February 2006
Volume 6, Issue 2
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Research Article  |   February 2006
Contribution of chromatic aberrations to color signals in the primate visual system
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Journal of Vision February 2006, Vol.6, 1. doi:10.1167/6.2.1
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      Jason D. Forte, Esther M. Blessing, Peter Buzás, Paul R. Martin; Contribution of chromatic aberrations to color signals in the primate visual system. Journal of Vision 2006;6(2):1. doi: 10.1167/6.2.1.

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Abstract

We measured responses to red–green color variation in parvocellular (PC) neurons in the lateral geniculate nucleus of dichromatic (“red–green color blind”) marmoset monkeys. Although these animals lack distinct visual pigments to distinguish between wavelengths in this range, many of the colored stimuli nevertheless produced robust responses in PC cells. We show that these responses, which are restricted to high stimulus spatial frequencies (fine image details), arise from chromatic aberrations in the eye. The neural signals produced by chromatic aberrations are of comparable magnitude to signals produced by high-frequency luminance (LUM) modulation and thus could influence cortical pathways for processing of color and object recognition. The fact that genetically “color-blind” primates are not necessarily blind to wavelength-dependent contours in the visual world may have enabled red–green color vision to become linked with high-acuity spatial vision during primate evolution.

Introduction
Retinal images are subject to longitudinal chromatic aberration (which causes wavelength-dependent defocus) and transverse chromatic aberration (which causes wavelength-dependent changes in image magnification and spatial displacement on the retina; Cottaris, 2003; Gullstrand, 1962; Thibos, 1987; Williams, Sekiguchi, Haake, Brainard, & Packer, 1991). Both these effects can produce wavelength-dependent image intensity (luminance) signals at the photoreceptor plane, even in the absence of luminance borders in the environment (Figure 1). 
Figure 1
 
Example of chromatic aberrations. (A) Relative to medium wavelengths (λ 500 nm), long wavelengths (λ 700 nm) show displacement away from the optic axis (transverse chromatic aberration, TCA) and reduced refraction (longitudinal chromatic aberration, LCA). At high spatial frequencies (right), aberrations cause wavelength-dependent changes in the phase (TCA) and contrast (LCA) of grating components (pale red and green lines). (B) Chromatic aberrations can introduce LUM contrast modulation when nominally isoluminant red (R) and green (G) grating components are combined.
Figure 1
 
