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Mathematical Problems in Engineering
Volume 2017, Article ID 5612743, 7 pages
https://doi.org/10.1155/2017/5612743
Research Article

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

1Tecnologico de Monterrey, Escuela de Ingeniería y Ciencias, Autopista del Sol Km 104, Real del Puente, 62790 Xochitepec, MOR, Mexico
2Facultad de Ingeniería, Universidad Autónoma del Carmen, 24180 Ciudad del Carmen, CAM, Mexico
3CONACyT-Centro de Investigación en Matemáticas, 97205 Mérida, YUC, Mexico

Correspondence should be addressed to Rafael Sanchez-Lara; moc.liamg@racanuafar

Received 13 March 2017; Revised 7 June 2017; Accepted 20 June 2017; Published 31 July 2017

Academic Editor: Pasquale Memmolo

Copyright © 2017 Agustín Pérez-Ramírez et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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 for the case of sparse matrices or binary images, where is the number of pixels other than zero and is the total of points in the image.