Assuming subjects indeed fixated on the target, the average eccentricity when the finger came out of the occluder was 17 degrees and the average pedestal disparity was 114 arcmin (crossed), corresponding to a position approximately 2.8 cm nearer to the observer than the geometric horopter, though this varied from trial to trial with a standard deviation of 126 arcmin. Though stereoacuity values are highly dependent on the measurement method and stimuli, and there are no direct data available at said eccentricity and pedestal disparity, extrapolating one measurement (Howard & Rogers,
1995), the threshold disparity difference for depth discrimination would be expected to be above 400 arcmin. The stereo acuity is, thus, very low compared to the acuity of position judgments on the retina—approximately 51 arcmin at that eccentricity—computed using an estimated Weber fraction for position estimates of 0.05 (Burbeck,
1987; Burbeck & Yap,
1990; Whitaker & Latham,
1997). Because of the markedly low acuity of binocular disparities in the periphery, it would take longer for an optimal controller to integrate the disparity signals into its estimate of finger position, explaining why subjects responded slower and more weakly to the in-depth step perturbation than the in-image one. A similar difference in delay was observed by Brenner and Smeets (
2006) as well. An alternative explanation of the apparent difference in the delay for corrective responses is that the visual system takes longer to process information about depth than position signals in the retinal plane. Measurements of the time constant for integrating inputs from the two eyes for stereopsis (Ludwig, Pieper, & Lachnit,
2007; Ogle,
1963) put the latency of binocular depth processing in perceptual tasks at 50 ms to 100 ms, which could explain the observed differences in delay. However, a recent study found that the latency can be much lower, about 14 ms, in visuomotor tasks (Wilson, Pearson, Matheson, & Marotta,
2008). Since the two factors lead to similar effects on performance, we cannot sort out from the current data the relative contribution of each one to the difference in apparent delay.