Counterphase dichoptic flicker is seen as its own second harmonic C. R. Cavonius Ahteilung Sinnes- und Neurophysiologie, Institut fur Arbeitsphysiologie, D-4600 Dortmund 7, Germany O. Estevez and L. H. van der Tweel Laboratory of Medical Physics, University of Amsterdam, Nl^I!05
Amsterdam, Netherlands
(Received 30 September 1991)
If a patterniess field is modulated sinusoidally In time so that the lumitiance change in one eye is in counterphase to that in the other, the resulting dicker appears faster than if the modulation to both eyes has the same phase. If observers set the frequency and the amplitude of a comparison in-phase field so that it matches a neighbouring counterphase field, modulated at, say. 2.5 x its threshold, they set the frequency to twice the counterphase frequency, and the amplitude to a value that is, for a given frequency, a constant ratio of the modulation of the counterphase field. Counterphase stimulation thus appears to cause an internal second-harmonic signal. However, it is not possible to cancel this by adding a second harmonic component to the stimulus.
Two experiments revolutionized visual psychophysics in this century: in 1954 Hendrik de Lange introduced the concept of tetnpora! modulation sensitivity', and in 1968 Fergus Campbell and John Robson extended this method to the broader domain of spatial vision". De Lange showed that linear systems theory could be used to account for flicker sensitivity to different waveforms, and Campbell and Robson explicitly introduced Fourier methods to the analysis of spatial patterns. Together these experiments freed visual science from the limitations inherent in measurements of critical flicker fusion frequency and visual acuity, which, since the previous century, had been the benchmark measures of temporal and spatial resolution. Most of de Lange's measurements were monocular determinations of the temporal luminance modulation that observers need to detect flicker at different frequencies, but he also investigated the effect of presenting modulation in opposite phase to the two eyes, and found that this increases the modulation needed to detect flicker-\ This effect was studied in detail by Van der Twecl and Estevez* and Cavonius^: they confirmed de Lange's results, and showed further that the difference between in-phase and counterphase sensitivity depends strongly on frequency. In the course of the latter two experiments, it was observed that the apparent rate offlicker is different when the modulation has the same phase in both eyes I in-phase) and when it is in counterphase: if the modulation is switched from in-phase to counterphase, the flicker seems to speed up. We have attempted to quantify this phenomenon and to explore its implications. Correspondence to: Dr C. R. Cavonitis. Instilut fiir Arbeitsphysiologic, Ardeystrasse 67. D-4600 Dortmund 1. Germany
© t992 Bulterworth-Heinemann for British College of Optometrisls 0275-5408/92/020153-04
Method Flickering stimuli were generated with factory-modified Philips 57 DeLuxe White ring fluorescent tubes mounted in integrating spheres, and driven by purpose-built power amplifiers. The luminanee within each sphere was monitored, and this signal was used to correct the driving current, so that within the range of frequeneies used in these experiments, sinusoidal modulation of up to 80% could be reached without measurable distortion. The stimulus frequency was set by a Hewlett Packard 203A variable-phase function generator, and its amplitude was adjusted by calibrated linear attenuators. To obtain dichoptie stimulation, the openings of two integrating spheres were reflected by mirrors to the rear of a circular aperture, so that an observer saw the left mirror with his right eye and the right mirror with his left eye. This obviates using a stereoscope or other special optics, and convergence is easily maintained on the single aperture. The comparison field filled a second aperture that was identical to, but above, the dichoptic field. Light from a third integrating sphere was seen binocuiarly through this aperture, so that the modulation to both eyes was always in-phase. This light source was controlled by a separate oscillator, and its frequency was measured with a Systron Donner 1034 counter. At a viewing distance of 57 cm both apertures had a diameter of 3.5 degrees and their centres were separated by 5 degrees. Their time-average luminance was 1500 cd m " ^ in a 180 cd m " -^ white surround. During informal observations, and during our earlier measurements of in-phase and counterphase modulation sensitivity, we noticed that at moderate levels of
Ophthal. Physiol. Opt., 1992, Vol. 12. April
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Dichoptic fiicker: C. R. Cavonius et al. modulation, observers were unable to tell whether flicker was in-phase or counterphase; but that with strong modulation, counterphase flicker had a qualitatively different appearance: observers usually described it as 'rough", as if it comprised more than one frequency. Observers could make matches between the dichoptic counterphase field and the in-phase field as long as the modulation was within a range of about I to 4x threshold: with stronger modulation no combination of modulation and frequency gave a satisfactory match. We therefore set the modulation of the in-phase field at each frequency to 2.5 x its threshold and let the observer match it by setting the frequency and modulation of the counterphase field. Results for two observers are shown by the upper row of data points in Figure L The lower set of data show similar matches, but in this case both fields were modulated in-phase. The two lines, at _v = 2x and y = .v. describe the data well; and the former shows that under these conditions counterphase flicker resembles in-phase flicker of twice the frequency. At these moderate depths of modulation the fundamental component of the counterphase stimulus is never seen, presumably because much of it is cancelled*'\ The remaining flicker must arise from non-linear processing of the neural signal before the signals from the two eyes are combined.
