- Email: [email protected]
Relation between flicker and two-pulse sensitivities for sinusoidal gratings
Vision Res. Vol. 28, No. 1, pp. 145-156, 1988 Printed in Great Britain. All rights reserved
0042-6989/88 $3.00 + 0.00 Copyright © 1988 Pergamon Journals Ltd
RELATION BETWEEN FLICKER AND TWO-PULSE SENSITIVITIES FOR SINUSOIDAL GRATINGS YOSHIO OHTANI a n d YOSHIMICHI EJIMA Department of Psychology, The College of Liberal Arts, Kyoto University, Yoshidanihonmatsu-cho, Sakyo-ku, Kyoto 606, Japan (Received 5 January 1987; in revised form 10 June 1987)
Abstract--Flicker and two-pulse sensitivities for sinusoidal gratings were determined with the same observers under the same experimental conditions of a wide range of spatial frequency ( 0 . 7 5 - 6 c/deg) and retinal illuminance (0.88-1100 td). The relations between the two sensitivities were analysed by using a model of multiple spatial-frequency-selective channels, each of which is composed of a linear filter, and an additive noise source and a threshold device. The model could explain well the relationship between the two sensitivities for the high spatial frequencies regardless of retinal illuminance and for the low spatial frequencies at the low retinal illuminances, but not for the low spatial frequencies at the high retinal illuminances. For the low spatial frequencies at the high retinal illuminances, the theoretical two-pulse sensitivities predicted from the flicker sensitivities deviated from the empirical data in the short range of SOA. The deviation was ascribed to the temporal duplicity of the sustained and transient mechanisms. Flicker sensitivity Two-pulse sensitivity Sustained and transient mechanisms
Sinusoidal grating
INTRODUCTION
Psychophysical investigations concerning the temporal property of the human visual system have been looking for a theory which can explain the relationship between different types of temporal measures, such as threshold vs temporal frequency function, threshold vs SOA function, and threshold vs duration function (Kelly, 1971a, b; Kelly and Savoie, 1978; Roufs, 1972a, b, 1973, 1974a, b; Bergen and Wilson, 1985; Gorea and Tyler, 1986; Georgeson, 1987). Difficulty often encountered in constructing such a comprehensive theory is due to the nonlinear performance of the visual system. The human visual system includes some nonlinear components in time domain as well as in space domain. In time domain, two types of nonlinear component have been documented; one is the temporal probability summation which is caused by noise inherent in the visual system. It has been well established that the temporal probability summation may be operative in the detection process over a wide range of experimental conditions (Watson, 1979; Bergen and Wilson, 1985; Gorea and Tyler, 1986; Georgeson, 1987). The other is the asymmetric rectifier-type nonlinearity which enhances the negative lobe
Temporal probability summation
of the filtered response relative to the positive lobe. There is no agreement concerning the property of the asymmetric rectifier. Kelly and Savoie (1978) showed that the sensitivity ratio of negative to positive lobe was 2.7 for a 8° circular uniform field, whereas Roufs (1974a) found that the ratio was 1 (no asymmetry) for a 1° uniform field. Bergen and Wilson (1985) indicated the sensitivity ratio of 1.4 for a triplet of low frequency DOG stimuli, but the ratio of 1 for high frequency stimuli. Legge and Kersten (1983) indicated the ratio of 1.1 for bar stimuli. These somewhat complicated properties of the asymmetric rectifier led us to ask the following questions, to which the present study is directed: (1) Is the asymmetric rectifier essentially required for the description of the detection process? (2) Are there any other nonlinear components involved in the detection process? In order to look for a comprehensive theory to explain the relationship between different temporal measures, we explored the nonlinearity in the detection process further. We determined sinusoidal flicker and two-pulse sensitivities for grating stimuli, and analysed the relations between the two sensitivities by using a temporal probability summation model which did not incorporate the asymmetric rectifier. The nonlinear model, taking notice of the tem-
145
146
YOSH10 OHTANI and YOSHIM1CHIEJIMA
poral duplicity of the sustained and transient mechanisms which may be operative for low spatial frequencies at high retinal illuminances, could explain successfully the relations in a wide range of spatial frequency (0.75-6 c/deg) and retinal illuminance (0.88-1100 td).
lowing equation (Quick, 1974; Watson, 1979)
S = I f ~ IR(t')IPdt'I ~/p
(2)
where S is the sensitivity through the visual pathway and p is a noise parameter. When the temporal waveform of a stimulus is a sinusoid, S is rewritten
GENERAL METHODS
(1) Conceptualframework The major purpose of the present study is to explore a functional relationship between two different kinds of temporal response. For this purpose, we start by assuming a model of the detection process as shown in Fig. 1. It resembles to the models of Sachs et aL (1971) and Watson and Nachmias (1977) in supposing a number of independent channels differing in their spatial sensitivities, and to the models of Watson (1979) and Gorea and Tyler (1986) in incorporating the temporal probability summation. The model consists of multiple spatialfrequency-specific channels, each of which is composed of a linear filter, an additive noise source, and a threshold device. Input signal is first passed through the linear filter at the initial stage of processing. Temporal response of the linear filter R(t) is given by convolving a temporal stimulus I(t) with an impulse response function of the linear filter H(t)
R(t)
=
foI(t')H(t
--
t') dt'.
(1)
Noise inherent in the visual system is then added to the output of the linear filter. The effect of the noise may be expressed as an effect of temporal probability summation by the fol-
where G ( f ) is the temporal modulation transfer function of the linear filter, f is a temporal frequency of a stimulus, and T is an exposure duration of the stimulus. An important simplification is that in case that T is chosen so as to be constant and to include a complete number of temporal cycles for all fs, equation (3) becomes (cf. Appendix) F ~T
= IG(f)IA(p)T lip.
(4)
Assuming that effect of noise is independent of input stimulus (i.e. p is the same for allfs), A(p) may be independent of temporal frequency fi resulting in that S is proportional to IG ( f ) IT1/P. This means that one can obtain IG(f)l from empirical modulation sensitivity functions for a constant T, bypassing the effect of probability summation (Georgeson, 1987). Further, if one may specify the functional form of G(f) with some assumptions, one can derive the impulse response function of the linear filter by the inverse Laplace transformation of G(f) and relate different temporal measures to each other by using the impulse response function. The
Response Stimulus
.I Noise
dt]
-i~lp
S : I G ( / ) I L J ° I sin(2nft)l'
b
1 /
Spatialfrequency Threshold selectivefilters devices Fig. 1. Conceptual framework of detection process for sinusoidal grating.
Flicker and two-pulse sensitivities
validity of the assumptions concerning the functional form of G ( f ) may be tested by asking how well the model can explain the relation between the different temporal measures.
(2) Stimulus and apparatus A vertical grating whose luminance was sinusoidally modulated along the horizontal dimension was electronically generated on a tv monitor at a frame frequency of 60 Hz. The spatial waveforms were produced by a function generator (Hewlett Packard, 3312A) by which the start-stop phase range was adjustable. The edge of a pattern was always at a zero-crossing of the spatial waveform. The screen of the monitor subtended 11.4 ° horizontally and 8.6 ° vertically. The mean retinal illuminance of the screen could be varied by placing an ND filter (Kodak Wratten gelatine filter) or by superimposing optically another white screen which was illuminated and had the same size and approximately the same color as the tv screen (x =0.2616, y =0.2913 on the CIE chromaticity coordinates). The mixed stimulus field gave an unscaled image'into the plane of an artificial pupil. The mean retinal illuminance was either 0~88, 8.8, 88 or l l00td. A grating pattern which appeared in the center of the screen subtended 4 ° x 4 ° from a viewing distance of 80 cm. A fixation point (a 0.2 ° black dot) was always presented in the center of the screen. The spatial frequency of the grating was either 0.75, 1.5, 3.0, or 6.0 c/deg. The pattern was viewed monocularly (right eye) through an artificial pupil of 2 mm in diameter. The contrast of a grating was defined as (Lmax -- Lmin) / (Lmax+ Lmi,) for a sine-wave temporal modulation, and as 4(Lmax- L~,)/rc (Zmax -k Zmin) for a square-wave temporal modulation in Experiment 1, and as (Zmax -Lmin)/(Zmax -4-Lmin) in Experiment 2. Measurements of detection threshold were carried out in the range of contrast over which harmonic distortions were little. The stimulus onset and offset were controlled by a microcomputer and a programmable digital device synchronized with the horizontal driving signal for the tv monitor. The contrast o f the stimulus grating was varied by the microcomputer with D/A converters, dB attenuators, and analog multipliers. The computer sequenced stimulus presentations and monitored observer's response.
(3) Procedure Contrast thresholds were measured by a
147
double random staircase method (Cornsweet, 1962). After 6min of initial adaptation to a homogeneous screen of a given retinal illuminance, a stimulus grating was presented repeatedly with an appropriate interval. By controlling the contrast of the grating, the observer set the starting points of two staircases, which bracketed the region containing the threshold contrast. The observer was then given a block of self-initiated trials. In the random staircase trial, the observer was required to make a binary decision whether he detected any change on the screen or not. Each staircase independently followed the same rule for change in grating contrast. The "yes" response was followed by a constant decrement in contrast, and the " n o " response was followed by a constant increment. The step size in the two staircases was set to 1/20 of the difference between the two starting contrasts. Each staircase was terminated when four reversals were made. The average of the last six contrast peaks and valleys in the resulting staircase sequences (last three from each sequence) was taken as a mean. Several staircase-pair means were then averaged to give an overall mean for each condition. An experimental session consisted of several consecutive blocks, in each of which one estimate of contrast threshold was obtained for a combination of a spatial frequency, a mean retinal illuminance, and a temporal frequency (Experiment 1) or an SOA (Experiment 2). Within a session, spatial frequency and mean retinal iUuminance were kept constant, while temporal frequency or SOA was varied between blocks. Spatial frequency and mean retinal illuminance were varied between sessions. Presentations of spatial frequency, mean retinal illuminance, temporal frequency, and SOA were made in an ascending and a descending order. The authors served as observers in all experiments; both were emmetropic. EXPERIMENT 1
(1) Method In Experiment 1, detection thresholds for sinusoidal gratings were measured as a function of temporal frequency for different spatial frequencies with mean retinal illuminance as a parameter. Temporal modulation of a grating pattern was accomplished by multiplying the spatial wave function by the desired temporal function which was sampled at a frame frequency of 60 Hz. Two kinds of temporal
148
Y o s m o OHTANI and YOSmMXCm EJIMA 1000
0.1
"~
o
I ooo
Y.E.
............................................................
Y.O.
100
,._..,/
0.1
................ , .................................................. 1
. .
