Phase retrieval with the transport of intensity equation. Part 2. Orthogonal series solution for non-uniform illumination

摘要

In this paper, the authors discuss the solution of the Transport of Intensity equation in the case of non-uniform intensity. The equation is solved using an approach based on Galerkin's method of orthogonal expansions. This technique also allows a matrix solution and, in the case of uniform illumination, the matrix is independent of the experimental data. However, this method also offers the advantage that separate boundary conditions are not required, as is the case with other methods. The discussion is primarily in terms of Zernike polynomials, however, it also discusses the approach using an expansion into Fourier harmonics which may have some substantial advantages given the availability of the fast Fourier Transform. 24 refs., 5 tabs., 4 figs. (Atomindex citation 27:020490)