Spline functions: an alternative representation of aspheric surfaces.

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.