Simulating paraxial optical systems using the linear canonical transform: properties, issues and applications

摘要

The linear canonical transform (also known as the quadratic phase integral and the special affine Fourier transform, among others) is an important tool for the modeling of quadratic phase systems for coherent optical signal processing, as it is a generalization of a number of important and widely used transforms such as the Fresnel transform, the Fourier transform and the fractional Fourier transform. We consider properties of the linear canonical transform which are important for numerical approximation of the integral transform, and thus for simulation of the related paraxial optical systems. Some of these properties have been previously developed in the literature, but are analyzed here in the context of linear canonical transform simulations, others are developed here for the first time. We examine these properties analytically, including how the support and bandwidth of the signal are related to transform parameters, a review of sampling issues and some new proposals in this area. Finally, we examine the effect of the linear canonical transform on the sparsity of signals, which is useful for efficient transmission or storage or to aid certain signal processing tools such as blind source separation.