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1 From the Department of Physiology, Institute for Biomedical Research, The University of Sydney, New South Wales, Australia; the 2 Department of Biological Sciences and the 3 Glaucoma Institute, State University of New York State College of Optometry, New York, New York; and the 4 Department of Neurobiology, Max Planck Institute for Biophysical Chemistry, Göttingen, Germany.
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Abstract |
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METHODS. Responses of macaque magnocellular (MC) retinal ganglion cells were recorded to counterphase-modulated sinusoidal gratings of various spatial frequencies, and linearity of spatial summation was assessed. Human psychophysical thresholds were measured for a variety of phase discrimination and matching tasks.
RESULTS. Consistent with lateral geniculate recordings reported by other authors, no evidence was found of a separate nonlinear (My) MC cell class. The small, spatially nonlinear responses found were least at the low spatial frequencies used in clinical testing. Further analysis showed that no spatially modulated signal can be expected from the nonlinear response of a ganglion cell; the nonlinearity of spatial summation gives a doubled response in time but not across space. Psychophysical performance was consistent with an inability to distinguish the temporal phase of counterphase-modulated gratings when the illusion occurs. From 4 to 40 Hz, the zero-crossings of the modulated sinusoidal grating provided a spatial cue and were matched to comparison patterns at twice the stimulus spatial frequency.
CONCLUSIONS. These results are inconsistent with the hypothesis that spatially nonlinear (My) retinal ganglion cells are the physiological substrate of the frequency-doubling illusion. A cortical loss of temporal phase discrimination may be the principle cause of the illusion.
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Introduction |
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The terms "X" and "Y" cell were originally coined to describe cat ganglion cells4 5 6 7 8 9 10 ; a characteristic feature of cat Y-cells is nonlinear spatial summation. This nonlinearity is thought to arise because of subunits within the field structure that rectify the visual signal.6 In studies in Old-World primates such as macaque, at the level of the lateral geniculate nucleus (LGN), only a small fraction of cells show some degree of nonlinear spatial summation.11 12 13 14 These cells were thought to be a subset of cells of the MC pathway and hence were termed Y-like MC (My) cells, with the remainder of spatially linear cells being termed X-like.13 It should be noted that spatial nonlinearity is not related to the temporal nonlinear summation of cone photoreceptor signals seen with chromatic stimuli, which is a property of all MC cells.15
Tests of linearity of spatial summation commonly involve a counterphase-modulated grating stimulus. An illustration of this stimulus and the response of a highly linear MC cell compared with that of a more nonlinear MC cell is shown in Figure 1 . Averaged responses to the stimulus at four grating positions are shown. For the spatially linear cell, there is a null position of the grating, where there is no response. The first harmonic response of the less-linear cell also shows a null position, but the second harmonic response (a temporally frequency-doubled response) shows no variation at different grating locations. Figure 1 also shows that the temporal phase of the linear cell’s response is quite different to gratings 180° spatially out of phase, whereas the temporally frequency-doubled response of the less-linear cell does not vary with spatial location. This inability of less-linear cells to distinguish between the onset and offset of light in terms of spatial phase led to a proposal that these cells may form the retinal substrate of the frequency-doubling illusion.3 It has been argued that if these cells were large and sparse across the retina, with limited redundancy, then retinal ganglion cell damage in the early stages of glaucoma could produce reduced sensitivity for the frequency-doubling illusion.3
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Methods |
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A tungsten-in-glass recording microelectrode was introduced to the retina through a scleral hole by established techniques. The details of the preparation can be found elsewhere.16 Cells were recorded both in the central and peripheral retina. The location of each cell’s receptive field was mapped onto a tangent screen 114 cm from the eye. Cells were initially characterized on the basis of both their antidromic latency after electrical stimulation of the optic chiasm and their responses to luminance and chromatic stimuli. Spatial dimensions of cells’ receptive fields were also measured by using drifting gratings of different spatial frequencies.
