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

Abstract

Using the Huygens-Fresnel principle the expressions for the intensity and the phase in Fresnel diffraction phenomena have been derived. The cases of spherical, cylindrical and plane scalar waves incident upon the plane diffraction screen have been investigated. The diffraction screen may consist of any number of parallel strips of different transmissivities and different phase shifts, the width of the individual strips being large compared with the wavelength. As special cases of the general formulae, the intensity and phase distributions in the diffraction patterns for the following forms of the diffraction screen have been calculated: opaque and partially transparent half-plane, slit, strip and double slit. By means of the derived expressions, the validity of Babinet's principle for Fresnel diffraction phenomena of this type has been verified.

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

“…If w > 0, the function O(w) does not differ from zero by more than 0-3 rad (see [15]) and thus, the first two terms in (25) are usually negligible compared to the third term. After inserting from (23), (14) and (19) into (25) the expression for ~ takes the form:…”

“…According to the previous part of the paper the disturbance Up is given by the sum of two disturbances: (a) of the disturbance U~I produced by diffracted wave ($1, hi), (b) of the disturbance Up~ produced by diffracted wave (Se, he). Using the results derived in [15] the disturbances Upt and Upz are given by,…”

“…The assumptions [15] under which the expressions in (1) and (2) These conditions (10) make it possible to perform the following simplifications :…”

“…§ 3. Substituting (20) into (15) we get the expression for the disturbance Up at a point of observation P(¢p, ~p, ~p) in the form :…”

“…(The properties (1), (2) and (3) can be seen, e.g., from [20], figures 8 and 9, [11], [10], figure 12, and from figures 11 and 12 of the present paper, the property (4) is described in [10], p. 362 and figure 15.) It is interesting to note that the properties (1) to (3) can be observed also in light optics in the interference patterns obtained in Fresnel bi-prism and mirrors experiments [2,3,13], and even there the explanation was unsatisfactory.…”