级数为2/3的分数傅里叶变换的单透镜法光学实现及其验证  

Optical realization and validation of fractional Fourier transform with order of 2/3 utilizing one lens

作　　者：范希智[1] 祝霁洺[1] 

机构地区：[1]武汉理工大学物理系,湖北武汉430070

出　　处：《光学仪器》2011年第4期42-48,共7页Optical Instruments

摘　　要：对于级数为2/3的分数傅里叶光学变换,一种简单的实现方式是将物置于一个焦距为f的正薄透镜一侧f/2处,在透镜的另一侧的同距离处即得到该物的变换。为了验证其正确性,利用其可加性和周期性的性质,分别将3和6个这种2/3的分数傅里叶光学变换相加与傅里叶光学变换的4f和8f系统比较,观察到相同的输出结果,从而说明这种2/3分数傅里叶光学变换的实现方式是正确的。文中还说明了这种装置的优点。Abstract： For the fractional Fourier transform（frFT）with order of 2/3, its optical implementwas realized, namely when a object has been placed at one side of a positive lens of loci f with distance of f/2, its 2/3 frFT is at another side of the lens with same distance. To confirm the exactness, basing on frFT＇s additivity and periodicity, through the same actionrs observation, three and six 2/3 order frFTs were connected and contrasting with 4f and 8f optical system,respectively. The frFT＇s advantage was also given.

关 键 词：傅里叶变换 分数傅里叶变换 单透镜法 4f系统 8f系统 

分 类 号：O438.2[机械工程—光学工程]