MATLAB Example of GS Algorithm Implementation

This document provides a practical MATLAB implementation example of the Gerchberg-Saxton (GS) algorithm. The code demonstrates simulation of a circular halo structure and includes configurable parameters documented within MATLAB comments: - Halo radius parameter defining the circular structure dimensions - Halo width specification for thickness control - Refractive index of the halo material for optical property simulation - Light source positioning coordinates - Number of rays used in the simulation for accuracy control The GS algorithm implementation utilizes iterative Fourier transform operations between object and Fourier domains to achieve phase retrieval. Key MATLAB functions include fft2/ifft2 for Fourier transformations and array manipulations for constraint enforcement. The code structure allows modification to simulate different halo geometries by adapting parameter values and constraint definitions. Detailed inline comments provide guidance for algorithm customization and parameter adjustment to suit various optical simulation requirements.