Abstract

Perfect reconstruction of a sine-wave grating requires at least two samples per cycle in order to determine the amplitude and phase. We have measured vernier acuity for discretely sampled sine-wave gratings. The stimulus was a pair of abutting horizontal sine-wave gratings, and the observers' task was to judge the direction of vertical offset between the two gratings. Each horizontal sample was 0.6 ft. (18.3 cm) wide and the luminance between samples was fixed at the mean luminance. The equally spaced samples were lined up in the two gratings, but the position of the gratings was random with respect to the samples. We found that reducing the number of discrete samples comprising the gratings has two effects: (1) grating visibility is reduced, and (2) vernier thresholds increase. When the visibility of the grating is held constant (by increasing the physical contrast) as the number of samples is reduced over a wide range of grating spatial frequencies, vernier thresholds are unimpaired with four samples per cycle and are only slightly impaired with three samples. Our results suggest that the human observer acts almost like an ideal observer in spatial localization tasks.

© 1990 Optical Society of America