10
1
10
1
10
1
10
Ternporot frequency ( H z )
Fig. 2. Contrast sensitivity as a function of temporal frequency for different spatial frequencies. Upper panels are for observer Y.E.: lower panels are for observer Y.O. Symbols signify the m e a n retinal illuminance: circles for 0.88 td, triangles for 8.8 td, squares for 88 td, and inverted triangles for 1 I00 td. Standard error bars are not shown since they were almost always smaller than the symbol size. Solid lines are predictions by using the equation (5) with parameter values listed in Table 1. Dashed lines are predictions based on the duplicity hypothesis obtained with parameter values listed in Table 2.
function were employed; one was a sine-wave function of 0.5-7.5 Hz, and the other was a square-wave function of 7.5-30 Hr. The sinewave function sampled at the frame frequency of 60 Hz is very nearly a pure sine-wave function for a low frequency range of 0.5-7.5 Hz, but not for a high frequency range of 7.5-30 Hz. For the high frequency range, the sampled sine-wave function deviates from a pure sinewave function with increase in temporal frequency. The higher order harmonics of the sampled sine-wave function are lower in frequency than those of the sampled square-wave function. This means that the effect of the higher order harmonics of the sampled sine-wave function is larger than that of the sampled squarewave function because the higher frequency components are largely filtered out by the human visual system. This is the reason why we used, for 7.5-30 Hz, the square-wave function rather than the sine-wave function. Our preliminary experiment showed that the higher order harmonics of a square-wave function with the fundamental frequency above 7.5 Hz did not produce any significant effect on the detection threshold. The multiplication of spatial wave
and temporal wave was made before adding the d.c. pedestal of the video signal. The remainder of the screen was maintained at the constant mean luminance level corresponding to the d.c. pedestal. Exposure duration was kept constant at 4 sec. The 4 sec duration contained complete cycles of temporal sinusoid for all temporal frequencies employed [2-120 cycles for 0.5-30 Hz; cf. equation (4)]. The duration was marked by an auditory tone of the same duration which started at 2 sec after the initiation of a trial. To eliminate effects of onset and offset transients, contrast of a grating was linearly increased and decreased in a 1-2 sec period before and after the 4 sec duration. Care was taken to avoid the possible effect of adaptation to the suprathreshold contrasts during the 4 sec period, especially at the early part of the staircase sequence; observer was required to set the suprathreshold starting point just above threshold. The average of the suprathreshold starting contrasts obtained was about 1.3 times of the threshold contrast for the two observers. For only 3% of all measurements, starting contrasts exceeded 1.78 times of the threshold contrast. Given the low starting contrasts ob-
Flicker and two-pulsesensitivities tained, one may say that the effect of adaptation is negligible for the present experiment.
(2) Results Figure 2 shows the sensitivities as a function of temporal frequency for two observers: the upper panels are for observer Y.E., and the lower panels for Y.O. The four panels represent the results for the four spatial frequencies separately. The ordinate denotes the contrast sensitivity expressed as reciprocal contrast detection threshold for a grating stimulus. The abscissa denotes the temporal frequency of the sine-wave function or the fundamental temporal frequency of square-wave function. Different symbols represent contrast sensitivities at different mean retinal illuminances. Each data point is the mean of 4 separate estimates collected in different runs, except the data for 7.5 Hz. For 7.5 Hz, since the sensitivities for the sine-wave and the square-wave temporal modulations were almost the same, the mean of 8 estimates (4 estimates for each wave form) was calculated. Standard error bars were not shown in the figure, because they were, in most of the cases, smaller than the symbol size. For the both observers, a general tendency of the present results is quite similar. For the low spatial frequencies, the contrast sensitivity function shows a systematic variation in shape with change in mean retinal illuminance. Early in the series of increasing the mean retinal illuminance, a low-pass function is obtained. Then the curve shows a single peak function, i.e. a band-pass function. An improvement in the delineation of the peak and a frequency shift of the peak towards high temporal frequencies occur at the high retinal illuminances. Such a tendency, however, becomes less prominent as the spatial frequency is increased. For the 6 c/deg grating, the sensitivity curve does not show a peak but shows a low-pass function even when the mean retinal illuminance of 1100 td is reached. These features of the present results are similar to those obtained by Kelly (1972) and Van Nes et al. (1967). Recently, similar functions have been obtained also in the electrophysiological studies of turtle retinal cells (Tranchina et al., 1984; Daly and Normann, 1985). According to the equation (4), the iempiricai temporal modulation sensitivity obtained here reflects directly the characteristics of the linear filter in Fig. 1. In order to describe the temporal modulation transfer function of the filter, we
149
assumed the following mathematical function of G ( f ) A G ( f ) = (1 +j2=fz)"+l[1--B/(1 +j2~fz)k] " (5) Equation (5) represents the transfer function of the minimum phase system which is composed of the excitatory pathway of n-stage ideal lowpass filters and the inhibitory pathway of the equivalent k-stage filters. The response of the filters is commonly characterized by the time constant (z) of the filter. A is a gain parameter of the whole system and B is a parameter which determines the gain of the inhibitory pathway relative to that of the excitatory pathway. The present form of the transfer function is open to substitution by appropriate alternatives. The reason why we prefer the present form is that it is mathematically convenient, and that the essentially similar functions have worked quite satisfactorily in a wide range of research on the relations among different temporal measures for grating as well as uniform field stimuli (Roufs, 1972a, b, 1973, 1974a, b; Roufs and Blommaert, 1981; Bergen and Wilson, 1985; Gorea and Tyler, 1986). Parameter values of A, B, ~, and k were estimated by means of least square so as to fit the absolute value of G ( f ) to the data for each combination of spatial frequency (4) and mean retinal illuminance (4), varying n from 1 to 20. Then the residuals for 16 conditions were summed Ul~ for each value of n. The minimum of the sums was obtained with n = 3 for observer Y.E. and with n = 2 for observer Y.O. In the estimation procedure, we allowed the value of k to be fractional. The overall property of the inhibitory pathway may be better described by a fractional value because different numbers of the linear filter are supposed to contribute to the inhibitory response in a stochastic manner (Bergen and Wilson, 1985). Table 1 shows the estimated parameter values for the two observers. It is shown in Table 1 that time constant of the linear filter becomes smaller (response becomes faster) with increase in retinal illuminance for all spatial frequencies. The values of the parameters related to the inhibitory pathway (B and k) also increase with increase in retinal illuminance. The effect of retinal illuminance on the inhibitory parameters is more marked for the low spatial frequencies than for the high spatial frequencies. The overall levels of the inhibitory parameters are higher for the low spatial frequencies. The pattern of
150
YOSHIO OHTANI a n d YOSHIMICHI EJIMA
xo~o
M
xo~o
xo~o
results shows that increase in retinal illuminance makes visual response faster irrespective of spatial frequency, while development of inhibitory response with retinal illuminance depends on spatial frequency. Solid lines in Fig. 2 show that good fits are obtained with equation (5) in conjunction with these parameter values. Having specified the temporal property of the linear filter, we can predict sensitivities for twopulse stimuli by appropriately estimating the effect of temporal probability summation• This is done in the next experiment.
xo~o
II EXPERIMENT 2 O xo~o
xo~i~5
x~5,--io
x~5.~o
9
8
_=
~x o ~ o
~ o~o
x o~ ~ oo ~
x ~ ~o
II
.{ 4 [..,
t'~l
xo¢,..;o
xoe.io
xe~--o
"
(I) Method For the same observers under the same conditions of spatial frequency and retinal illuminance, the detection thresholds for two-pulse grating stimuli were determined as a function of stimulus onset asynchrony (SOA). The test stimulus consisted of two brief gratings of the same spatial frequency, contrast, and duration (6.9 msec). The phase relation of the two gratings in a pair was either in-phase or 180° outof-phase. The two gratings were successively presented during a period of 700 msec marked by an auditory tone. The onset of t h e first grating was set so that the onset of the second grating might be 200 msec before the offset of the auditory tone. The observer was required to make a binary decision whether he detected any change on the screen or not during the interval marked by the tone. The detection thresholds were measured for 32 conditions [spatial frequency (4) x retinal iUuminance (4) x phase (2)].
xo,.zo
(2) Results _
xo~o
5,~-.
_= [.r., r~
~,-%
-
xo,4o
xo.do
xo
.__, :d
Figure 3 shows the two-pulse sensitivities (defined as the reciprocal of the detection threshold for the two-pulse gratings) as a function of SOA for the two observers; the upper panels for Y.E. and the lower panels for Y.O. The four panels represent the results for the four spatial frequencies separately• The four pairs of sensitivities in each panel show the data for different retinal illuminances. The solid and open circles signify the in-phase and the 180° out-of-phase conditions, respectively. Each data point, which is the mean of 4 separate estimates collected in different runs, is normalized by the average of the sensitivities for the longest three SOA conditions (128, 144, and 208 msec). Any significant difference was not observed between
Flicker and two-pulse sensitivities
151
Y.E. 0.75
~
cpd
1.5
cod
3.0
6.0
cod
cpd
0.88
2
0
,,
1100 td
0 I
I
100
0
I
I
200 0
I
I
I
200 0
100
I
100
l~
200 0
I
I
100
200
*,> O,
Y,
0.75 --I
3
t
cpd
1.5
3.0
cpd
cpd
6.0
cpd
4
8.8
Y 1100 td
~
o
~ I
0
100
I
I
200 0
I
100
I
/
200 0
I
100
I
i
200 0
I
I
100
200
StimuLus onset asynchrony ( m s )
Fig. 3. Two-pulse sensitivity as a function of SOA for two phase conditions, for different spatial frequencies. Upper panels are for observer Y.E.: lower panels are for observer Y.O. Parameter value, shown on the curve, is mean retinal illuminance. Open and solid circles represent the data of in-phase and out-of-phase pairs, respectively. Vertical bars show + 1 SE. Each set of data is normalized by the mean of the sensitivities for the longest 3 SOA conditions. The sets of data of 1100 td conditions are on a true scale, while the other sets have been displaced upwards by 1 log unit to prevent overlapping. Solid lines are the predictions obtained by using the equation (2) in conjuction with p ( = 4 ) and parameter values shown in Table 1.
