Shaped reflector antenna analysis using the Jacobi-Bessel series

TLDR

The authors propose a novel method to express the radiation integral of a doubly curved offset reflector as a sum of Fourier transforms of an effective aperture that incorporates surface curvature. Using physical optics, the authors derive the radiation integral for a doubly curved offset reflector illuminated by any source, then evaluate its Fourier transforms via a Jacobi‑Bessel series and compute all three Cartesian far‑field components in a unified manner. Extensive numerical tests confirm rapid evaluation of the derived expressions and reveal detailed scattering characteristics of symmetric and offset parabolic, spherical, and shaped reflectors, with comparisons to existing data.

Abstract

The physical optics approximation is employed to derive the radiation integral for a doubly curved offset reflector antenna illuminated by an arbitrary source. A novel procedure is presented for expressing the radiation integral in terms of a summation of Fourier transforms of an "effective" aperture distribution which includes the effect of the curvature of the surface. The Jacobi-Bessel series is used to evaluate the Fourier transforms. The vector nature of the far-field pattern is studied by evaluating its three Cartesian components in a unified fashion. The rapid numerical evaluations of the expressions obtained are demonstrated via extensive test cases. In particular, the scattering characteristics of symmetric and offset parabolic, spherical, and shaped reflectors are studied in detail, and comparisons are made with other available data.