Visual stimuli were generated through a graphics controller (Visual Stimulus Generator [VSG] series 3; Cambridge Research Systems, Cambridge, UK) and presented on a CRT monitor (Barco, Kortrijk, Belgium) 114 cm from the eye (frame rate 195 Hz, mean luminance 40 cd/m2). The stimuli were temporally counterphase-modulated sinusoidal gratings of various spatial frequencies. The temporal frequency was 3.68 or 17.44 Hz. The spatial frequency was 0.2, 0.4, 0.8, 1.6, 3.2, or 6.4 cyc/deg. The spatial phase of the grating was advanced from 0° to 360° across the receptive field in 45° increments.
Psychophysical Experiments
The same visual display system was used as that used in the physiological experiment, but with a viewing distance of 0.48 m. At this distance the visible area of the display subtended 40° by 26° of visual angle. Mean luminance of stimulus and background was 40 cd/m2, and chromaticity was (0.45, 0.47) in International Commission on Illumination (CIE) x, y coordinates.
Psychophysical experiments included measurements of phase-discrimination threshold, detection threshold, and zero-crossing matching. In all experiments, the observer viewed the targets monocularly.
In some experiments, we used rectified gratings generated with a graphics controller (VSG 2/5; Cambridge Research Systems) and presented on a 21-in. monitor (Trinitron; Sony, Tokyo, Japan) at a viewing distance of 148 cm. Other conditions were very similar to the main experimental set.
Phase Discrimination and Detection.
The stimuli consisted of a pair of temporally counterphase-modulated sinusoidal gratings. The two horizontal gratings (each 19° wide, 25° high) were presented simultaneously side by side with a 30-minute gap. In further experiments, sawtooth or square-wave gratings, or a rectified sine wave grating was used. Phase discrimination and detection contrast thresholds were measured with a two-alternative, forced-choice procedure involving randomly interleaved dual staircases.
For the discrimination task, each trial included two 300-ms presentations with a 200-ms interstimulus interval. One presentation contained a pair of gratings that were temporally in phase, and the other a pair of gratings 180° out of phase (for counterphase-modulated gratings, 180° temporally out of phase is equivalent to 180° spatially out of phase). The observer’s task was to indicate which of the two presentations contained the in-phase gratings.
For the detection task, similar stimuli were used, except that only one of the two presentations contained a pair of in-phase gratings, and the other presentation was blank. The observer’s task was to indicate which of the two presentations contained the gratings.
Contrast thresholds (71% correct responses) were computed as the means of 20 reversals of four staircases for both tasks. A complete data set was obtained with foveal fixation (spatial frequency: 0.2 and 1.0 cyc/deg, temporal frequency: 1, 2, 4, 8, 11, 16, 20, 30, and 40 Hz). For comparison, a partial data set was collected at 5°, 10°, and 20° eccentricity (spatial frequency: 0.2 cyc/deg, temporal frequency: 4–40 Hz).
In further experiments, discrimination thresholds were measured between pairs of in-phase gratings and pairs of temporally or spatially 90° phase-shifted gratings at 0.2 cyc/deg and 20 Hz.
Zero-Crossing Matching.
The stimuli consisted of a pair of horizontal gratings simultaneously presented side by side with a 30-minute gap. One grating, the test, was a counterphase-modulated sinusoidal or sawtooth grating (spatial frequency: 0.2 cyc/deg, temporal frequency: 4–20 Hz). The other grating, the comparison pattern, was a static square-wave grating with a restricted duty cycle (10%) so that it appeared on the screen as a series of equally spaced, thin, bright lines on a dark background. The test and comparison gratings were of equal contrast. The observer’s task was to adjust the spatial frequency and phase of the comparison grating until the bright bars aligned with the regions of minimal flicker (the zero-crossing regions) of the test grating. Initial training for all observers was with a 20-Hz test grating, because the zero-crossings were most prominent at this and higher temporal frequencies.
Matching spatial frequency and phase were measured with the method of adjustment. The temporal frequency and spatial phase of the reference gratings were randomized from trial to trial. Each matching result was an average of 10 settings. Data were collected with foveal fixation.
