Weak-scatterer generalization of the K-density function with application to laser scattering in atmospheric turbulence

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Abstract
The complex amplitude of scattered radiation at a point is modeled as a superposition of random amplitude, random phases, and random number of multipaths (or correlation areas) [see Eq. (2.1) ]. When the phases have uniform probability density (strong-scatterer regime) and the multipaths are governed by a negative binomial distribution, then Jakeman and Pusey [ Phys. Rev. Lett. 40, 546 ( 1978); IEEE Trans. Antennas Propag. AP-24, 806 ( 1976)] and associates have shown that the probability density of the intensity of the scattered radiation becomes K distributed as the average number of multipaths tends to infinity. This density function has the property that its normalized second moment is always greater than two. However, field measurements by Parry [ Opt. Acta 28, 715 ( 1981)] and Phillips and Andrews [ J. Opt. Soc. Am. 71, 1440 ( 1981); J. Opt. Soc. Am. 72, 864 ( 1982)] show that the normalized second moment can lie below two but must be greater than or equal to unity. The present paper is devoted to a generalization in which the phases are nonuniformly distributed (weak-scatterer regime) but the multipaths are still governed by the negative binomial distribution. In the limiting case, in which the average number of multipaths tends to infinity, the probability density of the scattered intensity is shown to be a generalization of the K-density function. This density function has the property that its second moment is greater than or equal to unity. Section 5 is devoted to the fit between this model and the Phillips–Andrews experimental data. Finally, the moments of the scattered intensity are evaluated when the average number of multipaths is finite.

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