Symmetrical group theory for mathematical complexity reduction of digital holograms

Abstract

This work presents the use of mathematical group theory through an algorithm to reduce the multiplicative computational complexity in the process of creating digital holograms. An object is considered as a set of point sources using mathematical symmetry properties of both the core in the Fresnel integral and the image, where the image is modeled using group theory. This algorithm has multiplicative complexity equal to zero and an additive complexity (k − 1) × N for the case of sparse matrices and binary images, where k is the number of pixels other than zero and N is the total points in the image.