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Theorem of Mannheim, formerly of Damien

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Abstract

A curious monograph entitled "Théorème sur les Surfaces d’Onde en Optique Géométrique” appeared in Paris in 1955. The author R. Damien claimed a novel theorem. Given a point source, a refracting surface, and the associated anticaustic (i.e., the refracted wavefront of algebraic path difference zero) an inversion in a sphere with the source as pole interchanges the transforms of the refracting surface and the anticaustic. The inverse of the refracting surface becomes an anticaustic and vice versa. S. Cornbleet in "Microwave and Optical Ray Geometry" (1984) and elsewhere dwelt a good deal upon this remarkable theorem and named it in honor of Damien.

© 1991 Optical Society of America

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