自成像魏格纳函数分析

Analysis of Self-Imaging Effect with Wigner Function

在空域-频域空间,基于魏格纳变换和魏格纳分布函数,分析讨论了一维物体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,给出了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两倍周期、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 and process is discussed in spatial-frequency domain using Wigner transform function. Unified explanation of the effects due to Talbot and Montgomery effect is presented in optical path difference between diffraction spatial frequency spectrums. The theory warrant is found, that how it can explanation the self-imaging phenomenon using Yang＇s double slit interference. The self-imaging of a period object is the interference result of the diffraction spatial frequency spectrums, which space between in object planar is two periods and optical path difference are integer＇s square of wavelength. The Montgomery effect is also, but which space between in object planar is parabola function of the order of the spectrums and optical path difference are integers of wavelength.