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Two pulses seen as three flashes: A superposition analysis
0042-6989/89$3.00+ 0.00 Copyright 0 1989Pergamon Press plc
VisionRes, Vol. 29, No. 4, pp.409-417, 1989 Printed in Great Britain. All rights reserved
TWO PULSES SEEN AS THREE FLASHES: A SUPERPOSITION ANALYSIS RICHARD
W. BOWEN
Department of Psychology, Loyola University of Chicago, Chicago, IL 60626, U.S.A. (Received 6 June 1988; in revisedform 16 September 1988) Abstract-If a single brief light pulse follows the offset of a light field by 0.14.3 set, the pulse is seen as a double flash. This “double flash effect” is a suprathreshold phenomenon: the pulse must exceed detection threshold by 10 times or more for this temporal illusion to occur. A special case of this effect is demonstrated here: two brief, high-luminance pulses separated by 0.1 set appear as three flashes. In a superposition analysis, hypothetical impulse response functions were added together with various delays to model flash perception. A biphasic impulse response (congruent with threshold flicker and pulse sensitivity) fails to predict perception of three flashes from two pulses. The analysis instead suggests that the visual response to a suprathreshold pulse has several alternating phases of excitation and inhibition. Temporal vision discrimination
Superposition/linear
Temporal impulse response
systems analysis
Two-pulse
baseline response level) with a trailing negative lobe (inhibitory, and below baseline) (Ikeda, Over the past three decades, linear systems 1965; Kelly, 1971). For the contrast sensitivity analysis has been vigorously applied to under- function, an inhibitory response component is standing human temporal vision at threshold. inferred from bandpass flicker sensitivity (deCritical data include detection and interaction creasing sensitivity at low temporal frequencies) of light pulses (Ikeda, 1965; Rashbass, 1970) (Kelly and Savoie, 1978; Swanson et al., 1987). and modulation sensitivity to sinusoidal flicker For pulse detection, a phase of inhibition is (de Lange, 1954; Kelly, 1961, 1971). Threshold inferred from the fact that two pulses separated data for pulses and for flickering sinusoids have by an intermediate interval require a higher been used to draw inferences about the nature luminance for threshold than if the interpulse of impulse responses, visual reactions to a the- interval is longer or shorter (Ikeda, 1965).* oretical light pulse of infinite height and Although a biphasic impulse response is cominfinitesimal width. As noted by Ikeda (1986), monly derived from threshold data, some analthe impulse response function commonly de- yses have suggested that the response is multirived from Fourier synthesis of a modulation phasic (Roufs and Blommaert, 1981; Stork and transfer function (i.e. from a measured temporal Falk, 1987). If the impulse response has several contrast sensitivity function) is similar to phases of excitation and inhibition, threshold that inferred from threshold summation of a data are perhaps not ideal for revealing their sequence of two light pulses. For luminance presence, since secondary “ringing” in the remodulation, under moderate light adaptation, sponse may be of too low an amplitude. Multithe impulse response is biphasic. The response ple phases in the impulse response may be more is initially positive (or excitatory, and above a readily distinguished at suprathreshold levels (Ueno, 1977). An important, and generally unexplored issue, is the nature of the response to *The form of an impulse response function inferred from stimuli that are significantly above detection or psychophysical data is very much dependent on the modulation threshold. stimulus conditions under study. For chromatic stimuINTRODUCTION
lation, for example, the impulse response function is sometimes characterized as monophasic, with only an excitatory lobe, since the modulation transfer function for equal-luminance chromatic modulation is nearly low-pass in form at moderate luminance levels (Kelly and van Norren, 1978; Swanson et al., 1987). 409
THE DOUBLE FLASH EFFECT
This paper is concerned with a perceptual effect that may reflect the form of temporal
RICHARD
410
31~5 :LASH
W.
BOWEN
ers JF and MP were naive as to the specific stimulus conditions studied and the purpose of the experiment. All observers had normal acuity with their customary refractive correction,
2 ‘71 5
1
:
TWO QASHES
ONE FLASH
12. TIME
Fig. 1. Schematic representation of the double flash effect as
reported by Bowenet al. (1980) and Bowen et al. (1987). Followingthe offset of a long-duration inducing light, a single probe pulse is presented. If the inducer-probe delay
is short (less than 0.1 set) or long (more than 0.3 set), a single flash is seen. If the probe is delayed by 0.1-0.3 set, it is perceived as a double flash.
responses to stimuli above detection threshold. The double flash effect (Bowen et al., 1980,1987) is elicited when a single brief suprathreshold light pulse follows the offset of a light field. With an appropriate delay (0.14.3 set) between light offset and pulse presentation, the single pulse is perceived as a double flash. Some activity or state of the visual system persists after light offset and interacts with the response to a subsequent brief light pulse so as to produce illusory flicker. The stimuli and the perceptions defining the double flash effect are represented schematically in Fig. 1. This temporal illusion has an important property. Double flashes are not seen if the brief probe pulse is near detection threshold (Bowen et al., 1987)-the pulse must be 10 times threshold or more in order to appear as a double flash. The effect thus requires a clearly suprathreshold stimulus, and it might therefore reflect a suprathreshold impulse response function. The present experiment establishes that illusory flashes can be observed using a simple sequence of two brief high-luminance suprathreshold pulses. In particular, two pulses are seen as three flashes when separated by about 0.1 sec. A temporal superposition analysis is used to ask whether impulse response functions of two basic forms-biphasic or multiphasiccan account for this finding. I conclude that the underlying suprathreshold impulse response function is likely multiphasic, with several WCcessive excitatory and inhibitory lobes. METHOD
Observers
The author (RB) and two laboratory assistants (MP and JF) served as observers. Observ-
Apparatus
Stimuli were generated by one channel of a two-channel Maxwellian-view optical system (Bowen et al., 1987). The light source was a high-brightness “orange” light-emitting diode (LED; dominant wavelength = 580 nm) located two focal lengths from a single Maxwellian lens (f = 125 mm). The source image was thus also located two focal lengths from the lens. A circular field stop located one focal length from the lens generated a well-focused image of a 25 min diameter target on the observer’s retina. The observer viewed the target through a 2 mm artificial pupil which completely contained the source image (LED cathode). The observer’s head was positioned with a chin rest. Fixation was further aided by the fact that between trials the target was continuously visible at a retinal illuminance of 10 td (see Procedure below). The optical system was interfaced to a microcomputer (IBM-PC). A 12-bit digital-to-analog converter (Data Translation) controlled the output of a precision voltage-to-frequency converter (Analog Devices) which generated 2 psec current pulses to drive the LED at a frequency linearly related to applied voltage. For a maximum 10 V signal from the computer, a pulse frequency of 85 kHz was produced which could generate a peak retinal illuminance of 20,000 td. In the present study, 1.3 log units of neutral density filters were placed in the optical path, so that a 10 V signal produced a maximum retinal illuminance of 1000 td. At a continuous illuminance level of 10 td, the stimulus pulse frequency was therefore 850 Hz. Retinal illuminance calibrations were made using the techSTIMULUS
CONDITIONS
Time
Fig. 2. The stimulus conditions. The 25 min dia. target was foveally fixated on a dark field. Pulses were changes in retinal illuminance from 10 to 1000 td. See text for further details.
