An expression is derived for the intensity correlation function of a partially coherent beam wave of arbitrary size and focus propagating through weak atmospheric turbulence. Because the derivation employs the quadratic structure function (QSF) approximation, it describes only long-term beam-wander effects. Calculated covariance results agree well with measured data and substantiate the importance of beam-wander effects on focused beam statistics. Illustrative results show the effects of the phase deviation, size, and phase curvature of the source as well as the strength of turbulence and range. The weak-turbulence formulas are used to calculate strong-turbulence statistics by iterative recalculation of the coherence parameters of the beam in a succession of weakly turbulent path intervals. Successively calculated values of the beam-phase deviation and correlation length effectively provide wave-tilt correlation information that is missing in the original QSF approximation. The iterative solution for the normalized beam-intensity variance saturates and asymptotically approaches unity in a manner predicted by other theories. Calculated covariance functions also exhibit the initial rapid falloff and subsequent long coherence tail typical of saturated covariance behavior. Some magnitude discrepancies between calculated results and reported measurements are apparent for strong turbulence conditions. The iteration analysis predicts that log-amplitude fluctuations are diminished for increasingly strong turbulence and that saturated conditions arise solely from phase effects, in agreement with Fante’s conclusions [ R, L. Fante, Radio Sci. 15, 757 ( 1980)].
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