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Illustration of the Use of Characteristic Functions in Lens Design

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Abstract

A method for investigating the image-forming characteristics of hypothetical optical systems by using Hamilton’s characteristic function, described previously, is applied to a simple optical system: the thick concentric single lens with media of equal refractive indices on either side of it. As a byproduct, the study yields a result that is surprising in view of well-known properties of the concentric lens: that, to a fifth-order approximation, a single lens of the kind described does exist, in theory, which sharply images a surface other than the aplanatic surface.

© 1967 Optical Society of America

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