the in-phase and out-of-phase average sensitivities. The vertical bars indicate _ 1 SE where it is sufficiently large to be displayed. For each retinal illuminance, the data have been successively displaced by 1 log unit to prevent overlapping. For the both observers, a general feature of the results is quite alike. The sensitivity function shows a systematic variation in shape with change in the spatial frequency and the retinal iUuminance. Consider first the features for the low spatial frequencies of 0.75 and 1.5 c/deg. When the retinal illuminance is 0.88 or 8.8 td,
the sensitivities show a monophasic gradual decrease for the in-phase condition (increase for the out-of-phase condition) with increasing the SOA up to 100-200 msec, and then asymptote a constant level. When the retinal iUuminance is 88 or l l00td, the sensitivities decrease for the in-phase condition (increase for the outof-phase condition), show a trough (a peak) around the SOA of 50 msec, then increase (decrease) or finally level off. The undershooting (overshooting) effects occur around the SOAs of 50-100 msec. Consider next the characteristics of the high
152
YOSHIO OHTANI and YosI-nMiCm EJIMA
spatial frequencies of 3 and 6 c/deg. When the retinal illuminance is 0.88 or 8.8 td, the sensitivities monotonically decrease for the in-phase condition (increase for the out-of-phase condition) and asymptote a constant level, showing a similar time-course as observed with the lower spatial frequencies. However, when the retinal illuminance is 88 or 1100 td, the sensitivities for the high spatial frequencies are in a sharp contrast to those observed for the low spatial frequencies, not showing any hint of undershooting (overshooting) effects. In the literature, similar spatial frequency dependencies have been obtained with mean luminances of 15-17cd/m 2. Georgeson (1987) found undershooting effect for in-phase pairs of 0.75 c/deg gratings at the SOAs of 40-60 msec, and no hint of such effects for pairs of 3-12c/deg gratings. Watson and Nachmias (1977) found that f o r low spatial frequencies, there was a range of temporal separation resuiting in facilitation between opposite-phase pairs, and inhibition between in-phase pairs. For high spatial frequencies, this range was absent or nearly absent. Breitmeyer and Ganz (1977) showed that subthreshold interaction of the two flashes at high spatial frequencies could be characterized by a monophasic function, but by a multiphasic function at low spatial frequencies. The present results also may be compared with those of the two-pulse studies for uniform fields. For a small field of 0.8' in diameter, Roufs and Blommaert (1981) found a monophasic function with the retinal illuminance of 1200 td, which is consonant with the present results for the high spatial frequencies. For a larger field, there has been a discrepancy between the sensitivity functions obtained. Roufs (1973, 1974a) obtained a biphasic function for a 1° uniform field at low (1 td) as well as high (1200 td) adaptational level. On the other hand, Uetsuki and Ikeda (1970) showed a monophasic function at low adaptation level (0-1 td) and a biphasic function at high adaptational level (18 and 300 td), for a 30' uniform field. The present results for the low spatial frequencies are not consonant with those of Roufs (1973, 1974a) but with those of Uetsuki and Ikeda (1970). By using the equation (2) in conjunction with the impulse response function derived by the inverse Laplace transformation of the equation (5), we can make predictions of the two-pulse sensitivities. We estimated the value of p in the equation (2) so as to minimize the sum of
differences between the predictions and the data over 32 conditions [spatial frequency (4) x mean retinal illuminance (4)x phase (2)], by the method of least square. The estimated value of p was 4 for the both observers. The value is in agreement with those derived from empirical psychometric functions (Legge, 1978; Watson, 1979; Bergen and Wilson, 1985; Gorea and Tyler, 1986), and with those used to describe two-pulse sensitivities (Watson and Nachmias, 1977; Georgeson, 1987). Solid lines in Fig. 3 show the predicted sensitivities. Making allowance for using only one parameter of p, general fits to the data are excellent. Our model predicts fairly well the tendencies in the empirical sensitivity functions. In detail, however, small but significant systematic deviations are observed in some conditions. For the conditions of spatial frequencies of 0.75 and 1.5 c/deg and retinal illuminances of 88 and l l00td, the predictions for the out-of-phase pairs are too low in the short range of SOA. Note here that such deviations are not observed for the other conditions of spatial frequency and retinal illuminance. By using a model similar to the present one, Georgeson (1987) showed that at a low adaptation level (16cd/m2), temporal modulation sensitivity and two-pulse sensitivity for in-phase pairs could be successfully related to each other for 0.75-12 c/deg gratings.
DISCUSSION
The present results demonstrate how the model based on the temporal probability summation can account for the relationship between the flicker sensitivity and the two-pulse sensitivity for grating stimulus. Three points should be noted. (1) The model can account for well the relationship for the high spatial frequencies, regardless of retinal illuminance. (2) The model can account for well the relationship for the low spatial frequencies at the low retinal illuminances, but not at the high retinal illuminances. (3) For the low spatial frequencies at the high retinal illuminances, the theoretical two-pulse sensitivities for the out-of-phase pairs are too low in the short range of SOA. These findings suggest that the detection process for grating stimuli may involve a nonlinear component other than the temporal probability summation, depending on stimulus condition.
Flicker and two-pulse sensitivities 2
1100
°\ ~
1100
~2 -~ 1 U
//o
/
~
~.5 ,;o
;
loo
Stimulus onset asynchrony (ms) Fig. 4. Predictions obtained by incorporatingthe asymmetric rectifier-typenonlinearity[g = 3, equation (6)] into the temporalprobabilitysummationmodelfor 0.75 c/deg at 1100 and 0.88 td. Solid lines indicate the predictions by incorporating the rectification nonlinearity, and broken lines indicate the predictions by the temporal probability summation model (the same as the solid lines in Fig. 3). Data points are replotted from Fig. 3. Left panels are for Y.E.: right panels are for Y.O. The data and the predictions for the SOA of 208 msec are omitted here.
(I) The asymmetric rectifier-type nonlinearity One possible reason for the discrepancies between the predictions and the empirical data for the low spatial frequencies at the high retinal illuminances may be the asymmetric rectifiertype nonlinearity that is supposed to enhance negative portions of the filtered visual response relative to positive parts. The nonlinearity may be described by the following equation (Bergen and Wilson, 1985)
R(t) = g Ig(t)l
(6)
where g = 1 for R (t) > 0, and g > 1 for R (t) < 0. The asymmetric rectifier-type nonlinearity can be introduced into the temporal probability summation model by using the equation (6) in conjunction with th e equation (2). For the low spatial frequencies at the high retinal illuminances, an appreciable improvement of prediction can be obtained by choosing an appropriate value of g. The upper panels in Fig. 4 represent the sensitivity functions for 0.75 c/deg at 1100 td, predicted by setting g = 3 (solid lines). In the panels, the predictions by the temporal probability summation model are also shown by the dashed lines. The predictions based on the asymmetric rectifier-type nonlinearity show an excellent improvement. Similar improvements can be obtained with the other conditions of the low spatial frequencies and high retinal illuminances, which are not shown here.
153
For the conditions of the high spatial frequencies and/or the low retinal illuminances, however, the introduction of the rectification function causes a systematically significant deviation of the prediction from the empirical data. The lower panels in Fig. 4 represent the sensitivity functions for 0.75 c/deg at 0.88 td predicted by setting g = 3, showing clearly such deviations. It is important to note here that the introduction of the asymmetric rectifier-type nonlinearity gives a substantial effect to the out-of-phase conditions, but not to the in-phase condition, because of small magnitude of the negative lobe of the filtered response. If we use the same value of g, much larger deviations are led to for the other out-of-phase conditions of the high spatial frequencies and/or low retinal illuminances. These findings show that the rectification law does not hold through the stimulus condition. Bergen and Wilson (1985) found that, to predict the sinusoidal flicker sensitivity from the temporal three-pulse data, the asymmetric rectifier-type nonlinearity was required for the low spatial frequency but not for the high spatial frequency. A further problem of the rectifier-type nonlinearity concerns the variation in the value of g among authors. The present study requires the value of g = 3 so as to obtain a good prediction for 0.75 c/deg at 1100 td. This value is comparable with that of Kelly and Savoie (1978; g = 2.7), but is much larger than the value of Bergen and Wilson (1985; g = 1.4), and far beyond the values of Legge and Kersten (1983; g = 1.1) and of Roufs (1974a; g = 1). Given the evidences of variation in the rectification function, one might not expect that the discrepancies between the predictions and the empirical data could be explained only by the asymmetric rectifier-type nonlinearity.
(2) Duplicity of temporal property The discrepancies between the predictions and the data for the low spatial frequencies at the high retinal illuminances may be ascribed to the assumption on which the present analysis is based. Our mathematical analysis is based on the assumption that the temporal processing for a given combination of spatial fre~quency and mean retinal illuminance is mediated only by a single channel but not by multiple channels. This assumption may not be valid for our conditions of the low spatial frequencies at the high retinal illuminances.
154
Y o s m o OHTANI and YOSHIMICItI EJIMA
It has been well established that the human visual system contains two distinct mechanisms, i.e. the sustained and transient mechanisms. The two mechanisms differ in their temporal properties and in the ranges of spatial frequencies over which they operate (Keesey, 1972; Tolhurst, 1973; Kulikowski and Tolhurst, 1973; Sharpe and Tolhurst, 1973; Pantle, 1973; Tolhurst et al., 1973; King-Smith and Kulikowski, 1975; Harwerth and Levi, 1978; Bodis-Wollner and Hendley, 1979). The transient mechanism is sensitive to rapid temporal change and to low spatial frequency, while the sustained mechanism responds better to steady or slowly changing stimuli and to high spatial frequency. It is likely that there exists a range of spatial frequency over which the both mechanisms contribute to detection of the stimulus gratings. For such a range of spatial frequency, temporal response property of the visual system would be determined by the changing contributions of the two mechanisms. The changing contributions of the two mechanisms to the detection process have been studied by using different detection criteria, i.e. the pattern and the flicker criterion. The sensitivity for the pattern deteclion (which is assumed to be mediated by the sustained mechanism) is higher than for the flicker detection (which is assumed to be mediated by the transient mechanism) in low temporal frequency region, while the flicker sensitivity becomes higher than the pattern sensitivity in high temporal frequency region (Kulikowski and Tolhurst, 1973; Wilson, 1980; Burbeck, 1981; Burbeck and Kelly, 1981). This implies that when the observer is required to detect any change on the stimulus field irrespective of the kind of percepts, the resulting temporal sensitivity may be a composite function of the underlying two mechanisms. This may be the case with the present experimental situation. Thus, it seems reasonable to assume that the temporal modulation function may be an envelope of two different functions of the sustained and transient mechanisms for the low spatial frequencies at the high retinal illuminances. On the other hand, the two-pulse sensitivity function for the conditions may be determined by the transient mechanisms, rather than the sustained mechanisms, because the two-pulse stimulus consists of rapid temporal changing stimuli. This may be the reason why the single channel analysis could not account for the relationship between the two sensitivities. The hypothesis that the temporal modulation sensitivity function consists of the
sustained and transient mechanisms is in line with Roufs' envelope assumption for uniform field (Roufs, 1974a, b; Roufs and Blommaert, 1981). According to the duplicity hypothesis, we modified the temporal modulation sensitivity function (or equivalently, the impulse response function) under the two constraints that; (1) the temporal modulation sensitivity at high temporal frequencies should be determined by the transient mechanism, and (2) the transient mechanisms should not show any sustained lobe in the temporal response to a step signal (i.e. the positive and the negative lobe of the impulse response are balanced) at high retinal illuminances. The latter constraint has been supported psychophysically (Roufs, 1974a; Tolhurst, 1975). The modification was done with the conditions of spatial frequencies of 0.75 and 1.5 c/deg at the retinal illuminances of 88 and 1100 td. Dashed lines in Fig. 2 show the modified modulation sensitivity functions. The solid lines in Fig. 5 show the resulting predictions obtained by using the values of parameters listed in Table 2. Note that the values of parameters remain almost the same as those in Table 1 except the value of B. Good fits are obtained at 1100 td for the two observers, while at 88 td, the predictions of the sensitivities for out-of-phase condition are somewhat highgr than the empirical data for the SOAs of 50-100msec. Predictions for the in-phase pairs are not affected so markedly by the modifi2 •
0,75 cpd
1.5 cpd
."2_ ._~
1100td to
"-J 1t ~ 0
' 100
0
11ootd 100
Stimulus onset asynchrony (ms)
Fig. 5. Predictions based on the duplicity hypothesis(solid lines) for 0.75 and 1.5 c/deg at 88 and 1100td. Data points are replotted from Fig. 3. Upper panels are for Y.E.: lower panels are for Y.O. Dashed lines are the predictions by the temporal probability summation model (the same as the solid lines in Fig. 3). The data and the predictions for the SOA of 208 msec are omitted here.
