PC and MC cell responses to compound gratings In this section we describe cell responses to chromatic, compound and luminance gratings. We recorded responses of 20 PC and 21 MC cells to luminance, chromatic and compound gratings over a range of spatial and temporal frequencies and contrasts.
Figure 3 shows responses of two typical PC cells (B, +L–M cell: C, +M–L cell). Responses are shown to a drifting grating at 75% of maximal modulation contrast at spatial frequencies as indicated; three out of the eight frequencies tested are shown. The luminance grating has twice the spatial and temporal frequency of the chromatic and compound gratings, in order to match the luminance component of the compound grating. Response amplitude decreased with spatial frequency for the chromatic and compound gratings. PC cell responses to compound and chromatic gratings were similar, as expected from the model results in Fig. 2, and there was no indication of a second-harmonic response (dual peaks) to the luminance component in the compound grating at any spatial frequency; responses to the compound grating were generally larger than to the chromatic grating, and tended to have more sharply defined peaks. This is largely due to the higher chromatic contrast of the former (see Appendix). Off-centre cells showed similar results, with some response waveform differences.
Figure 3. Responses of +L–M and +M–L cells to the chromatic red–green, compound red–green, and luminance gratings A, grating waveforms. The gratings drifted at 1.6 Hz (3.2 Hz for luminance grating) and 75% of maximal contrast. Responses are averaged over 30 cycles. B and C, responses of +L–M and +M–L cell, respectively, at three spatial frequencies. The response to the compound grating is similar to, but larger than, the response to the chromatic grating. There is no obvious second-harmonic response to the compound grating, even at the highest spatial frequency.
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Figure 4A shows Fourier spectra for the cells in Fig. 3 for each grating variety (0.8 cpd for chromatic and compound, 1.6 cpd for luminance gratings). The 1st harmonic response amplitude to the compound grating was greater than to the chromatic grating, and there was more energy in the higher harmonics. A larger response to the compound grating is expected since root-mean-square chromatic contrast (see eqn (4) in Appendix) is greater for the compound grating.
Figure 4. Harmonic composition of PC cell responses A, Fourier spectra of responses from Fig. 3 for the two cells shown (+L–M: 0.8 cpd; +M–L 1.6 cpd). There is a larger response of PC cells to the compound compared to the chromatic grating, expected from the higher chromatic contrast. B, spatial frequency tuning curves for the two cells for the different grating types. For the compound grating, the tuning curves for 1F and 2F response components are shown. For the luminance grating, the band-pass tuning is apparent, but this is not visible in the 2F response component. Curves represent fits of the model described in Fig. 2.
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The ‘double-duty’ hypothesis (e.g. Ingling & Martinez-Uriegas, 1985) suggests that both chromatic or luminance information might be multiplexed within signals carried by PC cells, with the luminance component dominant at higher spatial frequencies. If this were so, it might be expected that at high spatial frequencies there should be two response peaks per stimulus cycle for the compound gratings at high spatial frequencies. This was not apparent (Fig. 3). Figure 4B shows tuning curves for the two cells. For compound and chromatic gratings, 1st harmonic (1F) tuning curves are low pass, and for luminance gratings a band-pass character is apparent, as expected. However, the 2nd harmonic tuning curve for the compound grating is low pass and similar in shape to the 1F curve. This suggests that the 2F response reflects higher-harmonic distortion of the 1F response, i.e. the chromatic response to the compound grating is dominant at all spatial frequencies. The continuous curves associated with each set of points represent fits of the model sketched in Fig. 2. Rectified responses (as shown in Fig. 2) were Fourier analysed and response amplitudes fitted to the data with a least squares criterion using a grid search. Free parameters were centre and surround radii, centre/surround weighting, an amplitude scaling factor and the maintained activity level, which determines the degree of response rectification. The model provides a reasonable description of the data.
In most cells, the 2F response component to the compound grating did not show the band-pass character of the response to the luminance grating. This is attributable to the fact that, with balanced opponent mechanisms, the chromatic response is dominant, and higher harmonic components are associated with response rectification rather than the 2F luminance component of the compound grating. Only in 2 of 22 PC cells recorded was there a small indication of a 2F response to compound gratings at high spatial frequencies; in both these cells M/L cone balance was not close to one. These results suggest that luminance structure in compound chromatic patterns cannot be easily derived from PC cell activity.
MC cells are expected to respond to the luminance component of the compound grating, and this is illustrated in Fig. 5 for an on-centre and an off-centre MC cell; two spatial frequencies are shown. Responses were similar for the compound and luminance gratings. There was a small, frequency-doubled response to the chromatic grating (Lee et al. 1989a; Lee & Sun, 2009). Figure 6A shows Fourier spectra of the two MC cells of Fig. 5 at 0.2 cpd. For the compound grating, the energy in the response is in the even harmonics (connected points) and spectra resembled those for luminance gratings. There is a small 2F response to the chromatic grating.
Figure 5. Responses of MC cells to chromatic, compound and luminance gratings Stimulus parameters as in Fig. 3, except that only two spatial frequencies are shown. A, stimulus waveforms. B and C, responses of on- and off-centre cells, respectively. Responses to the compound and luminance gratings are very similar. There is a weak frequency-doubled response to the chromatic grating.
