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Temporal frequency discrimination above threshold
~~-6989~~ 53.00 + 0.00 Copyright C 198-I Pergamon Press ttd
k’irion Res. Vol. 24, No. 12. pp. 1873-1880. 1984 Printed in Great Britain. All rights resewed
TEMPORAL
FREQUENCY DISCRIMINATION THRESHOLD
ABOVE
MARC B. MANDLER+ Center for Visual Science and Department of Psychology, University of Rochester, Rochester. NY 14627. U.S.A. (Received 14 November 1983; in revised form 30 May 1984)
Ah&a&--Temporal frequency di~~~nation was measured above threshold with a two-alternative spatial forced-choice procedure. Stimuli were two 1 deg homogeneous fields modulated around a mean luminance of 3.7 log trolands. Observers determined which of the two stimuli was modulated at a higher frequency. To avoid differences in apparent moduiation depth as a cue for discrimination, all stimuli were matched in apparent modulation depth to an 11Hz standard that was 0.5 log units above its threshold. Adaptation, caused by repeated presentation of suprathreshold stimuli. was avoided by using a I5 set inter-trial interval. The relative difference thresholds (Af/f) were a non-monotonic function of frequency. Discrimination was best near 1.5, 4.0 and 30.0 Hz (As/J = 0.08) and worst near 20.0 Hz (Af/J= 0.50). Control experiments showed that the improvement in discrimination beyond 20.0 Hz was not an artifact of mismatches in apparent m~u~ation depth. These results demonstrate the existence of multiple channels
sensitive to different ranges of temporal frequency. Temporal frequency
Fticker
Discrimination
Channels
been derived from adaptation A fundamental property of sensory systems is multiplicity of parallel pathways. Behavioral evidence of
such multiplicity has led to a conceptuali~tion in the form of channels. As a genera1 definition, a channel can be thought of as a set of detectors with similar stimulus specificityt. Along a given stimulus dimension the sensory information tends to pass through different channels. It has been demonstrated that the human visual system possesses channels that differ in sensitivity to different wavelengths (Stiles, 1949), spatial frequencies (Pantie and Sekuier, 1968a; Blakemore and Campbell, 1969), temporal frequencies (Smith, 1970, 1971; Pantle, 197t), orientations (Campbell and Kulikowski, 1966), directions of motion (Sekular and Ganz, 1963; Pantle and Sekular, f968b), motions in depth (Beverley and Regan, 1973, 1975), and changes in size (Regan and Beverley, 1978). The channels that are tuned to different temporal frequencies are believed to be few in number and broadly tuned. Estimates of channel number have *Present address: Department of Transportation, USCG Research and Development Center, Avery Point, Groton, CT 06340, U.S.A. tMany different definitions of “channel” have been given in the past. I have used the term channel to refer to a collection of detectors with the same filtering characteristics. To be more specific, the input signa is first assumed to undergo filtering. It is assumed that the detector that follows each filter has a graded output that is proportional to the strength of the signal passing through the filter. Noise is added at the output of the detector. The output of the detector becomes the input to a decision stage.
(Mandler
and Bowker,
1980), masking (Pelli, 1981), subthreshofd summation (Gafni and Zeevi, 1980), threshold discrimination (Watson and Robson, 1981), and generalized colorimetry experiments (Richards, 1979). Estimates agree that at least two and no more than four channels are required. The observation that adaptation and masking elevate threshold across a wide range of frequencies suggests that the bandwidths of the channels are relatively broad. Bandwidths inferred from such observations are on the order of two to four octaves at half height. It has been argued that the channels are not uniformly distributed across the temporal frequency spectrum, as it appears that only a single channel samples the spectrum in the region between 15 and 30 Hz (Richards, 1979). Since the behavior of these channels has typically been measured near detection threshold, little is known about the manner in which the channels are related above threshold. Specifically, it is not known how the suprathreshold appearance of stimuli is related to the channel outputs. One hypothesis is that perceived frequency corresponds to that of the channel that is most active. This notion is supported by threshold behavior where it has been shown that the temporal frequency channels act as labeled lines (Watson and Robson, 1981). That is, observers have information about the channel through which the detection signal passes, as they can distinguish between some frequencies when ever they are detected. This idea, though, it not likely to be correct for suprathreshold perception, as it requires that the number of “percepts”, or unique sensations of frequency, equals the number of frequency-selective
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channels. For temporal frequency perception, we might expect there to be two, three or four percepts, as this is the number of channels that have been inferred. Above threshold, however, there are not discrete classes of percepts. Perceived frequency varies continuously with physical frequency, at least at frequencies below 15 Hz (Fukuda, 1977). An alternative hypothesis with respect to the appearance of temporally modulated stimuli is that the distribution of activity across all the channels is the means by which the temporal frequency content of the stimulus is coded. As perceived frequency is altered following temporal frequency adaptation (Mandler and Bowker, 1980). selective attenuation must change the distribution of channel activity. Evidently adaptation selectively attenuates the responses of some channels relative to that of others. If the perceived temporal frequency is determined by the distribution of channel activity, then discrimination of temporal frequencies should reflect the number, bandwidth and spectral distribution of those channels. A useful analogy is wavelength discrimination. It typically has been assumed that two wavelengths look different if the outputs from the three cone mechanisms differ by some threshold amount (Helmholtz, 1896; Stiles, 1946, Boynton, 1979). The minimum difference in wavelength that can be detected (difference threshold) will be proportional to the rate of change in the outputs of the cone classes as wavelength is varied. If a given change of wavelength causes a large change of the outputs, there should be a correspondingly small difference threshold. Similarly, regions in which the outputs change little with wavelength should have a large difference threshold. Discrimination of temporal frequencies must, in a similar way, reflect the rate of change in the outputs of the frequency selective channels with changes of temporal frequency. If there be regions where discrimination is superior, it must reflect a high rate of change of overlapping mechanisms. If the sensitivity profiles of the channels are unimodal, then any discontinuities in the discrimination function would not only constitute evidence for separate channels *As two stimuli that are flickering at the same frequency but different modulation depths can be discriminated from one another, and as two stimuli flickering at different frequencies can be discriminated from one another no matter what their relative modulation depths, the visual system has independent mechanisms for discriminating both frequency and modulation depth of flicker. However, if for example, the signal elicited by a flickering stimulus passed through some sort of temporal filter that attenuated modulation depths of different frequencies by different amounts (e.g. if it were a bandpass filter), then changes in frequency would be confounded at the output of the filter by changes of modulation depth. In order to limit discrimination to the mechanisms sensitive to differences of frequency, the effects of frequency changes on modulation depth must be compensated by appropriate changes of modulation depth at the input to the filter.
