Two-dimensional nonseparable linear canonical transform: sampling theorem and unitary discretization

作     者：Zhao, Liang Healy, John J. Sheridan, John T. 

作者机构：Univ Coll Dublin Sch Elect Elect & Commun Engn Coll Engn & Architecture Commun & Optoelect Res CtrSFI Strateg Res Cluste Dublin 4 Ireland Maynooth Univ Dept Elect Engn Maynooth Kildare Ireland 

出 版 物：《JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION》 (美国光学会志，A辑：光学、图象科学与视觉)

年 卷 期：2014年第31卷第12期

页      面：2631-2641页

核心收录：

学科分类：070207[理学-光学] 07[理学] 08[工学] 0803[工学-光学工程] 0702[理学-物理学] 

基　　金：UCD-China Scholarship Council (CSC) SPIE Optics and Photonics Education Scholarship National University of Ireland (NUI) Science Foundation Ireland Irish Research Council Enterprise Ireland under the National Development Plan 

主　　题：Numerical approximation and analysis ABCD transforms Digital holography Discrete optical signal processing 

摘      要：The two-dimensional (2D) nonseparable linear canonical transform (NS-LCT) is a unitary, linear integral transform that relates the input and output monochromatic, paraxial scalar wave fields of optical systems characterized by a 4 x 4 ray tracing matrix. In addition to the obvious generalizations of the 1D LCT (which are referred to as separable), the 2D-NS-LCT can represent a variety of nonaxially symmetric optical systems including the gyrator transform and image rotation. Unlike the 1D LCT, the numerical approximation of the 2D-NS-LCT has not yet received extensive attention in the literature. In this paper, (1) we develop a sampling theorem for the general 2D-NS-LCT which generalizes previously published sampling theorems for the 1D case and (2) we determine which sampling rates may be chosen to ensure that the obvious discrete transform is unitary. (C) 2014 Optical Society of America