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Vernier thresholds were measured with a pair of vertical sinusoidal gratings of one and a half cycles as targets. The amplitude was weighted by a one-dimensional Gaussian and contrast was set one log unit above contrast threshold. The vernier thresholds were estimated with the method of constant stimuli. Temporal frequency effects were introduced by movement of the vernier targets. It was found that vernier thresholds expressed in phase angle were unchanged in the effective range of spatial frequencies provided that the temporal frequency and the visibility were unchanged, and that thresholds deteriorated by increasing the temporal frequency. It is suggested that the detection of relative phase may be involved in the discrimination of vernier offsets and that it may be mediated by a sustained unit. Three possible types of mechanisms, edge-localization processes, orientation-selective units and phase-sensitive units, were considered in relation to vernier acuity.

This study investigated the case where a spatial offset was periodically and momentarily introduced between two vernier components during their excursion, to determine how such an offset affects the relative localization of the components. If the object in motion is perceived at a position averaged over a limited spatio-temporal range, spatial offsets in a moving vernier should be perceived accordingly. This prediction was confirmed by the outcome of the first experiment. A second experiment was performed to inquire into the relationship between vernier threshold and the averaging of spatial offset, and also the spatio-temporal limit of the integrative process. The upper temporal limit of the averaging was estimated to be about 50 ms, and the spatial extent of positional modulation was shown to have a significant effect on the detection of vernier offset. It was found that the larger the extent over which the vernier positions were distributed, the smaller the offset detected between them. It is suggested that spatial offset can be detected directly, perhaps by some mechanism sensitive to the phase relationship of the components of visual patterns.