Application of Mathematical Symmetrical Group Theory in the Creation Process of Digital Holograms

This work presents an algorithm to reduce the multiplicative computational complexity in the creation of digital holograms, where 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. The image is modeled using group theory. This algorithm has multiplicative complexity equal to zero and an additive complexity (k - 1)N-2 for the case of sparse matrices or binary images, where k is the number of pixels other than zero and N-2 is the total of points in the image.