Sparse-sampling of gratings in the visual cortex of strabismic amblyopes.

Strabismic amblyopes show losses in positional acuity that cannot be explained by their resolution or contrast sensitivities. One hypothesis for these losses is a reduction in the density of cortical neurons that are driven by the amblyopic eye (cortical undersampling). The question this study addressed was whether the foveal representation of the amblyopic eye is undersampled in the cortex of strabismic amblyopes. In order to assess spatial sampling psychophysically, we recorded the perceived orientation of a stationary grating as a function of grating orientation and frequency in three strabismic amblyopes. To ensure high retinal contrast, the grating was imaged on the fovea of each observer using a laser interferometer. We found that the strabismic amblyopes misperceived the orientation of the grating at spatial frequencies that are a factor of two to six lower than the sampling frequency of the foveal cones. Since the retina and LGN in strabismic amblyopes are presumably normal, this result suggests sparse cortical sampling in the foveal representation of the amblyopic eye. Undersampling by cortical neurons may contribute to the spatial distortions present in strabismic amblyopic eyes.

The spatial grain of motion perception in human peripheral vision.

Motion reversal effects (the apparent reversal of the direction of motion of a high frequency sinusoidal grating) have been attributed to aliasing by the cone mosaic [Coletta et al. (1990). Vision Research, 30, 1631-1648] and postreceptoral layers [Anderson & Hess (1990). Vision Research, 30, 1507-1515] in human observers. We present data and a new model which suggest that at least two sampling arrays of different densities affect direction discrimination out to 30 degrees eccentricity. The first sampling layer matches anatomical estimates of the cone density. The second sampling layer is too dense to be the parasol cells alone; midget ganglion cells certainly contribute to this task. This is further evidence that motion perception is not mediated exclusively by the magnocellular stream.

Effects of luminance and spatial noise on interferometric contrast sensitivity.

Optical properties of the eye contribute to the reduced visibility of spatial patterns at low luminance. To study the limits of spatial vision when optical factors are minimized, we measured contrast-sensitivity functions (CSF's) for 543.5-nm laser interference fringes imaged directly on the retina. Measurements were made in the fovea at four luminance levels, ranging from 0.3 to 300 photopic trolands (Td). At each luminance the fraction of coherent light in the stimulus pattern was varied to assess the masking effects of laser speckle, which is visible as spatial noise in fields of coherent light. Compared with published CSF's obtained under natural viewing conditions, interferometric CSF's were similar in height but broader, with the range of visibility being extended to higher spatial frequencies. The masking effects of speckle were greatest at the highest luminance and were negligible at the lowest luminance. For low coherent fractions, contrast sensitivity improved over the entire luminance range at a rate consistent with a square-root law; with purely coherent light, sensitivity tended to level off at approximately 30 Td because of speckle masking. The results indicate that the optical quality of the eye reduces the spatial bandwidth of vision even at luminances near the foveal threshold. The change in interference fringe visibility with luminance is consistent with noise-limited behavior, and the masking effects of speckle noise diminish as luminance decreases.

An oblique effect in parafoveal motion perception.

An observer's ability to discriminate the angular direction of a moving grating depends on the grating orientation. Observers can more accurately judge the angular direction of vertical or horizontal gratings than oblique gratings. We discovered that this oblique effect becomes very large at high spatial frequencies in the parafovea. Perceived direction was quantified with a direction matching task at spatial frequencies ranging from 7.6 to 22.6 c/deg. As spatial frequency increased, direction matches of oblique gratings deviated away from the diagonal and towards vertical or horizontal axes. Subjects reported that the higher spatial frequency gratings appeared as grainy noise, particularly at oblique orientations. Our results indicate that, in the parafovea, subjects perceive movement of high spatial frequencies mainly along principal meridians. One possible explanation for this effect is that the high frequency patterns are aliased by the irregular mosaic of parafoveal cones. The aliasing noise generated by irregular sampling contains spatial energy at all orientations, but perhaps only vertical and horizontal components of the noise are visible to the observer.

Consequences of spatial sampling for human motion perception.