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Figure 6. Fourier composition of MC cell responses A, Fourier spectra of responses from Fig. 5 for the lower spatial frequency shown. For the compound grating, the response energy is largely in the even harmonics due to the luminance response, and just these values have been connected by line segments. Spectra for luminance and even harmonic compound responses are similar. There is a small 2F response to the chromatic grating. B, ratios of 2F to 1F harmonic amplitude under different conditions for different cell types as a function of spatial frequency. Data for PC cells were also shown as a comparison. Ratios are highest for MC cells and compound gratings as expected (averaged over 10 cells, on and off cells combined, only responses greater than 10 impulses s−1 included; 2 Hz, 75% of maximal contrast). Ratio remains similar over spatial frequency for PC cells for compound gratings (average of 10 cells, only responses greater than 10 impulses s−1 included; 2 Hz, 75% of maximal contrast).
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Figure 6B shows the mean 2F/1F response ratio for the sample of PC and MC cells as a function of spatial frequency for the compound and chromatic grating types. This is greatest for MC cells with compound gratings, indicating they transfer the luminance component of the pattern, which has twice the spatial frequency. For compound gratings and PC cells, the ratio remains below one, and is similar over all frequencies, consistent with the analysis in Fig. 4 that indicated that a switch from chromatic (which has a fundamental frequency) to luminance signalling (which has twice the spatial frequency) does not occur as a function of spatial frequency. For comparison, the ratio is also shown for PC cells and chromatic modulation, and for MC cells for chromatic stimuli, for which the high 2F/1F ratio is indicative of the frequency-doubled responses of MC cells to the chromatic grating.
The results in Figs 3–6 were for gratings of 75% of maximal modulation contrast. The psychophysical data shown in a later section were obtained at or near detection threshold. We explored the responses to the different gratings as a function of contrast to ascertain if the pattern of responses shown was independent of contrast. By eye, this appeared to be the case. To analyse this further, we plot in Fig. 7A the amplitude of 1F and 2F responses as a function of contrast for compound gratings near the optimal spatial frequency. Data shown were averaged from both +L–M and +M–L cells (n= 10, 5 of each). The 1F and 2F amplitudes increased in a parallel manner; their ratio is shown in Fig. 7B and, apart from the lowest contrast when responses were weak and the estimate noisy, it remained stable. In Figs 3–6, it was shown that the 2F response was not obviously associated with the luminance component of the compound grating. A further issue is variability, i.e. the reliability, of the 2F response. If variability were lower than that of the 1F response then, despite low amplitude, they might deliver a useful signal. To test this, the signal-to-noise ratio was calculated. There is a convenient estimate for noise in responses to sinusoidal modulation (Croner et al. 1993), defined as
where di is the distance in the complex plane between each individual response and the mean response. Noise was calculated for the 1F and 2F responses. It is comparable for both (Fig. 7A) and independent of contrast (Croner et al. 1993; Sun et al. 2004). The signal-to-noise ratios for 1F and 2F responses are plotted in Fig. 7B and are a factor of 2–3 lower for the latter. This indicates that as contrast decreases, a significant 1F response persists to lower contrasts than does the 2F response; at low contrast the 2F signal becomes noisy. Figure 7C and D shows similar analyses for responses to chromatic gratings. Again the 2F amplitude increased parallel to the 1F response but was smaller than with the compound grating. These data suggest that 2F responses of PC cells to compound and chromatic gratings become less significant as contrast decreases. The ability of human observers to detect the difference between the gratings at detection threshold thus becomes of interest, and is discussed in a later section.
Figure 7. Responses of PC cells to compound and chromatic gratings as a function of contrast A, amplitude of 1F and 2F components as a function of stimulus contrast together with estimates of response variability (i.e. noise). 1F responses are larger than 2F responses but noise is similar for both. Mean of 10 PC cells, +L–M and +M–L cells combined). Error bars are 95% confidence limits of the sample mean; most variability is due to inter-cell variation in response amplitude. B, the ratio 1F/2F is similar at all contrasts. Signal-to-noise ratio curves of 1F and 2F components are similar in form though differing in amplitude. C and D, similar analysis for responses to chromatic gratings.
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The PC cells’ 1st harmonic response amplitude to the chromatic grating was consistently weaker than to the compound grating. We fitted curves for each cell with a Naka-Rushton function and calculated contrast gain (Naka & Rushton, 1966). This was 1.48 times larger for the compound than chromatic grating, a result that was highly significant (paired t test, P < 0.01%). This value approximates the theoretical ratio of 1.71 between the chromatic contrast measures in eqn (4a,b) (see Appendix) for these gratings. This is relevant to differences in observer sensitivity to chromatic and compound gratings, as discussed in the next section.
We also explored cell responses to the different gratings as a function of temporal frequency from 0.5 to 30 Hz. For PC cells, differences in the shape of response histograms between compound and chromatic gratings became less marked at higher frequencies because higher harmonic distortion increased with both types (not shown). Otherwise the results of the analyses in previous figures remained valid over the temporal frequency range tested. The temporal response of PC cells (Lee et al. 1990) was low pass, i.e. sustained, with compound gratings and resembled the chromatic temporal response (not shown). For MC cells, the temporal response to compound gratings was band pass, i.e. transient, and resembled their luminance temporal frequency tuning curve (Lee et al. 1990).