Asymmetric Phase Error in Circular Apertures

Abstract

The diffraction pattern of a circular aperture is determined under the condition that the aperture phase function is ξ(r) cos ф′, where (r, ф′) are polar coordinates in the aperture and function ξ(r) defines the radial variation of phase. The asymmetric phase error causes beam squint and distortion of the radiation pattern. The diffraction pattern is calculated by computer methods assuming ξ(r) = βr2 and ξ(r) = βr3, where β = 0, π/4, and π/2 rad. The edge taper of the aperture field is specified as 0 db, ‐12 db, and ‐20 db. An integral formula is derived for calculating um, the position of the pattern maximum. The analysis is used to determine the beam squint of a satellite‐mounted reflector antenna that undergoes asymmetric distortion in the space environment.