MANDLER
but, more importantly, provide spectral limits on channel distribution. The paper presents data of the kind that provides such limits, and the following paper derives these limits. Related experiments Frequency discrimination functions have been measured by the method of adjustment in the fovea (Mowbray and Gebhard, 1955; Gebhard er al., 1955) and in the periphery (Mowbray and Gebhard, 1960). In the fovea, the difference thresholds (Af), are a non-monotonic function of frequency. Local maxima, or points of poorest discrimination, are found near 5.0 and 22.5 Hz. Local minima are found at 7.5 and 35.0 Hz. The Weber fraction (Af//) is at a minimum of 0.005 at 35.0 Hz and a maximum of 0.031 at 22.5 Hz. These experiments have a number of defects. The two major problems are that the frequencies were all at equal physical modulation depths rather than equal apparent modulation depths, and the adaptation effects were not controlled. In terms of modulation depth, these experiments were performed at a constant modulation of 100%. Veringa (1958) and Marks (1970) showed that, at suprathreshold levels, stimuli of equal physical modulation depth can have unequal apparent modulation depths. They found the apparent modulation depth to be approximately proportional to the detection thresholds. Thus, when an observer adjusts the frequency of a variable stimulus to match that of a standard, a change in frequency may also cause a change in the apparent modulation depth. This change in apparent modulation depth could provide an additional cue to aid in matching two frequencies.* This will be most dramatic at high frequencies where the thresholds increase rapidly with frequency. The second potential artifact is that changes in the appearance of the stimuli may have resulted from prolonged exposure to the suprathreshold stimuli. If discrimination is derived from the outputs of the channels, then anything that alters the properties of the channels, such as prolonged viewing of suprathreshold stimuli, may also cause a change in discrimination. The following experiments were undertaken to evaluate suprathreshold temporal frequency discrimination. A number of preliminary experiments had to be performed so that the artifacts discussed above would not intrude. First, detection thresholds were established, as they were necessary for subsequent measures. Second, the adapting effects of suprathreshold stimuli were assessed so that steps could be taken to minimize their contribution to the results. Third, modulation matching between different frequencies was performed so that all stimuli could be presented at equal apparent modulation depth. Finally, difference thresholds for temporal frequencies of equal apparent modulation depth were measured across the frequency spectrum.
Temporal
frequency discrimination
GENERAL SIETHODS
Apparatus A two-channel optical system that was similar in principle to that used by Scott (1980) enabled two spatially distinct fields to be independently modulated in luminance. A schematic of the system is shown in Fig. 1. As an overview, the essential features of the system were two integrating-bar assemblies (IBI. IB2) and two mirror galvonometers (MGI, MGZ). Each integrating-bar assembly consisted of a rectangular prism of glass (1 x I x 3 cm) with a piece of flashed-opal glass attached to each end. The mirror galvanometers, under computer control. swept the image of square apertures Al and A2 (2.5 x 25 cm) across one end of each integrating-bar assembly. The amount of overlap between the image of the aperture and the integrating-bar assembly determined the luminance of each channel’s output. When the two overlapped completely, as at IB I of Fig. I, maximum luminance was achieved. The luminance was reduced when there was only partial overlap (IBZ, Fig. I) and was at a minimum when there was no overlap. The integrating-bar assemblies served to diffuse the image of the aperture so that the observer could directly view a uniform field on one end of each assembly. The system is described in more detail below. The source S, an Osram 64633 tungsten-halogen bulb was driven by a regulated power supply at I2 V. Lenses Ll and L2 collimated the beam, and lenses L3 and L4 brought the 5 mm square filament image to focus on the 7 mm square mirrors of the galvanometers. Apertures A I and A2, placed in the collimated portions of the beams, were brought to focus at the ends of each integrating-bar assembly. The flashed-opal glass attached to the integrating bars diffused the light in the image of the aperture as the first step towards a uniform distribution of light. The integrating bar diffused the light even further by multiple total
Fig. I. Schematic of optical system used to present sinusoidal luminance modulation. Mirror galvanometers MGI and MG2 swept images of apertures Al and A2 across the integrating-bar assemblies IBI and IB2. Maximum luminance was achieved when the image completely overlapped the integrating bar, as at IBI. The luminance was reduced when the image only partially overlapped the integrating bar, as at IB2.
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internal reflections. The final piece of gashed-opal glass was additional insurance of uniform luminance. The integrating-bar assemblies had a center-tocenter separation of 2.60 cm. The observer viewed the ends of the assemblies through two holes (0.875 cm) cut in mirror M3. This mirror (36 x 46cm) was oriented in a plane of 45 deg with respect to vertical. Elliptical holes cut in this mirror appeared circular when viewed in its proper orientation of 45 deg (bottom of the mirror closest to the observer). A surround field was provided by passing light from two 200 W tungsten bulbs through a piece of flashed-opal glass (36 x 52 cm). The image of the glass was reflected by mirror M3 so that the observer viewed a large uniform surround field that was closely matched in luminance and whiteness to the central test fields. The observer’s head was held in place with a dental impression at a distance of 47.6 cm from the center of M3. He/she viewed two I deg fields with center-tocenter separation of 3 deg through a 2.5 mm artificial pupil situated as close to the eye as was comfortable. The surround field was circular with a diameter of 24deg. The left eye was patched and the right eye fixated a small (approx. 2arc-min), black fixation point situated midway between the two test fields. A Data General 3/12 minicomputer provided stimulus control, as well as response recording. The movement of the mirror galvanometers was controlled by the computer through two ADAC 500/535 digital-to-analog converters. The position of each galvanometer was updated every 0.001 set by reading a value from a look-up table. This look-up table linearized the luminance output of each field, as the output was not linear at high and low luminances. This enabled sinusoidal luminance modulation to be achieved up to a modulation depth of 99.3%. Stimuli The stimuli in all experiments were 1 deg circular spots for which the luminance was modulated sinusoidally in time. The mean luminance of the stimulus and surround fields was 1600cd/m’. The sinusoids were multiplied by a window function so that the stimuli went on and off gradually. This mode of presentation has the advantages of limiting the bandwidth of the frequency spectrum of the stimulus, and so minimizing transients that give rise to the pseudoflash phenomenon (Levinson, 1968). In some experiments the window function was a simple linear ramp at onset and offset. In this case, the total stimulus duration was 3000 msec, with the ramps comprising the first and last 250 msec. In other experiments a gaussian window was used. The standard deviation of the gaussian was 500msec. Observers The author (M.B.M.) and a paid undergraduate (A.Z.) served as observers. M.B.M. is a wellcorrected myope with many hours of psychophysical
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observation. A.Z. needed no correction and was given sufficient practice on all tasks to reach a stable level of performance.