Flicker and two-pulse sensitivities
155
Table 2. Parameter values estimated to fit the two-pulse sensitivity on the basis of the duplicity hypothesis Subject Illuminance (td)
Y.E, 88
(n = 3) 1100
Y.O. 88
(n = 2) 1100
SF (c/deg) A B 0.75 k z (see) A B
1.5
5.6 x 1016 (6.0 x 1016) 1.13 (0.90) 3.5 0.012 3.1 x 1014 (3.3 x 1014) 1.13
2.5 x 1017 1.00 3.0 0.008 1.8 x 1023 1.00
(o.9o) k z (sec)
2.5 0.015
cations of the impulse response. This deviation for the 88 td condition suggests that the inhibitory lobe of the impulse response function of the transient mechanism may be overestimated. If the transient mechanisms, for the low retinal illuminances, might show a sustained lobe in the temporal response to a step signal, the inhibitory lobe of the impulse response should be reduced. This may be the case with the present 88 td condition. A smaller negative lobe gives a better fit, falling between the solid and dashed lines in Fig. 5. Paramete~ values which yield the best fits to the data on the basis of the least square, are shown in the parentheses in Table 2. Under the conditions of the high spatial frequencies and/or the low retinal illuminances, such introduction of temporal duplicity is not required, since the temporal probability summation model succeeds in predicting the relation between the temporal modulation sensitivities and the two-pulse sensitivities. This suggests that the temporal modulation sensitivity for the high spatial frequencies and/or the low retinal illuminances is determined by a single mechanism, presumably the sustained mechanisms, whereas the sensitivity for the low spatial frequencies at the high retinal illuminances is determined by multiple mechanisms, presumably the sustained and the transient mechanisms. This suggestion may be supported by physiological studies. Two types of cell, i.e. x and Y cells, are identified in the retina, and LGN of cat and primate visual system. The X cell which has been supposed to be a neural substrate of the sustained mechanisms is sensitive to high spatial frequencies and steady or slowly temporal change stimuli. The Y cell which has been supposed to be a neural substrate of the tran-
1.9 x 1012 (2.0 x 1012) 1.13 (0.85) 2.5 0.016 1.3 x 1012 (1.5 x 1012) 1.13
4.4 x 1014 1.00 3.0 0.010 4.8 x 1019 1.13
(0.7o) 6.0 0.009
2.5 0.018
5.5 0.010
sient mechanisms responds to low spatial frequencies and rapid temporal change stimuli. Further, the transient property of the Y cell is observed only at high luminance levels, diminishes with decrease in adapting luminance, and disappears when fully dark adapted. At low luminance levels, the response of the Y cell shows a similar temporal property to that of the X cell (Yoon, 1972; Enroth-Cugell and Shapley, 1973; Jakiela and Enroth-Cugell, 1976; Lennie, 1980). Thus it is for stimuli of low spatial frequencies at high luminance levels that the transient property of the Y cell is observed. The condition for the emergence of the transient property of the Y cell conforms to our conditions of the low spatial frequencies and high retinal illuminances where the temporal duplicity is required to relate the different temporal measures successfully. Acknowledgements--This work was supported in part by Grant-in-Aid for the Scientific Research (No. 61510044) from the Ministry of Education, by Nihon Housou Bunka Kikin, and by Yamamura-Tamura Foundation.
REFERENCES Bergen J. R. and Wilson H. R. (1985) Prediction of flicker sensitivities from temporal three-pulse data. Vision Res. 25, 577-582. Bodis-Wollner L and Hendley C. D. (1979) On the separability of two mechanisms involved in the detection of grating patterns in humans. J. Physiol., Lond. 291, 251-263. Breitmeyer B. G. and Ganz L. (1977) Temporal studies with flashed gratings: inferences about human transient and sustained channels. Vision Res. 17, 861-865. Burbeck C. A. (1981) Criterion-free pattern and flicker thresholds. J. opt. $oc. Am. 71, 1343-1350. Burbeck C. A. and Kelly D. H. (1981) Contrast gain
156
Yosmo OHTANI and YOSHIMICHIEJIMA
measurements and the transient/sustained dichotomy. J. opt. Soc. Am. 71, 1335-1342. Cornsweet T. N. (1962) The staircase-method in psychophysics. Am. J. Psychol. 75, 485-491. Daly S. J. and Normann R. A. (1985) Temporal information processing in cones: effects of light adaptation on temporal summation and modulation, t"ision Res. 25, 1197-1206. Enroth-CugeU C. and Shapley R. M. (1973) Adaptation and dynamics of cat retinal ganglion cells. J. Physiol., Lond. 233, 271-309. Georgeson M. A. (1987) Temporal properties of spatial contrast vision. Vision Res. 27, 765-780. Gorea A. and Tyler C. W. (1986) New look at Bloch's law for contrast, J. opt. Soc. Am. A3, 52-61. Harwerth R. S. and Levi D. M. (1978) Reaction time as a measure of suprathreshold grating detection. Vision Res. 18, 1579-1586. Jakiela H. G. and Enroth-Cugell C, (1976) Adaptation and dynamics in X-cells and Y-cells of the cat retina. Exp. Brain Res. 24, 335-342. Keesey U. T. (1972) Flicker and pattern detection: a comparison of thresholds. J. opt. Soc. Am. 62, 446-448. Kelly D. H. (1971a) Theory of flicker and transient responses, I. Uniform fields. J. opt. Soc. Am. 61, 537-546. Kelly D. H. (1971b) Theory of flicker and transient responses, II. Counterphase gratings. J. opt. Soc. Am. 61, 632-640. Kelly D. H. (1972) Adaptation effects on spatio-temporal sine-wave thresholds. Vision Res. 12, 89-101. Kelly D. H. and Savoie R. E. (1978) Theory of flicker and transient responses, III. An essential nonlinearity. J. opt. Soc. Am. 68, 1481-1490. King-Smith P, E. and Kulikowski J. J. (1975) Pattern and flicker detection analysed by subthreshold summation. J. Physiol., Lond. 249, 519-548. I Kulikowski J. J. and Tolhurst D. J. (1973) Psychophysical evidence for sustained and transient detectors in human vision. J. Physiol., Lond. 232, 149-162. Legge G. E. (1978) Sustained and transient mechanisms in human vision: temporal and spatial properties. Vision Res. 18, 69-81. Legge G. E. and Kersten D. (1983) Light and dark bars; contrast discrimination. Vision Res. 23, 473-483. Lennie P. (1980) Parallel visual pathways: a review. Vision Res. 20, 561-594. Pantle A. (1973) Visual effects of sinusoidaltcomponents of complex gratings: independent or additive? Vision Res. 13, 2195-2204. Quick R. F. (1974) A vector-magnitude model of contrast detection. Kybernetik 16, 65-67. Roufs J. A. J. (1972a) Dynamic properties of vision--I. Experimental relationships between flicker and flash thresholds. Vision Res. 12, 261-278. Roufs J. A, J. (1972b) Dynamic properties of vision--II. Theoretical relationships between flicker and flash thresholds. Vision Res. 12, 279-292. Roufs J. A. J. (1973) Dynamic properties of vision--Ill. Twin flashes, single flashes and flickerfusion. Vision Res. 13, 309-323. Roufs J. A. J. (1974a) Dynamic properties of vision--IV.
Thresholds of decremental flashes, incremental flashes and doublets in relation to flicker fusion. Vision Res. 14, 831-851. Roufs J. A. J. (1974b) Dynamic properties of vision--V. Perception lag and reaction time in relation to flicker and flash thresholds. Vision Res. 14, 853-869. Roufs J. A. J, and Blommaert F. J. J. (1981) Temporal impulse and step responses of the human eye obtained psychophysically by means of a drift-correcting perturbation technique. Vision Res. 21, 1203-1221. Sachs M. B., Nachmias J. and Robson J. G. (1971) Spatial-frequency channels in human vision. J. opt. Soc. Am. 61, 1176-1186. Sharpe C. R. and Tolhurst D. J. (1973) The effects of temporal modulation on the orientation channels of the human visual system. Perception 2, 23-29. Tolhurst D. J. (1973) Separate channels for the analysis of the shape and the movement of a moving stimulus. J. Physiol., Lond. 231, 385-402. Tolhurst D. J. (1975) Sustained and transient channels in human vision. Vision Res. 15, 1151-1155. Tolhurst D. J., Sharpe C. R. and Hart G. (1973) The analysis of the drift rate of moving sinusoidal gratings. Vision Res. 13, 2545-2555. Tranchina D., Gordon J. and Shapley R. M. (1984) Retinal light adaptation--evidence for a feedback mechanism. Nature, Lond. 310, 314-316. Uetsuki T. and Ikeda M. (1970) Study of temporal Visual response by the summation index. J. opt. Soe. Am. 60, 377-381. Van Nes F. L., Koenderink J. J., Nas H. and Bouman M. A. (1967) Spatiotemporal modulation transfer in the human eye. J. opt Soc. Am. 57, 1082-1088. Watson A. B. (1979) Probability summation over time. Vision Res. 19, 515-522. Watson A. B. and Nachmias J. (1977) Patterns of temporal interaction in the detection of gratings. Vision Res. 17, 893-902. Wilson H. R. (1980) Spatiotemporal characterization of a transient mechanism in the human visual system. Vision Res. 20, 443-452. Yoon M. (1972) Influence of adaptation level on response pattern and sensitivity of ganglion cells in the cat's retina. J. Physiol., Lond. 221, 93-104. APPENDIX
The second term of the right side of the equation (4) is rewritten as follows: I fr
.
-ll/p
Jo lSm(2nft)l'dtJ
.
where y = 2rift. It follows that I ~ "yr . _-I'/' I/2nfJ sm(y)l p dy /
=[l/2nf~/2[sin(y)l,dy× 4fTl'/'
F {
~,,12 .
= / T t 2 n J0
= TUPA(p).
ql/.
