Magnitude of perceived depth of multiple stereo transparent surfaces

According to the geometric relational expression of binocular stereopsis, for a given viewing distance the magnitude of the perceived depth of objects would be the same, as long as the disparity magnitudes were the same. However, we found that this is not necessarily the case for random-dot stereograms that depict parallel, overlapping, transparent stereoscopic surfaces (POTS). The data from five experiments indicated that (1) the magnitude of perceived depth between the two outer surfaces of a three- or a four-POTS configuration can be smaller than that for an identical pair of stereo surfaces of a two-POTS configuration for the range of disparities that we used (5.2-19.4 arcmin); (2) this phenomenon can be observed irrespective of the total dot density of a POTS configuration, at least for the range that we used (1.1-3.3 dots/deg(2)); and (3) the magnitude of perceived depth between the two outer surfaces of a POTS configuration can be reduced as the total number of stereo surfaces is increased, up to four surfaces. We explained these results in terms of a higher-order process or processes, with an output representing perceived depth magnitude, which is weakened when the number of its surfaces is increased.