Abstract:
A need for an optical transformation of coordinates arises in a number of problems of optical data processing, adaptive optics and reflecting antenna theory. For a plane element with (or without) a lens, this problem has been tackled in the paraxial approximation. This work demonstrates that, when the optical medium consists of two mirrors, under certain conditions the transformation problem has a solution outside the paraxial region. Explicit mirror equations are derived for the mirrors that realize any given transformation of coordinates. Application to reflecting antenna theory is also discussed.

References:

1. О. Bringdal. Avtometriya No. 2, 30 (1983).
   
2. A. E. Bereznyi and I. N. Sisakyan. Optical transformation of coordinates. In: Optical Recording and Data Processing. Kuibyshev (1981).
   
3. A. Gurvich and R. Kurant. Theory of Functions. Nauka, Moscow (1968).
   
4. F. Brickell and B. S. Westcott. Electron. Lett. 20, 588 (1984).

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