Optimal scale factors for Gaussian field expansions for a circular aperture

Gaussian field expansions for circular aperture antennas are reviewed, and a method for finding optimal scales in these expansions is given, paralleling the method for rectangular antennas presented in an earlier paper. This procedure is shown to lead to approximations structured in the sense that the number of lobes in the approximation corresponds to the number of terms retained in the expansion. An example is given of the development of a cosine distribution from the aperture, through the Fresnel region, to the far field.