Observers.
Three observers participated in the experiments. Observers AJRW and HS were authors, and JK was a naïve observer. All observers had normal color vision, as assessed with a Neitz anomaloscope, Ishihara pseudoisochromatic plates and Farnsworth-Munsell 100-Hue (Munsell Color Services, New Windsor, NY). Observer HS is myopic and wore corrective lenses. Observers AJRW and JK are emmetropic. Observers provided informed written consent according to a protocol conforming to the Declaration of Helsinki and approved by the State University of New York, State College of Optometry Institutional Review Board.
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Results |
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All cells were tested with counterphase luminance-modulated sinusoidal gratings at a spatial frequency twice that which gave the peak response. Typical cells from our sample are shown in Figure 1 and further examples are shown in Figure 2 . In the histograms (Fig. 1) , the amplitude of the first harmonic depended on the grating location, whereas the amplitude and phase of the second harmonic response appeared independent of grating position. In Figure 2 are plots of response amplitude and phase of a linear cell (Figs. 2A 2B) and less-linear cell (Figs. 2C 2D) which quantify these results. Amplitudes are made negative when the first harmonic phase changes by 180°.
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Spatial Nonlinearity as a Basis for the Frequency-Doubling Percept
In the previous section, we show that physiological evidence for a separate My class is weak. We then considered whether the frequency-doubling percept could be derived from such a nonlinear response, per se. Figure 4A
shows a further example of a temporally frequency-doubled response from a less-linear MC cell. The spatial nonlinearity caused a frequency-doubled response in time. There were two response peaks per temporal cycle of the stimulus. We then considered whether this implies a frequency-doubled response in space from a ganglion cell array.
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We considered whether the response phase of the second harmonic response could in any way act as a spatial cue. Response phase of first and second harmonic responses of two cells with differing nonlinearity indices were plotted as a function of grating position at 0.2 cyc/deg in Figure 2 . Response phase of the first harmonic varies with grating spatial phase, regardless of whether the cell has a high or low nonlinearity index. Phase of the second harmonic is independent of grating phase for both cells shown. To confirm this result, we compared the phases of the second harmonic at the two peaks of the first harmonic amplitude. At 0.2 cyc/deg, mean phase difference of the second harmonic at these two peaks was 32.7° ± 14.4° (SD; n = 11), which was not statistically significant (Watson and Williams test, P > 0.0519 ). The same analysis was repeated on the same cells at the highest spatial frequency that gave a response (average first harmonic or second harmonic response greater than 10 impules/sec). This yielded a similar result. The possibility that the second harmonic phase provides spatial information can thus be rejected.
We suggest that the notion that the frequency-doubling illusion can arise from a nonlinear spatial response is based on a confounding of the nature of the nonlinearity: Although it is a nonlinearity of spatial summation, it causes a temporal rather than a spatial doubling of frequency.
The Frequency-Doubling Illusion and Loss of Phase Information
Figure 4
showed responses of an array of ganglion cells as a function of spatial position. Observation of the frequency-doubling illusion suggests bars of intense flicker separated by regions of minimal flicker. These minima appear at approximately twice the spatial frequency of the test stimulus and correspond to the zero-crossings of the sinusoidal grating. A plausible explanation of the regions of minimum flicker would be minimal first harmonic responses of ganglion cells. On either side of these regions, ganglion cells respond vigorously. On- and off-center cells respond in counterphase. The doubled nature of the illusion implies that discrimination of the half-cycle temporal phase difference of neighboring flickering bars is difficult. We tested this by measuring the discrimination threshold of counterphase-modulated gratings at several spatial and temporal frequencies.
Two aligned gratings were presented side by side, each modulated in counterphase. In a two-alternative, forced-choice procedure, observers had to make the discrimination illustrated in Figure 5A . Contrast thresholds for the discrimination were measured at 0.2 and 1 cyc/deg.
