Clifton M. Schor

Disparity range for local stereopsis as a function of luminance spatial frequency

The disparity range for stereo sensitivity was investigated with spatially filtered bars, tuned narrowly over a broad range of spatial frequencies. When measured with narrow (high spatial frequency) bars the disparity range for stereopsis exceeded two orders of magnitude. The range was reduced with broad (low spatial frequency) bars by an elevation of stereothreshold that increased according to a constant 6 deg phase disparity. The upper disparity limit also increased at broad spatial periods but at a lower rate. These size disparity correlations illustrate quantitative stereopsis along a continuum from fine to coarse disparities (+/- 2 deg). A disparity matching task revealed that greater amounts of uncrossed than crossed disparity were required to match suprathreshold disparities. The ratio of standard/matched disparity was lower in both directions for small suprathreshold disparities subtended by broad than by narrow spatial periods. This selective reduction of stereo-efficiency ratio illustrates tuning to coarse disparities subtended by broad (low spatial frequency) stimuli and accounts for the marked reduction of stereoacuity caused by spectacle blur.

Binocular sensory fusion is limited by spatial resolution

Binocular sensory fusion which was previously thought to have a maximum spatial extent at the fovea of 1 deg is at least 600% larger when stimulated by low spatial frequency (coarse) detail. This upper limit for sensory fusion has a constant phase disparity limit of 90 deg which corresponds to the monocular Rayleigh criterion for spatial resolution of two diffraction patterns. At low spatial frequencies the sensory fusion limit equals the upper disparity limit for stereoscopic depth perception which suggests that a common mechanism underlies these two phenomena.

The relationship between fusional vergence eye movements and fixation disparity

Abstract The fusional vergence system is under the control of a fast neural integrator which aligns the eyes and a slow neural integrator which maintains binocular alignment. These controllers are distinguished by their decay time constants and their stimuli. Previous studies indicate that the fast fusional vergence controller responds to retinal image disparity and the slow fusional vergence controller responds to the output of the fast neural integrator. Slow fusional vergence as evidenced by adaptation of the phoria is unaffected by accommodative vergence when disparity vergence is open loop. Under closed loop conditions both accommodation and disparity induced vergence influence slow fusional vergence. These results indicate that the slow vergence controller is located before the site of interaction between convergence and accommodation. Fixation disparity is described as a steady-state error of the neural integrator controlling fast fusional vergence and its amplitude is shown to be inversely related to adaptation of the phoria to prism.

The influence of rapid prism adaptation upon fixation disparity

Abstract Small errors of fusional vergence (fixation disparity) were examined as a function of the magnitude of horizontal prism stimulating convergence or divergence for a short (30sec) duration. Marked differences were observed between the amplitude of fixation disparity resulting from convergent and divergent stimulus disparities. In another experiment, subjects wore a horizontal prism for 30 sec after which time one eye was occluded for 40 sec. Measurements of vergence eye movements revealed an incomplete relaxation of fusional vergence (prism adaptation) after 40 sec of occlusion. Marked differences were observed between the amplitude of prism adaptation resulting from convergent and divergent stimuli. Maximum prism adaptationand minimum fixation disparity occurred with the same direction of prism, suggesting that a slow fusional vergence mechanism minimizes errors of binocular vergence.

Dynamic interactions between accommodation and convergence are velocity sensitive

Aftereffects of accommodation and vergence occur following approximately 1 min of adaptation to lenses and prisms respectively. This observation can be interpreted to mean that accommodation and vergence responses have phasic and tonic components. We have examined the role that these proposed subcomponents play in mutual interactions between accommodation and vergence. Both accommodative vergence (AV) and vergence accommodation (VA) were unresponsive to low temporal frequency variations (less than 0.1 Hz) in defocus and disparity respectively. However, both AV and VA were responsive to higher temporal frequency stimuli (up to 0.5 Hz). When negative feedback to the stimulated system was cancelled electronically, both AV and VA become responsive to low temporal frequency stimuli. The ratio or gain of accommodative vergence/accommodation (AC/A) and vergence accommodation/vergence (CA/C) increased nonlinearly with stimulus amplitude. Vergence aftereffects resulted from stimulation of AV and accommodative aftereffects resulted from stimulation of VA. These results are interpreted to mean there could be a complementary relationship between the amplitude of the AC/A ratio and proposed tonic adaptation of accommodation, and between the amplitude of the CA/C ratio and proposed tonic adaptation of vergence. A low saturation limit or stimulus window for tonic adaptation may account for the amplitude dependent nonlinearities of the AC/A and CA/C ratios.

