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

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.