Example of chromatic aberrations. (A) Relative to medium wavelengths (λ 500 nm), long wavelengths (λ 700 nm) show displacement away from the optic axis (transverse chromatic aberration, TCA) and reduced refraction (longitudinal chromatic aberration, LCA). At high spatial frequencies (right), aberrations cause wavelength-dependent changes in the phase (TCA) and contrast (LCA) of grating components (pale red and green lines). (B) Chromatic aberrations can introduce LUM contrast modulation when nominally isoluminant red (R) and green (G) grating components are combined.
Chromatic aberrations are normally considered to degrade the quality of retinal images, but they potentially form a useful source of information about the visual environment. Indeed, color edges are an especially reliable indication of borders between objects because they are resistant to unpredictable changes in luminance such as caused by the shadows of other objects or by changes in illuminant intensity (Barbur, Harlow, & Plant, 1994; Hurlbert, 1989; Kingdom, 2003; Li & Lennie, 2001). Here we show that robust signals attributable to chromatic aberration are transmitted by neurons in the parvocellular (PC) division of the subcortical visual pathway. The PC pathway could therefore provide to the brain a wavelength-dependent signal for distinguishing objects, even in the absence of spectrally tuned outputs from distinct classes of cone photoreceptors. 
Methods
Adult common marmosets (Callithrix jacchus; four male, two female) were anaesthetized and extracellular recordings from PC cells were made using standard techniques (Blessing, Solomon, Hashemi-Nezhad, Morris, & Martin, 2004). Procedures were approved by institutional ethics committee and conformed to the Society for Neuroscience policy on the use of animals in neuroscience research. Measurement of PC cell responses in male marmoset monkeys can reveal the influence of chromatic aberration in the subcortical visual system. All male marmosets are dichromatic (“red–green color blind”; Hunt, Williams, Bowmaker, & Mollon, 1993; Jacobs, 1998). They express short wavelength-sensitive (S or “blue”) cones, as well as a single class of cone photoreceptor with maximum sensitivity in the medium–long (ML) range of the visible spectrum. Because PC cells receive little or no input from S cones, the functional input to PC-receptive fields in dichromatic marmosets derives from a single cone type and conform to the principle of univariance (Blessing et al., 2004; Kremers, Zrenner, Weiss, & Meierkord, 1998; Yeh et al., 1995). By contrast, female marmosets, in common with humans and other trichromatic primates, normally express both medium (M) and long wavelength-sensitive (L) cones as well as S cones. Most PC cells in female marmosets show red–green cone opponent responses, as a result of antagonistic interactions between M and L cones in the receptive field (Blessing et al., 2004; Tovée, Bowmaker, & Mollon, 1992; Yeh et al., 1995). 
Stimuli were presented on a CRT (computer monitor). To reveal the effects of chromatic aberrations, the relative intensity of the red and green phosphors of the CRT was set to produce equal quantal absorption (i.e., “silent substitution”) in the single ML range pigment (543, 556, or 563 nm) expressed by dichromatic marmosets. The silent substitution ratio was predicted by taking the dot product of the cone spectral sensitivity (Schnapf, Kraft, Nunn, & Baylor, 1988; Tovée et al., 1992) with the [x, y, Y] coordinates of the gratings, using the CIE 1931 color matching functions (Blessing et al., 2004; Nakano, 1996). In practice, the optics of individual eyes may produce small variations in the relative absorption of red and green wavelengths. We confirmed the validity of the silent substitution ratio by measuring the responses of most PC cells in each animal using a large, spatially uniform stimulus. We varied the ratio of red and green phosphor intensity to find the response minimum. The physiological null measure was typically very close to the theoretical silent substitution. If the discrepancy corresponded to greater than 10% cone contrast (see Results), the cell was excluded from further analysis. Using this method, we determined that three of the males expressed the 556-nm cone pigment and one expressed the 543-nm cone pigment. 
Prior to physiological recording, we established the cone type of the female marmosets using restriction fragment-length polymorphism following polymerase chain reaction (PCR) amplification of exons 2 and 5 of the cone opsin genes (Blessing et al., 2004; Hunt et al., 1993). One female animal expressed the 543-nm (M) and 563-nm (L) pigments. The other female was a dichromat expressing the 556-nm pigment. The physiological null measure and the PCR result for the dichromatic female were consistent. 
Stimuli were drifting (4 Hz) sine gratings, normally presented in a 4 deg aperture. Mean luminance was normally close to 25 cd/m2. For some experiments, the red and green grating components were presented alone to give “red–black” or “green–black” gratings at respective mean LUM close to 15 or 30 cd/m2. Refraction was optimized (using a pupil-concentric supplementary lens where necessary) by maximizing response amplitude of PC cells to high-frequency luminance (red + green, LUM) gratings. Pupil diameter was 2–4 mm; no systematic effects of pupil size were seen within this range. 
Results
Figure 2 shows responses of a PC cell in the lateral geniculate nucleus of a dichromatic female marmoset. When the red and green components of the grating are combined in the same spatial phase to give a luminance signal (Figure 2A, LUM), the modulation transfer function shows the expected broad band-pass form (Blessing et al., 2004; Derrington & Lennie, 1984; Jacobs & Blakemore, 1988). This is because center-surround spatial antagonism in the receptive field causes response attenuation below the optimum frequency, which is near 2 cycles/deg (cpd), and responses to high spatial frequencies (fine image details) are attenuated as they approach the resolution limit of the receptive field center. When the grating components are combined in opposite spatial phase (Figure 2A, RG), the response amplitude is close to the noise level at low spatial frequencies (Figure 2A, yellow line). However, a sharply band-pass “blip” RG response is evident, at higher spatial frequencies, with a peak near 2 cpd. 
Figure 2
 
Spatial and chromatic sensitivity of a PC cell in a dichromatic marmoset. Receptive field eccentricity, 7.4 deg. Error bars show ±1 SD. Amplitude of Fourier component (F1) at stimulus temporal frequency (4 Hz) is shown. (A) Spatial frequency tuning functions. Response to LUM modulation shows spatial band-pass characteristic. Solid black line shows difference-of-Gaussian fit. Fit parameters: center radius, 0.102 deg; surround radius, 0.856 deg; center/surround sensitivity ratio, 174.9. Response to red–green isoluminant (RG) modulation (solid red line) is limited to spatial frequencies near the high-frequency cut-off for the LUM response. Solid yellow line shows F1 at zero contrast. Dashed green line shows predicted response to 10% LUM modulation. (B) Determination of isoluminant point for cone input to this cell. Black line shows F1 for red–green gratings as a function of relative intensity of red grating component. Response is minimal close to the predicted isoluminant (“silent substitution”) point for the 556-nm cone pigment (s556). The isoluminant points for the other (543 and 563 nm) marmoset ML cone pigments are indicated. (C) Contrast–response function of this cell for LUM modulation. Spatial frequency 0.75 cpd. Solid line shows saturating hyperbolic (“Naka–Rushton”) function. Fit parameters: response maximum, 109 imp s−1; contrast at half maximum, 62.1%.
Figure 2
 
