Field fluctuations in the Fresnel zone of a circular focused aperture in the presence of phase errors

In this paper the field fluctuation of a circular aperture focused in the Fresnel zone caused by the phase errors of the aperture distribution is investigated. Analytic expressions for the amplitude and phase dispersions of the radiation field and also for the coordinates of the maximum of the field intensity are given. The relation between the amplitude and phase dispersions and the statistical parameters of the phase errors and also the focal distance are investigated. The presented results illustrate that the performance of an antenna in its Fresnel zone is notably limited by the phase errors of the aperture distribution.