On the Similarity between Object and Its Image

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Abstract
In this paper the problem of similarity between an optical object and its image for imaging with partially coherent quasi-monochromatic light according to the nth-order correlation is formulated. This problem leads to a non-linear homogeneous integral equation which is studied as a special case of algebraic integral equations or, on the other hand, by the method of successive approximation. It is shown that under certain assumptions there exists at most a countably infinite set of structures imaged similarly. Only a finite number of structures can be imaged similarly with sufficiently large intensity.

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