Dynamical Theory of Electron Diffraction for Finite Polyhedral Crystal III. Fresnel Diffraction Formula

Abstract

Following the first paper of the same title (J. Phys. Soc. Jap. 7 1952) 397), in which Bethe's dynamical theory of electron diffraction (Ann. d. Phys. Lpz. 87 (1928) 55) was extended to the case of finite polyhedral crystal and the general expressions of wave functions for transmitted and interfracted (=reflected by crystal net plane) wave were obtained, they have been rewritten in a form of the so-called Fresnel diffraction with the purpose that we might have better understanding of electron microscope images of crystallites. From these formulae, it is concluded that the striations due to “ Pendellosung ” are observed in the just-focused images of crystallites in which Bragg reflection occurs while in defocused image they are disturbed in the neighbourhood of a crystal edge by the Fresnel diffraction effect. In a special case where the parameter indicating the deviation from the Bragg condition is very large, the present formulation applies to the phase contrast fringes due to the edge of transparent wed...