Profiling the mirror surface from the Fraunhofer amplitude distribution that can be generated under coherent illumination

摘要

A procedure is proposed to profile the mirror surface needed to produce under coherent illumination, a pre-specified Fraunhofer amplitude distribution U(Ψ), The unknown optical path function O(x,y) in the diffraction integral is reconstructed from its stationary points {(xi,yi)}. The points {(xi,yi)} correspond to locations where the first Fresnel zone distribution F(x, y) is an extremum. The reconstruction utilizes the equivalence of the method-of stationary points and the method of Fresnel zones. In Fraunhofer diffraction, the F(x, y) has the functional distribution of the inverse Fourier transform of C7, We consider only Hermitian,U{t;, p)'s because they are generated by real F{x,y) distributions. The (fx,y) is deduced from the behaviour of its first derivatives, which are expressed as product series expansions of {(x,y.y,)}.1The path function