Onset of strong scintillation with application to remote sensing of turbulence inner scale

Numerical simulation of propagation through atmospheric turbulence of an initially spherical wave is used to calculate irradiance variance sigma(I)(2), variance of log irradiance sigma(lnI)(2), and mean of log irradiance (In 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 sigma(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 sigma(Rytov)(2) from 0.06 to 5.0. The irradiance Rytov probability distribution function (PDF) and, hence, sigma(I)(2), sigma(lnI)(2), and (In I) are shown to depend on only two 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 sigma(I)(2). We find that sigma(I)(2), sigma(lnI)(2), and (In I) are larger than their weak-scintillation asymptotes (namely, sigma(Rytov)(2), sigma(Rytov)(2) and - sigma(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 sigma(lnI)(2) to decrease relative to its weak-scintillation limit, sigma(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 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 < beta(0)(2) < 3 (where beta(0)(2) is sigma(Rytov)(2) for l(0) = 0); this is a condition for which retrieval of l(0) is problematic. (C) 1996 Optical Society of America