Spatial statistics of optical beams perturbed by aero-optical turbulence

We develop the spatial structure function (SSF) of the phase of an optical beam propagated through an aero-optically active turbulent boundary layer at a flying aircraft, which is characterized by anisotropic spatial fluctuations that arise from pressure fluctuations and are highly non-Kolmogoroff. We use the phase SSF to calculate in closed form the spatial statistics of a monochromatic Gaussian beam transmitted through such a turbulent layer and subsequently propagated in free space, discussing in particular the correlations of its amplitude and intensity fluctuations to arbitrary orders.