PRELIMINARY
EXPERIMENTS
Procedure Detection threshok. A two-alternative spatial forced-choice tracking procedure was employed for measuring detection thresholds. The observer, fixating between the two test fields, reported whether the stimulus appeared to the left or right of fixation. The side was randomly determined on each trial. In a given staircase the modulation depth of the stimulus was decreased by 0.05 log units when the observer made two successive correct responses. The modulation depth was increased by 0.05 log units when an incorrect response was made. A staircase terminated when there were eight reversals in the modulation depth. Threshold was taken to be the geometric mean of the four maximum and minimum modulation Two interleaved staircases were run in a single session so that two estimates of threshold were obtained. On each trial the computer randomly chose the staircase from which a stimulus was presented. A session began with at least 3 min of adaptation to the mean luminance of the display. The first stimulus was presented considerably above its detection threshold so that the observer could learn the frequency that was to be detected. A rapid approach was made toward threshold by decreasing the modulation depth by 0.15 log units after each correct response. Once an incorrect response was made, the staircase algorithm was instituted. The presentation of each stimulus was preceded by a 500 msec warning tone. A I set feedback tone was presented when an incorrect response was made. Trials were separated by a period of 4sec during which the test fields were held steady at the mean luminance. SupraAreshold adapling eficfs. Since all stimuli in the discrimination experiment were to be above threshold, they were capable of causing adaptation. To avoid artifacts introduced by adaptation, measurements were made to determine the inter-trial interval that would be sufficient to allow complete recovery from any temporal frequency adaptation. It was assumed that adaptation would be manifested as a change of threshold. Detection thresholds were measured at various times following cessation of a 3000msec adapting stimulus. The modulation depth of the adapting freauencv . < was 0.5 loe. units above its threshold. In a single session independent staircases were run for five different times following cessation of the adapting frequency. The adapting stimulus appeared simultaneously on both sides of the display while the test stimulus appeared on one randomly chosen side. The
I~~ANDLER
observer’s task was to detect the side on which the test stimulus occurred. The tracking algorithm was as given previously. Modulation matching. Matches of apparent modulation depth were made between stimuli of different frequencies by the method of adjustment. On every trial an I1 .O Hz standard that was 0.5 log units above its threshold was presented to one side of the display. At offset of this standard, a stimulus of variable modulation depth was presented to the other side of the display. The observer’s task was to adjust the modulation depth of the variable to match the apparent modulation depth of the standard. The change in modulation depth of the variable was controlled by a set of four switches, each with a different effect. Two switches raised or lowered the modulation depth by 0.05 log units while the other two switches raised or lowered it by 0.25 log units. Following an inter-trial interval of I3 set, the standard and variable were represented until a match was obtained.
Figure 2 shows modulation sensitivity as a function of frequency for observer M.B.M. Modulation sensitivity is defined as: (l/threshold modulation) x 100. Each point is the mean of six threshold determinations from three experimental sessions over a period of 2 weeks. The function has a characteristic bandpass shape (DeLange, 1958) with a maximum at about I I .O Hz. Results for observer A.Z. (not shown) were also bandpass in nature with a maximum at 10.0 Hz.
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Fig. 2. Temporal modulation sensitivity function for observer M.B.M. Measurements were made with a two alternative spatial forced-choice procedure. Each point is the mean of six threshold determinations. The bars represent + 1 standard error of the mean. The curve was drawn by
eye.
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Temporal frequency discrimination Figure 3 shows the time course of threshold recovery following a 3 set presentation of an adapting stimulus that was 0.5 log units above its detection threshold. Circles represent measurements taken when the adapting and test stimuli were 3.0 Hz and squares represent measurements taken when the adapting and test stimuli were 25.0 Hz. Threshold elevation is the ratio of the adapted to unadapted thresholds. A value of 1.O corresponds to an absence of a threshold change. Thresholds for both test stimuli recovered with a similar time course. Initially thresholds were elevated by a factor of 1.5. Within approx. 13 set thresholds returned to their unadapted values.
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Fig. 3. Time course of threshold recovery following a 3 set presentation of a 3.0 or 25.0 Hz stimulus that was 0.5 log units above its threshold.
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Results of modulation matching are shown in Fig. 4 for two observers. The ordinate represents the ratio of the modulation adjustment to the threshold in dB. The data show that stimuli match in apparent modulation depth when they are each 10 dB (0.5 log units) above their respective thresholds. DIFFERENCE
THRESHOLDS
Procedure
The observer’s task was to judge which of two temporally modulated stimuli was of a higher temporal frequency. In a single session a standard and a variable frequency were presented, one to each field of the display. The side of each stimulus was randomly assigned on each trial. A staircase tracking procedure was used so that the difference in frequency between the standard and variable (Af) was always near the threshold for discrimination. The Af was increased by 0.15 log units when an incorrect judgement was made, and decreased by 0.15 log units when three successive correct responses were given. Incorrect responses were marked by a 1 set auditory tone. Like the detection threshold experiment, the Af was well above threshold at the start of the session and decreased by 0.15 log units per trial until an incorrect response was made. The tracking procedure was then instituted and continued until 100 judgements were obtained. All temporal frequencies were equated in apparent modulation depth. This was accomplished by presenting all stimuli 0.5 log units above their detection thresholds, as previously determined. Threshold was interpolated at those frequencies for which detection thresholds had not been measured. A session always began with at least 3 min adaptation to the mean luminance of the display. The observer was required to maintain fixation on the central fixation point throughout the duration of each trial. The first stimulus of each trial was always presented to the left field of the display. Approximately IOOmsec after its termination, the second stimulus appeared on the right. In pilot experiments the two stimuli to be discriminated were presented simultaneously, one to each field of the display. Though this was a satisfactory method of displaying the stimuli, it was found that with successive presentation the observers not only found the task to be less difficult, the difference thresholds were lower. Thus the successive presentation was adopted. An intertrial interval of 15 set was used, as this was shown to be sufficient to allow recovery from adaptation (cf. Fig. 3).
(HZ)
Results Fig. 4. Modulation matching of two observers as a function of frequency. Observers adjusted the modulation depth of the frequency given by the abscissa to match an 11.OHz standard that was 0.5 log units above its threshold. The ordinate is the ratio of the modulation adjustment and threshold.
Data from each session were fit with a cumulative normal curve by using a probit analysis package (Finney, 1964; SAS User’s Guide, 1980). Threshold was taken to be the 75% probability of correct discrimination. There were some sessions in which
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convergence toward a best-fitting curve was not achieved in 100 iterations. Also, on occasion, the fits were poor, as assessed by a chi-square statistic (P < 0.05). When either of these situations were encountered, the data were discarded and another session was run in its place. For observer M.B.M. this occurred on 67; of the experimental sessions and for observer A.Z. on 4%. The variation in difference threshold with temporal frequency is shown in Fig. 5 for observer M.B.M. Each point is the mean of four experimental sessions of 100 trials each. The bars are the standard errors of the means. The difference threshold, Af, can be seen to increase with frequency between 0.75 and 4.0 Hz. Between 4.0 and 5.0 Hz Afdecreases slightly and then rises out to about 20.0 Hz. Beyond 20.0 Hz the thresholds decrease. Another way to look at these data is to consider the variation of the relative difference threshold (Af/f) with frequency. Figures 6a and 6b plot these ratios for the two observers. The two sets of data show local minima near 1.5, 4.5 and beyond 20.0 Hz. Over the range of frequencies tested, the relative difference thresholds vary by about a factor of six. The unexpected improvement in performance at the higher frequencies led to a closer examination of those frequencies. Since the apparent modulation depth changes rapidly with frequency above 20.0 Hz, it was possible that a small mismatch in apparent modulation depth could have provided a substantial cue for discrimination. To test this hypothesis, observers, as before, determined which of two stimuli was of a higher frequency. The frequencies of the two
Temporal
frequency
(Hz
I
Fig. 5. Difference thresholds for observer M.B.M. The observer judged which of two temporal frequencies was of a higher frequency. Threshold was-taken tobe the point of 75% correct discrimination as assessed with Probit analysis. Each point represents the estimates of threshold from &ur sessions of 100 trials each.
