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

Abstract

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.

Two-frequency analysis of interactions elicited by Vernier stimuli

“…As reported here, the Vernier displacements required to produce a significant change in the observed interactions was typically 4 min or more ( Fig. 6), beyond the hyperacuity range and the psychophysical thresholds for these stimuli (Ͻ 0.5 min, Victor & Conte, 1999a). The size of this displacement corresponds to a rotation of the center-to-center line of the bars with respect to their horizontal axis by 4 deg.…”

“…from the two bars, then multiplicative combination would generate even-parity mixed responses A~2,2!, but not the odd-parity mixed responses. Based on psychophysical studies, Victor and Conte (1999a) proposed a model to account for the dependence of Vernier threshold on stimulus dynamics, consisting of local processing followed by a productlike interaction across space. We showed that inclusion of partial rectification in the local processing stage was necessary to account for the dependence of Vernier threshold on relative phase and temporal frequency.…”

“…By examining how the VEP depended on the Vernier offset between the two bars and on colinear displacements across a gap, the specificity of the interaction for Vernier offsets could be assayed. By examining the characteristics of the Fourier components elicited by these stimuli, dynamical models (Victor & Conte, 1999a) for the interactions underlying Vernier acuity could be tested. Fig.…”

“…It is composed of a regular array of Vernier targets, each consisting of two bars. Across their width, the bars had a Gaussian profile, so that subpixel vertical displacements d could be produced (Krauskopf & Farell, 1991;Victor & Conte, 1999a). We used six such vertical displacements d (0, 0.5, 1, 2, 4, or 8 min), as diagrammed in Fig.…”

Temporal phase discrimination depends critically on separation

“…This strong polarity dependence falls off markedly when stimuli are separated by a gap (Levi, Jiang, & Klein, 1990;O'Shea & Mitchell, 1990;Waugh & Levi, 1993). An analogous observation holds for sinusoidally luminance-modulated vernier targets: there is a strong dependence of displacement thresholds on temporal phase when stimuli are abutting (Victor & Conte, 1999), but nearly no dependence with separations as small as 8 min (Victor & Conte, 2000a).…”