Σ-Separability of the far-field beam-pattern of an arbitrary excitation- function over an elliptical-rim aperture

This paper is first in the phase-mode analysis literature to analytically characterize the far-field azimuth-elevation beam-pattern due to any arbitrary excitation-function on a elliptical-rim aperture. The new findings include: Such an arbitrary excitation-functionpsilas far-field beam-pattern is not always phi-thetas separable. Nonetheless, this beam-pattern is Sigma-separable in the sense that it is a sum of phi-thetas separable terms.