Spatial resolution of stereopsis

Spatial resolution for modulations of stereoscopic depth is much worse than resolution for modulations of luminance. Resolution for disparity modulations has been measured with random-dot stereograms (RDS). The sampling pattern of random-dot stimuli constrains the range of spatial frequencies that can be represented. We examined the degree to which the observed low resolution for the detection/discrimination of disparity modulations is caused by stimulus constraints as opposed to neural limitations. Observers viewed RDSs depicting sinusoidal depth corrugations. We measured the highest spatial frequency (Fmax) at which observers could reliably discriminate two corrugation orientations at peak-to-trough amplitude of 16 min disparity. We made the measurements across a broad range of dot densities at different modulation amplitudes. We found that performance is scale-invariant (Fmax is proportional to the square root of density) across 2 log units of dot density. In the scale-invariant range, Fmax is predicted by the 2-d Nyquist limit of the sampling dot pattern (although ideally the task requires far fewer dots than the Nyquist limit). At the highest densities, Fmax reached asymptote at 1-2 cpd. This asymptote corresponded to a disparity gradient of ∼1 (measured from peak to trough, i.e., a peak gradient of nearly 3.14). When the modulation amplitude was reduced by a factor of three, the Fmax asymptote increased to 2-3 cpd (corresponding to the peak-to-trough disparity gradients of 0.35-0.55). Improving the optical quality of the stimuli led to a further slight improvement in Fmax in some observers, but all observers exhibited asymptotes up to ∼3.5 cpd. Thus, three factors limit spatial resolution to disparity modulations: sampling density, the disparity gradient, and another factor at high dot densities that probably reflects spatial averaging required to reduce noise from false matches in the correspondence process.