Two pulses seen as three flashes
nique described by Nygaard and Frumkes (1982), using an EG&G photometer (Model 450). Procedure
411 RESULTS
The results are given in Fig. 3. Each panel of the figure plots functions for-all three Observers that relate the frequency (in percent) of a given response to the interpulse interval. A data point legend is given in the top left panel: observer RB, squares; observer JF, crosses; observer MP, triangles. The panels (a) and (d) show frequency of reporting ‘&one flash” for the two procedures: three response alternatives, panel (a); two response alternatives, panel (d). The two data sets are similar; frequency of reports of “one flash” declines sharply between IPI values of 0.01 and 0.09 set, and the displacement of the functions along the IPI axis by observer follows the same ordering in each data set. The tendency of an observer to report “one flash” was not affected by whether two or three response alternatives were available. The data for reports of “two flashes” (panel (c)) were slowly and irregularly increasing functions from over nearly the entire IPI range. Only, in fact, at the longest IPI values do any of the observers report with complete certainty that they saw two flashes. All three observers made substantial use of the “three flashes” response category (panel (b)). The frequency of reporting three flashes is very low at IPI values less than 0.05 or greater than 0.15 sec. All three observers produced a maximum frequency of responding “three flashes” at IPI values in the range from 0.09 to 0.13 set (response frequency of 44-78%). Within this range, the perception of three flashes is a robust phenomenon. A pair of pulses separated by roughly 0.1 set often appears as a sequence of at least three flashes.
The observer viewed, in darkness, the 25 min dia. circular target illuminated at a level of 10 td. He depressed a button to initiate an experimental trial; after a fixed delay of 0.3 s, two 0.005 set, 1000 td pulses were presented at the target location, separated by an interval in a range from 0.01 to 0.19 sec. During the interpulse interval (IPI) and following the pulse sequence, the target was at the prevailing (initial) level of 10 td. These time-luminance relations are depicted in Fig. 2. In one stimulus series, 10 presentations each of IPI values of 0.01, 0.05, 0.09, 0.13 and 0.17 set occurred in a randomized order (a 50-trial sequence). A second 50-trial stimulus series consisted of 10 presentations of 0.03, 0.07, 0.11, 0.15, and 0.19 set IPI values, also completely randomized. During either series, following each trial at a particular IPI, the observer depressed one of three buttons to indicate whether he had seen “one flash, ” “two flashes” or “three flashes.” The naive observers (JF and MP) were unaware that on each trial the physical stimulus was always a pair of light pulses in sequence.* In addition to these “three alternative” experimental runs, a daily session also included a “two alternative” experimental series in which the observer responded “one flash” or “two flashes” on each trial. In this series, IPI values of 0.01,0.03, 0.05, 0.07 and 0.09 were tested, 10 trials each in a randomized order. This reduced range of IPI values was expected to encompass the normal two-alternative response variation in two-pulse discrimination (Boynton, 1972; Bowen and Hood, 1983). This series was included to check whether the probability of reporting “one flash” was affected to any appreANALYSIS ciable degree by a paradigm involving two To account for flash perception, we adopt versus three response categories. The three series of stimuli were run during these propositions: five daily sessions. Final data were based on 50 (1) The brief, high-luminance light pulses trials per IPI condition. used here can be treated as impulses. (2) The visual response to such a pulse will therefore be the impulse response of the system, if the system behaves linearly. *The response “three flashes” could also have been (3) With the assumption of visual system designated “more than two flashes,”but that seemed linearity, the principles of superposition and like a potentiallyconfusingcategory for naive observers. Reports of “three flashes” could have been given time invariance will apply (Watson, 1986), and for any perception of flash numerosity more than two the response to a sequence of two pulses at a flashes. particular interpulse interval can be calculated
RICHARD
412 Response
(a)
W.
BOWEN
: oneflash
Response
(b)
100
: two flashes +\
/ /+
P
60 o MP
+ JF
0.13 0.05 0.09 Interpulse interval ( set
0.01
(cl 100
Response
: three
0.17
0.05
1
0.09
Interpulse
flashes
(d)
ResDMse: one
r
60 -
0.13 interval
0.17
(set)
flash
60
0.13
0.09
0.05 Interpulse
interval
0.17
(set
0.05
0.09
Interpulse
1
0.13 interval
0.17
(set 1
Fig. 3. Data for three observers. Panels (a-c): data from the procedure with three response alternatives (“one flash”, “two flashes” or “three flashes”). Panel (d): data from the procedure with two response alternatives (“one flash” vs “two flashes”). Panel (a): frequency of reports of “one flash” as a function of IPI. Panel (c): frequency of reports of “two flashes” as a function of IPI. Panel (b): frequency of reports of “three flashes” as a function of IPI. In panels (as), for a given observer, frequency values for all three responses sum to 100% for any IPI.
by the addition of two impulse response functions separated by the appropriate time delay. (4) The perception of flashes will be determined by the presence of peaks in the calculated response function.
(a)
Biphasic
impulse
Time
response
The analysis evaluates two classes of impulse response: a biphasic response, congruent with threshold-level data, and a multiphasic response, composed of many cycles of damped oscillation. The biphasic impulse response
(b)
Multtphosic
Impulse response
Time
The hypothetical impulses responses used in the superposition analysis. Panel (a): a biphasic impulse response from the model of Watson (1986). Panel (b): a multiphasic impulse response, an exponentially-damped sin function.
