Fresnel Diffraction of Electrons by a Filament

Abstract Expressions for calculating the electron diffraction phenomena by a filament and at half-plane have been derived using the Huygens-Fresnel principle. It is shown that approximations usual in light optics for the calculation of Fresnel diffraction phenomena are justified also for electron optics. The intensity distributions in the diffraction pattern for various filament diameters and a half-plane have been calculated. It is demonstrated to what extent at different filament diameters the approximation of the two symmetrical parts of the diffraction pattern by the diffraction at a half-plane is admissible. Also, the intensity distribution in the zone of geometrical shadow as approximated by the interference from two straight line sources placed at the edges of the filament is discussed. Experiments are in good agreement with the theory for both the diffraction by a filament and by a half-plane.