空-频域中自成像分析和解释  

Analysis and explanation of self-imaging effect in spatial-frequency domain

作　　者：吕岑[1] 

机构地区：[1]陕西科技大学电气与信息工程学院,陕西西安710021

出　　处：《应用光学》2008年第1期152-155,共4页Journal of Applied Optics

基　　金：陕西科技大学基金资助(ZX05-42)

摘　　要：基于魏格纳变换和魏格纳分布函数,分析讨论一维物体在空域-频域空间的自成像及其形成过程。从成像过程中各衍射频谱分量的光程差出发,给出Talbot效应和Montgomery效应的统一解释。对于周期物的Talbot效应,得到了用杨氏双缝干涉解释自成像现象的理论依据。周期物的自成像是物平面上间距为2倍周期,光程差为波长的整数平方倍的各衍射频谱分量同相相干迭加的结果。Montgomery效应是物平面上间距为抛物线关系,光程差为波长整数倍的各衍射频谱分量同相相干迭加的结果。The self-imaging in spatial-frequency domain and its forming process are discussed, based on Weigner transform and distribution functions. A complete explanation for Talbot and Montgomery effect is presented by studying the optical path difference of each diffraction spectral component formed in the process of imaging. The theoretical basis, which can explain the self-imaging phenomenon with Yang＇s double-slit interference, was acquired. It is found that the self-imaging of a periodic object results from the same phase coherent overlap of various diffraction spectral components, whose space in object plane is twice the period and optical path difference is the square of integral multiple of wavelength. Montgomery effect is a result of the same phase coherent overlap of various diffraction spectrum components, which have a distance of parabolic relationship in the object plane and their optical path difference is the integral multiple of wavelength.

关 键 词：自成像 魏格纳分布函数 TALBOT效应 Montgomery效应 

分 类 号：O436.1[机械工程—光学工程]