=[f2o'~rl/2nflsln(y)l'dy j
\-Illp Ism(y)l'dy)J
0042-6989/88 $3.00 + 0.00 Copyright © 1988 Pergamon Journals Ltd
RELATION BETWEEN FLICKER AND TWO-PULSE SENSITIVITIES FOR SINUSOIDAL GRATINGS YOSHIO OHTANI a n d YOSHIMICHI EJIMA Department of Psychology, The College of Liberal Arts, Kyoto University, Yoshidanihonmatsu-cho, Sakyo-ku, Kyoto 606, Japan (Received 5 January 1987; in revised form 10 June 1987)
Abstract--Flicker and two-pulse sensitivities for sinusoidal gratings were determined with the same observers under the same experimental conditions of a wide range of spatial frequency ( 0 . 7 5 - 6 c/deg) and retinal illuminance (0.88-1100 td). The relations between the two sensitivities were analysed by using a model of multiple spatial-frequency-selective channels, each of which is composed of a linear filter, and an additive noise source and a threshold device. The model could explain well the relationship between the two sensitivities for the high spatial frequencies regardless of retinal illuminance and for the low spatial frequencies at the low retinal illuminances, but not for the low spatial frequencies at the high retinal illuminances. For the low spatial frequencies at the high retinal illuminances, the theoretical two-pulse sensitivities predicted from the flicker sensitivities deviated from the empirical data in the short range of SOA. The deviation was ascribed to the temporal duplicity of the sustained and transient mechanisms. Flicker sensitivity Two-pulse sensitivity Sustained and transient mechanisms
Sinusoidal grating
INTRODUCTION
Psychophysical investigations concerning the temporal property of the human visual system have been looking for a theory which can explain the relationship between different types of temporal measures, such as threshold vs temporal frequency function, threshold vs SOA function, and threshold vs duration function (Kelly, 1971a, b; Kelly and Savoie, 1978; Roufs, 1972a, b, 1973, 1974a, b; Bergen and Wilson, 1985; Gorea and Tyler, 1986; Georgeson, 1987). Difficulty often encountered in constructing such a comprehensive theory is due to the nonlinear performance of the visual system. The human visual system includes some nonlinear components in time domain as well as in space domain. In time domain, two types of nonlinear component have been documented; one is the temporal probability summation which is caused by noise inherent in the visual system. It has been well established that the temporal probability summation may be operative in the detection process over a wide range of experimental conditions (Watson, 1979; Bergen and Wilson, 1985; Gorea and Tyler, 1986; Georgeson, 1987). The other is the asymmetric rectifier-type nonlinearity which enhances the negative lobe
Temporal probability summation
of the filtered response relative to the positive lobe. There is no agreement concerning the property of the asymmetric rectifier. Kelly and Savoie (1978) showed that the sensitivity ratio of negative to positive lobe was 2.7 for a 8° circular uniform field, whereas Roufs (1974a) found that the ratio was 1 (no asymmetry) for a 1° uniform field. Bergen and Wilson (1985) indicated the sensitivity ratio of 1.4 for a triplet of low frequency DOG stimuli, but the ratio of 1 for high frequency stimuli. Legge and Kersten (1983) indicated the ratio of 1.1 for bar stimuli. These somewhat complicated properties of the asymmetric rectifier led us to ask the following questions, to which the present study is directed: (1) Is the asymmetric rectifier essentially required for the description of the detection process? (2) Are there any other nonlinear components involved in the detection process? In order to look for a comprehensive theory to explain the relationship between different temporal measures, we explored the nonlinearity in the detection process further. We determined sinusoidal flicker and two-pulse sensitivities for grating stimuli, and analysed the relations between the two sensitivities by using a temporal probability summation model which did not incorporate the asymmetric rectifier. The nonlinear model, taking notice of the tem-
145
146
YOSH10 OHTANI and YOSHIM1CHIEJIMA
poral duplicity of the sustained and transient mechanisms which may be operative for low spatial frequencies at high retinal illuminances, could explain successfully the relations in a wide range of spatial frequency (0.75-6 c/deg) and retinal illuminance (0.88-1100 td).
lowing equation (Quick, 1974; Watson, 1979)
S = I f ~ IR(t')IPdt'I ~/p
(2)
where S is the sensitivity through the visual pathway and p is a noise parameter. When the temporal waveform of a stimulus is a sinusoid, S is rewritten
GENERAL METHODS
(1) Conceptualframework The major purpose of the present study is to explore a functional relationship between two different kinds of temporal response. For this purpose, we start by assuming a model of the detection process as shown in Fig. 1. It resembles to the models of Sachs et aL (1971) and Watson and Nachmias (1977) in supposing a number of independent channels differing in their spatial sensitivities, and to the models of Watson (1979) and Gorea and Tyler (1986) in incorporating the temporal probability summation. The model consists of multiple spatialfrequency-specific channels, each of which is composed of a linear filter, an additive noise source, and a threshold device. Input signal is first passed through the linear filter at the initial stage of processing. Temporal response of the linear filter R(t) is given by convolving a temporal stimulus I(t) with an impulse response function of the linear filter H(t)
R(t)
=
foI(t')H(t
--
t') dt'.
(1)
Noise inherent in the visual system is then added to the output of the linear filter. The effect of the noise may be expressed as an effect of temporal probability summation by the fol-
where G ( f ) is the temporal modulation transfer function of the linear filter, f is a temporal frequency of a stimulus, and T is an exposure duration of the stimulus. An important simplification is that in case that T is chosen so as to be constant and to include a complete number of temporal cycles for all fs, equation (3) becomes (cf. Appendix) F ~T
= IG(f)IA(p)T lip.
(4)
Assuming that effect of noise is independent of input stimulus (i.e. p is the same for allfs), A(p) may be independent of temporal frequency fi resulting in that S is proportional to IG ( f ) IT1/P. This means that one can obtain IG(f)l from empirical modulation sensitivity functions for a constant T, bypassing the effect of probability summation (Georgeson, 1987). Further, if one may specify the functional form of G(f) with some assumptions, one can derive the impulse response function of the linear filter by the inverse Laplace transformation of G(f) and relate different temporal measures to each other by using the impulse response function. The
Response Stimulus
.I Noise
dt]
-i~lp
S : I G ( / ) I L J ° I sin(2nft)l'
b
1 /
Spatialfrequency Threshold selectivefilters devices Fig. 1. Conceptual framework of detection process for sinusoidal grating.
Flicker and two-pulse sensitivities
validity of the assumptions concerning the functional form of G ( f ) may be tested by asking how well the model can explain the relation between the different temporal measures.
(2) Stimulus and apparatus A vertical grating whose luminance was sinusoidally modulated along the horizontal dimension was electronically generated on a tv monitor at a frame frequency of 60 Hz. The spatial waveforms were produced by a function generator (Hewlett Packard, 3312A) by which the start-stop phase range was adjustable. The edge of a pattern was always at a zero-crossing of the spatial waveform. The screen of the monitor subtended 11.4 ° horizontally and 8.6 ° vertically. The mean retinal illuminance of the screen could be varied by placing an ND filter (Kodak Wratten gelatine filter) or by superimposing optically another white screen which was illuminated and had the same size and approximately the same color as the tv screen (x =0.2616, y =0.2913 on the CIE chromaticity coordinates). The mixed stimulus field gave an unscaled image'into the plane of an artificial pupil. The mean retinal illuminance was either 0~88, 8.8, 88 or l l00td. A grating pattern which appeared in the center of the screen subtended 4 ° x 4 ° from a viewing distance of 80 cm. A fixation point (a 0.2 ° black dot) was always presented in the center of the screen. The spatial frequency of the grating was either 0.75, 1.5, 3.0, or 6.0 c/deg. The pattern was viewed monocularly (right eye) through an artificial pupil of 2 mm in diameter. The contrast of a grating was defined as (Lmax -- Lmin) / (Lmax+ Lmi,) for a sine-wave temporal modulation, and as 4(Lmax- L~,)/rc (Zmax -k Zmin) for a square-wave temporal modulation in Experiment 1, and as (Zmax -Lmin)/(Zmax -4-Lmin) in Experiment 2. Measurements of detection threshold were carried out in the range of contrast over which harmonic distortions were little. The stimulus onset and offset were controlled by a microcomputer and a programmable digital device synchronized with the horizontal driving signal for the tv monitor. The contrast o f the stimulus grating was varied by the microcomputer with D/A converters, dB attenuators, and analog multipliers. The computer sequenced stimulus presentations and monitored observer's response.
(3) Procedure Contrast thresholds were measured by a
147
double random staircase method (Cornsweet, 1962). After 6min of initial adaptation to a homogeneous screen of a given retinal illuminance, a stimulus grating was presented repeatedly with an appropriate interval. By controlling the contrast of the grating, the observer set the starting points of two staircases, which bracketed the region containing the threshold contrast. The observer was then given a block of self-initiated trials. In the random staircase trial, the observer was required to make a binary decision whether he detected any change on the screen or not. Each staircase independently followed the same rule for change in grating contrast. The "yes" response was followed by a constant decrement in contrast, and the " n o " response was followed by a constant increment. The step size in the two staircases was set to 1/20 of the difference between the two starting contrasts. Each staircase was terminated when four reversals were made. The average of the last six contrast peaks and valleys in the resulting staircase sequences (last three from each sequence) was taken as a mean. Several staircase-pair means were then averaged to give an overall mean for each condition. An experimental session consisted of several consecutive blocks, in each of which one estimate of contrast threshold was obtained for a combination of a spatial frequency, a mean retinal illuminance, and a temporal frequency (Experiment 1) or an SOA (Experiment 2). Within a session, spatial frequency and mean retinal iUuminance were kept constant, while temporal frequency or SOA was varied between blocks. Spatial frequency and mean retinal illuminance were varied between sessions. Presentations of spatial frequency, mean retinal illuminance, temporal frequency, and SOA were made in an ascending and a descending order. The authors served as observers in all experiments; both were emmetropic. EXPERIMENT 1
(1) Method In Experiment 1, detection thresholds for sinusoidal gratings were measured as a function of temporal frequency for different spatial frequencies with mean retinal illuminance as a parameter. Temporal modulation of a grating pattern was accomplished by multiplying the spatial wave function by the desired temporal function which was sampled at a frame frequency of 60 Hz. Two kinds of temporal
148
Y o s m o OHTANI and YOSmMXCm EJIMA 1000
0.1
"~
o
I ooo
Y.E.
............................................................
Y.O.
100
,._..,/
0.1
................ , .................................................. 1
. .