MANDLER
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Fig. 6. Relative difference thresholds for observers M.B.M. and A.Z. The difference thresholds were divided by the base frequency.
stimuli were fixed while the modulation depth of one of them was varied on each trial by a method of constant stimuli. Consider a stimulus at 30.0 Hz. It was established previously that the difference threshold at 30.0 Hz was approx. 7.5 (Fig. 5). Thus 30.0 and 37.5 Hz could be correctly discriminated 75% of the time. If the discrimination was based on a difference in apparent modulation, there should be some modulation depth of the 37.5 Hz stimulus for which performance falls below this level. That this does not occur is illustrated in Fig. 7a. The proportion of correct discriminations is plotted against the modulation depth of the 37.5 Hz stimulus. The arrow represents the modulation depth of the 37.5 Hz stimulus that was used in the original measurements. Discrimination improves as the modulation depth is increased or decreased from this point. In Fig. 7b data are shown for frequencies of 40.0 and 45.9. These frequencies were correctly discriminated nearly lOO0/0of the time. If this discrimination was based on an apparent modulation depth difference, performance should get worse as the modulation depths become more nearIy equal. Here it is shown, however, that discrimination is independent of the modulation depth of the two stimuli.
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Fig. 7. Results of control experiments to determine if the high frequency improvement in discrimination was an artifact of mismatches of apparent modulation depth. Details are given in text.
Discussion
The initial premise of these experiments was that the difference threshold for temporal frequency discrimination must reflect the properties of the underlying channels. Specifically, it was supposed that the number of channels and their spectral distributions could be derived from such observations. This is possible if one makes assumptions about the shapes of the sensitivity profiles, as well as the manner in which channels interact to determine the appearance. One hypothesis that does not directly rely on assumptions about channel shape is that two frequencies will be discriminable only when they activate different channels. A consideration of the present results reveals that, given this hypothesis, 35-45 separate channels are required. This estimate was derived from the number of just noticeable differences in frequency over the range tested. It is clearly inconsistent with the two to four channels that have been inferred from other measures. An alternative hypothesis that was discussed earlier is that two frequencies will be discriminable if they cause some criterion change in the distribution of channel outputs. This is akin to a “line-element” model of wavelength discrimination (Wyszecki and Stiles, 1982, p. 654). This type of model requires
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discrimination to be better in those regions in which a small change in frequency produces a relatively large change in the outputs of the channels. That is, discrimination must be best when the slopes of the sensitivity profiles of the underlying channels are at a maximum. This type of model has been proposed for discrimination of motion in depth (Beverley and Regan, 1975), and spatial frequency (Regan, 1982). The present data show that frequency discrimination was better at I.5 and 4.5 Hz than at other frequencies. This means that there must be at least two channels with overlapping sensitivity at these frequencies. Moreover, the difference between the slopes of the sensitivity profiles of the underlying channels must be greatest at these frequencies. The data also show a substantial reduction in discrimination between 6.0 and 20.0 Hz. This poor discrimination could result from a decrease of the slopes of the underlying channels in this region, or the possibility that fewer channels have sensitivity at those frequencies. The most surprising aspect of these results is that discrimination improved dramatically at the highest frequencies. Observer M.B.M. could reliably distinguish 45.0 and 46.9 Hz. This discrimination was shown not to be based on differences in the apparent modulation depth. From the observers’ points of view the task became substantially less tedious at these frequencies. Observers reported a change in the subjective basis for the discrimination that was difficult to describe in words. One explanation for this high frequency improvement is that an additional very high frequency channel contributes to discrimination at these frequencies. It is shown in the following paper that this proposition is not required by the data. The high frequency behavior can be accounted for by a very broadly tuned low frequency channel. Finally, compared to earlier experiments that measured temporal frequency discrimination (Mowbray and Gebhard, 1955; Gebhard er al., 1955) the observers in the present experiment were about a factor of IO less sensitive to frequency differences. At least three factors may account for lower thresholds in the earlier experiments. First, differences in apparent modulation depth in the earlier experiments aided discrimination. Though there are no published data to support this notion in the temporal frequency domain, Campbell ef al. (1970) showed this to be the case for spatial frequency discrimination. Spatial discrimination was better by a factor of two when the gratings had equal physical contrasts than when they had equal apparent contrasts. Second, adaptation effects may have accentuated differences between stimuli. Third, the higher modulation depth used in the earlier experiments facilitated discrimination. Acknowledgemenfs-This work was submitted in partial fulfillment for the degree of Doctor of Philosophy at the University of Rochester in March,
1983. I thank Walt
ISSO
MARC B. MANDLER
hfakous, Dave Williams and Bill Merigan for their critical reviews of this work. Also. I thank Amy Zelazny for her many patient hours as an observer. This work was funded by grants EY03594 and EY01319 from the National Eye Insttrute. REFERENCES Beverley K, I. and Regan 0. (1973) Evidence for the existence of neural mechanisms selectively sensitive to the direction of movement in soace. J. Pkvsioi. 235. 17-29. Beverley K. 1. and Regan D.‘( 1975) The relation between discrimination and sensitivity in the perception of motion in deoth. J. Phvsiol. 249, 387-398. Blakembre C. and Campbell F. W. (1969) On the existence of neurons in the human visual system selectively sensitive to the orientation and size of retinal images. .I. Physioi. 203, 237-260. Boynton R. M. (1979) Human Color Vision. Rinehart & Winston, New York. Campbell F. W. and Kulikowski J. (1966) Orientational selectivity of the human visual system. J. Physiol 187, 437-44s.
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Gafni H. and Zeevi Y. Y. (1980) Temporal frequency channels in the visual system. Technical‘Repori nd. 394, Technion Israel Institute of Technology, Haifa, Israel. Gebhard L. W., Mowbray G. H. and Byham C. L. (1955) Difference-limens for photic intermittence. Q. J. up. PsychoI. 7, 49-55.
Helmhoitz H. van (1896) ~~nd~uch der Physioiogisc~en Oprik. Voss, Hamburg. Levinson J. Z. (1968) Flicker fusion phenomena. Science 160, 21-28. Mandler M. B. and Bowker D. 0. (1980) Shifts in apparent flicker rate following flicker adaptation. Inoesl. Ophthol. rimal Sci. 19, 45. Marks L. E. (1970) Apparent depth of modulation as a
function of frequency and amplitude of temporal modulations of luminance. J. opt. Sot. .4m. 60, 970-977. Mowbray G. H. and Gebhard J. W. (1955) Differential sensitivity of the eye to intermittent white light. Science 121, 373-175. Mowbray G. H. and Gebhard J. W. (1960) Differential sensitivity of peripheral retina to intermittent white light. Science 132, 672-674. Pantie A. (1971) Flicker adaptation--l. Et’lect on visual sensitivity to temporat ~uctuations in light intensity. Vision Res. 11, 943-9.52. Pantle A. and Sekuler R. (1968a) Size-detecting mechanisms in human vision. Science 162, 1146-I 148. Pantle A. and Sekuler R. (196Sb) Velocity sensitive elements in human vision: Initial psychophysical evidence. Vision Res. 8, 445-450. Pelli D. G. (1981) Effects of visual noise. Ph.D. thesis, Cambridge University, England. Regan D. (1982f Visual information channeling in normai and disordered vision. Pswhol. Rm. 89, 407-444. Regan D. and Beverley K. I. (1978) Looming detectors in the human visual pathway. Vision Res. 18, 415-421. Richards W. (1979) Quantifying sensory channels: Generalizing calorimetry to orientation and texture, touch, and tones. Sens. Proc. 3, 207-229. SAS Institute Inc. (1979) SrtS User’s Guide, 1979 edn. SAS Institute, Raleigh, N.C. Scott L. (1980) Center/surround interactions in the Benham’s top paradigm. Ph.D. thesis, University of Rochester, University Microfilms, Ann Arbor. Sekuler R. and Ganz L. (1963) Aftereffect of seen motion with stabilized retinal image. Science 139, 419-420. Smith R. A. (1970) Adaptation of visual contrast sensitivity to specific temporal frequencies. Vision Res. 10, 275-279. Smith R. A. (1971) Studies of temporal frequency adaptation in visual contrast sensitivity. j. Physioi 216,v237-i60. Stiles W. S. (1946) A modified Helmholtz line element in brightness-colour space. Proc. Phys. Sot. 58, 41-51. Stiles W. S. (1949) Increment thresholds and the mechanisms of colour vision. Dot. Ophthnf. 3, 138-163. Veringa F. (1958) On some properties of nonthreshold flicker. J. opt. Sot. Am. 48, 500-502. Watson A. B. and Robson J. G. (1981) Discrimination at threshold: Labelled detectors in human vision. Vision Res. 21, 1I IS-1122. Wyszecki G. and Stiles W. S. (1982) Color Science: Concepts and Methods, Quuntitatice Data and Formuiae. Wiley, New York.