413
Two pulses seen as three flashes
Time
Time
(d)
Time
Time
I
Time
Time
Fig. 5. Results of a superposition analysis with biphasic impulse responses. One response is delayed and added back to the other response (temporal superposition). In panels (a-f) the value of the delay increases progressively.
comes from the model of temporal sensitivity presented by Watson (1986). The response has two components-one excitatory, one inhibitory-and each is the output of a cascade of identical low-pass filter stages. The biphasic impulse response is depicted in Fig. 4a. The form of this response is consistent with threshold data structures (flicker and pulse detection). The multiphasic impulse response (Fig. 4b) is an exponentially-damped sine function. This response is oscillatory and has multiple peaks and troughs. The superposition analysis involved in summing two identical impulse responses, with one response lagging by a particular delay, short, intermediate and long in duration. The delays correspond to the psychophysical IPI parameter. The first aim of the superposition analysis
was qualitative: would the superposition of either impulse response simulate the flash perceptions reported in the experiment? Figure 5 shows the superposition of two biphasic impulse responses at various delays, with delay increasing from panels (a) to (f). The superposition response has two distinct positive peaks for intermediate and long delays, but at no delay is a third positive peak present. The visual responses synthesized by superposition of biphasic impulse responses do not show three positive peaks at any delay and thus do not predict the perception of three flashes from the presentation of two pulses. (The longest delay, in panel (f), was roughly twice the overall duration of the impulse response.) Figure 6 presents functions from the superposition of multiphasic impulse responses.
414
RICHARDW. BOWEN
.iP+=-j ---.--.--._ .-.._ (a)
(b)
3 3 0 ”
-__.._.______.
5
I+--
Time
Time
(d)
Time
(e)
Time
(f)
Time
Time
Fig. 6. As for Fig. 5, except with multiphasic impulse responses. The dashed line marks the amplitude of the second peak in the impulse response. See text for discussion.
Clearly, because of the form of the impulse response, the perception of three (or even more) flashes is predicted over a broad range of intervals. Therefore, a rule must be devised to decide whether a peak is seen as a flash. This amounts to embellishing proposition 4 above. We consider first a rule that holds that the amplitude of a peak must exceed threshold level for flash perception. In Fig. 6, the dashed horizontal line in each panel represents such a threshold. It corresponds to the amplitude of the second peak in the multiphasic impulse response (Fig. 4b). This is consistent with the observation that a single pulse presented to the fovea is seen as a single flash. The second and subsequent peaks in the oscillating impulse response are sub-threshold. In Fig. 6, at delay value d, there are three peaks in the response above the threshold level,
and thus three perceived flashes. Three flashes occur when the oscillating impulse response functions are superposed approximately “in phase,” so that sub-threshold response peaks sum to produce supra-threshold flash perceptions. At a shorter or longer delays, only two peaks exceed the threshold level. A discrepancy occurs in panel (a) of Fig. 6, where impulse responses are superposed at a very short IPI, in near temporal registration. The second peak of the superposition response is consequently above the threshold level. This predicts that two flashes will be seen but, of course, only one flash is perceived. We therefore consider an alternative rule for flash perception. The perception of a single flash could be due to masking of the second peak by the largeamplitude first peak. Masking effects are consistent with Ikeda’s observation (1965) that pulses
Two pulses seen as three flashes
with unequal amplitude interact in nonadditive fashion at threshold. To simulate a general masking effect, as an alternative to the rule of a fixed threshold amplitude, we calculated ratios of response peak amplitudes, second peak to first peak and third peak to first peak. At this point it becomes necessary to associate numerical parameters with the impulse response function. For the response functions in Fig. 6, the impulse response is given by: f(t) = sin(20 7tt) e -‘lo.‘.
(1)
The response is an exponentially-damped 10 Hz sin function with time constant of 0.1 sec. In Fig. 6, panels (a-f) represent IPI values of 0.01, 0.03, 0.05, 0.09, 0.13 and 0.17 set, respectively, based on the response of equation (1). Other IPI values from the experiment were also evaluated. Figure 7 gives the ratio of second peak amplitude to first peak amplitude (squares) and the ratio of third peak amplitude to first peak amplitude (diamonds) as a function of IPI. The dashed line represents the ratio of second peak to first peak amplitude in the impulse response function (Fig. 4b). Points above this line predict that flashes will be seen at that IPI. The predictions of Fig. 7 agree very well with the data of Fig. 3. At short interpulse intervals (0.01 and 0.03 set), both ratios are below the threshold level-one flash is seen. At very long interpulse intervals (0.15-O. 19 set), the third peak/first peak ratio is above the dashed line,
415
but the second peak/first peak ratio is not-two flashes are seen. And at intermediate interpulse intervals (0.07 to 0.11 s), both ratios are above the threshold line-three flashes are seen. With the assumption that the ratio of amplitudes among response peaks determines perception of flashes, we account for all crucial aspects of the data. (With a ratio rule, the degree of damping in the impulse response, which determines the amplitude relation of all peaks, does not affect the conclusions drawn from Fig. 7.) In the present linear analysis, the prediction of three flashes in response to two pulses requires three positive peaks in the impulse response, even though two of them are not seen. Were there only two peaks, in-phase addition would generate only two flashes, because the trailing third peak in the superposition response is at threshold (or is too small a fraction of the first peak amplitude). If, on the other hand, the superposition response were subjected to a subsequent compressive nonlinearity (such as Lehky, 1985, found for suprathreshold contrast responses), this would tend to reduce the amplitude of large peaks relative to small ones. Thus an impulse response that was only triphasic (as in Stork and Falk, 1987) might account for the perception of three flashes from two pulses. But a biphasic response is not adequate in either the present linear systems framework or in a model incorporating a plausible nonlinearity. To summarize, this analysis shows that, if we accept the applicability of the superposition principle for impulse light signals, a biphasic impulse response cannot account for the perception of three flashes for an input of two brief light pulses. Instead, the presence of illusory flashes is predicted by an oscillating impulse response having at least three phases of excitation and inhibition. DISCUSSION
0.05
0.09
0.13
0.17
Interpulse interval (see) Fig. 7. Predictions of flash perception from a quantitative version of the superposition analysis. Plot of ratios of peak response amplitudes as a function of IPI. Squares are the ratio of second peak to first peak; diamonds are the ratio of third peak to first peak. The dashed line represents the ratio of the second peak to the first peak in the multiphasic impulse response (equation 1). Ratio values above the dashed line predict flash perception due to one or both functions at a given IPI value.
