Abstract

Experiments connected with Luneburg theory as developed by the author are analyzed with the purpose of making explicit their underlying assumptions. In particular, the role of ad hoc assumptions is explored in detail and minimized wherever possible. It is shown that the special assumptions under which much of the experimental work was executed may be considerably broadened thereby indicating how the theory may be more directly founded upon experiment. The principal problem is the determination of the sensory visual transformation between the geometry of the binocular perception and that of the stimulus, and, in particular, the determination of the visual radial distance function. Three principal techniques, the double circumhoropters, the Blumenfeld alleys, and the equipartitioned geodesics are discussed from this generalized point of view. The specific experimental material treated here consists of results obtained by Zajaczkowska, Shipley, and the Knapp Laboratory group at Columbia University. Some of these results appear for the first time. Theoretical material presented for the first time consists most notably of the analysis of the equipartitioned geodesics, the two-point experiments for the determination of Gaussian curvature, and the meta-theoretical discussions of the several experiments.

© 1958 Optical Society of America

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