Spatial and chromatic sensitivity of a PC cell in a dichromatic marmoset. Receptive field eccentricity, 7.4 deg. Error bars show ±1 SD. Amplitude of Fourier component (F1) at stimulus temporal frequency (4 Hz) is shown. (A) Spatial frequency tuning functions. Response to LUM modulation shows spatial band-pass characteristic. Solid black line shows difference-of-Gaussian fit. Fit parameters: center radius, 0.102 deg; surround radius, 0.856 deg; center/surround sensitivity ratio, 174.9. Response to red–green isoluminant (RG) modulation (solid red line) is limited to spatial frequencies near the high-frequency cut-off for the LUM response. Solid yellow line shows F1 at zero contrast. Dashed green line shows predicted response to 10% LUM modulation. (B) Determination of isoluminant point for cone input to this cell. Black line shows F1 for red–green gratings as a function of relative intensity of red grating component. Response is minimal close to the predicted isoluminant (“silent substitution”) point for the 556-nm cone pigment (s556). The isoluminant points for the other (543 and 563 nm) marmoset ML cone pigments are indicated. (C) Contrast–response function of this cell for LUM modulation. Spatial frequency 0.75 cpd. Solid line shows saturating hyperbolic (“Naka–Rushton”) function. Fit parameters: response maximum, 109 imp s−1; contrast at half maximum, 62.1%.
The PCR analysis predicted that this female marmoset should express only one cone pigment (peak 556 nm) in the ML range. Responses of PC cells recorded in this animal were consistent with the prediction, as illustrated in Figure 2B. Here, the RG grating was presented at low spatial frequency, and the relative intensity of the red and green components was varied systematically. The response shows minimum amplitude at RG ratio 0.818; close to the ratio (0.808) predicted to give silent substitution in the 556-nm cone (“s556”). 
The RG tuning curve in Figure 2A was generated using the predicted s556 ratio of 0.808. Control measurements revealed no clear dependence of aperture size on the RG response minimum (data not shown). Other potential causes of deviation of the RG response minimum are incorrect stimulus specification, or preabsorption filters such as the macular pigment. These factors will generate contrast in the 556-nm cone at all spatial frequencies in the tested range. We calculated that for the PC cell in Figure 2A, the discrepancy between the predicted and empirically defined null points would correspond to ∼4% modulation in the 556-nm cone. However, such luminance artifacts cannot account for the RG response. Figure 2C shows the LUM contrast–response function for this PC cell at a spatial frequency (0.75 cpd) close to optimal. The initial part of the curve shows contrast gain close to 1 imp s−1 %−1. Thus, even a substantial luminance artifact of 10% contrast in the 556-nm cone would produce responses of lower amplitude than the RG peak. Note that the shape of the predicted response to 10% LUM contrast (Figure 2A, dashed line) is quite different to the shape of the RG response. Furthermore, the peak of the RG response is approximately 2 cpd, but the peak of the LUM response is about 0.8 cpd. In summary, the RG response is not simply a “scaled” version of the LUM response and thus cannot be attributed to unexpected luminance contrast in the distal stimulus. 
The procedures illustrated in Figure 2 were used to derive silent substitution points and measure RG spatial tuning functions for 19 PC cells in dichromatic marmosets. The average data (Figure 3A) are consistent with the example shown in Figure 2. However, PC cells recorded in the female trichromat show very different response characteristic to those recorded from dichromats. The RG responses in the trichromatic animal were greatest at low spatial frequencies (n = 11, Figure 3A). 
Figure 3
 
Properties of the RG response. (A) Average spatial frequency tuning functions for the RG response in dichromatic (DI, n = 19, black squares) and trichromatic (TRI, n = 11, red circles) marmosets. Error bars show ±1 SEM. Peak RG response for PC cells in dichromatic animals is close to 2 cpd. The PC cells recorded in a trichromatic animal show maximum RG response at low spatial frequency. (B) Responses of PC cells in dichromatic marmosets to RG isoluminant and S-cone-selective (S) gratings. Response amplitude is shown relative to amplitude for 10% LUM modulation at the same spatial frequency.
Figure 3
 
