Optimization using rational Bézier control points and weighting factors

Abstract

Optimization of traditional optical systems involves defining a merit function and a corresponding set of variables. The variables are changed to configure the optical system for optimum performance as required from the merit function. The typical variables used in lens design codes for designing classical optical systems are surface curvature, conic constant, aspheric coefficients, thickness, and refractive indices. The surface curvature, conic constant and aspheric coefficients are related directly to a polynomial equation representation of the surface. However, sometimes these variables are not the best choice for optimization especially in illumination system design where the required optical prescription is in the form of computer aided design (CAD) geometrical representation. As an alternative to these traditional variables, optimization using rational Bézier control points and weighting factors as variables is proposed and explored in this paper. Non-uniform rational B-splines (NURBs) using the Bézier basis are natural, graphical design curves exhibiting end-point interpolation whose interior control points and weighting factors are ideal variables for optical system optimization. Furthermore, optical designs created with NURBS are already in the language of CAD and numerical control machining environments and do not require the troublesome process of converting polynomial surfaces to their parametric representations.