10
1
10
1
10
1
10
Ternporot frequency ( H z )
Fig. 2. Contrast sensitivity as a function of temporal frequency for different spatial frequencies. Upper panels are for observer Y.E.: lower panels are for observer Y.O. Symbols signify the m e a n retinal illuminance: circles for 0.88 td, triangles for 8.8 td, squares for 88 td, and inverted triangles for 1 I00 td. Standard error bars are not shown since they were almost always smaller than the symbol size. Solid lines are predictions by using the equation (5) with parameter values listed in Table 1. Dashed lines are predictions based on the duplicity hypothesis obtained with parameter values listed in Table 2.
function were employed; one was a sine-wave function of 0.5-7.5 Hz, and the other was a square-wave function of 7.5-30 Hr. The sinewave function sampled at the frame frequency of 60 Hz is very nearly a pure sine-wave function for a low frequency range of 0.5-7.5 Hz, but not for a high frequency range of 7.5-30 Hz. For the high frequency range, the sampled sine-wave function deviates from a pure sinewave function with increase in temporal frequency. The higher order harmonics of the sampled sine-wave function are lower in frequency than those of the sampled square-wave function. This means that the effect of the higher order harmonics of the sampled sine-wave function is larger than that of the sampled squarewave function because the higher frequency components are largely filtered out by the human visual system. This is the reason why we used, for 7.5-30 Hz, the square-wave function rather than the sine-wave function. Our preliminary experiment showed that the higher order harmonics of a square-wave function with the fundamental frequency above 7.5 Hz did not produce any significant effect on the detection threshold. The multiplication of spatial wave
and temporal wave was made before adding the d.c. pedestal of the video signal. The remainder of the screen was maintained at the constant mean luminance level corresponding to the d.c. pedestal. Exposure duration was kept constant at 4 sec. The 4 sec duration contained complete cycles of temporal sinusoid for all temporal frequencies employed [2-120 cycles for 0.5-30 Hz; cf. equation (4)]. The duration was marked by an auditory tone of the same duration which started at 2 sec after the initiation of a trial. To eliminate effects of onset and offset transients, contrast of a grating was linearly increased and decreased in a 1-2 sec period before and after the 4 sec duration. Care was taken to avoid the possible effect of adaptation to the suprathreshold contrasts during the 4 sec period, especially at the early part of the staircase sequence; observer was required to set the suprathreshold starting point just above threshold. The average of the suprathreshold starting contrasts obtained was about 1.3 times of the threshold contrast for the two observers. For only 3% of all measurements, starting contrasts exceeded 1.78 times of the threshold contrast. Given the low starting contrasts ob-
Flicker and two-pulsesensitivities tained, one may say that the effect of adaptation is negligible for the present experiment.
(2) Results Figure 2 shows the sensitivities as a function of temporal frequency for two observers: the upper panels are for observer Y.E., and the lower panels for Y.O. The four panels represent the results for the four spatial frequencies separately. The ordinate denotes the contrast sensitivity expressed as reciprocal contrast detection threshold for a grating stimulus. The abscissa denotes the temporal frequency of the sine-wave function or the fundamental temporal frequency of square-wave function. Different symbols represent contrast sensitivities at different mean retinal illuminances. Each data point is the mean of 4 separate estimates collected in different runs, except the data for 7.5 Hz. For 7.5 Hz, since the sensitivities for the sine-wave and the square-wave temporal modulations were almost the same, the mean of 8 estimates (4 estimates for each wave form) was calculated. Standard error bars were not shown in the figure, because they were, in most of the cases, smaller than the symbol size. For the both observers, a general tendency of the present results is quite similar. For the low spatial frequencies, the contrast sensitivity function shows a systematic variation in shape with change in mean retinal illuminance. Early in the series of increasing the mean retinal illuminance, a low-pass function is obtained. Then the curve shows a single peak function, i.e. a band-pass function. An improvement in the delineation of the peak and a frequency shift of the peak towards high temporal frequencies occur at the high retinal illuminances. Such a tendency, however, becomes less prominent as the spatial frequency is increased. For the 6 c/deg grating, the sensitivity curve does not show a peak but shows a low-pass function even when the mean retinal illuminance of 1100 td is reached. These features of the present results are similar to those obtained by Kelly (1972) and Van Nes et al. (1967). Recently, similar functions have been obtained also in the electrophysiological studies of turtle retinal cells (Tranchina et al., 1984; Daly and Normann, 1985). According to the equation (4), the iempiricai temporal modulation sensitivity obtained here reflects directly the characteristics of the linear filter in Fig. 1. In order to describe the temporal modulation transfer function of the filter, we
149
assumed the following mathematical function of G ( f ) A G ( f ) = (1 +j2=fz)"+l[1--B/(1 +j2~fz)k] " (5) Equation (5) represents the transfer function of the minimum phase system which is composed of the excitatory pathway of n-stage ideal lowpass filters and the inhibitory pathway of the equivalent k-stage filters. The response of the filters is commonly characterized by the time constant (z) of the filter. A is a gain parameter of the whole system and B is a parameter which determines the gain of the inhibitory pathway relative to that of the excitatory pathway. The present form of the transfer function is open to substitution by appropriate alternatives. The reason why we prefer the present form is that it is mathematically convenient, and that the essentially similar functions have worked quite satisfactorily in a wide range of research on the relations among different temporal measures for grating as well as uniform field stimuli (Roufs, 1972a, b, 1973, 1974a, b; Roufs and Blommaert, 1981; Bergen and Wilson, 1985; Gorea and Tyler, 1986). Parameter values of A, B, ~, and k were estimated by means of least square so as to fit the absolute value of G ( f ) to the data for each combination of spatial frequency (4) and mean retinal illuminance (4), varying n from 1 to 20. Then the residuals for 16 conditions were summed Ul~ for each value of n. The minimum of the sums was obtained with n = 3 for observer Y.E. and with n = 2 for observer Y.O. In the estimation procedure, we allowed the value of k to be fractional. The overall property of the inhibitory pathway may be better described by a fractional value because different numbers of the linear filter are supposed to contribute to the inhibitory response in a stochastic manner (Bergen and Wilson, 1985). Table 1 shows the estimated parameter values for the two observers. It is shown in Table 1 that time constant of the linear filter becomes smaller (response becomes faster) with increase in retinal illuminance for all spatial frequencies. The values of the parameters related to the inhibitory pathway (B and k) also increase with increase in retinal illuminance. The effect of retinal illuminance on the inhibitory parameters is more marked for the low spatial frequencies than for the high spatial frequencies. The overall levels of the inhibitory parameters are higher for the low spatial frequencies. The pattern of
150
YOSHIO OHTANI a n d YOSHIMICHI EJIMA
xo~o
M
xo~o
xo~o
results shows that increase in retinal illuminance makes visual response faster irrespective of spatial frequency, while development of inhibitory response with retinal illuminance depends on spatial frequency. Solid lines in Fig. 2 show that good fits are obtained with equation (5) in conjunction with these parameter values. Having specified the temporal property of the linear filter, we can predict sensitivities for twopulse stimuli by appropriately estimating the effect of temporal probability summation• This is done in the next experiment.
xo~o
II EXPERIMENT 2 O xo~o
xo~i~5
x~5,--io
x~5.~o
9
8
_=
~x o ~ o
~ o~o
x o~ ~ oo ~
x ~ ~o
II
.{ 4 [..,
t'~l
xo¢,..;o
xoe.io
xe~--o
"
(I) Method For the same observers under the same conditions of spatial frequency and retinal illuminance, the detection thresholds for two-pulse grating stimuli were determined as a function of stimulus onset asynchrony (SOA). The test stimulus consisted of two brief gratings of the same spatial frequency, contrast, and duration (6.9 msec). The phase relation of the two gratings in a pair was either in-phase or 180° outof-phase. The two gratings were successively presented during a period of 700 msec marked by an auditory tone. The onset of t h e first grating was set so that the onset of the second grating might be 200 msec before the offset of the auditory tone. The observer was required to make a binary decision whether he detected any change on the screen or not during the interval marked by the tone. The detection thresholds were measured for 32 conditions [spatial frequency (4) x retinal iUuminance (4) x phase (2)].
xo,.zo
(2) Results _
xo~o
5,~-.
_= [.r., r~
~,-%
-
xo,4o
xo.do
xo
.__, :d
Figure 3 shows the two-pulse sensitivities (defined as the reciprocal of the detection threshold for the two-pulse gratings) as a function of SOA for the two observers; the upper panels for Y.E. and the lower panels for Y.O. The four panels represent the results for the four spatial frequencies separately• The four pairs of sensitivities in each panel show the data for different retinal illuminances. The solid and open circles signify the in-phase and the 180° out-of-phase conditions, respectively. Each data point, which is the mean of 4 separate estimates collected in different runs, is normalized by the average of the sensitivities for the longest three SOA conditions (128, 144, and 208 msec). Any significant difference was not observed between
Flicker and two-pulse sensitivities
151
Y.E. 0.75
~
cpd
1.5
cod
3.0
6.0
cod
cpd
0.88
2
0
,,
1100 td
0 I
I
100
0
I
I
200 0
I
I
I
200 0
100
I
100
l~
200 0
I
I
100
200
*,> O,
Y,
0.75 --I
3
t
cpd
1.5
3.0
cpd
cpd
6.0
cpd
4
8.8
Y 1100 td
~
o
~ I
0
100
I
I
200 0
I
100
I
/
200 0
I
100
I
i
200 0
I
I
100
200
StimuLus onset asynchrony ( m s )
Fig. 3. Two-pulse sensitivity as a function of SOA for two phase conditions, for different spatial frequencies. Upper panels are for observer Y.E.: lower panels are for observer Y.O. Parameter value, shown on the curve, is mean retinal illuminance. Open and solid circles represent the data of in-phase and out-of-phase pairs, respectively. Vertical bars show + 1 SE. Each set of data is normalized by the mean of the sensitivities for the longest 3 SOA conditions. The sets of data of 1100 td conditions are on a true scale, while the other sets have been displaced upwards by 1 log unit to prevent overlapping. Solid lines are the predictions obtained by using the equation (2) in conjuction with p ( = 4 ) and parameter values shown in Table 1.
