Asymmetric Phase Error in Circular Apertures

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 ) = β r 2 and ξ( r ) = β r 3 , 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 u m , 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.