Abstract

Numerical simulation of propagation through atmospheric turbulence of an initially spherical wave is used to calculate irradiance variance σI2, variance of log irradiance σlnI2, and mean of log irradiance 〈ln I〉 for 13 values of l 0/RF (i.e., of turbulence inner scale l 0 normalized by Fresnel scale RF) and 10 values of Rytov variance σRytov2, which is the irradiance variance, including the inner-scale effect, predicted by perturbation methods; l 0/RF was varied from 0 to 2.5 and σRytov2 from 0.06 to 5.0. The irradiance probability distribution function (PDF) and, hence, σI2, σlnI2, and 〈ln I〉 are shown to depend on only two dimensionless parameters, such as l 0/RF and σRytov2. Thus the effects of the onset of strong scintillation on the three statistics are characterized completely. Excellent agreement is obtained with previous simulations that calculated σI2. We find that σI2, σlnI2, and 〈ln I〉 are larger than their weak-scintillation asymptotes (namely, σRytov2,σRytov2, and σRytov2/2, respectively) for the onset of strong scintillation for all l 0/RF. An exception is that for the largest l 0/RF, the onset of strong scintillation causes σlnI2 to decrease relative to its weak-scintillation limit, σRytov2. We determine the efficacy of each of the three statistics for measurement of l 0, taking into account the relative difficulties of measuring each statistic. We find that measuring σI2 is most advantageous, although it is not the most sensitive to l 0 of the three statistics. All three statistics and, hence, the PDF become insensitive to l 0 for roughly 1<β02<3 (where β02 is σRytov2 for l 0 = 0); this is a condition for which retrieval of l 0 is problematic.

© 1996 Optical Society of America

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