Properties of the RG response. (A) Average spatial frequency tuning functions for the RG response in dichromatic (DI, n = 19, black squares) and trichromatic (TRI, n = 11, red circles) marmosets. Error bars show ±1 SEM. Peak RG response for PC cells in dichromatic animals is close to 2 cpd. The PC cells recorded in a trichromatic animal show maximum RG response at low spatial frequency. (B) Responses of PC cells in dichromatic marmosets to RG isoluminant and S-cone-selective (S) gratings. Response amplitude is shown relative to amplitude for 10% LUM modulation at the same spatial frequency.
For these measurements, the components of the grating were adjusted to give approximately equal and opposite contrast in the M and L cones (M contrast, 0.183; L contrast, 0.162). The low-pass spatial frequency tuning curve is consistent with opponent interaction between M and L cones in center and surround components of the PC-receptive field, as previously reported for trichromatic marmosets and macaque monkeys (Blessing et al., 2004; Derrington, Krauskopf, & Lennie, 1984; Yeh et al., 1995). The large difference in response properties between dichromats and trichromats could help to explain why the effects of chromatic aberration were not previously reported in experimental studies of the macaque visual system. In macaques, color-blind individuals are very rare (Jacobs, 1998) and the effects of chromatic aberration would be combined with the effects of genuine cone opponent inputs to PC cells (Flitcroft, 1989). 
In dichromats, the average RG response amplitude was close to 40% of the LUM response amplitude at the same spatial frequency [0.36 ± 0.16 (mean ± SD), n = 19]. The average spatial frequency yielding maximum RG response in dichromats was 1.73 ± 0.67 cpd (n = 19), which is higher than the optimum spatial frequency for LUM modulation (0.97 ± 0.52, p < .01, Wilcoxon rank-sum test). Because the surround mechanism of the receptive field responds negligibly to spatial frequencies above the LUM optimum, these results imply that the RG response is mediated by the receptive field center mechanism. 
Previous analysis of the responses of PC cells in dichromatic marmosets (Blessing et al., 2004; Kremers et al., 1998; Yeh et al., 1995) showed that for the great majority of PC cells, functional input to the receptive field (at photopic luminance levels) is derived only from ML class cones, with negligible input from S cones. During recording, we routinely tested all cells encountered for signs of S cone input, by presenting a grating that delivered high contrast (66%) to the S cones and low (∼4%) contrast to ML class cones. None of the PC cells we describe in the present study showed signs of input from S cones. A subgroup (n = 13) of the dichromat PC cells shown in Figure 3A was tested using this “S-cone-selective” stimulus at a range of spatial frequencies. Figure 3B shows the peak amplitude of responses to RG- and S-cone-selective gratings in these cells. Responses to these stimuli are compared with responses to 10% LUM contrast at the optimum spatial frequency. The peak responses to S-cone-selective gratings (mean 4.21 ± 2.53 imp s−1) are close to half the amplitude of responses to 10% LUM contrast (8.25 ± 3.18 imp s−1), consistent with the low (∼4%) ML cone contrast present in the stimulus. The S cone stimulus also modulates rods with 28% contrast, so the lack of response also confirms that rods are not providing functional input to these cells under these stimulus conditions. Peak responses to RG gratings (mean 15.42 ± 6.57 imp s−1) are, however, in almost all cases, greater than the response to 10% LUM contrast (mean 7.98 ± 4.02 imp s−1) and much greater than expected from the (nominally zero) cone contrast present in the RG stimulus. In the following, we present evidence that both longitudinal and transverse chromatic aberrations could underlie the RG response in dichromatic PC cells. 
Transverse chromatic aberrations vary with retinal eccentricity and angle relative to the optic axis, so the luminance signals they produce are dependent on stimulus eccentricity and orientation (Thibos, 1987). As expected, we found variability for LUM orientation tuning among PC cells (Figures 4AC), suggesting that any effects of chromatic aberrations would be superimposed on receptive field anisotropies that have other origins (Leventhal & Schall, 1983; Martin, Lee, White, Solomon, & Rüttiger, 2001; Passaglia, Troy, Rüttiger, & Lee, 2002; Smith, Chino, Ridder, Kitagawa, & Langston, 1990). Such anisotropies make it difficult to predict precisely the effects of chromatic aberrations. Nonetheless, for the majority of PC cells, the orientation tuning of the RG response was sharper than the orientation tuning for LUM modulation (Figure 4D). This is evidence for the presence of transverse chromatic aberrations because the RG orientation tuning curve would simply be an amplitude-scaled version of the LUM response if longitudinal chromatic aberrations were the only underlying cause. 
Figure 4
 
Evidence for contribution of transverse chromatic aberration to the RG response. (A–C) Examples of orientation tuning curves for a PC cells recorded in dichromatic marmosets. The orientation index (OI; a direction-independent vector average of response amplitude) for RG gratings is higher than the OI for LUM modulation at the same spatial frequency. Receptive field eccentricities (deg): (A) 2.46; (B) 9.41; (C) 4.39. (D) Orientation selectivity for RG modulation is greater than selectivity for LUM modulation in the great majority of PC cells recorded in dichromats.
Figure 4
 
