Ding J-J, Pei S-C
The Institute of Optics, University of Rochester, Rochester, New York 14627, USA.
J Opt Soc Am A Opt Image Sci Vis. 2011 Feb 1;28(2):82-95. doi: 10.1364/JOSAA.28.000082.
The two-dimensional (2D) nonseparable linear canonical transform (NSLCT) is a generalization of the fractional Fourier transform (FRFT) and the LCT. It is useful in signal analysis and optics. The eigenfunctions of both the FRFT and the LCT have been derived. In this paper, we extend the previous work and derive the eigenfunctions of the 2D NSLCT. Although the 2D NSLCT is very complicated and has 16 parameters, with the proposed methods, we can successfully find the eigenfunctions of the 2D NSLCT in all cases. Since many optical systems can be represented by the 2D NSLCT, our results are useful for analyzing the self-imaging phenomena of optical systems.
二维（2D）不可分离线性规范变换（NSLCT）是分数傅里叶变换（FRFT）和线性规范变换（LCT）的推广。它在信号分析和光学中很有用。FRFT和LCT的本征函数都已推导出来。在本文中，我们扩展了先前的工作并推导了二维NSLCT的本征函数。尽管二维NSLCT非常复杂且有16个参数，但通过所提出的方法，我们可以在所有情况下成功找到二维NSLCT的本征函数。由于许多光学系统可以用二维NSLCT来表示，我们的结果对于分析光学系统的自成像现象很有用。
