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Optica Acta International Journal of Optics

The Source Width and Its Influence on Interference Phenomena in a Fresnel Electron Bi-prism

V. Drahoš, A. Delong

Published Jul 1, 1964• 13 citations
Publisher

Abstract

Expressions for the dependence of interference fringes contrast in a Fresnel electron bi-prism on source width or virtual sources distance are stated in the first part of the paper. For given working conditions the influence of the virtual sources distance on interference fringes contrast at different source widths is given. First disappearance of the contrast at a constant source width is experimentally verified.

DOI
10.1080/713817876

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Expressions for the dependence of interference fringes contrast in a Fresnel electron bi-prism on source width or virtual sources distance are stated in the first part of the paper. For given working conditions the influence of the virtual sources distance on interference fringes contrast at different source widths is given. First disappearance of the contrast at a constant source width is experimentally verified.
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.
Is it possible to detect the interference from an extended incoherent source with Young's slits when the source-slits distance is such that all dimensions of the coherence area of the incident light beam are smaller than the distance between the slits? We have experimentally demonstrated that, under the above conditions, interference fringes can be obtained with a controlled degree of visibility by means of coincidence measurements between conujugated beams of the down-conversion luminescence.