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If a loss of temporal phase discrimination is indeed responsible for the frequency-doubling illusion, under certain conditions an observer should be unable to distinguish between a counterphase-modulated sinusoid and reversal of a rectified sinusoid at high stimulus temporal frequencies, as illustrated in Figure 5B . A linear ganglion cell’s response amplitude for this waveform would go through a minimum near the minimum of the rectified sinusoid but not null out completely. The residual response would be dependent on receptive field center size and contrast. We calculated that in central retina (±10°) a grating of 0.1 cyc/deg at 30% contrast would evoke a negligible response in an MC cell positioned at the crossover (equivalent to <1% contrast for an optimally positioned sinusoid). Under these conditions, five observers compared the contrast-reversed rectified sine wave paired with the standard grating reversal stimulus. At low temporal frequencies, the gratings were clearly distinguishable. At 20 Hz, they appeared very similar.
Possible Mechanisms for Loss of Phase Discrimination
These results show that observers are unable to distinguish the temporal phase of counterphase-modulated gratings at and above 20 Hz, although the modulation is easily detectable. A possible cause for this loss of phase sensitivity would be variation in response phase at the ganglion cell level. To analyze this further, we examined variation of response phase on a cycle-by-cycle basis for each cell. For peak responses (i.e., Fig. 1
spatial phases 0° and 180°), the standard deviation of phase from cycle to cycle was 32.3° (n = 11). Phase difference for the peak responses (at 0.2 cyc/deg) was 176.1° ± 2.7°, n = 11). For a single sweep, based on responses of a single ganglion cell at each counterphase location, a central mechanism would reliably (P < 0.001) distinguish the phase of counterphase modulation.
Thus, ganglion cell data do not support the hypothesis that the psychophysical loss in temporal phase sensitivity is due to phase variation among members of the ganglion cell array. An alternative hypothesis is that there is a loss of temporal phase sensitivity at a cortical site.
Other studies have suggested temporal rectification as the origin of the frequency-doubling illusion.3 20 21 One mechanism by which this might occur is by summation at high temporal frequencies of on- and off-center cell signals in the cortical mechanism responsible for detecting high-frequency flicker. In the retina, two MC cell arrays are present, one each for on- and off-center ganglion cells. Summation at a cortical site of responses of these two cell types would be equivalent to full-wave rectification of the stimulus. This model would account for the psychophysical discrimination results described so far.
The hypothesis is shown in more detail in Figure 7 . Signals from on- and off-center cells combine to give a full-wave rectified response. This would be indistinguishable from the counterphase condition. However the quadrature (90°) condition should be discriminable. To test this, observers were asked to perform the discrimination task for a pair of counterphase gratings with the temporal phase difference set at 90° instead of 180°. The two gratings should appear different if a straightforward temporal rectification is taking place. None of the three observers could make the discrimination at 100% contrast, which suggests that the temporal rectification hypothesis does not account for the loss of phase discriminability. We propose that this evidence shows that the frequency-doubling illusion is due to a loss of phase sensitivity at a cortical locus. The reason for this loss remains uncertain.
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To test the hypothesis that at high temporal frequencies, spatial information is preserved in the zero-crossings of counterphase-modulated sinusoidal gratings, the phase-discrimination task was repeated for two sinusoidal gratings. This time, the gratings were temporally in phase but spatially in quadrature—that is, offset by 90°. The hypothesis was that for 20-Hz counterphase gratings, if only spatial information were preserved in the zero-crossings then a spatial offset of the gratings would always be obvious. This was the case. The discrimination threshold was comparable to the detection threshold (discrimination threshold: 7.91% contrast, 0.7 log unit above detection threshold, n = 3). This suggests that the absolute response amplitude to the counterphase flicker is available for spatial discrimination; it is only temporal phase information that is unavailable.
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Discussion |
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Second, if such a class of cells were to exist, it is unclear why they should dominate the percept of the counterphase grating while responses of other cells (e.g., linear MC cells) are perceptually ignored.
