The radiation characteristics of a partially coherent illuminated antenna are found for both a circular aperture and a linear antenna. The antenna illumination function is assumed to be Gaussian, and the phase structure function in the plane of the antenna is assumed to be of the form

, with

, and 2. The beam broadening and reduction in gain in decibels are found to be of the form

, where

and

are functions of the antenna illumination and the "law" of the phase structure function, and

is a function of the "level" of the phase structure function.