'Mental Holography': Stereograms Portraying Ambiguously Perceivable Surfaces

There are many limitations in portraying our three-dimensional environment on a two-dimensional surface. One of the primary shortcomings is the difficulty of effectively representing the hidden surfaces of objects together with the visible ones. Perspective drawings and even stereoscopic images did not alleviate this limitation. The cubist 2075 2076 T H E BELL SYSTEM TECHNICAL JOURNAL, DECEMBER 1968 artists tried to place the hidden surfaces of their objects side by side with the visible ones, but the results were rather confusing. The usual representation by multiple projections solves the problem geometrically yet it is very difficult to combine these projections into a unified spatial percept. The invention of panoramagrams using lenticular screens by Ives 1 and multiple lens arrays (fly's eye) by Lippmann 2 portrayed the three-dimensional objects within a wide angle, but in order to inspect some hidden surfaces the observer still has to move around the panoramagram. Furthermore, certain hidden surfaces (such as the boundaries of inside cavities of opaque objects) stayed invisible. Since holograms (invented by Gabor 3 and improved by Leith and Upatnieks) 4 are similar to panoramagrams only more simply made, some change in the geometry of the optical rays has to be initiated in order to obtain various stored organizations. This is usually achieved by the observer when inspecting the hologram from various angles. This article describes a method of generating ambiguously perceivable stereograms.