vision which may reflect the activity of direction-selective cortical cells (e.g. Hubel & Wiesel, 1968; Zeki, 1974). A mechanism which responds to movement independent of contrast must be non-linear, because a linear system must give opposite responses for bright and dark stimuli; it is possible therefore that the nonlinearity observed in our experiments may correspond to this essential non-linearity of such a motion detection system (cf. also the essentially non-linear models of Reichardt, 1961 and Barlow & Levick, 1965). Rashbass (1970) has shown that the thresholds for double pulses of diffuse light can be explained in terms of a mechanism which involves squaring of the visual signal; this non-linearity may be related to that observed for the 'pure flicker' detector of Fig. 8. Kelly (1966) proposed a non-linear element to explain the phenomenon of apparent spatial frequency doubling for modulated high-contrast gratings ofhigh temporal and low spatial frequencies. However, it seems likely that the nonlinearity proposed by Kelly has a different origin from that described in this paper; for, in the case of spatial frequency doubling, Kelly proposes that non-linearity causes an apparent darkening at the antinodes of the modulated grating, while, in the present study, the non-linearity is a general excitatory effect tending to lower the threshold for a flickering test target (Fig. 3b, c and d). These examples emphasize that non-linearities within the visual system could have different functional effects and presumably may originate at different sites.

26 544 P. E. KING-SMITH AND J. J. KULIKOWSKI We thank Mr D. Carden for expert technical assistance, Professor J. R. Cronly- Dillon and Drs Hisako Ikeda, M. J. Wright, W. R. Levick and P. Hammond for their careful reading of the manuscript and the Simons Engineering Laboratory and the Electrical Engineering Department, U.M.I.S.T. for lending function generators. This project was sponsored by S.R.C. grant No. BI RG/1511. APPENDIX 1 Contribution of different detectors to the non-linearity of contrast interrelation curves Fig. 6 illustrates that a wide range of detectors of varying widths are available for the detection of a combination of test and background stimuli; to determine the test threshold in the presence of a weak background we must first determine which detector is most sensitive to the combined stimulus. Let S(x2) be the sensitivity, at position x, of the detector which is most sensitive to the central test line (the 'threshold-line detector', circles, Fig. 6). Both broader and narrower detectors will have lower central sensitivity so we may represent their sensitivities by S((1 +A) x2)/(1 +ka2), (A 1) where A is a parameter determining the width of the detectors and k determines how much the sensitivity of broader and narrower detectors falls below that of the threshold-line detector; a value of k of 034 allows a fairly good fit for the broad and narrow curves in Fig. 6 represented by squares and open triangles. If we assume that these detectors respond linearly to test and background contrasts then the response of any detector to a test stimulus of contrast CT will be RT = CT.S(O)/(l +ka2) (A 2) while its response to the two background lines of contrast CB, with spacing x, will be RB = 2CB.S((1 +AA) X2)/(1 +ka2). (A 3) The total response of this detector will be determined by the sum of RT and RB (again assuming linearity), and this response will be at threshold when it equals the threshold response of the 'threshold-line detector' (circles, Fig. 6) to the test line alone, i.e. Co. S(O) where CO is the threshold for the test stimulus on its own. Thus Ca.S(O) = CT.S(O)/(1 +ka2) +2CB.S((l +A) X2)/(1 +ka2). (A 4) This equation may be simplified by expressing sensitivity in relative terms, i.e. S(O) = 1.

27 PATTERN AND FLICKER DETECTION 545 The contrast threshold may thus be expressed in terms of the width parameter A, and by standard differential calculus, the value of A yielding lowest threshold may be determined and hence the corresponding contrast threshold. This is expressed as a function of CB and so the corresponding 'curvature index' of the contrast interrelation (eqn. (7)) may be derived and shown to be ds Q =Ik d((1 +A)X2) This may be evaluated using the sensitivity curve fitted to the data of Fig. 6 (continuous curve) and the corresponding curvature index is represented by the dashed curve in Fig. 9c; this curve assumes linear processing in the detectors (see above) so any additional non-linearity represented in Fig. 9c presumably corresponds to non-linear processing within the detectors. APPENDIX 2 A contribution to non-linearity of the contrast interrelation for background phase Imagine a detector which processes test and background contrasts linearly, and which is stimulated by a test line of contrast CT cos 2nrft flanked by two background lines of contrast CB sin 2nft. The total response of the detector will be ST.CT cos 27rft +2SB.CB sin 2nft, where ST and SB are the sensitivities to test and background lines respectively. Using standard trigonometrical theory, the amplitude of the response is given by (ST2.C2 +S2.C2 )1. The test contrast will be at threshold when this response equals the response to a threshold test stimulus on its own i.e. ST AC Equating these two responses, we obtain CT = (CT-4SB CBIST. Thus there will be a curvature in the contrast interrelation (CT as a function of CB), and the corresponding curvature index (eqn. (7)) may be shown to be Q = 2SB/S2. This function has been plotted as the dashed lines in Fig. 9b and d, the latter curve corresponding to a frequency of 12 Hz.

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