Linear canonical transform sampling: analysis

摘要

A new sampling criterion for the linear canonical transform (LCT) was recently proposed by the authors. This criterion was based on an analysis of the consequences of sampling the LCT of a discrete signal. Previous LCT sampling work in the literature considered only sampling the LCT of continuous, band limited signals. This analysis has great significance for numerical simulations of first order optical systems using the LCT, as these simulations must necessarily consider a sampled input function, and evaluate only a sampled output function. It is also significant for the analysis of periodic structures such as gratings. We present a review of this new sampling criterion and the associated analysis. We clarifying its meaning and consider its applications. In particular, we consider the consequences of the analysis for fast LCT algorithms, and for the use of the discrete Fresnel transform in digital holography. We conclude that the spectral method of calculating Fresnel transforms may benefit greatly from recent advances to LCT sampling theory.