Evidence for contribution of transverse chromatic aberration to the RG response. (A–C) Examples of orientation tuning curves for a PC cells recorded in dichromatic marmosets. The orientation index (OI; a direction-independent vector average of response amplitude) for RG gratings is higher than the OI for LUM modulation at the same spatial frequency. Receptive field eccentricities (deg): (A) 2.46; (B) 9.41; (C) 4.39. (D) Orientation selectivity for RG modulation is greater than selectivity for LUM modulation in the great majority of PC cells recorded in dichromats.
For drifting gratings, the timing of PC cells' responses relative to the stimulus (neuronal response phase) can be used to give a sensitive measure of stimulus position on the retina (Lee, Elepfandt, & Virsu, 1981). Furthermore, PC cells show little response compression at high contrasts (Blessing et al., 2004; Derrington & Lennie, 1984; Kaplan & Shapley, 1986; Yeh et al., 1995). Thus, neuronal response phase and amplitude can be used to calculate the position and amplitude of the luminance signals introduced by chromatic aberrations. For a sample of PC cells (n = 17), we measured responses to the individual (red and green) components of the grating as a function of spatial frequency. For the PC cell shown in Figures 5A and B, the frequency phase gradient is steeper for the red component of the grating than for the green component, giving a frequency-dependent phase offset. The luminance contrast delivered by grating components of frequency f with phase offset Δ is given by sin(f/2Δ). Extrapolation of the phase gradients for this cell thus predicts that substantial luminance contrast (>50%) would be generated by frequencies above 10 cpd. For the PC cells that were tested, vector combination of the responses to the red and green components of the grating gave a good prediction of the peak spatial frequency of the RG response (r = .70, p < .01, n = 17). For those cells within 16 deg of the fovea, the average spatial offset predicted from the response phase difference (0.020 ± 0.085 deg, Figure 5C) corresponds to 11.2 ± 9.3% of the PC cell center diameter (0.201 ± 0.085 deg, n = 19). Finally, there was a negative correlation (r = −.74, p < .01, n = 19) between RG response amplitude and receptive field center radius as estimated from the LUM response. These data suggest that the high spatial resolving capacity of foveal PC cells for luminance contrast may be at least partly constrained by chromatic aberrations. 
Figure 5
 
Magnitude of spatial offset. (A) Spatial frequency tuning functions for a PC cell recorded in a dichromatic marmoset. Receptive field eccentricity 6.1 deg. Response amplitude for RG grating (black diamonds) is well predicted (black dashed line) from vector sum of responses to the green (G, green squares) and red (R, red circles) components of the grating presented independently. (B) Response phase for the R and G gratings shows a difference in the linear relationship with spatial frequency (solid lines), consistent with a constant spatial offset. The lines are curved because the data are plotted on a log axis to match the data in panel A. The linear interpolation (dashed lines) shows the point where the red and green phosphors will be in the same phase. (C) Spatial offset calculated from phase regression for 17 PC cells recorded in dichromats. Arrow shows the offset predicted for the PC cell shown in panels A and B.
Figure 5
 
Magnitude of spatial offset. (A) Spatial frequency tuning functions for a PC cell recorded in a dichromatic marmoset. Receptive field eccentricity 6.1 deg. Response amplitude for RG grating (black diamonds) is well predicted (black dashed line) from vector sum of responses to the green (G, green squares) and red (R, red circles) components of the grating presented independently. (B) Response phase for the R and G gratings shows a difference in the linear relationship with spatial frequency (solid lines), consistent with a constant spatial offset. The lines are curved because the data are plotted on a log axis to match the data in panel A. The linear interpolation (dashed lines) shows the point where the red and green phosphors will be in the same phase. (C) Spatial offset calculated from phase regression for 17 PC cells recorded in dichromats. Arrow shows the offset predicted for the PC cell shown in panels A and B.
The response phase analysis allows the “blip” shape of the RG response to be interpreted as follows. With increasing spatial frequency, the luminance contrast delivered to ML class cones begins to increase, as a result of phase and amplitude changes due to chromatic aberrations. However, responses to frequencies above the RG peak are sharply attenuated, as they approach the resolution limit of the receptive field center mechanism. A large degree of intercell variability in phase of response at the RG peak was seen (Figure 5C). This is consistent with psychophysical evidence for variability of chromatic aberrations across eyes and observers (Rynders, Lidkea, Chisholm, & Thibos, 1995), and it shows that chromatic aberrations arising in the eye's optics must be much greater than any systematic deviation caused by the refraction-correcting lens through which the stimulus was viewed. In some informal measurements, we tested the effect of changing refraction on the RG response by changing the power of the correcting lens. Results were consistent with the presence of longitudinal chromatic aberration in the natural optics, but technical limitations prevented a systematic study of the influence of refractive state. 
Discussion
The effects of chromatic aberration are barely noticeable in normal vision, and it is a long-standing hypothesis (Hay, Pick, & Rosser, 1963) that the brain must learn to compensate for the eye's chromatic aberrations. Such compensatory mechanisms are thought to be made manifest in perceptual phenomena such as edge colors and the McCollough effect (Broerse, Vladusich, & O'Shea, 1999; Grossberg, Hwang, & Mingolla, 2002; Hay et al., 1963). Our results support these hypotheses by showing that neural signals resulting from chromatic aberrations are indeed present in the main afferent pathway to the visual cortex. The idea that chromatic aberrations are mitigated by higher-order optical aberrations (McLellan, Marcos, Prieto, & Burns, 2002) or by postreceptoral spatial pooling within the retina (Gullstrand, 1962; Nagle & Osorio, 1993; Williams et al., 1991) is only partly supported by our data (Figures 2A, 3A, B, and 5AC), which show that the sampling aperture of PC-receptive fields in the retina can attenuate, but does not eliminate, neural signals induced by high-frequency red–green contrast. 
The marmoset eye is close to half the size of the human eye. Chromatic aberrations scale with eye size (Smith & Atchinson, 1997), and the other optical properties of the marmoset eye are quantitatively comparable to the human eye (Troilo, Howland, & Judge, 1993). The position of the RG response peak is thus broadly consistent with psychophysical evidence that aberration-induced luminance contrast can influence red–green grating detection tasks at spatial frequencies above 8 cpd (Anderson, Mullen, & Hess, 1991; Sekiguchi, Williams, & Brainard, 1993). 
Our results show that even without input from distinct classes of cone photoreceptors, responses in PC cells can arise not only from fine spatial details but also from strong chromatic borders in the environment. What happens to these signals as they ascend to higher processing levels of the visual system? Because high-acuity spatial signals from PC cells are preserved during the early stages of cortical processing (Jacobs & Blakemore, 1988), the neural signals arising from chromatic aberrations could have access to brain pathways for object border detection (Figure 6), as well as to early cortical stages of color signal processing (Barbur et al., 1994; Derrington et al., 2002; Flitcroft, 1989; Lennie, Krauskopf, & Sclar, 1990; Wachtler, Sejnowski, & Albright, 2003). The distinct spatial and orientation tuning of the LUM and RG responses (Figures 2 and 3) means that luminance and color borders would create distinct patterns of response timing and amplitude in the PC population. Such timing differences might enable cortical mechanisms to extract both chromatic and luminance information from the afferent signals, but the neural network mechanism by which this could be achieved has not yet been investigated. 
Figure 6
 
