Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media

TLDR

The irradiance fluctuations of optical waves in turbulence are modeled by a two‑parameter distribution derived from a doubly stochastic scintillation theory, where small‑scale fluctuations are modulated by large‑scale gamma‑distributed variations. We develop a model for the probability density function of the irradiance fluctuations of an optical wave propagating through a turbulent medium. The resulting irradiance pdf is a generalized K distribution, termed the gamma‑gamma distribution, whose two parameters are obtained from a recent scintillation theory using only the refractive‑index structure parameter Cn (or Rytov variance) and inner scale l0, enabling direct calculation of log‑irradiance moments and comparison with plane‑wave and spherical‑wave simulation data across weak to strong turbulence with inner‑scale effects. The gamma‑gamma pdf generally fits the simulation data well in nearly all tested turbulence conditions. © 2001 Society of Photo‑Optical Instruments.

Abstract

We develop a model for the probability density function (pdf) of the irradiance fluctuations of an optical wave propagating through a turbulent medium. The model is a two-parameter distribution that is based on a doubly stochastic theory of scintillation that assumes that small-scale irradiance fluctuations are modulated by large-scale irradi- ance fluctuations of the propagating wave, both governed by indepen- dent gamma distributions. The resulting irradiance pdf takes the form of a generalized K distribution that we term the gamma-gamma distribution. The two parameters of the gamma-gamma pdf are determined using a recently published theory of scintillation, using only values of the refractive-index structure parameter C n (or Rytov variance) and inner scale l 0 provided with the simulation data. This enables us to directly calculate various log-irradiance moments that are necessary in the scaled plots. We make a number of comparisons with published plane wave and spherical wave simulation data over a wide range of turbu- lence conditions (weak to strong) that includes inner scale effects. The gamma-gamma pdf is found to generally provide a good fit to the simu- lation data in nearly all cases tested. © 2001 Society of Photo-Optical Instrumen-