k’irion Res. Vol. 24, No. 12. pp. 1873-1880. 1984 Printed in Great Britain. All rights resewed
TEMPORAL
FREQUENCY DISCRIMINATION THRESHOLD
ABOVE
MARC B. MANDLER+ Center for Visual Science and Department of Psychology, University of Rochester, Rochester. NY 14627. U.S.A. (Received 14 November 1983; in revised form 30 May 1984)
Ah&a&--Temporal frequency di~~~nation was measured above threshold with a two-alternative spatial forced-choice procedure. Stimuli were two 1 deg homogeneous fields modulated around a mean luminance of 3.7 log trolands. Observers determined which of the two stimuli was modulated at a higher frequency. To avoid differences in apparent moduiation depth as a cue for discrimination, all stimuli were matched in apparent modulation depth to an 11Hz standard that was 0.5 log units above its threshold. Adaptation, caused by repeated presentation of suprathreshold stimuli. was avoided by using a I5 set inter-trial interval. The relative difference thresholds (Af/f) were a non-monotonic function of frequency. Discrimination was best near 1.5, 4.0 and 30.0 Hz (As/J = 0.08) and worst near 20.0 Hz (Af/J= 0.50). Control experiments showed that the improvement in discrimination beyond 20.0 Hz was not an artifact of mismatches in apparent m~u~ation depth. These results demonstrate the existence of multiple channels
sensitive to different ranges of temporal frequency. Temporal frequency
Fticker
Discrimination
Channels
been derived from adaptation A fundamental property of sensory systems is multiplicity of parallel pathways. Behavioral evidence of
such multiplicity has led to a conceptuali~tion in the form of channels. As a genera1 definition, a channel can be thought of as a set of detectors with similar stimulus specificityt. Along a given stimulus dimension the sensory information tends to pass through different channels. It has been demonstrated that the human visual system possesses channels that differ in sensitivity to different wavelengths (Stiles, 1949), spatial frequencies (Pantie and Sekuier, 1968a; Blakemore and Campbell, 1969), temporal frequencies (Smith, 1970, 1971; Pantle, 197t), orientations (Campbell and Kulikowski, 1966), directions of motion (Sekular and Ganz, 1963; Pantle and Sekular, f968b), motions in depth (Beverley and Regan, 1973, 1975), and changes in size (Regan and Beverley, 1978). The channels that are tuned to different temporal frequencies are believed to be few in number and broadly tuned. Estimates of channel number have *Present address: Department of Transportation, USCG Research and Development Center, Avery Point, Groton, CT 06340, U.S.A. tMany different definitions of “channel” have been given in the past. I have used the term channel to refer to a collection of detectors with the same filtering characteristics. To be more specific, the input signa is first assumed to undergo filtering. It is assumed that the detector that follows each filter has a graded output that is proportional to the strength of the signal passing through the filter. Noise is added at the output of the detector. The output of the detector becomes the input to a decision stage.
(Mandler
and Bowker,
1980), masking (Pelli, 1981), subthreshofd summation (Gafni and Zeevi, 1980), threshold discrimination (Watson and Robson, 1981), and generalized colorimetry experiments (Richards, 1979). Estimates agree that at least two and no more than four channels are required. The observation that adaptation and masking elevate threshold across a wide range of frequencies suggests that the bandwidths of the channels are relatively broad. Bandwidths inferred from such observations are on the order of two to four octaves at half height. It has been argued that the channels are not uniformly distributed across the temporal frequency spectrum, as it appears that only a single channel samples the spectrum in the region between 15 and 30 Hz (Richards, 1979). Since the behavior of these channels has typically been measured near detection threshold, little is known about the manner in which the channels are related above threshold. Specifically, it is not known how the suprathreshold appearance of stimuli is related to the channel outputs. One hypothesis is that perceived frequency corresponds to that of the channel that is most active. This notion is supported by threshold behavior where it has been shown that the temporal frequency channels act as labeled lines (Watson and Robson, 1981). That is, observers have information about the channel through which the detection signal passes, as they can distinguish between some frequencies when ever they are detected. This idea, though, it not likely to be correct for suprathreshold perception, as it requires that the number of “percepts”, or unique sensations of frequency, equals the number of frequency-selective
1873
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MARC
B.
channels. For temporal frequency perception, we might expect there to be two, three or four percepts, as this is the number of channels that have been inferred. Above threshold, however, there are not discrete classes of percepts. Perceived frequency varies continuously with physical frequency, at least at frequencies below 15 Hz (Fukuda, 1977). An alternative hypothesis with respect to the appearance of temporally modulated stimuli is that the distribution of activity across all the channels is the means by which the temporal frequency content of the stimulus is coded. As perceived frequency is altered following temporal frequency adaptation (Mandler and Bowker, 1980). selective attenuation must change the distribution of channel activity. Evidently adaptation selectively attenuates the responses of some channels relative to that of others. If the perceived temporal frequency is determined by the distribution of channel activity, then discrimination of temporal frequencies should reflect the number, bandwidth and spectral distribution of those channels. A useful analogy is wavelength discrimination. It typically has been assumed that two wavelengths look different if the outputs from the three cone mechanisms differ by some threshold amount (Helmholtz, 1896; Stiles, 1946, Boynton, 1979). The minimum difference in wavelength that can be detected (difference threshold) will be proportional to the rate of change in the outputs of the cone classes as wavelength is varied. If a given change of wavelength causes a large change of the outputs, there should be a correspondingly small difference threshold. Similarly, regions in which the outputs change little with wavelength should have a large difference threshold. Discrimination of temporal frequencies must, in a similar way, reflect the rate of change in the outputs of the frequency selective channels with changes of temporal frequency. If there be regions where discrimination is superior, it must reflect a high rate of change of overlapping mechanisms. If the sensitivity profiles of the channels are unimodal, then any discontinuities in the discrimination function would not only constitute evidence for separate channels *As two stimuli that are flickering at the same frequency but different modulation depths can be discriminated from one another, and as two stimuli flickering at different frequencies can be discriminated from one another no matter what their relative modulation depths, the visual system has independent mechanisms for discriminating both frequency and modulation depth of flicker. However, if for example, the signal elicited by a flickering stimulus passed through some sort of temporal filter that attenuated modulation depths of different frequencies by different amounts (e.g. if it were a bandpass filter), then changes in frequency would be confounded at the output of the filter by changes of modulation depth. In order to limit discrimination to the mechanisms sensitive to differences of frequency, the effects of frequency changes on modulation depth must be compensated by appropriate changes of modulation depth at the input to the filter.
