Abstract

Binocular visual space is, according to Luneburg, a hyperbolic space; two personal constants determine the geometry of subjective space of individual observers. Personal constants σ (the degree of depth perception) and K (the curvature of binocular space) were obtained by Luneburg’s 3 and 4 point tests and served as predictors for frontal plane horopter and alley experiments. In the result, the observed distances of the straight-line horopters agreed with values predicted within certain limits of confidence. The predictions concerning the shapes of concave and convex horopters and the shapes of alleys tended to hold in the case of observers of good depth perception and a relatively low absolute value of K. Three different alley experiments yielded values of personal constants agreeing with values obtained by the 3 and 4 point tests again only within certain limits of confidence. Good agreement with prediction for all observers was obtained from an alley experiment in which physiological and technical difficulties were reduced. While a study of the constancy of σ and improvement of experimental conditions are needed, the measure of agreement obtained in the experiments reported gives considerable support for the hypothesis that binocular visual space is metric and hyperbolic.

© 1956 Optical Society of America

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