Illustration of the potential role of signals originating from chromatic aberrations. (A) Original image. (B and C) Utility of chromatic border detection. The top row shows a region of interest from the original image (indicated by the yellow square in panel A). Center and lower rows show the effect of a band-pass spatial filter (schematics in panel B) on the LUM signal (center row) and red–green chromatic difference signal (lower row). Grayscale in the lower two panels represents signal output from a univariant (single cone) spectral mechanism. The spatial characteristic of the filter was designed to approximate the shape of the RG response in PC cells recorded in dichromatic marmosets. The chromatic border signal is resistant to LUM variation due to shadows. (D) Effect of the RG spatial band-pass filter on the original image. Note recovery of chromatic edges and image outlines. Low spatial frequencies removed by Gaussian filtering (SD = 10 pixels) and subtraction (MatLAB image processing toolbox, Mathworks, Natick, NJ). Original image courtesy Pony Express, Inc., modified with permission.
Figure 6
 
Illustration of the potential role of signals originating from chromatic aberrations. (A) Original image. (B and C) Utility of chromatic border detection. The top row shows a region of interest from the original image (indicated by the yellow square in panel A). Center and lower rows show the effect of a band-pass spatial filter (schematics in panel B) on the LUM signal (center row) and red–green chromatic difference signal (lower row). Grayscale in the lower two panels represents signal output from a univariant (single cone) spectral mechanism. The spatial characteristic of the filter was designed to approximate the shape of the RG response in PC cells recorded in dichromatic marmosets. The chromatic border signal is resistant to LUM variation due to shadows. (D) Effect of the RG spatial band-pass filter on the original image. Note recovery of chromatic edges and image outlines. Low spatial frequencies removed by Gaussian filtering (SD = 10 pixels) and subtraction (MatLAB image processing toolbox, Mathworks, Natick, NJ). Original image courtesy Pony Express, Inc., modified with permission.
Severely red–green color-blind (dichromatic) humans perform better than expected by chance on tasks requiring red–green chromatic discrimination and consistently use the color terms “red” and “green” to describe their color percepts (Scheibner & Boynton, 1968; Wachtler, Dohrmann, & Hertel, 2004). Even as adults, many color-defective humans are unaware of their color vision anomaly until they are specifically tested (Steward & Cole, 1989). We speculate that the PC cell signals arising from chromatic aberrations could contribute to a perceptual color space (Derrington et al., 2002; Wachtler et al., 2004) that is not specifically dependent on three tuned receptor mechanisms. In this way, the PC pathway may have become associated with brain mechanisms for extracting wavelength-dependant signals, at a stage in primate evolution that was prior to the recent evolutionary divergence (Nathans, 1999; Shyue et al., 1995) of distinct medium and long wavelength-tuned (M and L) receptor mechanisms. Therefore, chromatic aberrations may have contributed to the yoking of red–green color vision with high-acuity spatial vision (Mollon, 1989; Wässle & Boycott, 1991) in the functional role of the PC pathway. 
Acknowledgments
We thank A. Lara and D. Matin for technical assistance, B. Szmajda and P. Jusuf for assistance with recordings, and R. Masland, A. Metha, J. Victor, and T. R. Vidyasagar for helpful comments and discussion. Supported by Australian NHMRC grant 253621 and Australian Research Council grant A00104053. 
Commercial relationships: none. 
Corresponding author: Paul R. Martin. 
Email: prmartin@unimelb.edu.au. 
Address: Cnr Keppel & Cardigan Streets, Carlton, VIC 3053, Australia. 
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Figure 1
 
