Abstract

A set of algorithms is proposed for determining the first-order derivatives of a skew ray with respect to all the independent variables of an aspherical boundary surface in a general 3D optical system. Ellipsoidal, paraboloidal, hyperboloidal, and cylindrical boundary surfaces are given as examples. The proposed method has important applications in the analysis of aspherical surfaces and enables a detailed understanding of a wide variety of optical effects, including reflection and refraction, the modulation transfer function, and aberrations.

© 2012 Optical Society of America

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