Composite method for precise freeform optical beam shaping

We present a composite freeform SURFACE construction method for creating a high-accuracy irradiance distribution from a given incident beam under the influence of diffraction. The main idea is that we first determine a fully continuous freeform surface estimate by solving a standard Monge-Ampère equation and then refine it using an iterative Fourier-transform algorithm associated with over-compensation. Although this method can only be implemented in the paraxial approximation, it can significantly simplify the design and is applicable to many examples that fulfill this restriction. The resulting optical surface, unwrapped from the final phase, is an unusual discontinuous freeform surface that can produce very promising performances in terms of surface roughness and irradiance accuracy.