Electron Ptychography. II. Theory of Three-Dimensional Propagation Effects

The interpretation of image reconstructions obtained by ptychography in a scanning transmission electron microscope (STEM) is investigated. In this technique, a number of coherent electron diffraction patterns are obtained from adjacent points of a crystalline sample by scanning a focused electron beam. The phase problem is solved by using an interference phenomenon, thus obtaining a very high resolution (0.136 nm) reconstruction of the specimen. Simulations presented here assist experiments described in a previous paper [Nellist & Rodenburg (1998). Acta Cryst. A54, 49-60]. In this paper, the simulation method which is best suited for the calculation of ptychographical reconstructions for perfect crystals is described. Simulation results are presented for the simplest case of diffraction beams with single overlap and it is shown that the reconstruction does not match the exit-surface wave function for axial plane-wave illumination but instead resembles the image wave function with a fixed focus setting on the middle section of the specimen. A second reconstruction method is described, in which a greater angular diameter of the aperture is used and every beam is re-interfered with the central beam. The variation of the amplitude and phase of all reconstructed beams with crystal thickness is very similar up to a thickness of about 25 nm. It is argued that such a simple relationship can only be expected for projected structures containing identical atomic columns.