Three experiments were performed to examine positional acuity and the role of spatial sampling in central, peripheral and amblyopic vision. In the first experiment, 3-line bisection acuity was compared to grating acuity. In normal foveal vision bisection acuity represents a hyperacuity. In anisometropic amblyopes, bisection acuity is reduced in rough proportion to their grating acuity. In strabismic amblyopes, and in the normal periphery, bisection acuity is reduced to a greater extent than grating acuity. This result implies that reduced contrast sensitivity of the spatial filters is not sufficient to account for the increased positional uncertainty found in peripheral vision and in strabismic amblyopia. In order to test the hypothesis that the high degree of positional uncertainty evident in these visual systems is a consequence of sparse spatial sampling, bisection thresholds and width discrimination thresholds were measured with stimuli comprised of discrete samples. The results showed that normal foveal vision and the vision of anisometropic amblyopes show little benefit from adding discrete samples to the stimulus. In contrast, the normal periphery, and the central field of strabismic amblyopes demonstrate marked positional uncertainty which can be efficiently reduced in proportion to the square root of the number of samples (up to about 10) comprising the stimulus in the direction orthogonal to the discrimination cue. In aggregate the results suggest that anisometropic and strabismic amblyopia are fundamentally different. The positional uncertainty in anisometropic amblyopia is consistent with the reduced sensitivity of the spatial filters. The data of the normal periphery and of the central field of strabismic amblyopes suggest that the cortical sampling grain imposes a fundamental limit upon their positional acuity.