Last, we argue that any temporally frequency-doubled response of putative My cells must be spatially invariant and thus cannot be a substrate for the illusion. Other mechanisms for the frequency-doubling illusion must be considered. Our findings are consistent with a cortical loss of temporal phase-discrimination ability. In a study of primary visual cortex, the temporal response was slower than in the retina or LGN,23 but the investigators did not comment on the precision of the cells’ response phase. The locus of the cortical loss of phase information thus remains uncertain.
A psychophysical examination of the temporal and spatial parameters of the frequency-doubling illusion, based on phase-discrimination ability, substantially conformed to the original description made by Kelly.1 The rapid elevation in grating phase-discrimination threshold (Fig. 5) quantifies an abrupt onset of the frequency-doubling illusion over a restricted temporal frequency range, as in previous descriptions.1 24 25 We suggest that the location of zero-crossings, separated by regions of perceived flicker, provides the spatial cue for the illusion when phase discrimination is not possible. By matching the zero-crossings to bars, it was possible to show that not only were they at twice the grating spatial frequency, but the bars did not appear to change in perceived spatial frequency or phase at temporal frequencies from 4 to 20 Hz. Over this same region of temporal frequencies, temporal phase discrimination changed from good (within 0.5 log unit of detection threshold) to poor (nonmeasurable, >2 log units above detection threshold). Investigators in several studies have reported that in this temporal frequency range the perceived spatial frequency of counterphased gratings is intermediate—between one and two times the fundamental.24 25 26 Because we did not find evidence that the apparent spacing of the zero-crossings changes with temporal frequency, we suggest that the finding of intermediate apparent spatial frequencies may be due to the observer’s being forced to reconcile conflicting cues. Parker,27 based on an adaptation paradigm, also suggested that the illusion arises in processing by central mechanisms, rather than in the retina.
There has been a report28 of a frequency-doubling illusion with chromatic gratings. This would be a puzzling finding if nonlinear ganglion cells gave rise to the percept, because PC-cells, for example, show linear summation properties.12 13 However, loss of phase discrimination at a cortical locus might also occur with chromatic mechanisms and give rise to a similar illusion.
Cortical mechanisms can detect flicker up to at least 40 to 50 Hz.23 However, in the discrimination tasks reported in the current study, phase information appeared to be lost at much lower frequencies. In contrast, with rapidly moving targets in a Vernier task, the temporal precision achieved by the observers is in the millisecond range, with rapidly drifting gratings. Mechler and Victor29 recently showed that, in a Vernier task, it is the spatiotemporal context that enables such precise temporal assessment; temporal information alone is not sufficient. The current results fit with this suggestion.
The current commercially available clinical test uses a decrease in contrast sensitivity to detect visual field loss.2 17 The clinical test does not depend on perception of the frequency-doubling illusion, per se.17 30 Recent evidence suggests that the mechanisms underlying the illusion resemble to some extent those for detection of full-field flicker, which appears to be accomplished through the MC pathway.30 Thus, the test is most likely a probe of contrast sensitivity of the MC pathway.
In summary, the present study builds on previous physiological studies in primate LGN to show that, as in LGN, spatial nonlinearity is found to a very limited extent in the primate retina. Unlike Y-cells in the cat, which form a physiologically and anatomically separate population of ganglion cells, spatially nonlinear MC cells in primate are the extremes of a unimodal distribution of spatial nonlinearity. Furthermore, we have shown that spatially nonlinear cells are unlikely to be the origin of the frequency-doubling illusion. Instead, we postulate an alternate model for the illusion, which may occur because of a reduced cortical sensitivity to the temporal phase of achromatic counterphased gratings. This has important implications for the design of future clinical screening tests for glaucoma.
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Footnotes |
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Submitted for publication April 5, 2002; revised June 12, 2002; accepted June 18, 2002.
Commercial relationships policy: N.
The publication costs of this article were defrayed in part by page charge payment. This article must therefore be marked "advertisement" in accordance with 18 U.S.C. 
1734 solely to indicate this fact.
Corresponding author: Barry B. Lee, State University of New York (SUNY) State College of Optometry, 33 West 42nd Street, New York, NY 10036; blee{at}sunyopt.edu.
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