Ординатура / Офтальмология / Английские материалы / Seeing_De Valois_2000

44 Larry N. Thibos

Further evidence that retinal undersampling is responsible for perceptual aliasing e ects comes from the close correlation between psychophysical and anatomical estimates of sampling density of the cone mosaic in the parafoveal retina (Williams & Coletta, 1987) and the ganglion cell mosaic in the periphery (Thibos, Cheney, & Walsh, 1987). Given that the visual system consists of a series of anatomically distinct stages (e.g., photoreceptors, bipolars, ganglion cells), each of which sample the preceding stage, it stands to reason that the lowest sampling limit will be set by the coarsest array of the visual pathway. Over most of the retina, excluding the foveal and parafoveal region, cone photoreceptors and midget bipolar cells greatly outnumber midget ganglion cells, which implies that peripheral ganglion cells subsample the photoreceptor array. Consequently, if retinal undersampling is the limiting factor for spatial resolution, rather than optical or neural filtering mechanisms, then human resolution acuity should match the Nyquist frequency of the cone array in central vision but the ganglion cell array for peripheral vision.

Results of a systematic exploration of the limits to contrast detection and resolution across the visual field in human vision are summarized in Figure 23a. Cuto spatial frequency was measured for two di erent tasks (contrast, detection, pattern resolution), for two di erent types of visual targets (interference fringes, sinusoidal grating displayed on a computer monitor with the eye’s refractive error corrected by spectacle lenses), at various locations along the horizontal nasal meridian of the visual field (Thibos, Cheney, & Wash, 1987;Thibos,Walsh, & Cheney, 1987). These results show that for the resolution task, cuto spatial frequency was the same regardless of whether the visual stimulus was imaged on the retina by the eye’s optical system (natural view) or produced directly on the retina as high-contrast, interference fringes. This evidence supports the view that, for a well-focused eye, resolution of high-contrast patterns is limited by the ambiguity of aliasing caused by undersampling, rather than by contrast attenuation due to optical or neural filtering. Aliasing occurs for frequencies just above the resolution limit, so the triangles in Figure 23a also mark the lower limit to the aliasing portion of the spatial frequency spectrum. This lower boundary of the aliasing zone is accurately predicted by the Nyquist limit calculated for human P-ganglion cells in peripheral retina beyond about 15 of eccentricity (Curcio & Allen, 1990).

The upper limit to the aliasing zone in Figure 23a is determined by performance on the contrast-detection task. Detection acuity is significantly lower for natural viewing than for interferometric viewing at all eccentricities. Consequently, the spectrum of frequencies for which aliasing occurs is narrower for natural viewing than for interference fringes. This di erence is directly attributable to imperfections of the eye’s optical system, since all else is equal. In both cases the neural system is faced with identical tasks (contrast detection) of the same stimulus (sinusoidal gratings). Notice that for natural viewing the aliasing zone narrows with decreasing field angle and vanishes completely at the fovea, where contrast sensitivities for detection and for resolution of gratings are nearly identical. Thus we may conclude that under natural viewing conditions, the fovea is protected from aliasing by optical

Summary of optical and neural limits to pattern detection and pattern resolution across the visual field in humans. (a) Symbols show psychophysical performance (mean of three subjects from Thibos et al., 1987) for grating detection (squares) and resolution (triangles) tasks under normal viewing conditions (open symbols) or when viewing interference fringes (closed symbols). The aliasing zone extends from the resolution to the detection limits. Solid curve drawn through open squares indicates the optical cuto of the eye and marks the upper limit to the aliasing zone for natural viewing (horizontal hatching). The expanded aliasing zone observed with interference fringes (vertical hatching) extends beyond the optical cuto to a higher value set by neural factors. Dashed curve shows computed detection limit of individual cones (from Curcio et al., 1990), and dotted curve shows computed Nyquist limit of retinal ganglion cells (RGC; from Curcio & Allen, 1990). (b) Topography of visual resolution for radially oriented interference fringes. Iso-acuity contour lines were interpolated from measurements at eight eccentricities along eight meridia. Contours are spaced at 0.2 log cyc/deg intervals as indicated by numbers on curves. Black spot indicates location of optic nerve head in the visual field.

low-pass filtering. However, in the periphery, the optical bandwidth of the retinal image exceeds the neural Nyquist frequency (assuming refractive errors are corrected), and so the eye’s optical system fails to protect the relatively coarse sampling array of the peripheral retinal ganglion cells against undersampling.

If it is true that resolution acuity in peripheral retina is determined by the sam-

46 Larry N. Thibos

pling density of retinal ganglion cells, then we should expect to see a close similarity between the topography of visual resolution and the topography of retinal ganglion cells determined anatomically. An example of a resolution topographic map obtained using the interference fringe method is shown in Figure 23b. This map, obtained for the author when viewing through his right eye (Wilkinson, 1994), contains all of the major features of the anatomical topographic map of ganglion cells described by Curcio and Allen (1990). The isodensity contours are elongated along the horizontal meridian, the contours are displaced into temporal field by an amount which increases with eccentricity, and the contours are displaced inferiorly in the visual field. The visual streak (an anatomical feature of retinas from many di erent species in which cell density on the horizontal meridian is slightly higher than in neighboring areas just above or just below the horizon) is clearly evident along the horizontal meridian, and the nasal/temporal asymmetry expected for retinal ganglion cell density is also apparent psychophysically. In the central portion of the visual field (inside 15 of eccentricity), these characteristic asymmetries are not as strong in either the topographic map of resolution or the corresponding map of photoreceptor density (Curcio et al., 1990).

