Abstract

Numerical simulation of propagation through atmospheric turbulence of an initially spherical wave is used to calculate irradiance variance ${\text{σ}}_I^2$, variance of log irradiance ${\text{σ}}_{\text{ln}I}^2$, 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_F) and 10 values of Rytov variance ${\text{σ}}_{\text{Rytov}}^2$, which is the irradiance variance, including the inner-scale effect, predicted by perturbation methods; l ₀/R_F was varied from 0 to 2.5 and ${\text{σ}}_{\text{Rytov}}^2$ from 0.06 to 5.0. The irradiance probability distribution function (PDF) and, hence, ${\text{σ}}_I^2$, ${\text{σ}}_{\text{ln}I}^2$, and 〈ln I〉 are shown to depend on only two dimensionless parameters, such as l ₀/R_F and ${\text{σ}}_{\text{Rytov}}^2$. 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 ${\text{σ}}_I^2$. We find that ${\text{σ}}_I^2$, ${\text{σ}}_{\text{ln}I}^2$, and 〈ln I〉 are larger than their weak-scintillation asymptotes (namely, ${\text{σ}}_{\text{Rytov}}^2,{\text{σ}}_{\text{Rytov}}^2$, and $-{\text{σ}}_{\text{Rytov}}^2/2$, respectively) for the onset of strong scintillation for all l ₀/R_F. An exception is that for the largest l ₀/R_F, the onset of strong scintillation causes ${\text{σ}}_{\text{ln}I}^2$ to decrease relative to its weak-scintillation limit, ${\text{σ}}_{\text{Rytov}}^2$. 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 ${\text{σ}}_I^2$ 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 $1<{{\text{β}}_0}^2<3$ (where ${{\text{β}}_0}^2$ is ${\text{σ}}_{\text{Rytov}}^2$ for l ₀ = 0); this is a condition for which retrieval of l ₀ is problematic.

© 1996 Optical Society of America

Probability distribution of irradiance for the onset of strong scintillation

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Inner-scale effect on irradiance variance measured for weak-to-strong atmospheric scintillation

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