Analysis of antennas with elliptical apertures using Fourier-Bessel expansion

The Fourier-Bessel expansion technique for elliptical apertures is described. The elliptical coordinate system is introduced and the radiation integral of a reflector antenna is expressed in terms of radial and angular Mathieu functions. However, the integrals can be simplified, and the final integrals are written in terms of Bessel functions only. An effort is also made to compare the Jacobi-Bessel expansion and Fourier-Bessel techniques and to find the convergence behaviors of both methods for various sizes and shapes of the elliptical aperture. The procedures discussed are also applicable to any elliptically shaped aperture-type antennas with known aperture distributions.<>