This paper describes evidence for spatial aliasing in human motion perception. For a certain range of spatial frequencies, interference fringes drifting across the extrafoveal retina resemble two-dimensional spatial noise drifting in the opposite direction. For retinal locations within 10 deg of the fovea, the perceived direction of motion is veridical up to spatial frequencies near the cone Nyquist frequency, reverses between one and two times the cone Nyquist frequency, and sometimes reverses back to the correct direction at still higher frequencies. Thus two "motion nulls", or spatial frequencies at which the direction of motion is ambiguous, are typically observed at each retinal eccentricity. A computational model is described in which sinusoidal gratings are sampled by a cone mosaic and the direction of motion of the filtered output is computed. The model predicts that the second motion null, but not the first, should be relatively immune to postreceptoral processing and should roughly equal twice the cone Nyquist frequency. This prediction is confirmed by psychophysical experiments, providing a new technique to estimate cone spacing in the living human eye.

Psychophysical estimate of extrafoveal cone spacing.

In the extrafoveal retina, interference fringes at spatial frequencies higher than the resolution limit look like two-dimensional spatial noise, the origin of which has not been firmly established. We show that over a limited range of high spatial frequencies this noise takes on a striated appearance, with the striations running perpendicular to the true fringe orientation. A model of cone aliasing based on anatomical measurements of extrafoveal cone position predicts that this orientation reversal should occur when the period of the interference fringe roughly equals the spacing between cones, i.e., when the fringe spatial frequency is about twice the cone Nyquist frequency. Psychophysical measurements of the orientation reversal at retinal eccentricities from 0.75 to 10 deg are in quantitative agreement with this prediction. This agreement implies that at least part of the spatial noise observed under these conditions results from aliasing by the cone mosaic. The orientation reversal provides a psychophysical method for estimating spacing in less regular mosaics, complementing another psychophysical technique for measuring spacing in the more regular mosaic of foveal cones [D.R. Williams, Vision Res. 25, 195 (1985); Vision Res. (submitted)].

Cone spacing and the visual resolution limit.

It is commonly assumed that the visual resolution limit must be equal to or less than the Nyquist frequency of the cone mosaic. However, under some conditions, observers can see fine patterns at the correct orientation when viewing interference fringes with spatial frequencies that are as much as about 1.5 times higher than the nominal Nyquist frequency of the underlying cone mosaic. The existence of this visual ability demands a closer scrutiny of the sampling effects of the cone mosaic and the information that is sufficient for an observer to resolve a sinusoidal grating. The Nyquist frequency specifies which images can be reconstructed without aliasing by an imaging system that samples discretely. However, it is not a theoretical upper bound for psychophysical measures of visual resolution because the observer's criteria for resolving sinusoidal gratings are less stringent than the criteria specified by the sampling theorem for perfect, alias-free image reconstruction.

Clinical measurement of saturation discrimination.

In this paper, we describe how a circular reflective neutral-density wedge can be used to construct an apparatus which provides a relatively rapid procedure for the clinical measurement of saturation discrimination. Subsequent to an initial measurement of the patient's relative luminosity function, the patient need only turn a single control which varies the colorimetric purity of a test field which remains luminance matched to a white light reference field.

Dark adaptation in age-related maculopathy.

Dark adaptation was measured for patients with age-related maculopathy (ARM) and for age-matched controls; green and red test stimuli were flashed 15 degrees from the fovea to examine differential effects of ARM on rod and cone functions, respectively. The ARM patients showed decreases in sensitivity for both rods and cones (0.5-1.5 log units) and an increased time constant of recovery for rod function. After 20 min in the dark, sensitivity to both red and green stimuli was depressed at the fovea and at 5, 10, 15 and 25 degrees eccentric to the fovea. The greatest sensitivity loss was found in the macular area (fovea and 5 degrees eccentric). Our data suggest that the ARM patients have an abnormality in both rod- and cone-adaptation systems over a relatively large retinal area which extends beyond the zone of visual field abnormality.

Spatial extent of rod-cone and cone-cone interactions for flicker detection.

