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arXiv · 1706.09173

Propagation of waves from an arbitrary shaped surface -- a generalization of the Fresnel diffraction integral

R M Feshchenko·A V Vinogradov·I A Artyukov
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Abstract

Using the method of Laplace transform the field amplitude in the paraxial approximation is found in the two-dimensional free space using initial values of the amplitude specified on an arbitrary shaped monotonic curve. The obtained amplitude depends on one {\it a priori} unknown function, which can be found from a Volterra first kind integral equation. In a special case of field amplitude specified on a concave parabolic curve the exact solution is derived. Both solutions can be used to study the light propagation from arbitrary surfaces including grazing incidence X-ray mirrors. They can find applications in the analysis of coherent imaging problems of X-ray optics, in phase retrieval algorithms as well as in inverse problems in the cases when the initial field amplitude is sought on a curved surface.

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R M Feshchenko, A V Vinogradov, I A Artyukov. 2017-06-28. Propagation of waves from an arbitrary shaped surface -- a generalization of the Fresnel diffraction integral. https://doi.org/10.1016/j.optcom.2017.12.070

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