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Factorization of the phase-space transformation produced by an arbitrary refracting surface

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Abstract

We study the transformation produced on optical phase space by an arbitrary refracting surface. We show that this factorizes into two root canonical transformations, one representing the propagation from a reference plane to the refracting surface in the first medium, and the other, the inverse propagation back to the reference surface in the second medium. This factorization allows for a simple parameterization of the effect of a refracting surface to some aberration order, illustrated for cubic surfaces and Dragt’s Lie-algebraic description of a quartic surface and its Seidel aberration coefficients.

© 1986 Optical Society of America

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