## Abstract

Numerical simulation of propagation through atmospheric turbulence of an
initially spherical wave is used to calculate irradiance variance ${\text{\sigma}}_{I}^{2}$, variance of log irradiance ${\text{\sigma}}_{\text{ln}I}^{2}$, and mean of log irradiance 〈ln
*I*〉 for 13 values of
*l*
_{0}/*R _{F}* (i.e., of
turbulence inner scale

*l*

_{0}normalized by Fresnel scale

*R*) and 10 values of Rytov variance ${\text{\sigma}}_{\text{Rytov}}^{2}$, which is the irradiance variance, including the inner-scale effect, predicted by perturbation methods;

_{F}*l*

_{0}/

*R*was varied from 0 to 2.5 and ${\text{\sigma}}_{\text{Rytov}}^{2}$ from 0.06 to 5.0. The irradiance probability distribution function (PDF) and, hence, ${\text{\sigma}}_{I}^{2}$, ${\text{\sigma}}_{\text{ln}I}^{2}$, and 〈ln

_{F}*I*〉 are shown to depend on only two dimensionless parameters, such as

*l*

_{0}/

*R*and ${\text{\sigma}}_{\text{Rytov}}^{2}$. 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 ${\text{\sigma}}_{I}^{2}$. We find that ${\text{\sigma}}_{I}^{2}$, ${\text{\sigma}}_{\text{ln}I}^{2}$, and 〈ln

_{F}*I*〉 are larger than their weak-scintillation asymptotes (namely, ${\text{\sigma}}_{\text{Rytov}}^{2},{\text{\sigma}}_{\text{Rytov}}^{2}$, and $-{\text{\sigma}}_{\text{Rytov}}^{2}/2$, respectively) for the onset of strong scintillation for all

*l*

_{0}/

*R*. An exception is that for the largest

_{F}*l*

_{0}/

*R*, the onset of strong scintillation causes ${\text{\sigma}}_{\text{ln}I}^{2}$ to decrease relative to its weak-scintillation limit, ${\text{\sigma}}_{\text{Rytov}}^{2}$. We determine the efficacy of each of the three statistics for measurement of

_{F}*l*

_{0}, taking into account the relative difficulties of measuring each statistic. We find that measuring ${\text{\sigma}}_{I}^{2}$ 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 $1<{{\text{\beta}}_{0}}^{2}<3$ (where ${{\text{\beta}}_{0}}^{2}$ is ${\text{\sigma}}_{\text{Rytov}}^{2}$ 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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