the in-phase and out-of-phase average sensitivities. The vertical bars indicate _ 1 SE where it is sufficiently large to be displayed. For each retinal illuminance, the data have been successively displaced by 1 log unit to prevent overlapping. For the both observers, a general feature of the results is quite alike. The sensitivity function shows a systematic variation in shape with change in the spatial frequency and the retinal iUuminance. Consider first the features for the low spatial frequencies of 0.75 and 1.5 c/deg. When the retinal illuminance is 0.88 or 8.8 td,
the sensitivities show a monophasic gradual decrease for the in-phase condition (increase for the out-of-phase condition) with increasing the SOA up to 100-200 msec, and then asymptote a constant level. When the retinal iUuminance is 88 or l l00td, the sensitivities decrease for the in-phase condition (increase for the outof-phase condition), show a trough (a peak) around the SOA of 50 msec, then increase (decrease) or finally level off. The undershooting (overshooting) effects occur around the SOAs of 50-100 msec. Consider next the characteristics of the high
152
YOSHIO OHTANI and YosI-nMiCm EJIMA
spatial frequencies of 3 and 6 c/deg. When the retinal illuminance is 0.88 or 8.8 td, the sensitivities monotonically decrease for the in-phase condition (increase for the out-of-phase condition) and asymptote a constant level, showing a similar time-course as observed with the lower spatial frequencies. However, when the retinal illuminance is 88 or 1100 td, the sensitivities for the high spatial frequencies are in a sharp contrast to those observed for the low spatial frequencies, not showing any hint of undershooting (overshooting) effects. In the literature, similar spatial frequency dependencies have been obtained with mean luminances of 15-17cd/m 2. Georgeson (1987) found undershooting effect for in-phase pairs of 0.75 c/deg gratings at the SOAs of 40-60 msec, and no hint of such effects for pairs of 3-12c/deg gratings. Watson and Nachmias (1977) found that f o r low spatial frequencies, there was a range of temporal separation resuiting in facilitation between opposite-phase pairs, and inhibition between in-phase pairs. For high spatial frequencies, this range was absent or nearly absent. Breitmeyer and Ganz (1977) showed that subthreshold interaction of the two flashes at high spatial frequencies could be characterized by a monophasic function, but by a multiphasic function at low spatial frequencies. The present results also may be compared with those of the two-pulse studies for uniform fields. For a small field of 0.8' in diameter, Roufs and Blommaert (1981) found a monophasic function with the retinal illuminance of 1200 td, which is consonant with the present results for the high spatial frequencies. For a larger field, there has been a discrepancy between the sensitivity functions obtained. Roufs (1973, 1974a) obtained a biphasic function for a 1° uniform field at low (1 td) as well as high (1200 td) adaptational level. On the other hand, Uetsuki and Ikeda (1970) showed a monophasic function at low adaptation level (0-1 td) and a biphasic function at high adaptational level (18 and 300 td), for a 30' uniform field. The present results for the low spatial frequencies are not consonant with those of Roufs (1973, 1974a) but with those of Uetsuki and Ikeda (1970). By using the equation (2) in conjunction with the impulse response function derived by the inverse Laplace transformation of the equation (5), we can make predictions of the two-pulse sensitivities. We estimated the value of p in the equation (2) so as to minimize the sum of
differences between the predictions and the data over 32 conditions [spatial frequency (4) x mean retinal illuminance (4)x phase (2)], by the method of least square. The estimated value of p was 4 for the both observers. The value is in agreement with those derived from empirical psychometric functions (Legge, 1978; Watson, 1979; Bergen and Wilson, 1985; Gorea and Tyler, 1986), and with those used to describe two-pulse sensitivities (Watson and Nachmias, 1977; Georgeson, 1987). Solid lines in Fig. 3 show the predicted sensitivities. Making allowance for using only one parameter of p, general fits to the data are excellent. Our model predicts fairly well the tendencies in the empirical sensitivity functions. In detail, however, small but significant systematic deviations are observed in some conditions. For the conditions of spatial frequencies of 0.75 and 1.5 c/deg and retinal illuminances of 88 and l l00td, the predictions for the out-of-phase pairs are too low in the short range of SOA. Note here that such deviations are not observed for the other conditions of spatial frequency and retinal illuminance. By using a model similar to the present one, Georgeson (1987) showed that at a low adaptation level (16cd/m2), temporal modulation sensitivity and two-pulse sensitivity for in-phase pairs could be successfully related to each other for 0.75-12 c/deg gratings.
DISCUSSION
The present results demonstrate how the model based on the temporal probability summation can account for the relationship between the flicker sensitivity and the two-pulse sensitivity for grating stimulus. Three points should be noted. (1) The model can account for well the relationship for the high spatial frequencies, regardless of retinal illuminance. (2) The model can account for well the relationship for the low spatial frequencies at the low retinal illuminances, but not at the high retinal illuminances. (3) For the low spatial frequencies at the high retinal illuminances, the theoretical two-pulse sensitivities for the out-of-phase pairs are too low in the short range of SOA. These findings suggest that the detection process for grating stimuli may involve a nonlinear component other than the temporal probability summation, depending on stimulus condition.
Flicker and two-pulse sensitivities 2
1100
°\ ~
1100
~2 -~ 1 U
//o
/
~
~.5 ,;o
;
loo
Stimulus onset asynchrony (ms) Fig. 4. Predictions obtained by incorporatingthe asymmetric rectifier-typenonlinearity[g = 3, equation (6)] into the temporalprobabilitysummationmodelfor 0.75 c/deg at 1100 and 0.88 td. Solid lines indicate the predictions by incorporating the rectification nonlinearity, and broken lines indicate the predictions by the temporal probability summation model (the same as the solid lines in Fig. 3). Data points are replotted from Fig. 3. Left panels are for Y.E.: right panels are for Y.O. The data and the predictions for the SOA of 208 msec are omitted here.
(I) The asymmetric rectifier-type nonlinearity One possible reason for the discrepancies between the predictions and the empirical data for the low spatial frequencies at the high retinal illuminances may be the asymmetric rectifiertype nonlinearity that is supposed to enhance negative portions of the filtered visual response relative to positive parts. The nonlinearity may be described by the following equation (Bergen and Wilson, 1985)
R(t) = g Ig(t)l
(6)
where g = 1 for R (t) > 0, and g > 1 for R (t) < 0. The asymmetric rectifier-type nonlinearity can be introduced into the temporal probability summation model by using the equation (6) in conjunction with th e equation (2). For the low spatial frequencies at the high retinal illuminances, an appreciable improvement of prediction can be obtained by choosing an appropriate value of g. The upper panels in Fig. 4 represent the sensitivity functions for 0.75 c/deg at 1100 td, predicted by setting g = 3 (solid lines). In the panels, the predictions by the temporal probability summation model are also shown by the dashed lines. The predictions based on the asymmetric rectifier-type nonlinearity show an excellent improvement. Similar improvements can be obtained with the other conditions of the low spatial frequencies and high retinal illuminances, which are not shown here.
153
For the conditions of the high spatial frequencies and/or the low retinal illuminances, however, the introduction of the rectification function causes a systematically significant deviation of the prediction from the empirical data. The lower panels in Fig. 4 represent the sensitivity functions for 0.75 c/deg at 0.88 td predicted by setting g = 3, showing clearly such deviations. It is important to note here that the introduction of the asymmetric rectifier-type nonlinearity gives a substantial effect to the out-of-phase conditions, but not to the in-phase condition, because of small magnitude of the negative lobe of the filtered response. If we use the same value of g, much larger deviations are led to for the other out-of-phase conditions of the high spatial frequencies and/or low retinal illuminances. These findings show that the rectification law does not hold through the stimulus condition. Bergen and Wilson (1985) found that, to predict the sinusoidal flicker sensitivity from the temporal three-pulse data, the asymmetric rectifier-type nonlinearity was required for the low spatial frequency but not for the high spatial frequency. A further problem of the rectifier-type nonlinearity concerns the variation in the value of g among authors. The present study requires the value of g = 3 so as to obtain a good prediction for 0.75 c/deg at 1100 td. This value is comparable with that of Kelly and Savoie (1978; g = 2.7), but is much larger than the value of Bergen and Wilson (1985; g = 1.4), and far beyond the values of Legge and Kersten (1983; g = 1.1) and of Roufs (1974a; g = 1). Given the evidences of variation in the rectification function, one might not expect that the discrepancies between the predictions and the empirical data could be explained only by the asymmetric rectifier-type nonlinearity.
(2) Duplicity of temporal property The discrepancies between the predictions and the data for the low spatial frequencies at the high retinal illuminances may be ascribed to the assumption on which the present analysis is based. Our mathematical analysis is based on the assumption that the temporal processing for a given combination of spatial fre~quency and mean retinal illuminance is mediated only by a single channel but not by multiple channels. This assumption may not be valid for our conditions of the low spatial frequencies at the high retinal illuminances.
154
Y o s m o OHTANI and YOSHIMICItI EJIMA
It has been well established that the human visual system contains two distinct mechanisms, i.e. the sustained and transient mechanisms. The two mechanisms differ in their temporal properties and in the ranges of spatial frequencies over which they operate (Keesey, 1972; Tolhurst, 1973; Kulikowski and Tolhurst, 1973; Sharpe and Tolhurst, 1973; Pantle, 1973; Tolhurst et al., 1973; King-Smith and Kulikowski, 1975; Harwerth and Levi, 1978; Bodis-Wollner and Hendley, 1979). The transient mechanism is sensitive to rapid temporal change and to low spatial frequency, while the sustained mechanism responds better to steady or slowly changing stimuli and to high spatial frequency. It is likely that there exists a range of spatial frequency over which the both mechanisms contribute to detection of the stimulus gratings. For such a range of spatial frequency, temporal response property of the visual system would be determined by the changing contributions of the two mechanisms. The changing contributions of the two mechanisms to the detection process have been studied by using different detection criteria, i.e. the pattern and the flicker criterion. The sensitivity for the pattern deteclion (which is assumed to be mediated by the sustained mechanism) is higher than for the flicker detection (which is assumed to be mediated by the transient mechanism) in low temporal frequency region, while the flicker sensitivity becomes higher than the pattern sensitivity in high temporal frequency region (Kulikowski and Tolhurst, 1973; Wilson, 1980; Burbeck, 1981; Burbeck and Kelly, 1981). This implies that when the observer is required to detect any change on the stimulus field irrespective of the kind of percepts, the resulting temporal sensitivity may be a composite function of the underlying two mechanisms. This may be the case with the present experimental situation. Thus, it seems reasonable to assume that the temporal modulation function may be an envelope of two different functions of the sustained and transient mechanisms for the low spatial frequencies at the high retinal illuminances. On the other hand, the two-pulse sensitivity function for the conditions may be determined by the transient mechanisms, rather than the sustained mechanisms, because the two-pulse stimulus consists of rapid temporal changing stimuli. This may be the reason why the single channel analysis could not account for the relationship between the two sensitivities. The hypothesis that the temporal modulation sensitivity function consists of the
sustained and transient mechanisms is in line with Roufs' envelope assumption for uniform field (Roufs, 1974a, b; Roufs and Blommaert, 1981). According to the duplicity hypothesis, we modified the temporal modulation sensitivity function (or equivalently, the impulse response function) under the two constraints that; (1) the temporal modulation sensitivity at high temporal frequencies should be determined by the transient mechanism, and (2) the transient mechanisms should not show any sustained lobe in the temporal response to a step signal (i.e. the positive and the negative lobe of the impulse response are balanced) at high retinal illuminances. The latter constraint has been supported psychophysically (Roufs, 1974a; Tolhurst, 1975). The modification was done with the conditions of spatial frequencies of 0.75 and 1.5 c/deg at the retinal illuminances of 88 and 1100 td. Dashed lines in Fig. 2 show the modified modulation sensitivity functions. The solid lines in Fig. 5 show the resulting predictions obtained by using the values of parameters listed in Table 2. Note that the values of parameters remain almost the same as those in Table 1 except the value of B. Good fits are obtained at 1100 td for the two observers, while at 88 td, the predictions of the sensitivities for out-of-phase condition are somewhat highgr than the empirical data for the SOAs of 50-100msec. Predictions for the in-phase pairs are not affected so markedly by the modifi2 •
0,75 cpd
1.5 cpd
."2_ ._~
1100td to
"-J 1t ~ 0
' 100
0
11ootd 100
Stimulus onset asynchrony (ms)
Fig. 5. Predictions based on the duplicity hypothesis(solid lines) for 0.75 and 1.5 c/deg at 88 and 1100td. Data points are replotted from Fig. 3. Upper panels are for Y.E.: lower panels are for Y.O. Dashed lines are the predictions by the temporal probability summation model (the same as the solid lines in Fig. 3). The data and the predictions for the SOA of 208 msec are omitted here.