raised in steps, and at each the observer matched it by setting the modulation of the 40 Hz field. Although for this pair of frequencies nearly five times as much modulation is needed in the 40 Hz field, the ratio of the modulations, which we call k^, remains constant; and an extrapolation of the regression line intersects the origin. While kf is constant for any pair of frequencies, it varies greatly across frequencies. If after the internal second harmonic is generated it is processed in the same way as a conventional binocular signal of the same frequency, and if the distortion is static, it should be possible to predict thresholds for detection of the physical second harmonic from the counterphase thresholds. The logic is shown in Figure 3: the frequency of the matching signal is 2 x the counterphase frequency (cf. Figure I) and its threshold modulation is kf times the counterphase threshold. Two examples are shown schematically: one at low frequencies, where kf < 1, and one at high frequencies, where kf> 1. The crosses in Figures 4 and 5 show the calculated thresholds for two observers; these agree quite well with the open circles, which are the measured in-phase thresholds.
We next asked what ratio of modulation depths is needed at various frequencies if the two fields are to match. If after the stage at which the second harmonic is generated the visual system processes this signal in the same way as it does a binocular in-phase stimulus at the same frequency as the second harmonic, this ratio should remain constant when the modulation in both fields is changed. Figure 2 shows that this holds within experimental error. Thresholds for the detection of counterphase (20 H^l and in-phase (40 Hz) flicker were first measured separately, and plotted as the lowest point. The modulation of the 20 Hz counterphase field was then
Observers can accurately match a binocular in-phase flickering field either to another in-phase field or to a dichoptic counterphase field. Although we agree with Mandler and Bowker's finding that modulation depth influences the apparent speed of flicker^, observers can make unique matches if they are allowed to vary both the frequency and the amplitude of modulation. Mandler also reported later that matches can be made at high frequencies if the depths of modulation at all frequencies are first adjusted so that they appear equar. As long as the depth of modulation was not greater than about 4x the detection threshold, counterphase
100 r
Discussion
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.
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Figure I Frequency of binocular in-phase flicker that is required to match a second field {f\,\ when the latter is modulated in-phase (open symbols) or in counlerphase (filled symbols|. Observers O.E. (circles) and D.C (diamonds). The upper and lower tines arc y = 2x and >• = .\. respectively
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4
5
counterphase(%)
Figure 2 An example of contrast-matching. The upper and lower fields were modulated at 20 and 40 Hz. and their separate thresholds for flicker detection were measured. The modulation of the eouiiterphase field was then increased in steps, and at each the subject set the modulation of the in-phase field to a visual match
Dichoptic ficker: C. R. Cavonius et al. 0.1
09
o • +
10 Figure 3 Schematic examples of how iti-phasc thresholds were predicted by multiplying the frequency of the counterphase modukition by 2. and multiplying its threshold modulation by k.
0.1
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100 10
:oo
Frequency (Hz)
Figure 5 Counlerphase thresholds # . in-phase thresholds. O. and predicted in-ph:ise thresholds. + . for observer D,C.
10
100 10 Frequency
100 (Hz)
Figure 4 Counterphase thresholds. # , in-phase thresholds. O and predicted in-phase thresholds, +, for observer O.E,
flicker could be completely matched by in-phase flicker at twice the frequency: under these conditions the two fields are indistinguishable. At high modulation depths the flelds arc qualitatively different, and no match is possible. Two possible causes arc that cancellation of the fundamental of the counterphase signal is incomplete, so that when modulation is strong the fundamental may be detected; and that the distortion products that are produced by the non-linear processing of the input may reach their own detection thresholds. So far, the results are consistent with a simple model in which counterphase stimulation cancels the fundamental component of the neural signal and the sensation of flicker is produced by higher even-harmonics. Of these, the second harmonic dominates, and our results suggest that
it is processed by the visual system in the same way as a binocular signal of the same frequency. Because the in-phase and counterphase modulation depths that yield visual matches are linearly related (e.g.. Fii/ure 2). the non-linearity involved in producing the second harmonic must be of a linear-rectifier type, since a square-law or logarithmic transform would cause a non-linear increase of modulation. The ratios o{ counter- and in-phase sensitivity (e.g.. Figures 4 and 5) give the relative amplitude of the internal second harmonic, which is frequency-dependent: at higher frequencies the two sensitivities are similar, so the relative amplitude of the second-harmonic is large. However, this cannot be the whole story, for if it were, one could cancel the internal second harmonic by adding to the stimulus the same frequency, at an appropriate amplitude and phase. We tried this, without success: if a near-threshold second harmonic is added to the counterphase stimulus and its phase rotated through 360 degrees, the perceived flicker never waxes or wanes. We tested this more systematically by adding various amounts of second harmonic, from below its own threshold to above, lo the counterphase stimulus and measuring thresholds for the detection of the latter at 30 degree steps of phase advance. We never found systematic changes in threshold. Acknowledgements Preparation of this manuscript was aided by a Deutscher Akademischcr Austauschdienst British Council Academic Research Collaboration grant (312 arc/lz). Part of the results were presented at the 1983 meeting of the Association for Research in Vision and Ophthalmology^ with support from the Deutsche Forschungsgemeinschaft.