Over a large range of light adaptation levels, sensitivity to 25 Hz flicker improves as the light level of the background increases. Using small background discs and annular surrounds, this effect was shown to be mediated by the surround and not the average luminance of the test region, in agreement with recent reports. The effect is due to two types of lateral interaction: at mesopic light levels (from 0.1 to 1.0 td), cone-mediated flicker resolution is enhanced by the stimulation of surrounding rods; at photopic light levels (above 10 td), flicker sensitivity improves with light stimulation of adjacent cones. The spatial zone, or extent, over which the surround contributes to the flicker threshold was measured. The spatial area over which rods influence the cone 25 Hz flicker threshold is larger than the analogous spatial area of cone influence. In the parafovea, at 5 deg eccentricity, cone flicker sensitivity for a 20' spot is influenced by cones in a 1 deg diameter area centered on the spot; the corresponding area of rod influence is about 3 deg. In the fovea, flicker sensitivity for a 10' spot is influenced by cone stimulation in an area of about 20' diameter. Rods which affect foveal flicker sensitivity appear to occupy an annular zone with about a 2 deg outer diameter and 1 deg inner diameter, centered on the fovea.

Adaptation of a color-opponent mechanism increases parafoveal sensitivity to luminance flicker.

Sensitivity to 25 Hz luminance flicker is enhanced as the intensity of a background is increased. This effect is due, in part, to light adaptation of cones. Preliminary studies suggested that, in the parafovea, the enhancement of flicker sensitivity is due to the adaptation of a color-opponent mechanism rather than a single cone mechanism or achromatic mechanism. In the present study, action spectra and field additivity experiments demonstrated that the enhancing effect was opponent in nature. The field sensitivity function had a notch at 570 nm; fields on either side of the notch acted subadditively. This suggests that, in the parafovea, the sensitivity of an achromatic flicker mechanism is influenced by the adaptation of a chromatic mechanism.

Spatial contrast sensitivity. Importance of controlling the patient's visibility criterion.

Clinical spatial contrast sensitivity measurements are typically made using psychophysical methods that do not specify the response criterion being used by the patient in judging grating visibility. Results of this report show the necessity of such methods for (1) maximizing detectability of early contrast sensitivity deficits by minimizing normal sample variance, and (2) ensuring that changes in an individual's contrast sensitivity reflect changes in vision and not simply fluctuations in the patient's criterion for judging grating visibility.

Rod-cone interaction in flicker detection.

There is considerable evidence in the literature that rod-cone interaction occurs when both rods and cones simultaneously detect a test target. More recent evidence, however, has shown a parafoveal rod-cone interaction during dark adaptation for a purely cone-detected flickering test stimulus; this influence on cone threshold appears to be mediated by surrounding rods. In this study, we demonstrate a similar rod-mediated influence on parafoveal cone-detected flicker threshold. More surprisingly, foveal cone-detected thresholds are also influenced by rods. This effect occurs over at least a 2 log unit intensity range of mesopic background level; cone-detected 25 Hz flicker sensitivity is enhanced by increasing the radiance of the background. The action spectrum of this effect fits the scotopic spectral sensitivity curve. At higher background levels, this rod-cone interaction disappears and surrounding cone activity then influences the cone flicker threshold. The results suggest that, as rods recover sensitivity, they reduce cone-detected flicker sensitivity, even at the fovea. The rod influence on cone flicker is most apparent for long wavelength test stimuli. Our results, in agreement with recent reports, suggest that the rod-cone interaction is laterally-mediated and may be specific for the long wavelength-sensitive cone type.

Effect of artificial central scotoma on the spatial contrast sensitivity of normal subjects.

Spatial contrast sensitivity was measured in normal subjects with and without a retinally stabilized artificial scotoma (either circular or rectangular), which precluded foveal vision. Our results indicate that the type of contrast sensitivity loss obtained (predominantly high frequency or overall) depended on temporal factors associated with grating presentation. A predominantly high frequency loss was obtained when grating contrast was turned on and off gradually. An additional low frequency difference was obtained when grating contrast was turned on and off abruptly.