Antenna radiation characteristics with partially coherent illumination

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
cr^{\nu}
, with
\nu = 1, 5/3
, and 2. The beam broadening and reduction in gain in decibels are found to be of the form
Kb^{\alpha}
, where
K
and
\alpha
are functions of the antenna illumination and the "law" of the phase structure function, and
b
is a function of the "level" of the phase structure function.