Two Evolutionary Approaches to Design Phase Plate for Tailoring Focal-Plane Irradiance Profile

Abstract

The goal is to design the 2-dimensional profile of an optical lens in order to control focal-plane irradiance of some laser beam. The numerical simulation of the irradiance of the beam through the lens, including some technological constraints on the correlation radius of the phase of the lens, involves two FFT computations, whose computational cost heavily depends on the chosen discretization.

A straightforward representation of a solution is that of a matrix of thicknesses, based on a N  x N (with N = 2^p) discretization of the lens. However, even though some technical simplifications allow us to reduce the size of that search space, its complexity increases quadratically with N, making physically realistic cases (e.g. N  ≥ 256) almost untractable (more than 2000 variables). An alternative representation is brought by GP parse trees, searching in some functional space: the genotype does not depend any more on the chosen discretization.

The implementation of both parametric representation (using ES algorithms) and functional approach (using “standard” GP) for the lens design problem are described. Both achieve good results compared to the state-of-the-art methods for small to medium values of the discretization parameter N (up to 256). Moreover, preliminary comparative results are presented between the two representations, and some counter-intuitive results are discussed.