Example of chromatic aberrations. (A) Relative to medium wavelengths (λ 500 nm), long wavelengths (λ 700 nm) show displacement away from the optic axis (transverse chromatic aberration, TCA) and reduced refraction (longitudinal chromatic aberration, LCA). At high spatial frequencies (right), aberrations cause wavelength-dependent changes in the phase (TCA) and contrast (LCA) of grating components (pale red and green lines). (B) Chromatic aberrations can introduce LUM contrast modulation when nominally isoluminant red (R) and green (G) grating components are combined.
Figure 1
 
Example of chromatic aberrations. (A) Relative to medium wavelengths (λ 500 nm), long wavelengths (λ 700 nm) show displacement away from the optic axis (transverse chromatic aberration, TCA) and reduced refraction (longitudinal chromatic aberration, LCA). At high spatial frequencies (right), aberrations cause wavelength-dependent changes in the phase (TCA) and contrast (LCA) of grating components (pale red and green lines). (B) Chromatic aberrations can introduce LUM contrast modulation when nominally isoluminant red (R) and green (G) grating components are combined.
Figure 2
 
Spatial and chromatic sensitivity of a PC cell in a dichromatic marmoset. Receptive field eccentricity, 7.4 deg. Error bars show ±1 SD. Amplitude of Fourier component (F1) at stimulus temporal frequency (4 Hz) is shown. (A) Spatial frequency tuning functions. Response to LUM modulation shows spatial band-pass characteristic. Solid black line shows difference-of-Gaussian fit. Fit parameters: center radius, 0.102 deg; surround radius, 0.856 deg; center/surround sensitivity ratio, 174.9. Response to red–green isoluminant (RG) modulation (solid red line) is limited to spatial frequencies near the high-frequency cut-off for the LUM response. Solid yellow line shows F1 at zero contrast. Dashed green line shows predicted response to 10% LUM modulation. (B) Determination of isoluminant point for cone input to this cell. Black line shows F1 for red–green gratings as a function of relative intensity of red grating component. Response is minimal close to the predicted isoluminant (“silent substitution”) point for the 556-nm cone pigment (s556). The isoluminant points for the other (543 and 563 nm) marmoset ML cone pigments are indicated. (C) Contrast–response function of this cell for LUM modulation. Spatial frequency 0.75 cpd. Solid line shows saturating hyperbolic (“Naka–Rushton”) function. Fit parameters: response maximum, 109 imp s−1; contrast at half maximum, 62.1%.
Figure 2
 
Spatial and chromatic sensitivity of a PC cell in a dichromatic marmoset. Receptive field eccentricity, 7.4 deg. Error bars show ±1 SD. Amplitude of Fourier component (F1) at stimulus temporal frequency (4 Hz) is shown. (A) Spatial frequency tuning functions. Response to LUM modulation shows spatial band-pass characteristic. Solid black line shows difference-of-Gaussian fit. Fit parameters: center radius, 0.102 deg; surround radius, 0.856 deg; center/surround sensitivity ratio, 174.9. Response to red–green isoluminant (RG) modulation (solid red line) is limited to spatial frequencies near the high-frequency cut-off for the LUM response. Solid yellow line shows F1 at zero contrast. Dashed green line shows predicted response to 10% LUM modulation. (B) Determination of isoluminant point for cone input to this cell. Black line shows F1 for red–green gratings as a function of relative intensity of red grating component. Response is minimal close to the predicted isoluminant (“silent substitution”) point for the 556-nm cone pigment (s556). The isoluminant points for the other (543 and 563 nm) marmoset ML cone pigments are indicated. (C) Contrast–response function of this cell for LUM modulation. Spatial frequency 0.75 cpd. Solid line shows saturating hyperbolic (“Naka–Rushton”) function. Fit parameters: response maximum, 109 imp s−1; contrast at half maximum, 62.1%.
Figure 3
 
Properties of the RG response. (A) Average spatial frequency tuning functions for the RG response in dichromatic (DI, n = 19, black squares) and trichromatic (TRI, n = 11, red circles) marmosets. Error bars show ±1 SEM. Peak RG response for PC cells in dichromatic animals is close to 2 cpd. The PC cells recorded in a trichromatic animal show maximum RG response at low spatial frequency. (B) Responses of PC cells in dichromatic marmosets to RG isoluminant and S-cone-selective (S) gratings. Response amplitude is shown relative to amplitude for 10% LUM modulation at the same spatial frequency.
Figure 3
 
