Abstract

Analytical results are found for irradiance statistics of a plane wave propagating through uniformly turbulent air. They result from a new error analysis of approximations made in selective summation of diagram contributions to the iterated moment equations (in integral form). The results are determined by three regimes of the parameter k7/6L11/6Cn2 determined by its location with respect to powers of the micro- and macroscale Fresnel numbers (κm2L/k)1/60.3 and (kL02/L)104 (the numerical values are for 0.6-μm radiation and a horizontal pathlength L ∾ 1 km). The modified-Rytov result is found in the lowest regime. Irradiance I is log-normal in the intermediate (saturation) regime and the log-amplitude variance decays asymptotically as 0.41 (κm7/3L3Cn2)1/6. When k7/6L11/6Cn2 far exceeds the macroscale Fresnel number kL02/L, the irradiance tends to an exponential distribution (in agreement with previous results).

© 1973 Optical Society of America

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