Short-range vernier acuity: interactions of temporal frequency, temporal phase, and stimulus polarity

We examined how vernier thresholds for flickering bars depend on the temporal frequency and relative temporal phase of the bars. The largest effect of relative phase (up to a fivefold increase in displacement thresholds) was seen at 2 Hz, and for most subjects, relative phase had little effect at 16 Hz and above. The effect of relative phase was essentially independent of contrast and trial duration. Thresholds were elevated by the greatest amount when bars were presented in antiphase, but at 1 and 4 Hz, quadrature phase offsets also led to substantial elevations in displacement thresholds. An experiment designed to examine the interaction of the vernier judgment with apparent motion failed to identify a role for mechanisms sensitive to apparent motion in threshold elevation. Another experiment in which the bars were modulated with sawtooth waveforms indicated that temporal correlation between the bars, rather than the ON versus OFF distinction, underlies the phase sensitivity. A simple dynamical model that posits partial rectification prior to a cross-correlation-like interaction accounts for the observed results.