Nancy J. Coletta

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 observers criteria for resolving sinusoidal gratings are less stringent than the criteria specified by the sampling theorem for perfect, alias-free image reconstruction.

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)].

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 15d̀ 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 25d̀ eccentric to the fovea. The greatest sensitivity loss was found in the macular area (fovea and 5d̀ 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.

Effect of myopia on visual acuity measured with laser interference fringes

The aim was to determine how visual acuity is affected by myopia when optical factors of the eye are controlled. Grating acuity was measured with interference fringes to avoid the effects of aberrations, and ocular biometry was used to compensate for differences in retinal image size among subjects. Distance spectacle refractions ranged from +2.25 to -14.75 D. The retinal magnification factor (RMF) in mm/deg was computed for each eye from the distance refraction, central corneal power and ultrasound biometry. A forced-choice orientation discrimination method was used to measure acuity for high-contrast 543 nm laser interference fringes in three retinal locations: the fovea, and at 4 deg and 10 deg eccentricity in the temporal retina. Acuity, expressed in c/deg and adjusted for spectacle magnification, was not significantly correlated with refraction at any of the three retinal locations. When acuity was converted to retinal spatial frequency units (c/mm) via the RMF, acuity decreased with increasing myopia at all three retinal locations (significantly at the fovea and at 10 deg eccentricity). Retinal acuity values in highly myopic subjects (>6 D) are consistent with retinal sampling distances that are larger than published values of human cone or ganglion cell spacing. The results imply that a highly myopic eye has retinal neurons that are more widely spaced than normal, but the increased axial length enlarges the retinal image enough to compensate for the retinal stretching. The data are consistent with a retinal stretching model that primarily affects the posterior pole.

An oblique effect in parafoveal motion perception

An observers 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.

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.

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.

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 (CSFs) 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 CSFs obtained under natural viewing conditions, interferometric CSFs 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.

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.

Ocular wavefront aberrations in the common marmoset Callithrix jacchus: effects of age and refractive error

The common marmoset, Callithrix jacchus, is a primate model for emmetropization studies. The refractive development of the marmoset eye depends on visual experience, so knowledge of the optical quality of the eye is valuable. We report on the wavefront aberrations of the marmoset eye, measured with a clinical Hartmann-Shack aberrometer (COAS, AMO Wavefront Sciences). Aberrations were measured on both eyes of 23 marmosets whose ages ranged from 18 to 452 days. Twenty-one of the subjects were members of studies of emmetropization and accommodation, and two were untreated normal subjects. Eleven of the 21 experimental subjects had worn monocular diffusers and 10 had worn binocular spectacle lenses of equal power. Monocular deprivation or lens rearing began at about 45 days of age and ended at about 108 days of age. All refractions and aberration measures were performed while the eyes were cyclopleged; most aberration measures were made while subjects were awake, but some control measurements were performed under anesthesia. Wavefront error was expressed as a seventh-order Zernike polynomial expansion, using the Optical Society of Americas naming convention. Aberrations in young marmosets decreased up to about 100 days of age, after which the higher-order RMS aberration leveled off to about 0.10 μm over a 3 mm diameter pupil. Higher-order aberrations were 1.8 times greater when the subjects were under general anesthesia than when they were awake. Young marmoset eyes were characterized by negative spherical aberration. Form-deprived eyes of the monocular deprivation animals had greater wavefront aberrations than their fellow untreated eyes, particularly for asymmetric aberrations in the odd-numbered Zernike orders. Both lens-treated and form-deprived eyes showed similar significant increases in Z3(-3) trefoil aberration, suggesting the increase in trefoil may be related to factors that do not involve visual feedback.