Abstract

In this note, we apply the concept of dynamic programming to derive the eikonal equation from Fermat’s principle of least time for anisotropic media. The derivation for isotropic media was given by Kalaba and the result of the present paper is a natural extension of his treatment. The key to the derivation is Bellman’s principle of optimality, which is stated below. First, we derive the eikonal equation for isotropic media, for three dimensions, because Kalaba’s derivation was restricted to two dimensions. After this we establish the result for anisotropic media. We follow Kalaba’s derivation closely.

© 1974 Optical Society of America

Dynamic Programming, Fermat’s Principle, and the Eikonal Equation

Robert Kalaba
J. Opt. Soc. Am. 51(10) 1150-1151 (1961)

Fermat's principle, the general eikonal equation, and space geometry in a static anisotropic medium

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J. Opt. Soc. Am. A 14(10) 2850-2854 (1997)

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Optical Refraction and Fermat’s Principle at a Point*

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J. Opt. Soc. Am. 40(4) 244-245 (1950)

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