On the Similarity between Object and Its Image

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.