MANDLER
but, more importantly, provide spectral limits on channel distribution. The paper presents data of the kind that provides such limits, and the following paper derives these limits. Related experiments Frequency discrimination functions have been measured by the method of adjustment in the fovea (Mowbray and Gebhard, 1955; Gebhard er al., 1955) and in the periphery (Mowbray and Gebhard, 1960). In the fovea, the difference thresholds (Af), are a non-monotonic function of frequency. Local maxima, or points of poorest discrimination, are found near 5.0 and 22.5 Hz. Local minima are found at 7.5 and 35.0 Hz. The Weber fraction (Af//) is at a minimum of 0.005 at 35.0 Hz and a maximum of 0.031 at 22.5 Hz. These experiments have a number of defects. The two major problems are that the frequencies were all at equal physical modulation depths rather than equal apparent modulation depths, and the adaptation effects were not controlled. In terms of modulation depth, these experiments were performed at a constant modulation of 100%. Veringa (1958) and Marks (1970) showed that, at suprathreshold levels, stimuli of equal physical modulation depth can have unequal apparent modulation depths. They found the apparent modulation depth to be approximately proportional to the detection thresholds. Thus, when an observer adjusts the frequency of a variable stimulus to match that of a standard, a change in frequency may also cause a change in the apparent modulation depth. This change in apparent modulation depth could provide an additional cue to aid in matching two frequencies.* This will be most dramatic at high frequencies where the thresholds increase rapidly with frequency. The second potential artifact is that changes in the appearance of the stimuli may have resulted from prolonged exposure to the suprathreshold stimuli. If discrimination is derived from the outputs of the channels, then anything that alters the properties of the channels, such as prolonged viewing of suprathreshold stimuli, may also cause a change in discrimination. The following experiments were undertaken to evaluate suprathreshold temporal frequency discrimination. A number of preliminary experiments had to be performed so that the artifacts discussed above would not intrude. First, detection thresholds were established, as they were necessary for subsequent measures. Second, the adapting effects of suprathreshold stimuli were assessed so that steps could be taken to minimize their contribution to the results. Third, modulation matching between different frequencies was performed so that all stimuli could be presented at equal apparent modulation depth. Finally, difference thresholds for temporal frequencies of equal apparent modulation depth were measured across the frequency spectrum.
Temporal
frequency discrimination
GENERAL SIETHODS
Apparatus A two-channel optical system that was similar in principle to that used by Scott (1980) enabled two spatially distinct fields to be independently modulated in luminance. A schematic of the system is shown in Fig. 1. As an overview, the essential features of the system were two integrating-bar assemblies (IBI. IB2) and two mirror galvonometers (MGI, MGZ). Each integrating-bar assembly consisted of a rectangular prism of glass (1 x I x 3 cm) with a piece of flashed-opal glass attached to each end. The mirror galvanometers, under computer control. swept the image of square apertures Al and A2 (2.5 x 25 cm) across one end of each integrating-bar assembly. The amount of overlap between the image of the aperture and the integrating-bar assembly determined the luminance of each channel’s output. When the two overlapped completely, as at IB I of Fig. I, maximum luminance was achieved. The luminance was reduced when there was only partial overlap (IBZ, Fig. I) and was at a minimum when there was no overlap. The integrating-bar assemblies served to diffuse the image of the aperture so that the observer could directly view a uniform field on one end of each assembly. The system is described in more detail below. The source S, an Osram 64633 tungsten-halogen bulb was driven by a regulated power supply at I2 V. Lenses Ll and L2 collimated the beam, and lenses L3 and L4 brought the 5 mm square filament image to focus on the 7 mm square mirrors of the galvanometers. Apertures A I and A2, placed in the collimated portions of the beams, were brought to focus at the ends of each integrating-bar assembly. The flashed-opal glass attached to the integrating bars diffused the light in the image of the aperture as the first step towards a uniform distribution of light. The integrating bar diffused the light even further by multiple total
Fig. I. Schematic of optical system used to present sinusoidal luminance modulation. Mirror galvanometers MGI and MG2 swept images of apertures Al and A2 across the integrating-bar assemblies IBI and IB2. Maximum luminance was achieved when the image completely overlapped the integrating bar, as at IBI. The luminance was reduced when the image only partially overlapped the integrating bar, as at IB2.
1875
internal reflections. The final piece of gashed-opal glass was additional insurance of uniform luminance. The integrating-bar assemblies had a center-tocenter separation of 2.60 cm. The observer viewed the ends of the assemblies through two holes (0.875 cm) cut in mirror M3. This mirror (36 x 46cm) was oriented in a plane of 45 deg with respect to vertical. Elliptical holes cut in this mirror appeared circular when viewed in its proper orientation of 45 deg (bottom of the mirror closest to the observer). A surround field was provided by passing light from two 200 W tungsten bulbs through a piece of flashed-opal glass (36 x 52 cm). The image of the glass was reflected by mirror M3 so that the observer viewed a large uniform surround field that was closely matched in luminance and whiteness to the central test fields. The observer’s head was held in place with a dental impression at a distance of 47.6 cm from the center of M3. He/she viewed two I deg fields with center-tocenter separation of 3 deg through a 2.5 mm artificial pupil situated as close to the eye as was comfortable. The surround field was circular with a diameter of 24deg. The left eye was patched and the right eye fixated a small (approx. 2arc-min), black fixation point situated midway between the two test fields. A Data General 3/12 minicomputer provided stimulus control, as well as response recording. The movement of the mirror galvanometers was controlled by the computer through two ADAC 500/535 digital-to-analog converters. The position of each galvanometer was updated every 0.001 set by reading a value from a look-up table. This look-up table linearized the luminance output of each field, as the output was not linear at high and low luminances. This enabled sinusoidal luminance modulation to be achieved up to a modulation depth of 99.3%. Stimuli The stimuli in all experiments were 1 deg circular spots for which the luminance was modulated sinusoidally in time. The mean luminance of the stimulus and surround fields was 1600cd/m’. The sinusoids were multiplied by a window function so that the stimuli went on and off gradually. This mode of presentation has the advantages of limiting the bandwidth of the frequency spectrum of the stimulus, and so minimizing transients that give rise to the pseudoflash phenomenon (Levinson, 1968). In some experiments the window function was a simple linear ramp at onset and offset. In this case, the total stimulus duration was 3000 msec, with the ramps comprising the first and last 250 msec. In other experiments a gaussian window was used. The standard deviation of the gaussian was 500msec. Observers The author (M.B.M.) and a paid undergraduate (A.Z.) served as observers. M.B.M. is a wellcorrected myope with many hours of psychophysical
IYi6
h’hRC
B.
observation. A.Z. needed no correction and was given sufficient practice on all tasks to reach a stable level of performance.
