The Problem of Phase Retrieval in Light and Electron Microscopy of Strong Objects: IV. Checking of algorithms by means of simulated objects

In this paper we will present numerical results of the reconstruction of the wave function P(ξ) in the exit pupil from two intensity distributions in the image plane, corresponding to two exposures taken at different values of the defocusing of the microscope. In [7] we reduced the relation between the image intensities and P(ξ) to a system of non-linear Volterra integral equations, which can be solved uniquely [1, 2]. We will show the computations for an imaging process with one transverse spatial dimension. We use for the reconstruction procedures two algorithms, developed in [3]. The first method, the so-called direct method, gives for two simulated examples a correct solution for both examples. For the second algorithm, the Newton-Kantorovich approximation, we also find the correct solution for the wave function in the exit pupil. However, the direct method is by a factor of about 800 faster than the Newton-Kantorovich approximation.