In the analysis presented here, the temporal form of an impulse response function is inferred from a psychophysical paradigm with transient stimuli. The logic of this approach was pioneered by Ikeda (1965). Ikeda showed that a pair of brief pulses separated by 0.07 set (at a low adaptation level) required more threshold radiance than when separated by a longer interpulse interval. He inferred that an inhibitory process was present at that interval, in which a trailing negative phase of the first response subtracted from the leading positive phase of a
RICHARD W. BOWEN
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second response. This inference is the basis of the now widely accepted view that the impulse response at detection threshold is biphasic for luminance signals (Ikeda, 1986; Rashbass, 1970). In a study directly related to the present one, Ueno (1977) made analogous inferences for reaction time data to suprathreshold double pulses of light. With pulses separated by 0.1 set (at a low adapting level), reaction times were longer than at longer IPI values, implying an inhibitory process. At higher adapting levels, the inferred inhibitory phase of the response moves to shorter delays, and the reaction time function oscillates at still longer delays. From this, Ueno concluded that the underlying impulse response was multiphasic with at least two successive positive-negative components. Here we deduce a multiphasic impulse response from the perception of flashes more numerous than the physical light pulses. The temporal structure of the oscillating impulse response (equation 1) was suggested, of course, by the temporal structure of the data (Fig. 3). How well does this particular impulse response function predict the temporal structure of the double flash effect (see Fig. 1; Bowen et al., 1980, 1987), when a single brief pulse follows the offset of a long duration (0.5 set) light? Figure 8 shows a temporal convolution of the multiphasic impulse response with a 0.5 set pulse (the “inducer” for the double flash effect). A principal peak follows light offset by 0.1 sec. Were a multiphasic impulse response added in phase with this peak, given the amplitude ratio rule discussed above, only a single flash would Convolution : 0.5 set pulse 24
-0.6
t A
0
I 0.2
I
I 0.4 Time
1 0.6
1 0.6
I
( set 1
Fig. 8. Temporal convolution of the multiphasic impulse response (equation 1) with a 0.5 s pulse (the inducing pulse of Fig. 1). The arrow marks the delay of a probe pulse that will most effectively produce illusory flashes, given the amplitude ratio rule depicted in Fig. 7. See text.
be seen (secondary peaks would be masked). But if the impulse response were added in phase with a secondary trailing peak (marked by the arrow at about 0.18 set following light offset), as depicted in Fig. 6, this would cause the perception of two flashes for a single probe pulse. In data (Bowen et al., 1987), delays near 0.2 set are in fact optimal for producing illusory flashes to a probe pulse. Thus the temporal structure of the hypothetical impulse response also applies reasonably well to the original double flash effect. What mechanism might cause an oscillating impulse response function is an open issue. Recently, Stelmach et al. (1987), postulated that the double flash effect was due to alternate activation of “On” and “Off’ channels following light offset (see Jung, 1973; Krauskopf, 1980). This “parallel mechanism” model has positive and negative components of an impulse response in separate channels (Stelmach et al., 1987). The biphasic impulse response inferred from threshold data may actually be oscillatory in form. Possibly secondary and tertiary positive and negative phases are of such low amplitude that they do not contribute to measurable threshold values (except, perhaps, through probability summation, Watson, 1982). Stork and Falk (1987) have presented calculations of impulse responses from flicker sensitivity data; the temporal structure of many of these responses actually is oscillatory, and the impulse is at least triphasic at most adapting levels. The present analysis suggests that suprathreshold stimulus conditions allow more detailed evaluation of impulse responses. If the visual response to a strong signal is oscillatory, as suggested here, then the modulation transfer function for suprathreshold sinusoidal signals would be strongly bandpass in form. (We confirmed this with a fast Fourier transform of the impulse response (equation l).) Various studies have estimated the overall modulation transfer function for suprathreshold flicker. These have used brightness matching, with a steady reference field, of light and dark cycles in the flicker stimulus (Magnussen and Glad, 1975; Magnussen and Bjorklund, 1979) and direct scaling of apparent depth of modulation versus frequency (Marks, 1970). When mean luminance of a suprathreshold flickering stimulus is increased, the function remains bandpass in form, and the peak of the function shifts to higher frequencies (Magnussen and
Two pulses seen as three flashes
Glad, 1975). This follows threshold-level effects of adapting luminance (e.g. Kelly, 1961). But when adapting level is held constant, and modulation depth is increased, the function becomes low-pass at higher temporal contrast levels (above 50% according to Magnussen and Bjorklund, 1979; above 14% for a range of adapting levels, according to Marks, 1970). The finding of low-pass temporal filtering at high contrast level, implying a monophasic impulse response, is not consistent with analysis of the double flash effect. This raises the interesting possibility that the steady-state response and the transient response of the visual system for strong signals are governed by different processes. Acknowledgernears-Preparation of this manuscript was aided by a research leave of absence from Loyola University of Chicago. I thank Joel Pokomy and Vivianne C. Smith for a number of valuable comments and a critical reading of the manuscript. William Swanson also suggested a variety of significant improvements to the paper. REFERENCES Bowen R. W. and Hood D. C. (1983) Improvements in visual performance following a pulsed field of light: a test of the equivalent background principle. J. opt. Sot. Am. 73, 1551-1556. Bowen R. W., Markell K. A. and Schoon C. S. (1980) Two-pulse discrimination and rapid light adaptation: complex effects on temporal resolution and a new visual temporal illusion. J. opt. Sot. Am. 70, 1453-1458. Bowen R. W., Mallow J. and Harder P. J. (1987) Some properties of the double flash illusion. J. opt. Sot. Am. A 4, 746755. Boynton R. M. (1972) Discrimination of homogeneous double pulses of light. In Handbook of Sensory Physiology, Vol. VII/4, Visual Psychophysics (Edited by Jameson D. and Hurvich L.). Springer, Berlin. Ikeda M. (1965) Temporal summation of positive and negative flashes in the visual system. J. opr. Sot. Am. 55, 527-534. Ikeda M. (1986) Temporal impulse response. Vision Res. 26, 1431-1440. Jung R. (1973) Visual perception and neurophysiology. In Handbook of Sensory Physiology, Vol. VII/3, Central Visual Information A (Edited by Jung R.). Springer, Berlin. Kelly D. H. (1961) Visual responses to time-dependent
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stimuli. I. Amplitude sensitivity measurements. J. opt. Sot. Am. 51, 422429. Kelly D. H. (1971) Theory of flicker and transient responses. I. Uniform fields. J. opt. Sot. Am. 61, 537-546. Kelly D. H. and Savoie R. E. (1978) Theory of flicker and transient responses. III. An essential nonlinearity. J. opt. Sot. Am. 68, 1481-1490. Kelly D. H. and Norren D. van (1977) Two-band model of heterochromatic flicker. J. opt. Sot. Am. 67, 1081-1091. Krauskopf J. (1980) Discrimination and detection of changes in luminance. Vision Res. 24l, 671-677. de Lange H. (1954) Relationship between critical flicker frequency and a set of low frequency characteristics of the eye. J. opt. Sot. Am. 44, 38&389. Lehky S. R. (1985) Temporal properties of visual channels measured by masking. J. opt. Sot. Am. A 2, 1260-1272. Magnussen S. and Bjorklund R. A. (1979) The perception of suprathreshold sinusoidal flicker measured by lightand dark-phase matching. Vision Res. 19, 335-338. Magnussen S. and Glad A. (1975) Brightness and darkness enhancement during flicker: Perceptual correlates of neuronal B- and D-systems in human vision. ExpI Brain Res. 22, 399413. Marks L. E. (1970) Apparent depth of modulation as a function of frequency and amplitude of temporal modulation of luminance. J. opt. Sot. Am. 60, 970-977. Nygaard R. W. and Frumkes T. E. (1982) Calibration of the retinal illuminance provided by Maxwellian views. Vision Res. 22, 433434. Rashbass C. (1970) The visibility of transient changes in luminance. J. Physiol. Lond. 210, 165186. 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. Stelmach L. B., Bourassa C. M. and Di Lo110V. (1987) Gn and off systems in human vision. Vision Res. 27,919928. Stork D. G. and Falk D. S. (1987) Temporal impulse responses from flicker sensitivities. J. opt. Sot. Am. A 4, 113&1135. Swanson W. H., Ueno T., Smith V. C. and Pokomy J. (1987) Temporal modulation sensitivity and pulsedetection thresholds for chromatic and luminance perturbations. J. opt. Sot. Am. A 4, 1992-2005. Ueno T. (1977) Temporal characteristics of the human visual system as revealed by reaction time to double pulses of light. Vision Res. 17, 591-596. Watson A. B. (1982) Derivation of the impulse response: comments on the method of Roufs and Blommaert. Vision Res. 22, 133551337. Watson A. B. (1986) Temporal sensitivity. In Handbook of Perception and Human Performance, Vol. I, Sensory Processes and Perception (Edited by Boff K., Kaufman L. and Thomas J. P.). Wiley, New York.