PRELIMINARY
EXPERIMENTS
Procedure Detection threshok. A two-alternative spatial forced-choice tracking procedure was employed for measuring detection thresholds. The observer, fixating between the two test fields, reported whether the stimulus appeared to the left or right of fixation. The side was randomly determined on each trial. In a given staircase the modulation depth of the stimulus was decreased by 0.05 log units when the observer made two successive correct responses. The modulation depth was increased by 0.05 log units when an incorrect response was made. A staircase terminated when there were eight reversals in the modulation depth. Threshold was taken to be the geometric mean of the four maximum and minimum modulation Two interleaved staircases were run in a single session so that two estimates of threshold were obtained. On each trial the computer randomly chose the staircase from which a stimulus was presented. A session began with at least 3 min of adaptation to the mean luminance of the display. The first stimulus was presented considerably above its detection threshold so that the observer could learn the frequency that was to be detected. A rapid approach was made toward threshold by decreasing the modulation depth by 0.15 log units after each correct response. Once an incorrect response was made, the staircase algorithm was instituted. The presentation of each stimulus was preceded by a 500 msec warning tone. A I set feedback tone was presented when an incorrect response was made. Trials were separated by a period of 4sec during which the test fields were held steady at the mean luminance. SupraAreshold adapling eficfs. Since all stimuli in the discrimination experiment were to be above threshold, they were capable of causing adaptation. To avoid artifacts introduced by adaptation, measurements were made to determine the inter-trial interval that would be sufficient to allow complete recovery from any temporal frequency adaptation. It was assumed that adaptation would be manifested as a change of threshold. Detection thresholds were measured at various times following cessation of a 3000msec adapting stimulus. The modulation depth of the adapting freauencv . < was 0.5 loe. units above its threshold. In a single session independent staircases were run for five different times following cessation of the adapting frequency. The adapting stimulus appeared simultaneously on both sides of the display while the test stimulus appeared on one randomly chosen side. The
I~~ANDLER
observer’s task was to detect the side on which the test stimulus occurred. The tracking algorithm was as given previously. Modulation matching. Matches of apparent modulation depth were made between stimuli of different frequencies by the method of adjustment. On every trial an I1 .O Hz standard that was 0.5 log units above its threshold was presented to one side of the display. At offset of this standard, a stimulus of variable modulation depth was presented to the other side of the display. The observer’s task was to adjust the modulation depth of the variable to match the apparent modulation depth of the standard. The change in modulation depth of the variable was controlled by a set of four switches, each with a different effect. Two switches raised or lowered the modulation depth by 0.05 log units while the other two switches raised or lowered it by 0.25 log units. Following an inter-trial interval of I3 set, the standard and variable were represented until a match was obtained.
Figure 2 shows modulation sensitivity as a function of frequency for observer M.B.M. Modulation sensitivity is defined as: (l/threshold modulation) x 100. Each point is the mean of six threshold determinations from three experimental sessions over a period of 2 weeks. The function has a characteristic bandpass shape (DeLange, 1958) with a maximum at about I I .O Hz. Results for observer A.Z. (not shown) were also bandpass in nature with a maximum at 10.0 Hz.
i
<
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i
2 Test lleld 7.350 Id
1’
1
I
I
I
5
10
50
Temporal
frequency
Fig. 2. Temporal modulation sensitivity function for observer M.B.M. Measurements were made with a two alternative spatial forced-choice procedure. Each point is the mean of six threshold determinations. The bars represent + 1 standard error of the mean. The curve was drawn by
eye.
1877
Temporal frequency discrimination Figure 3 shows the time course of threshold recovery following a 3 set presentation of an adapting stimulus that was 0.5 log units above its detection threshold. Circles represent measurements taken when the adapting and test stimuli were 3.0 Hz and squares represent measurements taken when the adapting and test stimuli were 25.0 Hz. Threshold elevation is the ratio of the adapted to unadapted thresholds. A value of 1.O corresponds to an absence of a threshold change. Thresholds for both test stimuli recovered with a similar time course. Initially thresholds were elevated by a factor of 1.5. Within approx. 13 set thresholds returned to their unadapted values.
. cl . .
a
- --------
>_P_o__‘+__a
:
a OOOS Time
offer
onset
(set)
Fig. 3. Time course of threshold recovery following a 3 set presentation of a 3.0 or 25.0 Hz stimulus that was 0.5 log units above its threshold.
! i
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,o___o_---._~__4--*-~-_
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1 50
Results of modulation matching are shown in Fig. 4 for two observers. The ordinate represents the ratio of the modulation adjustment to the threshold in dB. The data show that stimuli match in apparent modulation depth when they are each 10 dB (0.5 log units) above their respective thresholds. DIFFERENCE
THRESHOLDS
Procedure
The observer’s task was to judge which of two temporally modulated stimuli was of a higher temporal frequency. In a single session a standard and a variable frequency were presented, one to each field of the display. The side of each stimulus was randomly assigned on each trial. A staircase tracking procedure was used so that the difference in frequency between the standard and variable (Af) was always near the threshold for discrimination. The Af was increased by 0.15 log units when an incorrect judgement was made, and decreased by 0.15 log units when three successive correct responses were given. Incorrect responses were marked by a 1 set auditory tone. Like the detection threshold experiment, the Af was well above threshold at the start of the session and decreased by 0.15 log units per trial until an incorrect response was made. The tracking procedure was then instituted and continued until 100 judgements were obtained. All temporal frequencies were equated in apparent modulation depth. This was accomplished by presenting all stimuli 0.5 log units above their detection thresholds, as previously determined. Threshold was interpolated at those frequencies for which detection thresholds had not been measured. A session always began with at least 3 min adaptation to the mean luminance of the display. The observer was required to maintain fixation on the central fixation point throughout the duration of each trial. The first stimulus of each trial was always presented to the left field of the display. Approximately IOOmsec after its termination, the second stimulus appeared on the right. In pilot experiments the two stimuli to be discriminated were presented simultaneously, one to each field of the display. Though this was a satisfactory method of displaying the stimuli, it was found that with successive presentation the observers not only found the task to be less difficult, the difference thresholds were lower. Thus the successive presentation was adopted. An intertrial interval of 15 set was used, as this was shown to be sufficient to allow recovery from adaptation (cf. Fig. 3).
(HZ)
Results Fig. 4. Modulation matching of two observers as a function of frequency. Observers adjusted the modulation depth of the frequency given by the abscissa to match an 11.OHz standard that was 0.5 log units above its threshold. The ordinate is the ratio of the modulation adjustment and threshold.
