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Spline Functions: an Alternative Representation of Aspheric Surfaces

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Abstract

This paper offers an alternative to current practice in the specification of aspheric optical surfaces. Spline functions, a numerical analog of a flexible draftsman’s curve, are used to represent a rotationally symmetric aspheric surface. We develop the interpolation formulas pertinent to ray tracing and apply an optimization procedure to design a simple Schmidt system as an illustration. We conclude by showing that the new formulation seems to be more compatible with the optimization process than the usual polynomial aspheric.

© 1971 Optical Society of America

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