VisionRes, Vol. 29, No. 4, pp.409-417, 1989 Printed in Great Britain. All rights reserved
TWO PULSES SEEN AS THREE FLASHES: A SUPERPOSITION ANALYSIS RICHARD
W. BOWEN
Department of Psychology, Loyola University of Chicago, Chicago, IL 60626, U.S.A. (Received 6 June 1988; in revisedform 16 September 1988) Abstract-If a single brief light pulse follows the offset of a light field by 0.14.3 set, the pulse is seen as a double flash. This “double flash effect” is a suprathreshold phenomenon: the pulse must exceed detection threshold by 10 times or more for this temporal illusion to occur. A special case of this effect is demonstrated here: two brief, high-luminance pulses separated by 0.1 set appear as three flashes. In a superposition analysis, hypothetical impulse response functions were added together with various delays to model flash perception. A biphasic impulse response (congruent with threshold flicker and pulse sensitivity) fails to predict perception of three flashes from two pulses. The analysis instead suggests that the visual response to a suprathreshold pulse has several alternating phases of excitation and inhibition. Temporal vision discrimination
Superposition/linear
Temporal impulse response
systems analysis
Two-pulse
baseline response level) with a trailing negative lobe (inhibitory, and below baseline) (Ikeda, Over the past three decades, linear systems 1965; Kelly, 1971). For the contrast sensitivity analysis has been vigorously applied to under- function, an inhibitory response component is standing human temporal vision at threshold. inferred from bandpass flicker sensitivity (deCritical data include detection and interaction creasing sensitivity at low temporal frequencies) of light pulses (Ikeda, 1965; Rashbass, 1970) (Kelly and Savoie, 1978; Swanson et al., 1987). and modulation sensitivity to sinusoidal flicker For pulse detection, a phase of inhibition is (de Lange, 1954; Kelly, 1961, 1971). Threshold inferred from the fact that two pulses separated data for pulses and for flickering sinusoids have by an intermediate interval require a higher been used to draw inferences about the nature luminance for threshold than if the interpulse of impulse responses, visual reactions to a the- interval is longer or shorter (Ikeda, 1965).* oretical light pulse of infinite height and Although a biphasic impulse response is cominfinitesimal width. As noted by Ikeda (1986), monly derived from threshold data, some analthe impulse response function commonly de- yses have suggested that the response is multirived from Fourier synthesis of a modulation phasic (Roufs and Blommaert, 1981; Stork and transfer function (i.e. from a measured temporal Falk, 1987). If the impulse response has several contrast sensitivity function) is similar to phases of excitation and inhibition, threshold that inferred from threshold summation of a data are perhaps not ideal for revealing their sequence of two light pulses. For luminance presence, since secondary “ringing” in the remodulation, under moderate light adaptation, sponse may be of too low an amplitude. Multithe impulse response is biphasic. The response ple phases in the impulse response may be more is initially positive (or excitatory, and above a readily distinguished at suprathreshold levels (Ueno, 1977). An important, and generally unexplored issue, is the nature of the response to *The form of an impulse response function inferred from stimuli that are significantly above detection or psychophysical data is very much dependent on the modulation threshold. stimulus conditions under study. For chromatic stimuINTRODUCTION
lation, for example, the impulse response function is sometimes characterized as monophasic, with only an excitatory lobe, since the modulation transfer function for equal-luminance chromatic modulation is nearly low-pass in form at moderate luminance levels (Kelly and van Norren, 1978; Swanson et al., 1987). 409
THE DOUBLE FLASH EFFECT
This paper is concerned with a perceptual effect that may reflect the form of temporal
RICHARD
410
31~5 :LASH
W.
BOWEN
ers JF and MP were naive as to the specific stimulus conditions studied and the purpose of the experiment. All observers had normal acuity with their customary refractive correction,
2 ‘71 5
1
:
TWO QASHES
ONE FLASH
12. TIME
Fig. 1. Schematic representation of the double flash effect as
reported by Bowenet al. (1980) and Bowen et al. (1987). Followingthe offset of a long-duration inducing light, a single probe pulse is presented. If the inducer-probe delay
is short (less than 0.1 set) or long (more than 0.3 set), a single flash is seen. If the probe is delayed by 0.1-0.3 set, it is perceived as a double flash.
