Fresnel zone approach to self-Fourier transforming.
The phenomenon of self-imaging and (in the case of coherent illumination) self-Fourier transforming was first observed over a century and a half ago. [H. Talbot, "Facts Relating to Optical Science NoIV.," Philos. Mag. 9,403-407 (1836).] There has since been a steady stream of publications in which the phenomenon has been noted and a theoretical analysis presented. Most noteworthy of these papers in recent years have been those by Kolodziejczyk, Kalestynski, and Smolinska. [A. Kolodziejczyk, "Realization of Fourier Images Without Using A Lens By Sampling The Optical Object," Opt. Acta. 32, 741-746 (1985); and A. Kalestynski and B. Smolinska, "Multiple Image Formation By Sampling Fraunhoffer Diffraction Patterns," Opt. Acta. 24,1115-1124 (1977).].
Willson
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