Quadratic Bézier curve method for continuous freeform optical surface design

Abstract

A novel approach is introduced for the design of freeform axisymmetric optical surfaces using an optimization technique based on quadratic Bézier curves. Notably, the continuity (or lack thereof) of the freeform surface produced using the proposed technique is largely unaffected by the source-target mapping function. The validity of the proposed methodology is demonstrated through its application to the design of several laser beam shapers. The results show that the proposed technique requires only a small number of structural points to converge to the optimum design solution. The freeform design method presented herein is mathematically straightforward and can be easily implemented in code. Thus, it offers significant advantages for the design and analysis of a diverse range of optical systems.