responses to stimuli above detection threshold. The double flash effect (Bowen et al., 1980,1987) is elicited when a single brief suprathreshold light pulse follows the offset of a light field. With an appropriate delay (0.14.3 set) between light offset and pulse presentation, the single pulse is perceived as a double flash. Some activity or state of the visual system persists after light offset and interacts with the response to a subsequent brief light pulse so as to produce illusory flicker. The stimuli and the perceptions defining the double flash effect are represented schematically in Fig. 1. This temporal illusion has an important property. Double flashes are not seen if the brief probe pulse is near detection threshold (Bowen et al., 1987)-the pulse must be 10 times threshold or more in order to appear as a double flash. The effect thus requires a clearly suprathreshold stimulus, and it might therefore reflect a suprathreshold impulse response function. The present experiment establishes that illusory flashes can be observed using a simple sequence of two brief high-luminance suprathreshold pulses. In particular, two pulses are seen as three flashes when separated by about 0.1 sec. A temporal superposition analysis is used to ask whether impulse response functions of two basic forms-biphasic or multiphasiccan account for this finding. I conclude that the underlying suprathreshold impulse response function is likely multiphasic, with several WCcessive excitatory and inhibitory lobes. METHOD
Observers
The author (RB) and two laboratory assistants (MP and JF) served as observers. Observ-
Apparatus
Stimuli were generated by one channel of a two-channel Maxwellian-view optical system (Bowen et al., 1987). The light source was a high-brightness “orange” light-emitting diode (LED; dominant wavelength = 580 nm) located two focal lengths from a single Maxwellian lens (f = 125 mm). The source image was thus also located two focal lengths from the lens. A circular field stop located one focal length from the lens generated a well-focused image of a 25 min diameter target on the observer’s retina. The observer viewed the target through a 2 mm artificial pupil which completely contained the source image (LED cathode). The observer’s head was positioned with a chin rest. Fixation was further aided by the fact that between trials the target was continuously visible at a retinal illuminance of 10 td (see Procedure below). The optical system was interfaced to a microcomputer (IBM-PC). A 12-bit digital-to-analog converter (Data Translation) controlled the output of a precision voltage-to-frequency converter (Analog Devices) which generated 2 psec current pulses to drive the LED at a frequency linearly related to applied voltage. For a maximum 10 V signal from the computer, a pulse frequency of 85 kHz was produced which could generate a peak retinal illuminance of 20,000 td. In the present study, 1.3 log units of neutral density filters were placed in the optical path, so that a 10 V signal produced a maximum retinal illuminance of 1000 td. At a continuous illuminance level of 10 td, the stimulus pulse frequency was therefore 850 Hz. Retinal illuminance calibrations were made using the techSTIMULUS
CONDITIONS
Time
Fig. 2. The stimulus conditions. The 25 min dia. target was foveally fixated on a dark field. Pulses were changes in retinal illuminance from 10 to 1000 td. See text for further details.
Two pulses seen as three flashes
nique described by Nygaard and Frumkes (1982), using an EG&G photometer (Model 450). Procedure
411 RESULTS
The results are given in Fig. 3. Each panel of the figure plots functions for-all three Observers that relate the frequency (in percent) of a given response to the interpulse interval. A data point legend is given in the top left panel: observer RB, squares; observer JF, crosses; observer MP, triangles. The panels (a) and (d) show frequency of reporting ‘&one flash” for the two procedures: three response alternatives, panel (a); two response alternatives, panel (d). The two data sets are similar; frequency of reports of “one flash” declines sharply between IPI values of 0.01 and 0.09 set, and the displacement of the functions along the IPI axis by observer follows the same ordering in each data set. The tendency of an observer to report “one flash” was not affected by whether two or three response alternatives were available. The data for reports of “two flashes” (panel (c)) were slowly and irregularly increasing functions from over nearly the entire IPI range. Only, in fact, at the longest IPI values do any of the observers report with complete certainty that they saw two flashes. All three observers made substantial use of the “three flashes” response category (panel (b)). The frequency of reporting three flashes is very low at IPI values less than 0.05 or greater than 0.15 sec. All three observers produced a maximum frequency of responding “three flashes” at IPI values in the range from 0.09 to 0.13 set (response frequency of 44-78%). Within this range, the perception of three flashes is a robust phenomenon. A pair of pulses separated by roughly 0.1 set often appears as a sequence of at least three flashes.
The observer viewed, in darkness, the 25 min dia. circular target illuminated at a level of 10 td. He depressed a button to initiate an experimental trial; after a fixed delay of 0.3 s, two 0.005 set, 1000 td pulses were presented at the target location, separated by an interval in a range from 0.01 to 0.19 sec. During the interpulse interval (IPI) and following the pulse sequence, the target was at the prevailing (initial) level of 10 td. These time-luminance relations are depicted in Fig. 2. In one stimulus series, 10 presentations each of IPI values of 0.01, 0.05, 0.09, 0.13 and 0.17 set occurred in a randomized order (a 50-trial sequence). A second 50-trial stimulus series consisted of 10 presentations of 0.03, 0.07, 0.11, 0.15, and 0.19 set IPI values, also completely randomized. During either series, following each trial at a particular IPI, the observer depressed one of three buttons to indicate whether he had seen “one flash, ” “two flashes” or “three flashes.” The naive observers (JF and MP) were unaware that on each trial the physical stimulus was always a pair of light pulses in sequence.* In addition to these “three alternative” experimental runs, a daily session also included a “two alternative” experimental series in which the observer responded “one flash” or “two flashes” on each trial. In this series, IPI values of 0.01,0.03, 0.05, 0.07 and 0.09 were tested, 10 trials each in a randomized order. This reduced range of IPI values was expected to encompass the normal two-alternative response variation in two-pulse discrimination (Boynton, 1972; Bowen and Hood, 1983). This series was included to check whether the probability of reporting “one flash” was affected to any appreANALYSIS ciable degree by a paradigm involving two To account for flash perception, we adopt versus three response categories. The three series of stimuli were run during these propositions: five daily sessions. Final data were based on 50 (1) The brief, high-luminance light pulses trials per IPI condition. used here can be treated as impulses. (2) The visual response to such a pulse will therefore be the impulse response of the system, if the system behaves linearly. *The response “three flashes” could also have been (3) With the assumption of visual system designated “more than two flashes,”but that seemed linearity, the principles of superposition and like a potentiallyconfusingcategory for naive observers. Reports of “three flashes” could have been given time invariance will apply (Watson, 1986), and for any perception of flash numerosity more than two the response to a sequence of two pulses at a flashes. particular interpulse interval can be calculated
RICHARD
412 Response
(a)
W.
BOWEN
: oneflash
Response
(b)
100
: two flashes +\
/ /+
P
60 o MP
+ JF
0.13 0.05 0.09 Interpulse interval ( set
0.01
(cl 100
Response
: three
0.17
0.05
1
0.09
Interpulse
flashes
(d)
ResDMse: one
r
60 -
0.13 interval
0.17
(set)
flash
60
0.13
0.09
0.05 Interpulse
interval
0.17
(set
0.05
0.09
Interpulse
1
0.13 interval
0.17
(set 1
Fig. 3. Data for three observers. Panels (a-c): data from the procedure with three response alternatives (“one flash”, “two flashes” or “three flashes”). Panel (d): data from the procedure with two response alternatives (“one flash” vs “two flashes”). Panel (a): frequency of reports of “one flash” as a function of IPI. Panel (c): frequency of reports of “two flashes” as a function of IPI. Panel (b): frequency of reports of “three flashes” as a function of IPI. In panels (as), for a given observer, frequency values for all three responses sum to 100% for any IPI.
by the addition of two impulse response functions separated by the appropriate time delay. (4) The perception of flashes will be determined by the presence of peaks in the calculated response function.
