SPATIAL CORRELATION OF PHASE-EXPANSION COEFFICIENTS FOR PROPAGATION THROUGH ATMOSPHERIC-TURBULENCE

Spatial correlation functions of phase-expansion coefficients for phase fluctuations of a wave that has propagated through a layer of atmospheric turbulence are derived. First, a general expression is derived giving the correlation of the coefficients phase-expansion functions orthogonal over an arbitrary circularly symmetric weighting function for an isotropic turbulence spectrum. Second, the correlations are evaluated analytically for a Gaussian weight and numerically for a uniform circular weight. Results applicable to ground-to-space propagation are obtained by integrating some of the correlations for a layer over the Hufnagel 1974 structure constant model.