Unitary rotation and gyration of pixelated images on rectangular screens

摘要

In the two space dimensions of screens in optical systems, rotations, gyrations, and fractional Fourier transformations form the Fourier subgroup of the symplectic group of linear canonical transformations: U(2)(F) subset of Sp(4,R). Here, we study the action of this Fourier group on pixelated images within generic rectangular N-x x N-y screens; its elements here compose properly and act unitarily, i.e., without loss of information. (C) 2016 Optical Society of America