(a)
Biphasic
impulse
Time
response
The analysis evaluates two classes of impulse response: a biphasic response, congruent with threshold-level data, and a multiphasic response, composed of many cycles of damped oscillation. The biphasic impulse response
(b)
Multtphosic
Impulse response
Time
The hypothetical impulses responses used in the superposition analysis. Panel (a): a biphasic impulse response from the model of Watson (1986). Panel (b): a multiphasic impulse response, an exponentially-damped sin function.
413
Two pulses seen as three flashes
Time
Time
(d)
Time
Time
I
Time
Time
Fig. 5. Results of a superposition analysis with biphasic impulse responses. One response is delayed and added back to the other response (temporal superposition). In panels (a-f) the value of the delay increases progressively.
comes from the model of temporal sensitivity presented by Watson (1986). The response has two components-one excitatory, one inhibitory-and each is the output of a cascade of identical low-pass filter stages. The biphasic impulse response is depicted in Fig. 4a. The form of this response is consistent with threshold data structures (flicker and pulse detection). The multiphasic impulse response (Fig. 4b) is an exponentially-damped sine function. This response is oscillatory and has multiple peaks and troughs. The superposition analysis involved in summing two identical impulse responses, with one response lagging by a particular delay, short, intermediate and long in duration. The delays correspond to the psychophysical IPI parameter. The first aim of the superposition analysis
was qualitative: would the superposition of either impulse response simulate the flash perceptions reported in the experiment? Figure 5 shows the superposition of two biphasic impulse responses at various delays, with delay increasing from panels (a) to (f). The superposition response has two distinct positive peaks for intermediate and long delays, but at no delay is a third positive peak present. The visual responses synthesized by superposition of biphasic impulse responses do not show three positive peaks at any delay and thus do not predict the perception of three flashes from the presentation of two pulses. (The longest delay, in panel (f), was roughly twice the overall duration of the impulse response.) Figure 6 presents functions from the superposition of multiphasic impulse responses.
414
RICHARDW. BOWEN
.iP+=-j ---.--.--._ .-.._ (a)
(b)
3 3 0 ”
-__.._.______.
5
I+--
Time
Time
(d)
Time
(e)
Time
(f)
Time
Time
Fig. 6. As for Fig. 5, except with multiphasic impulse responses. The dashed line marks the amplitude of the second peak in the impulse response. See text for discussion.
Clearly, because of the form of the impulse response, the perception of three (or even more) flashes is predicted over a broad range of intervals. Therefore, a rule must be devised to decide whether a peak is seen as a flash. This amounts to embellishing proposition 4 above. We consider first a rule that holds that the amplitude of a peak must exceed threshold level for flash perception. In Fig. 6, the dashed horizontal line in each panel represents such a threshold. It corresponds to the amplitude of the second peak in the multiphasic impulse response (Fig. 4b). This is consistent with the observation that a single pulse presented to the fovea is seen as a single flash. The second and subsequent peaks in the oscillating impulse response are sub-threshold. In Fig. 6, at delay value d, there are three peaks in the response above the threshold level,
and thus three perceived flashes. Three flashes occur when the oscillating impulse response functions are superposed approximately “in phase,” so that sub-threshold response peaks sum to produce supra-threshold flash perceptions. At a shorter or longer delays, only two peaks exceed the threshold level. A discrepancy occurs in panel (a) of Fig. 6, where impulse responses are superposed at a very short IPI, in near temporal registration. The second peak of the superposition response is consequently above the threshold level. This predicts that two flashes will be seen but, of course, only one flash is perceived. We therefore consider an alternative rule for flash perception. The perception of a single flash could be due to masking of the second peak by the largeamplitude first peak. Masking effects are consistent with Ikeda’s observation (1965) that pulses
Two pulses seen as three flashes
with unequal amplitude interact in nonadditive fashion at threshold. To simulate a general masking effect, as an alternative to the rule of a fixed threshold amplitude, we calculated ratios of response peak amplitudes, second peak to first peak and third peak to first peak. At this point it becomes necessary to associate numerical parameters with the impulse response function. For the response functions in Fig. 6, the impulse response is given by: f(t) = sin(20 7tt) e -‘lo.‘.
(1)
The response is an exponentially-damped 10 Hz sin function with time constant of 0.1 sec. In Fig. 6, panels (a-f) represent IPI values of 0.01, 0.03, 0.05, 0.09, 0.13 and 0.17 set, respectively, based on the response of equation (1). Other IPI values from the experiment were also evaluated. Figure 7 gives the ratio of second peak amplitude to first peak amplitude (squares) and the ratio of third peak amplitude to first peak amplitude (diamonds) as a function of IPI. The dashed line represents the ratio of second peak to first peak amplitude in the impulse response function (Fig. 4b). Points above this line predict that flashes will be seen at that IPI. The predictions of Fig. 7 agree very well with the data of Fig. 3. At short interpulse intervals (0.01 and 0.03 set), both ratios are below the threshold level-one flash is seen. At very long interpulse intervals (0.15-O. 19 set), the third peak/first peak ratio is above the dashed line,
415
but the second peak/first peak ratio is not-two flashes are seen. And at intermediate interpulse intervals (0.07 to 0.11 s), both ratios are above the threshold line-three flashes are seen. With the assumption that the ratio of amplitudes among response peaks determines perception of flashes, we account for all crucial aspects of the data. (With a ratio rule, the degree of damping in the impulse response, which determines the amplitude relation of all peaks, does not affect the conclusions drawn from Fig. 7.) In the present linear analysis, the prediction of three flashes in response to two pulses requires three positive peaks in the impulse response, even though two of them are not seen. Were there only two peaks, in-phase addition would generate only two flashes, because the trailing third peak in the superposition response is at threshold (or is too small a fraction of the first peak amplitude). If, on the other hand, the superposition response were subjected to a subsequent compressive nonlinearity (such as Lehky, 1985, found for suprathreshold contrast responses), this would tend to reduce the amplitude of large peaks relative to small ones. Thus an impulse response that was only triphasic (as in Stork and Falk, 1987) might account for the perception of three flashes from two pulses. But a biphasic response is not adequate in either the present linear systems framework or in a model incorporating a plausible nonlinearity. To summarize, this analysis shows that, if we accept the applicability of the superposition principle for impulse light signals, a biphasic impulse response cannot account for the perception of three flashes for an input of two brief light pulses. Instead, the presence of illusory flashes is predicted by an oscillating impulse response having at least three phases of excitation and inhibition. DISCUSSION
0.05
0.09
0.13
0.17
Interpulse interval (see) Fig. 7. Predictions of flash perception from a quantitative version of the superposition analysis. Plot of ratios of peak response amplitudes as a function of IPI. Squares are the ratio of second peak to first peak; diamonds are the ratio of third peak to first peak. The dashed line represents the ratio of the second peak to the first peak in the multiphasic impulse response (equation 1). Ratio values above the dashed line predict flash perception due to one or both functions at a given IPI value.
