Multiple-image formation by Fresnel-Dirac sampling.
The theory of lensless formation of multiple images from a single object by Fresnel-Dirac sampling is reexamined. It is concluded that the multiple-image formation does not really occur in principle. However, reasonably good image arrays can be obtained if the sampling filter is properly designed. These image arrays appear when the reduced length Q satisfies the Montgomery zone-plate condition for self-imaging of a periodic grating. The explicit formula for the quasi multiple images is derived within the framework of the Fresnel diffraction. The results are to some extent different from those given previously in the literature. A simple interpretation of the results in terms of geometric optics confirms their acceptability.
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