Propagation of waves from an arbitrary shaped surface -- a generalization of the Fresnel diffraction integral
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.
Keywords
Cite
@article{arxiv.1706.09173,
title = {Propagation of waves from an arbitrary shaped surface -- a generalization of the Fresnel diffraction integral},
author = {R M Feshchenko and A V Vinogradov and I A Artyukov},
journal= {arXiv preprint arXiv:1706.09173},
year = {2018}
}
Comments
8 pages, 1 figure, accepted by Optics Communication