In the analysis presented here, the temporal form of an impulse response function is inferred from a psychophysical paradigm with transient stimuli. The logic of this approach was pioneered by Ikeda (1965). Ikeda showed that a pair of brief pulses separated by 0.07 set (at a low adaptation level) required more threshold radiance than when separated by a longer interpulse interval. He inferred that an inhibitory process was present at that interval, in which a trailing negative phase of the first response subtracted from the leading positive phase of a
RICHARD W. BOWEN
416
second response. This inference is the basis of the now widely accepted view that the impulse response at detection threshold is biphasic for luminance signals (Ikeda, 1986; Rashbass, 1970). In a study directly related to the present one, Ueno (1977) made analogous inferences for reaction time data to suprathreshold double pulses of light. With pulses separated by 0.1 set (at a low adapting level), reaction times were longer than at longer IPI values, implying an inhibitory process. At higher adapting levels, the inferred inhibitory phase of the response moves to shorter delays, and the reaction time function oscillates at still longer delays. From this, Ueno concluded that the underlying impulse response was multiphasic with at least two successive positive-negative components. Here we deduce a multiphasic impulse response from the perception of flashes more numerous than the physical light pulses. The temporal structure of the oscillating impulse response (equation 1) was suggested, of course, by the temporal structure of the data (Fig. 3). How well does this particular impulse response function predict the temporal structure of the double flash effect (see Fig. 1; Bowen et al., 1980, 1987), when a single brief pulse follows the offset of a long duration (0.5 set) light? Figure 8 shows a temporal convolution of the multiphasic impulse response with a 0.5 set pulse (the “inducer” for the double flash effect). A principal peak follows light offset by 0.1 sec. Were a multiphasic impulse response added in phase with this peak, given the amplitude ratio rule discussed above, only a single flash would Convolution : 0.5 set pulse 24
-0.6
t A
0
I 0.2
I
I 0.4 Time
1 0.6
1 0.6
I
( set 1
Fig. 8. Temporal convolution of the multiphasic impulse response (equation 1) with a 0.5 s pulse (the inducing pulse of Fig. 1). The arrow marks the delay of a probe pulse that will most effectively produce illusory flashes, given the amplitude ratio rule depicted in Fig. 7. See text.
be seen (secondary peaks would be masked). But if the impulse response were added in phase with a secondary trailing peak (marked by the arrow at about 0.18 set following light offset), as depicted in Fig. 6, this would cause the perception of two flashes for a single probe pulse. In data (Bowen et al., 1987), delays near 0.2 set are in fact optimal for producing illusory flashes to a probe pulse. Thus the temporal structure of the hypothetical impulse response also applies reasonably well to the original double flash effect. What mechanism might cause an oscillating impulse response function is an open issue. Recently, Stelmach et al. (1987), postulated that the double flash effect was due to alternate activation of “On” and “Off’ channels following light offset (see Jung, 1973; Krauskopf, 1980). This “parallel mechanism” model has positive and negative components of an impulse response in separate channels (Stelmach et al., 1987). The biphasic impulse response inferred from threshold data may actually be oscillatory in form. Possibly secondary and tertiary positive and negative phases are of such low amplitude that they do not contribute to measurable threshold values (except, perhaps, through probability summation, Watson, 1982). Stork and Falk (1987) have presented calculations of impulse responses from flicker sensitivity data; the temporal structure of many of these responses actually is oscillatory, and the impulse is at least triphasic at most adapting levels. The present analysis suggests that suprathreshold stimulus conditions allow more detailed evaluation of impulse responses. If the visual response to a strong signal is oscillatory, as suggested here, then the modulation transfer function for suprathreshold sinusoidal signals would be strongly bandpass in form. (We confirmed this with a fast Fourier transform of the impulse response (equation l).) Various studies have estimated the overall modulation transfer function for suprathreshold flicker. These have used brightness matching, with a steady reference field, of light and dark cycles in the flicker stimulus (Magnussen and Glad, 1975; Magnussen and Bjorklund, 1979) and direct scaling of apparent depth of modulation versus frequency (Marks, 1970). When mean luminance of a suprathreshold flickering stimulus is increased, the function remains bandpass in form, and the peak of the function shifts to higher frequencies (Magnussen and
Two pulses seen as three flashes
Glad, 1975). This follows threshold-level effects of adapting luminance (e.g. Kelly, 1961). But when adapting level is held constant, and modulation depth is increased, the function becomes low-pass at higher temporal contrast levels (above 50% according to Magnussen and Bjorklund, 1979; above 14% for a range of adapting levels, according to Marks, 1970). The finding of low-pass temporal filtering at high contrast level, implying a monophasic impulse response, is not consistent with analysis of the double flash effect. This raises the interesting possibility that the steady-state response and the transient response of the visual system for strong signals are governed by different processes. Acknowledgernears-Preparation of this manuscript was aided by a research leave of absence from Loyola University of Chicago. I thank Joel Pokomy and Vivianne C. Smith for a number of valuable comments and a critical reading of the manuscript. William Swanson also suggested a variety of significant improvements to the paper. REFERENCES Bowen R. W. and Hood D. C. (1983) Improvements in visual performance following a pulsed field of light: a test of the equivalent background principle. J. opt. Sot. Am. 73, 1551-1556. Bowen R. W., Markell K. A. and Schoon C. S. (1980) Two-pulse discrimination and rapid light adaptation: complex effects on temporal resolution and a new visual temporal illusion. J. opt. Sot. Am. 70, 1453-1458. Bowen R. W., Mallow J. and Harder P. J. (1987) Some properties of the double flash illusion. J. opt. Sot. Am. A 4, 746755. Boynton R. M. (1972) Discrimination of homogeneous double pulses of light. In Handbook of Sensory Physiology, Vol. VII/4, Visual Psychophysics (Edited by Jameson D. and Hurvich L.). Springer, Berlin. Ikeda M. (1965) Temporal summation of positive and negative flashes in the visual system. J. opr. Sot. Am. 55, 527-534. Ikeda M. (1986) Temporal impulse response. Vision Res. 26, 1431-1440. Jung R. (1973) Visual perception and neurophysiology. In Handbook of Sensory Physiology, Vol. VII/3, Central Visual Information A (Edited by Jung R.). Springer, Berlin. Kelly D. H. (1961) Visual responses to time-dependent
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