This study was concerned with the manner in which perceived depth and perceived frontoparallel size varied with physical distance and hence with each other. An equation expressing the relation between perceived size and physical depth was developed and applied to size judgments determined with four observers under two viewing conditions. By use of that equation and an expression of the size-distance invariance hypothesis, an additional equation was developed which related perceived and physical depth. The additional equation, when applied to judgments of perceived depth from the same observers under the same viewing conditions, produced results not in agreement with those expected from the size-distance invariance hypothesis. This is interpreted as evidence against the validity of the size-distance invariance hypothesis in its usual form. The data from the apparent depth judgments also were applied to the problem of the discrepancies in results that have been found in experiments on the perceptual bisection of depth intervals.
WALTER C. GOGEL, "Visual Perception of Spatial Extent," J. Opt. Soc. Am. 54, 411-416 (1964)