Intensity Distributions in Electron Interference Phenomena Produced by an Electrostatic Bi-prism

Abstract

The paper describes a model of electron interference obtained using an electrostatic bi-prism. The model is an approximation to the actual interference process, in which two diffracted waves, each representing the diffraction of electrons emerging from a single source by an opaque half-plane, are superposed in such a way that the half-planes are of opposite orientation and overlap by a distance equal to the width of the bi-prism filament. The intensity distribution in the interference pattern calculated according to the formula derived from this model is in an exact agreement with the intensity distribution found experimentally. This makes it possible to present a consistent quantitative explanation of all the special properties of the interference pattern, including intensity modulation of the fringes. The model may also serve for detailed interpretation of some interference phenomena in light optics, such as those observed with the help of Fresnel mirrors or a Fresnel bi-prism.

Interferometric methods for mapping static electric and magnetic fields

“…The justification for the use of the POA to describe the interaction between the electron beam and electromagnetic fields is based on knowledge gained from several case studies, some of which are now described briefly. By applying the POA to the electrostatic potential of an electron biprism, which can be described either as a cylindrical capacitor [5,6] or using the Septier model (as a thin electrically biased wire between two vertical planes) [7], T can be calculated in analytical form [8,9], revealing that the biprism splits the electron wavefunction and allows the coherent superposition of two half-waves, each of which describes the diffraction and refraction of the electrons, originating from a virtual point source, by an opaque half-plane [10]. Very good agreement between theoretical predictions and experimental measurements has been confirmed, both by older [10] and by more recent [11] experiments, suggesting that the POA is applicable in a situation where the (electric) field extends over several microns and its magnitude is on the order of a few kV/m.…”

Intensity and Phase in Fresnel Diffraction by a Plane Screen Consisting of Parallel Strips

“…light interference in Fresnel biprism and mirror experiments, or electron interference obtained by means of electrostatic or magnetostatic biprisms: A development of the idea expressed by the relation (39) makes possible the detailed interpretation of these phenomena, including the interpretation of modulation of the intensity of interference maxima and other details [13 ]. In the case of electron interference produced by an electrostatic biprism, the derived expressions for the intensity and the phase have been found to be in exact agreement with experiment [12,13].…”

“…Lately, however, it has been shown [12,13] that a knowledge of both the intensity and the phase is indispensable for a detailed interpretation of electron interference phenomena produced by an electiostatic biprism.…”

Progress in electron- and ion-interferometry

“…The developmental phase of electron interferometry was followed by one concerned with its application for measurement purposes and questions of purely fundamental interest: Fresnel diffraction by circular diaphragms, by Faget and Fert [24,25], determination of mean inner potentials [38] in solids, interference microscopy [39] or the phase shifts of electron waves by a magnetic flux [40][41][42] enclosed between the coherent beams were typical applications [43][44][45][46]78] in these early days. The Brno group, Komrska, Drahos, Delong and Vlachova, contributed a consistent theoretical interpretation of the electron interference phenomena produced by an electrostatic biprism and demonstrated the validity of their model by impressive experimental interference patterns [47][48][49][50].…”