The Problem of Phase Retrieval in Light and Electron Microscopy of Strong Objects: III. Developments of methods for numerical solution

In this paper we will develop procedures for solving the system of non-linear Volterra integral equations, which describe the relations between the complex wave functions in the exit pupil and the Fourier transforms of two intensity distributions in the image plane, corresponding to two images of the same object taken at different values of the defocusing of the optical system. The first method reduces the Volterra integral equations to a finite system of linear algebraic equations which can be solved successively. The second algorithm is based on the Newton-Kantorovich approximation for functional equations, which gives a system of recurrence relations by means of which the Volterra equations can be solved.