Theory of saturation of optical scintillation by strong turbulence: plane-wave variance and covariance and spherical-wave covariance

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Abstract
The heuristic theory of covariance of log amplitude for saturation of scintillation, which was originally developed for spherical waves, is extended to the plane-wave case. Comparison of calculated log-amplitude variance of plane waves with observation is good, but measurements of this specific quantity are scarce. For strong refractive turbulence, the log-amplitude variance tends to increase as the inner scale of turbulence increases relative to the Fresnel-zone size; for spherical waves this behavior is in quantitative agreement with data. In strong turbulence the path-weighting functions of the log-amplitude variance tend to be uniform with localized peaks near the transmitter and receiver for spherical waves but only one localized peak near the receiver for plane waves. The dependence of the log-amplitude covariance on a minimum number of nondimensional parameters is found (similarity relationships), and this set of parameters is shown to be nonunique. The specialization of this parameter set to the case of strong refractive turbulence reveals important differences between cases in which the coherence length ρ0 is larger as opposed to smaller than the inner scale l0. In strong refractive turbulence the covariance function has three distinct ranges: at sufficiently large separations it has the same form as in the weak refractive-turbulence limit, at intermediate separations it is nearly independent of the separation, and at small separations r it rises sharply. For ρ0 ≫ l0, the conventional strong-turbulence result of covariance depending only on r/ρ0 is obtained, but for ρ0 ≪ l0 the covariance depends on both r/ρ0 and ρ0/l0. The lack of scaling of measured intensity covariance with r/ρ0 corresponds to the case ρ0 ≪ l0. There is no reason to prefer the transverse scale (k3Cn2)−3/11 to ρ0 for ρ0 ≫ l0, and there is no reason for using this transverse scale for ρ0 ≪ l0 because of the strong inner-scale effect on the covariance.