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Optica Acta International Journal of Optics

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

Jiřı́ Komrska, V. Drahoš, A. Delong

Published Apr 1, 1967• 26 citations
Publisher

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.

DOI
10.1080/713818023

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Journal of Guangdong Polytechnic Normal University•Jan 1, 2015•0 citations
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.
The wave function describing the electron interference produced by an electrostatic biprism derived from the perturbation theory involves an integral which is not easy to evaluate numerically. Using the method of stationary phase it is shown in the paper that the expression of this integral in terms of the Fresnel integrals considerably facilitates the calculations. Physically this expression corresponds to the superposition of two waves emerging from two virtual images of the source diffracted by two opaque half-planes of opposite orientation. In such a way the model widely used for discussions of the interference of this type is justified.
Using the Fresnel–Kirchhoff integral, we express the state of the light that diffracts from an aperture to a point, by superposition of two or more waves. The amplitudes of the waves are determined by the distances of the point from the ray optics borders of the emerging beams. The interference approach to the Fresnel diffraction leads to a universal formulation of the normalized intensity distribution on the diffraction pattern that determines the state of the incident light, the parameters of the aperture, and its distance from the observation plane, uniquely. In the photon approach, according to the uncertainty principle, confining the position of a photon to an aperture changes the probable propagation direction of the photon in an interval that leads to the diffraction of the photon or light. Thus, the normalized intensity distribution on the diffraction pattern is the probability distribution of a photon. To this probability distribution, a probability amplitude distribution is associated that diffracts similar to a wave in Fresnel diffraction. Applying the introduced approach to the study of the diffraction, from different simple apertures and phase steps, we deduce general behaviors of the Fresnel diffraction and show it is involved in all aspects of light phenomena.
Diffraction patterns of electrons are believed to resemble those of electromagnetic waves (EMW). I performed a series of experiments invoked to show that the periodicity of peaks in the diffraction diagram of electrons is concerned with the periodicity of the arrangement of scattering centers in the diffraction grating in combination with the supposed character of the spatial structure of the electron as a system of regularly spaced concentric shells of elasticity. I started from the experiment on the diffraction of electrons and EMWs at the sharp edge of the opaque half-plane. This simple scattering configuration enabled me to discriminate between the re-radiation mechanism of the wave diffraction and ricochet scattering of electrons on the edge of the half-plane. Then I made experiments with scattering on composite objects proceeding step by step from a single straight edge to a couple of edges (one slit) and then to four edges (two slits). Thus I succeeded in interpretation of the double-slit diffraction (four straight edges) in terms of the scattering on a single edge. I managed also to observe the electron's trajectory. Equipping the slit's edge with a semiconductor sensors I registered the passing of the electron through the slit detecting simultaneously a weaker signal at another slit. This technique appeared not to destroy or disturb the "interference" pattern. Closing one slit by inserting therein a transparent for EMWs piece of dielectric I have found that the scattering pattern beneath this slit vanishes while the scattering pattern under the open slit remains as before when both slits were open. This experiment indicates that the electron "interferes" with its electromagnetic component passed via the slit plugged by the transparent for it dielectric.
Considering double-slit interference as an optical wave passing a through double-slit hard aperture, the intensity expression of Young's double-slit interference is derived based on Collins diffraction integral. The intensity distribution of Young's double-slit interference is graphically demonstrated. The interference fringes will be changes by adjusting the parameter of slit width, double-slit separation, incident wavelength, etc. Meanwhile, the causes for the different brightness at bright fringe center in Young's double-slit interference are discussed. Additionally, the interference fringe width is calculated. The result agrees well with optical interference theory. As an expanding teach method, it will be helpful to understand the double-slit interference characteristics.