The two stimuli simulated in this paper are not the only ones in which interocular delay leads to a perception of depth, but they are those most often cited in support of the view that joint encoding of motion and depth is required to explain the Pulfrich effect. We believe that the principles of the explanation we develop here can account for depth perception in all other Pulfrich-like stimuli, without invoking space/time-inseparable binocular filters. This implies that there is currently no evidence suggesting a privileged role for joint encoding of motion and disparity in depth perception. Although space does not permit us to demonstrate the model's behavior to all possible variants of the Pulfrich effect, it is instructive to consider briefly one or two additional examples. (1) Applying interocular delay to dynamic random-dot stereograms results in a decrease in stereoacuity, with no shift in the point of subjective equivalence, on a forced-choice front/back discrimination task. Both features are predicted by the behavior of pure disparity sensors in V1; the decrease in stereoacuity with interocular delay agrees well with the binocular integration time estimated physiologically (Read & Cumming,
2005a). (2) Morgan & Ward (
1980) argued against Tyler's (
1977) disparity-averaging hypothesis based on a variant of the dynamic noise stimulus, in which dots moved horizontally for
n frames before being replaced by a new dot in a random position. They reported that perceived depth increases with
n. Many authorities still consider this compelling evidence in favor of joint motion disparity encoding. However, when one considers the changes that occur between any pair of frames in this stimulus, it is easy to see why our model accounts for the results equally well. On each frame only 100/
n% of the dots are replaced, whereas in a standard noise stimulus 100% of the dots are replaced on each frame. The dots that are not replaced move coherently and hence produce a spatial disparity as in the classic Pulfrich effect. The dots that are replaced behave just like the dynamic noise we simulated above. Thus, the stimulus of Morgan and Ward is a simple sum of a standard interocularly delayed noise stimulus (to which it reduces when
n=1) and a random-dot strobe Pulfrich stimulus (to which it asymptotes as
n→∞,
Figure 15). Morgan and Ward asked their subjects to match a probe to the depth of the dots. They do not report results for
n=1, but it seems clear that in this case, the matching depth must be zero because there is symmetry about fixation. Our own results with this stimulus confirm that interocular delay in zero-disparity noise does not bias depth perception (see
Figure 10 of Read & Cumming,
2005a). As
n increases above 1, the symmetry about fixation is broken, because there is now more power in horizontal motion to the right than in other directions. In terms of depth, this places more power at the virtual disparity (blue arrows in
Figure 15). It therefore does not seem surprising that the matching depth reported by Morgan and Ward's subjects moved away from zero towards this virtual disparity. For large
n, the matching disparity was equal to the virtual disparity implied by the apparent motion of the stimulus, as expected because the stimulus is now a strobe Pulfrich stimulus with a short interflash interval (25 ms) (Morgan,
1979; Read & Cumming,
2005b). Thus, the results of Morgan and Ward follow naturally from the percepts elicited by dynamic noise and the Pulfrich effect, both of which can be explained with separate motion/disparity encoding. We are not aware of any stimuli that require joint motion/disparity encoding to explain them.