Flicker and two-pulse sensitivities
155
Table 2. Parameter values estimated to fit the two-pulse sensitivity on the basis of the duplicity hypothesis Subject Illuminance (td)
Y.E, 88
(n = 3) 1100
Y.O. 88
(n = 2) 1100
SF (c/deg) A B 0.75 k z (see) A B
1.5
5.6 x 1016 (6.0 x 1016) 1.13 (0.90) 3.5 0.012 3.1 x 1014 (3.3 x 1014) 1.13
2.5 x 1017 1.00 3.0 0.008 1.8 x 1023 1.00
(o.9o) k z (sec)
2.5 0.015
cations of the impulse response. This deviation for the 88 td condition suggests that the inhibitory lobe of the impulse response function of the transient mechanism may be overestimated. If the transient mechanisms, for the low retinal illuminances, might show a sustained lobe in the temporal response to a step signal, the inhibitory lobe of the impulse response should be reduced. This may be the case with the present 88 td condition. A smaller negative lobe gives a better fit, falling between the solid and dashed lines in Fig. 5. Paramete~ values which yield the best fits to the data on the basis of the least square, are shown in the parentheses in Table 2. Under the conditions of the high spatial frequencies and/or the low retinal illuminances, such introduction of temporal duplicity is not required, since the temporal probability summation model succeeds in predicting the relation between the temporal modulation sensitivities and the two-pulse sensitivities. This suggests that the temporal modulation sensitivity for the high spatial frequencies and/or the low retinal illuminances is determined by a single mechanism, presumably the sustained mechanisms, whereas the sensitivity for the low spatial frequencies at the high retinal illuminances is determined by multiple mechanisms, presumably the sustained and the transient mechanisms. This suggestion may be supported by physiological studies. Two types of cell, i.e. x and Y cells, are identified in the retina, and LGN of cat and primate visual system. The X cell which has been supposed to be a neural substrate of the sustained mechanisms is sensitive to high spatial frequencies and steady or slowly temporal change stimuli. The Y cell which has been supposed to be a neural substrate of the tran-
1.9 x 1012 (2.0 x 1012) 1.13 (0.85) 2.5 0.016 1.3 x 1012 (1.5 x 1012) 1.13
4.4 x 1014 1.00 3.0 0.010 4.8 x 1019 1.13
(0.7o) 6.0 0.009
2.5 0.018
5.5 0.010
sient mechanisms responds to low spatial frequencies and rapid temporal change stimuli. Further, the transient property of the Y cell is observed only at high luminance levels, diminishes with decrease in adapting luminance, and disappears when fully dark adapted. At low luminance levels, the response of the Y cell shows a similar temporal property to that of the X cell (Yoon, 1972; Enroth-Cugell and Shapley, 1973; Jakiela and Enroth-Cugell, 1976; Lennie, 1980). Thus it is for stimuli of low spatial frequencies at high luminance levels that the transient property of the Y cell is observed. The condition for the emergence of the transient property of the Y cell conforms to our conditions of the low spatial frequencies and high retinal illuminances where the temporal duplicity is required to relate the different temporal measures successfully. Acknowledgements--This work was supported in part by Grant-in-Aid for the Scientific Research (No. 61510044) from the Ministry of Education, by Nihon Housou Bunka Kikin, and by Yamamura-Tamura Foundation.
REFERENCES Bergen J. R. and Wilson H. R. (1985) Prediction of flicker sensitivities from temporal three-pulse data. Vision Res. 25, 577-582. Bodis-Wollner L and Hendley C. D. (1979) On the separability of two mechanisms involved in the detection of grating patterns in humans. J. Physiol., Lond. 291, 251-263. Breitmeyer B. G. and Ganz L. (1977) Temporal studies with flashed gratings: inferences about human transient and sustained channels. Vision Res. 17, 861-865. Burbeck C. A. (1981) Criterion-free pattern and flicker thresholds. J. opt. $oc. Am. 71, 1343-1350. Burbeck C. A. and Kelly D. H. (1981) Contrast gain
156
Yosmo OHTANI and YOSHIMICHIEJIMA
measurements and the transient/sustained dichotomy. J. opt. Soc. Am. 71, 1335-1342. Cornsweet T. N. (1962) The staircase-method in psychophysics. Am. J. Psychol. 75, 485-491. Daly S. J. and Normann R. A. (1985) Temporal information processing in cones: effects of light adaptation on temporal summation and modulation, t"ision Res. 25, 1197-1206. Enroth-CugeU C. and Shapley R. M. (1973) Adaptation and dynamics of cat retinal ganglion cells. J. Physiol., Lond. 233, 271-309. Georgeson M. A. (1987) Temporal properties of spatial contrast vision. Vision Res. 27, 765-780. Gorea A. and Tyler C. W. (1986) New look at Bloch's law for contrast, J. opt. Soc. Am. A3, 52-61. Harwerth R. S. and Levi D. M. (1978) Reaction time as a measure of suprathreshold grating detection. Vision Res. 18, 1579-1586. Jakiela H. G. and Enroth-Cugell C, (1976) Adaptation and dynamics in X-cells and Y-cells of the cat retina. Exp. Brain Res. 24, 335-342. Keesey U. T. (1972) Flicker and pattern detection: a comparison of thresholds. J. opt. Soc. Am. 62, 446-448. Kelly D. H. (1971a) Theory of flicker and transient responses, I. Uniform fields. J. opt. Soc. Am. 61, 537-546. Kelly D. H. (1971b) Theory of flicker and transient responses, II. Counterphase gratings. J. opt. Soc. Am. 61, 632-640. Kelly D. H. (1972) Adaptation effects on spatio-temporal sine-wave thresholds. Vision Res. 12, 89-101. Kelly D. H. and Savoie R. E. (1978) Theory of flicker and transient responses, III. An essential nonlinearity. J. opt. Soc. Am. 68, 1481-1490. King-Smith P, E. and Kulikowski J. J. (1975) Pattern and flicker detection analysed by subthreshold summation. J. Physiol., Lond. 249, 519-548. I Kulikowski J. J. and Tolhurst D. J. (1973) Psychophysical evidence for sustained and transient detectors in human vision. J. Physiol., Lond. 232, 149-162. Legge G. E. (1978) Sustained and transient mechanisms in human vision: temporal and spatial properties. Vision Res. 18, 69-81. Legge G. E. and Kersten D. (1983) Light and dark bars; contrast discrimination. Vision Res. 23, 473-483. Lennie P. (1980) Parallel visual pathways: a review. Vision Res. 20, 561-594. Pantle A. (1973) Visual effects of sinusoidaltcomponents of complex gratings: independent or additive? Vision Res. 13, 2195-2204. Quick R. F. (1974) A vector-magnitude model of contrast detection. Kybernetik 16, 65-67. Roufs J. A. J. (1972a) Dynamic properties of vision--I. Experimental relationships between flicker and flash thresholds. Vision Res. 12, 261-278. Roufs J. A, J. (1972b) Dynamic properties of vision--II. Theoretical relationships between flicker and flash thresholds. Vision Res. 12, 279-292. Roufs J. A. J. (1973) Dynamic properties of vision--Ill. Twin flashes, single flashes and flickerfusion. Vision Res. 13, 309-323. Roufs J. A. J. (1974a) Dynamic properties of vision--IV.
Thresholds of decremental flashes, incremental flashes and doublets in relation to flicker fusion. Vision Res. 14, 831-851. Roufs J. A. J. (1974b) Dynamic properties of vision--V. Perception lag and reaction time in relation to flicker and flash thresholds. Vision Res. 14, 853-869. Roufs J. A. J, and Blommaert F. J. J. (1981) Temporal impulse and step responses of the human eye obtained psychophysically by means of a drift-correcting perturbation technique. Vision Res. 21, 1203-1221. Sachs M. B., Nachmias J. and Robson J. G. (1971) Spatial-frequency channels in human vision. J. opt. Soc. Am. 61, 1176-1186. Sharpe C. R. and Tolhurst D. J. (1973) The effects of temporal modulation on the orientation channels of the human visual system. Perception 2, 23-29. Tolhurst D. J. (1973) Separate channels for the analysis of the shape and the movement of a moving stimulus. J. Physiol., Lond. 231, 385-402. Tolhurst D. J. (1975) Sustained and transient channels in human vision. Vision Res. 15, 1151-1155. Tolhurst D. J., Sharpe C. R. and Hart G. (1973) The analysis of the drift rate of moving sinusoidal gratings. Vision Res. 13, 2545-2555. Tranchina D., Gordon J. and Shapley R. M. (1984) Retinal light adaptation--evidence for a feedback mechanism. Nature, Lond. 310, 314-316. Uetsuki T. and Ikeda M. (1970) Study of temporal Visual response by the summation index. J. opt. Soe. Am. 60, 377-381. Van Nes F. L., Koenderink J. J., Nas H. and Bouman M. A. (1967) Spatiotemporal modulation transfer in the human eye. J. opt Soc. Am. 57, 1082-1088. Watson A. B. (1979) Probability summation over time. Vision Res. 19, 515-522. Watson A. B. and Nachmias J. (1977) Patterns of temporal interaction in the detection of gratings. Vision Res. 17, 893-902. Wilson H. R. (1980) Spatiotemporal characterization of a transient mechanism in the human visual system. Vision Res. 20, 443-452. Yoon M. (1972) Influence of adaptation level on response pattern and sensitivity of ganglion cells in the cat's retina. J. Physiol., Lond. 221, 93-104. APPENDIX
The second term of the right side of the equation (4) is rewritten as follows: I fr
.
-ll/p
Jo lSm(2nft)l'dtJ
.
where y = 2rift. It follows that I ~ "yr . _-I'/' I/2nfJ sm(y)l p dy /
=[l/2nf~/2[sin(y)l,dy× 4fTl'/'
F {
~,,12 .
= / T t 2 n J0
= TUPA(p).
ql/.
=[f2o'~rl/2nflsln(y)l'dy j
\-Illp Ism(y)l'dy)J