Y. S. Shifrin, V. V. Dolzhikov
Results of the analysis of mean field characteristics of a circular uniformly excited aperture antenna focused to the Fresnel zone under phase fluctuations in its aperture are given. The phase fluctuations are assumed to be described by the homogeneous over aperture function being random with the normal distribution and the zero mean. The correlation coefficient is assumed to be in the Gaussian form.
Expressions for angular and longitudinal (along the focal axis) distributions of mean field intensity being invariant with respect to the focal distance are obtained. Consequently, they are equally applicable when analyzing both the field of antennas focused to the Fresnel zone and when studying field statistics of ordinary (focused to infinity) antennas in their Fresnel and far zones.
Formulas are found for parameters characterizing a kind of these distributions: the main maximum location and value, the width of main lobe (focal spot) in longitudinal and transversal directions, spurious extreme locations and levels. Plots of these parameters versus the dispersion and correlation radius of phase fluctuations and position of focusing and observation are given. The results for the circular aperture antenna are compared with the analogous ones obtained by the authors for a linear antenna and for a square aperture antenna.
Appendix contains most complicated and bulky derivations of relations used in the work