The transmission coefficient of elliptical and rectangular apertures for electromagnetic waves

A simple scalar method using Kirchhoff's boundary values is applied to the diffraction problems of circular, elliptical, and rectangular apertures for normally incident electromagnetic waves. As far as circular apertures are concerned, a simple formula can be derived not only for the diffraction pattern but also for the transmission coefficient. This formula yields good results for apertures greater than
0.8\lambda
. Even in the ease of elliptical apertures a simple formula can he derived for the diffraction pattern. For the elliptical aperture, as well as the rectangular one, the transmission coefficient was found in the form of an integral. Relief models and diagrams are given for the transmission coefficients of the elliptical and the rectangular apertures as a function of the two aperture parameters. Diagrams are given which explain the dependence of the transmission coefficient on the aperture parameters. A comparison with other more complicated methods of approximation and with measurements shows both good agreement and the great practical value of the simple method of approximation used.