"Weber's law" for position: the role of spatial frequency and contrast

We used Gabor bars to measure the effects of spatial bandwidth, spatial scale, contrast and separation on three-line spatial interval discrimination (bisection). In the first experiment, we used stimuli that were well above threshold. Our results show that at all spatial scales, spatial interval discrimination (three-line bisection) thresholds are proportional to the separation of the Gabor patches (i.e. Weber's law) when the separation exceeds approximately 2.5 times the standard deviation (sigma) of the Gaussian envelope. The optimal threshold occurs when the separation is approx. 2-2.5 sigma, and for separations larger than the optimal, bisection thresholds are equal to a more or less constant Weber fraction (delta s/s) of approx. 0.02-0.04. These results are consistent with a number of previous studies. In the second experiment, we examined the effect of contrast. Our results show an interaction between separation and stimulus visibility. Reducing the stimulus contrast has a marked effect on spatial interval thresholds at small separations (e.g. separations less than about 3 sigma), and much less effect at larger separations. Thus, the Weber's law relationship appears to depend on the visibility of the stimuli, but does not depend on the spatial frequency or bandwidth of the stimuli. These results can be predicted by an ideal observer model of spatial interval discrimination.