Ophthal. Physiol. Opt.. 1992, Vol. 12, April
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Dichoptic flicker: C. R. Cavonius et al. References de Lange, H, Relationship between critical flicker frequency and a sel of low-frequency characteristics of the eye, J. Opt. Soc. Am. 44. 380-389(1954). Campbell, F, W, and Robson, J. G, Application of Fourier analysis lo Ihe visibility of gratings, J. Physiol. 197. 551-566 (1968). de Lange, H. Attenuation characteri.stics and phase-shift characteristics of the human fovea-cortex systems in relation to the flicker-fusion phenomena. Doctoral dissertation, Technische Hogeschool, Delfl, pp. 64-66 (1957).
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Van der Tweel. L, H, and Estevez. O, Subjective and objective evalualion of flicker. Ophthalmotoc/ica 169. 70 81 (1974). Cavonius, C. R. Binocular interactions in flicker, Q. J. Exper. P.svrW. 31, 273-280(19791, Mandler. M. B. and Bowkcr, D, O, Fields flickering at different rates can appear identical. Invest. Ophthalmoi. Vi.sual Sci. 20(SuppL), 49(1981). Mandler, M. B. Temporal frequency discrimination above threshold. Vision Re.-i. 24. 1873 1880 (1984). Estevez, O, and Cavonius, C. R, Binocular counterphase flicker is seen as ils own second harmonic. Invest. Ophthalmol. Visual Sci. 24tSuppl.), 97(1983).
Amsterdam, Netherlands
(Received 30 September 1991)
If a patterniess field is modulated sinusoidally In time so that the lumitiance change in one eye is in counterphase to that in the other, the resulting dicker appears faster than if the modulation to both eyes has the same phase. If observers set the frequency and the amplitude of a comparison in-phase field so that it matches a neighbouring counterphase field, modulated at, say. 2.5 x its threshold, they set the frequency to twice the counterphase frequency, and the amplitude to a value that is, for a given frequency, a constant ratio of the modulation of the counterphase field. Counterphase stimulation thus appears to cause an internal second-harmonic signal. However, it is not possible to cancel this by adding a second harmonic component to the stimulus.
Two experiments revolutionized visual psychophysics in this century: in 1954 Hendrik de Lange introduced the concept of tetnpora! modulation sensitivity', and in 1968 Fergus Campbell and John Robson extended this method to the broader domain of spatial vision". De Lange showed that linear systems theory could be used to account for flicker sensitivity to different waveforms, and Campbell and Robson explicitly introduced Fourier methods to the analysis of spatial patterns. Together these experiments freed visual science from the limitations inherent in measurements of critical flicker fusion frequency and visual acuity, which, since the previous century, had been the benchmark measures of temporal and spatial resolution. Most of de Lange's measurements were monocular determinations of the temporal luminance modulation that observers need to detect flicker at different frequencies, but he also investigated the effect of presenting modulation in opposite phase to the two eyes, and found that this increases the modulation needed to detect flicker-\ This effect was studied in detail by Van der Twecl and Estevez* and Cavonius^: they confirmed de Lange's results, and showed further that the difference between in-phase and counterphase sensitivity depends strongly on frequency. In the course of the latter two experiments, it was observed that the apparent rate offlicker is different when the modulation has the same phase in both eyes I in-phase) and when it is in counterphase: if the modulation is switched from in-phase to counterphase, the flicker seems to speed up. We have attempted to quantify this phenomenon and to explore its implications. Correspondence to: Dr C. R. Cavonitis. Instilut fiir Arbeitsphysiologic, Ardeystrasse 67. D-4600 Dortmund 1. Germany
© t992 Bulterworth-Heinemann for British College of Optometrisls 0275-5408/92/020153-04
Method Flickering stimuli were generated with factory-modified Philips 57 DeLuxe White ring fluorescent tubes mounted in integrating spheres, and driven by purpose-built power amplifiers. The luminanee within each sphere was monitored, and this signal was used to correct the driving current, so that within the range of frequeneies used in these experiments, sinusoidal modulation of up to 80% could be reached without measurable distortion. The stimulus frequency was set by a Hewlett Packard 203A variable-phase function generator, and its amplitude was adjusted by calibrated linear attenuators. To obtain dichoptie stimulation, the openings of two integrating spheres were reflected by mirrors to the rear of a circular aperture, so that an observer saw the left mirror with his right eye and the right mirror with his left eye. This obviates using a stereoscope or other special optics, and convergence is easily maintained on the single aperture. The comparison field filled a second aperture that was identical to, but above, the dichoptic field. Light from a third integrating sphere was seen binocuiarly through this aperture, so that the modulation to both eyes was always in-phase. This light source was controlled by a separate oscillator, and its frequency was measured with a Systron Donner 1034 counter. At a viewing distance of 57 cm both apertures had a diameter of 3.5 degrees and their centres were separated by 5 degrees. Their time-average luminance was 1500 cd m " ^ in a 180 cd m " -^ white surround. During informal observations, and during our earlier measurements of in-phase and counterphase modulation sensitivity, we noticed that at moderate levels of