Properties of the RG response. (A) Average spatial frequency tuning functions for the RG response in dichromatic (DI, n = 19, black squares) and trichromatic (TRI, n = 11, red circles) marmosets. Error bars show ±1 SEM. Peak RG response for PC cells in dichromatic animals is close to 2 cpd. The PC cells recorded in a trichromatic animal show maximum RG response at low spatial frequency. (B) Responses of PC cells in dichromatic marmosets to RG isoluminant and S-cone-selective (S) gratings. Response amplitude is shown relative to amplitude for 10% LUM modulation at the same spatial frequency.
Figure 4
 
Evidence for contribution of transverse chromatic aberration to the RG response. (A–C) Examples of orientation tuning curves for a PC cells recorded in dichromatic marmosets. The orientation index (OI; a direction-independent vector average of response amplitude) for RG gratings is higher than the OI for LUM modulation at the same spatial frequency. Receptive field eccentricities (deg): (A) 2.46; (B) 9.41; (C) 4.39. (D) Orientation selectivity for RG modulation is greater than selectivity for LUM modulation in the great majority of PC cells recorded in dichromats.
Figure 4
 
Evidence for contribution of transverse chromatic aberration to the RG response. (A–C) Examples of orientation tuning curves for a PC cells recorded in dichromatic marmosets. The orientation index (OI; a direction-independent vector average of response amplitude) for RG gratings is higher than the OI for LUM modulation at the same spatial frequency. Receptive field eccentricities (deg): (A) 2.46; (B) 9.41; (C) 4.39. (D) Orientation selectivity for RG modulation is greater than selectivity for LUM modulation in the great majority of PC cells recorded in dichromats.
Figure 5
 
Magnitude of spatial offset. (A) Spatial frequency tuning functions for a PC cell recorded in a dichromatic marmoset. Receptive field eccentricity 6.1 deg. Response amplitude for RG grating (black diamonds) is well predicted (black dashed line) from vector sum of responses to the green (G, green squares) and red (R, red circles) components of the grating presented independently. (B) Response phase for the R and G gratings shows a difference in the linear relationship with spatial frequency (solid lines), consistent with a constant spatial offset. The lines are curved because the data are plotted on a log axis to match the data in panel A. The linear interpolation (dashed lines) shows the point where the red and green phosphors will be in the same phase. (C) Spatial offset calculated from phase regression for 17 PC cells recorded in dichromats. Arrow shows the offset predicted for the PC cell shown in panels A and B.
Figure 5
 
Magnitude of spatial offset. (A) Spatial frequency tuning functions for a PC cell recorded in a dichromatic marmoset. Receptive field eccentricity 6.1 deg. Response amplitude for RG grating (black diamonds) is well predicted (black dashed line) from vector sum of responses to the green (G, green squares) and red (R, red circles) components of the grating presented independently. (B) Response phase for the R and G gratings shows a difference in the linear relationship with spatial frequency (solid lines), consistent with a constant spatial offset. The lines are curved because the data are plotted on a log axis to match the data in panel A. The linear interpolation (dashed lines) shows the point where the red and green phosphors will be in the same phase. (C) Spatial offset calculated from phase regression for 17 PC cells recorded in dichromats. Arrow shows the offset predicted for the PC cell shown in panels A and B.
Figure 6
 
Illustration of the potential role of signals originating from chromatic aberrations. (A) Original image. (B and C) Utility of chromatic border detection. The top row shows a region of interest from the original image (indicated by the yellow square in panel A). Center and lower rows show the effect of a band-pass spatial filter (schematics in panel B) on the LUM signal (center row) and red–green chromatic difference signal (lower row). Grayscale in the lower two panels represents signal output from a univariant (single cone) spectral mechanism. The spatial characteristic of the filter was designed to approximate the shape of the RG response in PC cells recorded in dichromatic marmosets. The chromatic border signal is resistant to LUM variation due to shadows. (D) Effect of the RG spatial band-pass filter on the original image. Note recovery of chromatic edges and image outlines. Low spatial frequencies removed by Gaussian filtering (SD = 10 pixels) and subtraction (MatLAB image processing toolbox, Mathworks, Natick, NJ). Original image courtesy Pony Express, Inc., modified with permission.
Figure 6
 
Illustration of the potential role of signals originating from chromatic aberrations. (A) Original image. (B and C) Utility of chromatic border detection. The top row shows a region of interest from the original image (indicated by the yellow square in panel A). Center and lower rows show the effect of a band-pass spatial filter (schematics in panel B) on the LUM signal (center row) and red–green chromatic difference signal (lower row). Grayscale in the lower two panels represents signal output from a univariant (single cone) spectral mechanism. The spatial characteristic of the filter was designed to approximate the shape of the RG response in PC cells recorded in dichromatic marmosets. The chromatic border signal is resistant to LUM variation due to shadows. (D) Effect of the RG spatial band-pass filter on the original image. Note recovery of chromatic edges and image outlines. Low spatial frequencies removed by Gaussian filtering (SD = 10 pixels) and subtraction (MatLAB image processing toolbox, Mathworks, Natick, NJ). Original image courtesy Pony Express, Inc., modified with permission.
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