Image degradation with random wavefront tilt compensation

The perturbations on electromagnetic wavefronts resulting from the propagation of plane waves through a random medium are resolved into two components: a random tilt and a random residual phase perturbation. This analysis permits the determination of the mean square angle of arrival from knowledge of the aperture plane phase correlation. It also suggests the use of the statistics of the residual phase perturbation in calculations of resolution and of antenna power patterns. The mean square angle of arrival is calculated for linear and circular apertures with various exponential weightings using the description of phase statistics derived by Tatarski from the Obukhov-Kolmogorov theory of locally homogeneous turbulence. Integrals for tilt-compensated average power patterns are derived. It is demonstrated that a significant reduction in the image degradation results when the aperture tracks the random tilt of the wavefront.