Ophthal. Physiol. Opt., 1992, Vol. 12. April
153
Dichoptic fiicker: C. R. Cavonius et al. modulation, observers were unable to tell whether flicker was in-phase or counterphase; but that with strong modulation, counterphase flicker had a qualitatively different appearance: observers usually described it as 'rough", as if it comprised more than one frequency. Observers could make matches between the dichoptic counterphase field and the in-phase field as long as the modulation was within a range of about I to 4x threshold: with stronger modulation no combination of modulation and frequency gave a satisfactory match. We therefore set the modulation of the in-phase field at each frequency to 2.5 x its threshold and let the observer match it by setting the frequency and modulation of the counterphase field. Results for two observers are shown by the upper row of data points in Figure L The lower set of data show similar matches, but in this case both fields were modulated in-phase. The two lines, at _v = 2x and y = .v. describe the data well; and the former shows that under these conditions counterphase flicker resembles in-phase flicker of twice the frequency. At these moderate depths of modulation the fundamental component of the counterphase stimulus is never seen, presumably because much of it is cancelled*'\ The remaining flicker must arise from non-linear processing of the neural signal before the signals from the two eyes are combined.
raised in steps, and at each the observer matched it by setting the modulation of the 40 Hz field. Although for this pair of frequencies nearly five times as much modulation is needed in the 40 Hz field, the ratio of the modulations, which we call k^, remains constant; and an extrapolation of the regression line intersects the origin. While kf is constant for any pair of frequencies, it varies greatly across frequencies. If after the internal second harmonic is generated it is processed in the same way as a conventional binocular signal of the same frequency, and if the distortion is static, it should be possible to predict thresholds for detection of the physical second harmonic from the counterphase thresholds. The logic is shown in Figure 3: the frequency of the matching signal is 2 x the counterphase frequency (cf. Figure I) and its threshold modulation is kf times the counterphase threshold. Two examples are shown schematically: one at low frequencies, where kf < 1, and one at high frequencies, where kf> 1. The crosses in Figures 4 and 5 show the calculated thresholds for two observers; these agree quite well with the open circles, which are the measured in-phase thresholds.
We next asked what ratio of modulation depths is needed at various frequencies if the two fields are to match. If after the stage at which the second harmonic is generated the visual system processes this signal in the same way as it does a binocular in-phase stimulus at the same frequency as the second harmonic, this ratio should remain constant when the modulation in both fields is changed. Figure 2 shows that this holds within experimental error. Thresholds for the detection of counterphase (20 H^l and in-phase (40 Hz) flicker were first measured separately, and plotted as the lowest point. The modulation of the 20 Hz counterphase field was then
Observers can accurately match a binocular in-phase flickering field either to another in-phase field or to a dichoptic counterphase field. Although we agree with Mandler and Bowker's finding that modulation depth influences the apparent speed of flicker^, observers can make unique matches if they are allowed to vary both the frequency and the amplitude of modulation. Mandler also reported later that matches can be made at high frequencies if the depths of modulation at all frequencies are first adjusted so that they appear equar. As long as the depth of modulation was not greater than about 4x the detection threshold, counterphase
100 r
Discussion
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Figure I Frequency of binocular in-phase flicker that is required to match a second field {f\,\ when the latter is modulated in-phase (open symbols) or in counlerphase (filled symbols|. Observers O.E. (circles) and D.C (diamonds). The upper and lower tines arc y = 2x and >• = .\. respectively
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counterphase(%)
Figure 2 An example of contrast-matching. The upper and lower fields were modulated at 20 and 40 Hz. and their separate thresholds for flicker detection were measured. The modulation of the eouiiterphase field was then increased in steps, and at each the subject set the modulation of the in-phase field to a visual match
Dichoptic ficker: C. R. Cavonius et al. 0.1
09
o • +
10 Figure 3 Schematic examples of how iti-phasc thresholds were predicted by multiplying the frequency of the counterphase modukition by 2. and multiplying its threshold modulation by k.