Interocular correlation, luminance contrast and cyclopean processing

We have investigated the nature and viability of interocular correlation as a measure of signal strength in the cyclopean domain. Thresholds for the detection of interocular correlation in dynamic random element stereograms were measured as a function of luminance contrast, a more traditional measure of stimulus strength. At high contrasts, correlation thresholds were independent of contrast. At low contrasts, correlation thresholds were inversely proportional to the square of contrast. Stereothresholds were also measured as a function of both contrast and interocular correlation. At low contrasts, stereoacuity was inversely proportional to both interocular correlation and the square of contrast. These results are consistent with an inherently multiplicative mechanism of binocular combination, such as a cross-correlation of the two eyes inputs.

ocular Dominance and the Interocular Suppression of Blur in Monovision

ABSTRACT Presbyopic contact lens patients with monocular corrections (monovision) see clearly at all distances by virtue of an interocular suppression of anisometropic blur that occurs regionally between corresponding retinal areas. This suppression fails to occur with small highcontrast targets viewed under low luminance conditions. The effect of target size and contrast upon interocular suppression of blur was quantified by reducing contrast of a bright test spot, viewed binocularly while wearing various plus lenses monocularly, until the out‐of‐focus image was suppressed. The strength of interocular suppression was equivalent when the plus lens was before either eye. However, after subjects wore a plus lens over their nonsighting eye for one day, interocular suppression of blur became enhanced when the nonsighting eye was blurred, and it became reduced when the sighting eye was blurred. Succcessful monovision subjects suppressed blur at higher contrast levels than did unsuccessful subjects. These results suggest a possible clinical test for quantifying adaptation to monovision.

Depth-increment detection function for individual spatial channels.

We have used stimuli with difference-of-Gaussian (DOG) luminance profiles to measure depth-increment thresholds within postulated spatial channels as functions of depth from the fixation plane. Stereoacuity was best with high-frequency DOGs presented at the fixation plane. Performance was relatively constant for spatial frequency above 2.4 cycles/deg, but it deteriorated as spatial frequency was decreased. Regardless of spatial frequency, stereo sensitivity declined rapidly as stimuli were presented away from the horopter. The falloff occurred more rapidly over the 0-20-arc-min range than over the 20-80-arc-min range. Depth was perceived over a broader range of disparity pedestals with low-spatial-frequency stimuli; however, the lowest thresholds were always obtained with the highest-frequency stimuli. Both the falloff of sensitivity with disparity pedestal and the disparity range of quantitative stereo depth lead to the conclusion that different size-tuned channels process disparity differently.

A Dynamic Model of Cross-Coupling Between Accommodation and Convergence : Simulations of Step and Frequency Responses

The near triad consists of an increase in accommodation, vergence, and pupillary constriction. All three motor systems exhibit phasic and tonic responses. The tonic response adapts readily to phasic efforts of accommodation and vergence. Cross-coupling between accommodation and vergence provides a means of dynamically adjusting the tonic set points of the two motor systems to a common near or far working distance. Accommodative vergence cross-links play a dominant role in coordinating proximal changes in accommodation and convergence. The magnitude of cross-link interactions can be modified by imbalanced strength of tonic adaptation by accommodation and vergence. Reducing adaptation of tonic accommodation increases the AC/A ratio and decreases the CA/C ratio. Reducing adaptation of tonic vergence has the opposite effect. A model is able to predict these and other interactions simply by reducing the decay time constant of one of the two motor systems. For example, reducing the time constant for tonic accommodation results in an increased AC/A ratio and decreased CA/C ratio. Reducing the time constant for tonic vergence has the opposite effect. The model predicts transient step responses by accommodative vergence when the AC/A ratio is low and transient step responses of vergence accommodation when the CA/C ratio is low. It also predicts a reciprocal relationship between the AC/A and CA/C ratios. When one cross-link ratio is high the other cross-link ratio is low. Simulated frequency responses predict the low frequency roll off of low AC/A and low CA/C ratios. The step and frequency responses of cross-link ratios are shown to be the same for proximal (perceived distance) and retinal (blur and disparity) stimuli. The model suggests that physiological variations of tonic decay time constants may play an important role in determining clinically abnormal values of AC/A and CA/C ratios.

Spatial tuning of static and dynamic local stereopsis

The range of spatial tuning for channels that process static and dynamic disparities was investigated in the central visual field by measuring stereoscopic thresholds as a function of the difference in size of spatially filtered bar-like patterns presented to the two eyes. Spatial tuning functions were revealed by an elevation of stereothreshold as the difference between the widths of bar patterns increased. Functions tuned to low spatial frequencies (0.075-2 c/deg) were classified as transient since their stereosensitivity was greater for dynamic (1 Hz) than static disparities. Functions tuned to high spatial frequencies (2.4-19 c/deg) were classified as sustained since their stereosensitivity was equal for dynamic and static disparities. When equal width patterns were presented to the two eyes, stereothreshold increased with spatial periods greater than 0.4 deg according to a constant 6 deg phase disparity. This size-disparity correlation suggests that large disparities are processed by spatial filters tuned to disparities proportional to their receptive field dimensions.