Yi-Zhong Wang

Oblique (off-axis) astigmatism of the reduced schematic eye with elliptical refracting surface

The oblique (off-axis) astigmatism of the Indiana Eye, an aspheric reduced-eye model of ocular chromatic aberration and spherical aberration, is computed across the visual field by using Coddingtons equations for nonspherical surfaces of revolution. Our results show that the amount of astigmatism varies significantly with the shape of the refracting surface and with the axial location of the pupil. For a pupil located 1.91 mm from the apex of the refracting surface (as originally specified for the model), the calculated Sturms interval was larger than that reported in the literature. However, by moving the models pupil 0.84 mm axially away from the apex toward the nodal point, a close match was achieved between Sturms interval of the model eye and published data from human eyes for eccentricities up to 60°. These results demonstrate that the aspheric reduced-eye model is capable of simultaneously accounting for the chromatic, spherical, and oblique astigmatic aberrations typically found in human eyes.

Undersampling produces non-veridical motion perception, but not necessarily motion reversal, in peripheral vision

We investigated motion perception in peripheral vision (10-40 deg eccentricity) for drifting gratings above and below the Nyquist limit set by neural sampling of the retinal image. We found that psychometric functions for motion discrimination rarely exhibited worse-than-chance performance indicative of motion reversal. A series of control experiments indicated that failure to demonstrate motion reversal could not be attributed to: (1) failure to detect the contrast of the stimulus; (2) failure to detect the motion of the stimulus; (3) use of an inappropriate range of spatial frequencies. Although consistent motion reversal was not observed, additional experiments demonstrated that motion perception was nevertheless non-veridical for spatial frequencies above the Nyquist limit. These seemingly contradictory results were reconciled by the observation that aliased patterns could appear to move in several different directions, all of which were different from the direction of stimulus, but only of which was opposite to the stimulus direction. Nyquist limits inferred from motion discrimination lie near the predictions for P-ganglion cells in human retina and well above M-cell predictions, which implies the M-cell array is too sparse to account for the limits to verdical motion perception in peripheral vision.

Aliased Frequencies Enable the Discrimination of Compound Gratings in Peripheral Vision

Although gratings beyond the Nyquist limit of the peripheral retina are visible as aliased percepts when presented in isolation, the reported lack of aliasing for targets with complex spectra (edges, lines, letters) suggests that aliased frequency components are invisible in the presence of sub-Nyquist image components. We tested this hypothesis by systematically exploring a range of stimulus parameters in search of conditions which would enable subjects to detect the supra-Nyquist components of a compound grating. A three-alternative forced-choice masking paradigm was used, which required subjects to discriminate a 2.5 deg patch of compound grating (mask + test) from a simple grating (mask only). Using a 2 c/deg grating as the masking component, which is well below the 4 c/deg Nyquist limit to veridical perception at 20 deg in the horizontal nasal field, we varied the spatial frequency of the test grating over a range extending above and below the Nyquist frequency. We found that aliased, supra-Nyquist components are reliably detected in the presence of high contrast, sub-Nyquist gratings, provided they have sufficient contrast. Contrast threshold for detecting the aliased gratings was higher when presented as a component of the compound grating than when presented in isolation. This masking effect of the sub-Nyquist component was not specific to supra-Nyquist test targets, however, since a similar masking effect also occurred for sub-Nyquist targets. These results suggest that the invisibility of aliasing described previously for edges or square wave gratings is due primarily to the combination of the low amplitudes of supra-Nyquist harmonics in such stimuli and a high contrast threshold of the peripheral retina. The additional masking effects of the sub-Nyquist, fundamental component of a square wave on the supra-Nyquist harmonics make the detection of aliasing impossible even for very high contrast square wave gratings presented in the periphery.

Interaction between sub- and supra-Nyquist spatial frequencies in peripheral vision

In peripheral vision, high-frequency gratings beyond the Nyquist limit are visible as aliased patterns but, as shown previously, their visibility can be masked by superimposed sub-Nyquist gratings. Is the converse also true? Can supra-Nyquist gratings affect the detectability of sub-Nyquist gratings? In this study, we investigated the masking effect of high contrast, supra-Nyquist components of a compound grating on the contrast detection of sub-Nyquist components by employing a temporal three-alternative, forced-choice (3AFC) masking paradigm. We found that high-frequency, aliased gratings with contrast just 2 or 3 times above threshold can have a powerful masking effect on low-frequency, resolved gratings in peripheral vision. This result was surprising because prior results from sub-Nyquist masking studies in the fovea and the periphery have indicated that masking occurs only when the mask contrast is at least 5 times greater than threshold. Strong masking by supra-Nyquist gratings that are only just visible may be accounted for by an irregular sampling model in which the alias of the mask is distributed over a band of frequencies in the sub-Nyquist range. Furthermore, if undersampling is the explanation for the results of this study, then masking must occur after spatial sampling.

Effect of Sampling Array Irregularity and Window Size on the Discrimination of Sampled Gratings

The effect of sampling irregularity and window size on orientation discrimination was investigated using discretely sampled gratings as stimuli. For regular sampling arrays, visual performance could be accounted for by a theoretical analysis of aliasing produced by undersampling. For irregular arrays produced by adding noise to the location of individual samples, the incidence of perceived orientation reversal declined and the spatial frequency range of flawless performance expanded well beyond the nominal Nyquist frequency. These results provide a psychophysical method to estimate the spatial density and the degree of irregularity in the neural sampling arrays that limit human visual resolution.