0.1
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Figure 5 Counlerphase thresholds # . in-phase thresholds. O. and predicted in-ph:ise thresholds. + . for observer D,C.
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100 (Hz)
Figure 4 Counterphase thresholds. # , in-phase thresholds. O and predicted in-phase thresholds, +, for observer O.E,
flicker could be completely matched by in-phase flicker at twice the frequency: under these conditions the two fields are indistinguishable. At high modulation depths the flelds arc qualitatively different, and no match is possible. Two possible causes arc that cancellation of the fundamental of the counterphase signal is incomplete, so that when modulation is strong the fundamental may be detected; and that the distortion products that are produced by the non-linear processing of the input may reach their own detection thresholds. So far, the results are consistent with a simple model in which counterphase stimulation cancels the fundamental component of the neural signal and the sensation of flicker is produced by higher even-harmonics. Of these, the second harmonic dominates, and our results suggest that
it is processed by the visual system in the same way as a binocular signal of the same frequency. Because the in-phase and counterphase modulation depths that yield visual matches are linearly related (e.g.. Fii/ure 2). the non-linearity involved in producing the second harmonic must be of a linear-rectifier type, since a square-law or logarithmic transform would cause a non-linear increase of modulation. The ratios o{ counter- and in-phase sensitivity (e.g.. Figures 4 and 5) give the relative amplitude of the internal second harmonic, which is frequency-dependent: at higher frequencies the two sensitivities are similar, so the relative amplitude of the second-harmonic is large. However, this cannot be the whole story, for if it were, one could cancel the internal second harmonic by adding to the stimulus the same frequency, at an appropriate amplitude and phase. We tried this, without success: if a near-threshold second harmonic is added to the counterphase stimulus and its phase rotated through 360 degrees, the perceived flicker never waxes or wanes. We tested this more systematically by adding various amounts of second harmonic, from below its own threshold to above, lo the counterphase stimulus and measuring thresholds for the detection of the latter at 30 degree steps of phase advance. We never found systematic changes in threshold. Acknowledgements Preparation of this manuscript was aided by a Deutscher Akademischcr Austauschdienst British Council Academic Research Collaboration grant (312 arc/lz). Part of the results were presented at the 1983 meeting of the Association for Research in Vision and Ophthalmology^ with support from the Deutsche Forschungsgemeinschaft.
Ophthal. Physiol. Opt.. 1992, Vol. 12, April
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Dichoptic flicker: C. R. Cavonius et al. References de Lange, H, Relationship between critical flicker frequency and a sel of low-frequency characteristics of the eye, J. Opt. Soc. Am. 44. 380-389(1954). Campbell, F, W, and Robson, J. G, Application of Fourier analysis lo Ihe visibility of gratings, J. Physiol. 197. 551-566 (1968). de Lange, H. Attenuation characteri.stics and phase-shift characteristics of the human fovea-cortex systems in relation to the flicker-fusion phenomena. Doctoral dissertation, Technische Hogeschool, Delfl, pp. 64-66 (1957).
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Van der Tweel. L, H, and Estevez. O, Subjective and objective evalualion of flicker. Ophthalmotoc/ica 169. 70 81 (1974). Cavonius, C. R. Binocular interactions in flicker, Q. J. Exper. P.svrW. 31, 273-280(19791, Mandler. M. B. and Bowkcr, D, O, Fields flickering at different rates can appear identical. Invest. Ophthalmoi. Vi.sual Sci. 20(SuppL), 49(1981). Mandler, M. B. Temporal frequency discrimination above threshold. Vision Re.-i. 24. 1873 1880 (1984). Estevez, O, and Cavonius, C. R, Binocular counterphase flicker is seen as ils own second harmonic. Invest. Ophthalmol. Visual Sci. 24tSuppl.), 97(1983).
