Chinese Journal of Lasers B, 1999, 8 (2): 167, 网络出版: 2006-08-08  

Wigner Transforms and Fractional Fourier Transforms of the First Order Optical Systems

Wigner Transforms and Fractional Fourier Transforms of the First Order Optical Systems
作者单位
Shanghai Institute of Optics and Fine Mechanics, the Chinese Academy of Sciences, Shanghai 201800, China
摘要
Abstract
Based on the Collins formula, the relationship between the coordinate transform matrix (WCTM) of the Wigner distribution function (WDF) and the ray transfer matrix (RTM) of an arbitrary first-order optical system has been derived. By using this relation and the definition of fractional Fourier transform (FRT) in terms of WDF rotation, it is concluded that an arbitrary first-order optical system can be generally decomposed into a thin lens and a FRT sub-system whose order is not unique and depends on two concrete decomposing operations on the system. And when the system is reciprocally symmetric, a FRT can be implemented by it. In addition, the composition, that is also the decomposition condition of the complicated FRT optical system by cascading a series of FRT subsystems has also been derived by using the operations of RTM.

LIU Zhongyong, FAN Dianyuan. Wigner Transforms and Fractional Fourier Transforms of the First Order Optical Systems[J]. Chinese Journal of Lasers B, 1999, 8(2): 167. LIU Zhongyong, FAN Dianyuan. Wigner Transforms and Fractional Fourier Transforms of the First Order Optical Systems[J]. 中国激光(英文版), 1999, 8(2): 167.

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