Spatial Periodicities in Coherent and Partially Coherent Fields

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Abstract
The propagation of light in free space yields images of a certain class of objects. This effect, discovered 150 years ago by Talbot, is known as ‘self-imaging’. The self-imaging phenomenon, or the periodic properties of coherent and partially coherent fields, are described in this paper as eigenfunctions of the operator that represents the solution of the Helmholtz equation. Using this simple treatment, we state the necessary and sufficient conditions for self-imaging in coherent and partially coherent fields. We indicate that certain laterally aperiodical, partially coherent fields also exhibit self-imaging properties. Our treatment is exact, but it disregards evanescent waves.

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