In summary, recent evidence indicates that not only does neural sampling limit visual resolution everywhere in the visual field (provided optical limitations are avoided), but the limiting neural array is in the retina itself. Thus, the long-stand- ing theory of visual resolution as a sampling-limited process is now well substantiated experimentally, thus providing a clear link between the neural architecture of the retina and visual perception.

IV. OPTICAL VERSUS SAMPLING LIMITS TO VISION

The evidence reviewed herein indicates that despite the declining optical quality of the peripheral retinal image due to o -axis aberrations, the quality of the retinal image is much higher than the corresponding neural resolution limit, provided the o -axis astigmatism and defocus of the eye are corrected. However, in daily life this is an unlikely circumstance because peripheral refractive errors are not routinely corrected with spectacles or contact lenses. If an individual wears corrective lenses, they are prescribed for the refractive errors of central vision, not peripheral vision. The distinction here is important because the appropriate prescription for di erent parts of the visual field varies systematically over a range of several diopters, including large changes in astigmatism, depending on the angle of eccentricity of peripheral targets (Ferree, Rand, & Hardy, 1931). Furthermore, in our three-dimensional world objects may lie at various distances relative to the foveal stimulus which drives the accommodative reflex to focus the eye. For these reasons, we must conclude that the retinal image will be habitually out-of-focus over most of the visual field most of the time. Since defocus reduces the quality of the retinal image, it is important to inquire how much optical defocus is required to abolish aliasing from our perceptual experience.

48 Larry N. Thibos

limit can be positioned without a ecting their resolvability. Although resolution acuity is constant throughout the shaded region, detection acuity varies signifi- cantly, being maximum at the retinal conjugate distance marked by the thick line. Outside the shaded region, gratings at the resolution limit are so badly blurred that they are not detectable, which prevents aliasing and reduces resolution acuity below the retinal sampling limit.

A great deal of individual variability would be expected in the position of the shaded area in Figure 24b along the dioptric viewing distance axis because of di - erences in peripheral refractive errors of di erent eyes. However, the dioptric extent of the depth of field for resolution would be expected to be similar across individuals because it is primarily an optical consequence of defocus. Since the mean refractive error of eyes varies by less than 3 D for eccentricities up to 40 (Ferree et al., 1931), which is less than half of the depth of focus for resolution, we may conclude that for the average person the depth of focus is likely to include a large range on either side of the fixation distance. Thus, contrary to the expectation that aliasing might be abolished in daily life by optical defocus, the evidence suggests that perceptual aliasing of high-contrast patterns is to be expected of peripheral vision.

For low-contrast targets the moiré e ects of undersampling are not as conspicuous for several reasons. First, the optical depth of focus for peripheral vision illustrated in Figure 24 will be shorter because reducing the contrast of the target adds to the contrast-attenuating e ects of defocus. Second, natural scenes have continuous contrast spectra which fall inversely with spatial frequency (Barton & Moorehead, 1987; Field, 1987), and therefore the higher frequency components that are eligible for undersampling may produce too little contrast on the retina to cause perceptual aliasing. This happens for bar patterns and edges, for example, partly because the contrast threshold for detection is relatively high in peripheral vision, but also because of masking of high-frequency patterns by low-frequency patterns (Galvin & Williams, 1992; Wang, Bradley, & Thibos, 1997a).

The neural e ects of undersampling described above are primarily a feature of peripheral vision, which is commonly regarded as inferior to central vision. Yet, in many regards just the opposite is true. Night vision is an obvious example for which the central blind spot is attributed to the lack of rods in the retinal fovea. Another broad area in which peripheral vision excels is in the sensing and control of selfmovement. For example, the visual control of posture, locomotion, head, and eye movements are largely under the control of motor mechanisms sensitive to peripheral stimulation (Howard, 1986; Matin, 1986). Many of these functions of peripheral vision are thought of as reflex-like actions which, although they can be placed under voluntary control, largely work in an “automatic-pilot” mode with minimal demands for conscious attention.This suggests that information regarding body attitude, self-motion through the environment, and moving objects are ideally matched to the natural ability of the peripheral visual system to extract such information. The cost of retinal undersampling, therefore, is the possibility of erroneous perception of space, motion, or depth, which may have unintended or undesirable con-

sequences. Evidently this risk of occasional misperception is outweighed by the pressure to maximize the quality of vision by maximizing retinal image contrast over a large visual field, which has led to the evolution of eyes of remarkable high quality over a panoramic field of view (Snyder, Bossomaier, & Hughes, 1986).

Acknowledgments

This manuscript was prepared with the support of the National Eye Institute (grant R01 EY05109) of the U.S. National Institutes of Health. A. Bradley provided valuable suggestions and critical comments. Y. Wang created the computer programs for illustrating retinal images in the presence of optical aberrations.

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