Data from each session were fit with a cumulative normal curve by using a probit analysis package (Finney, 1964; SAS User’s Guide, 1980). Threshold was taken to be the 75% probability of correct discrimination. There were some sessions in which
1578
MARC
B.
convergence toward a best-fitting curve was not achieved in 100 iterations. Also, on occasion, the fits were poor, as assessed by a chi-square statistic (P < 0.05). When either of these situations were encountered, the data were discarded and another session was run in its place. For observer M.B.M. this occurred on 67; of the experimental sessions and for observer A.Z. on 4%. The variation in difference threshold with temporal frequency is shown in Fig. 5 for observer M.B.M. Each point is the mean of four experimental sessions of 100 trials each. The bars are the standard errors of the means. The difference threshold, Af, can be seen to increase with frequency between 0.75 and 4.0 Hz. Between 4.0 and 5.0 Hz Afdecreases slightly and then rises out to about 20.0 Hz. Beyond 20.0 Hz the thresholds decrease. Another way to look at these data is to consider the variation of the relative difference threshold (Af/f) with frequency. Figures 6a and 6b plot these ratios for the two observers. The two sets of data show local minima near 1.5, 4.5 and beyond 20.0 Hz. Over the range of frequencies tested, the relative difference thresholds vary by about a factor of six. The unexpected improvement in performance at the higher frequencies led to a closer examination of those frequencies. Since the apparent modulation depth changes rapidly with frequency above 20.0 Hz, it was possible that a small mismatch in apparent modulation depth could have provided a substantial cue for discrimination. To test this hypothesis, observers, as before, determined which of two stimuli was of a higher frequency. The frequencies of the two
Temporal
frequency
(Hz
I
Fig. 5. Difference thresholds for observer M.B.M. The observer judged which of two temporal frequencies was of a higher frequency. Threshold was-taken tobe the point of 75% correct discrimination as assessed with Probit analysis. Each point represents the estimates of threshold from &ur sessions of 100 trials each.
MANDLER
35 (ai
t
l
04 i
t
$ 06b/
(b)
/
T
05 t 04
03
~
I
5 Temoorol
$0 frequency
50 (Hz
1
Fig. 6. Relative difference thresholds for observers M.B.M. and A.Z. The difference thresholds were divided by the base frequency.
stimuli were fixed while the modulation depth of one of them was varied on each trial by a method of constant stimuli. Consider a stimulus at 30.0 Hz. It was established previously that the difference threshold at 30.0 Hz was approx. 7.5 (Fig. 5). Thus 30.0 and 37.5 Hz could be correctly discriminated 75% of the time. If the discrimination was based on a difference in apparent modulation, there should be some modulation depth of the 37.5 Hz stimulus for which performance falls below this level. That this does not occur is illustrated in Fig. 7a. The proportion of correct discriminations is plotted against the modulation depth of the 37.5 Hz stimulus. The arrow represents the modulation depth of the 37.5 Hz stimulus that was used in the original measurements. Discrimination improves as the modulation depth is increased or decreased from this point. In Fig. 7b data are shown for frequencies of 40.0 and 45.9. These frequencies were correctly discriminated nearly lOO0/0of the time. If this discrimination was based on an apparent modulation depth difference, performance should get worse as the modulation depths become more nearIy equal. Here it is shown, however, that discrimination is independent of the modulation depth of the two stimuli.
10
09
1
.
Temporal frequency discrimination .
.
00
.
.
t 07
300 an3 37 5 HZ 06
t
a
t
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06
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125
3.35
40.0
an4
459
H.7
b
055 135
Log
1.45
155
modulation
1.65 depth
175 of
165
variable
Fig. 7. Results of control experiments to determine if the high frequency improvement in discrimination was an artifact of mismatches of apparent modulation depth. Details are given in text.
Discussion
The initial premise of these experiments was that the difference threshold for temporal frequency discrimination must reflect the properties of the underlying channels. Specifically, it was supposed that the number of channels and their spectral distributions could be derived from such observations. This is possible if one makes assumptions about the shapes of the sensitivity profiles, as well as the manner in which channels interact to determine the appearance. One hypothesis that does not directly rely on assumptions about channel shape is that two frequencies will be discriminable only when they activate different channels. A consideration of the present results reveals that, given this hypothesis, 35-45 separate channels are required. This estimate was derived from the number of just noticeable differences in frequency over the range tested. It is clearly inconsistent with the two to four channels that have been inferred from other measures. An alternative hypothesis that was discussed earlier is that two frequencies will be discriminable if they cause some criterion change in the distribution of channel outputs. This is akin to a “line-element” model of wavelength discrimination (Wyszecki and Stiles, 1982, p. 654). This type of model requires
1879
discrimination to be better in those regions in which a small change in frequency produces a relatively large change in the outputs of the channels. That is, discrimination must be best when the slopes of the sensitivity profiles of the underlying channels are at a maximum. This type of model has been proposed for discrimination of motion in depth (Beverley and Regan, 1975), and spatial frequency (Regan, 1982). The present data show that frequency discrimination was better at I.5 and 4.5 Hz than at other frequencies. This means that there must be at least two channels with overlapping sensitivity at these frequencies. Moreover, the difference between the slopes of the sensitivity profiles of the underlying channels must be greatest at these frequencies. The data also show a substantial reduction in discrimination between 6.0 and 20.0 Hz. This poor discrimination could result from a decrease of the slopes of the underlying channels in this region, or the possibility that fewer channels have sensitivity at those frequencies. The most surprising aspect of these results is that discrimination improved dramatically at the highest frequencies. Observer M.B.M. could reliably distinguish 45.0 and 46.9 Hz. This discrimination was shown not to be based on differences in the apparent modulation depth. From the observers’ points of view the task became substantially less tedious at these frequencies. Observers reported a change in the subjective basis for the discrimination that was difficult to describe in words. One explanation for this high frequency improvement is that an additional very high frequency channel contributes to discrimination at these frequencies. It is shown in the following paper that this proposition is not required by the data. The high frequency behavior can be accounted for by a very broadly tuned low frequency channel. Finally, compared to earlier experiments that measured temporal frequency discrimination (Mowbray and Gebhard, 1955; Gebhard er al., 1955) the observers in the present experiment were about a factor of IO less sensitive to frequency differences. At least three factors may account for lower thresholds in the earlier experiments. First, differences in apparent modulation depth in the earlier experiments aided discrimination. Though there are no published data to support this notion in the temporal frequency domain, Campbell ef al. (1970) showed this to be the case for spatial frequency discrimination. Spatial discrimination was better by a factor of two when the gratings had equal physical contrasts than when they had equal apparent contrasts. Second, adaptation effects may have accentuated differences between stimuli. Third, the higher modulation depth used in the earlier experiments facilitated discrimination. Acknowledgemenfs-This work was submitted in partial fulfillment for the degree of Doctor of Philosophy at the University of Rochester in March,
1983. I thank Walt
ISSO
MARC B. MANDLER
hfakous, Dave Williams and Bill Merigan for their critical reviews of this work. Also. I thank Amy Zelazny for her many patient hours as an observer. This work was funded by grants EY03594 and EY01319 from the National Eye Insttrute. REFERENCES Beverley K, I. and Regan 0. (1973) Evidence for the existence of neural mechanisms selectively sensitive to the direction of movement in soace. J. Pkvsioi. 235. 17-29. Beverley K. 1. and Regan D.‘( 1975) The relation between discrimination and sensitivity in the perception of motion in deoth. J. Phvsiol. 249, 387-398. Blakembre C. and Campbell F. W. (1969) On the existence of neurons in the human visual system selectively sensitive to the orientation and size of retinal images. .I. Physioi. 203, 237-260. Boynton R. M. (1979) Human Color Vision. Rinehart & Winston, New York. Campbell F. W. and Kulikowski J. (1966) Orientational selectivity of the human visual system. J. Physiol 187, 437-44s.
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