1 August 2001 Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media
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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 independent gamma distributions. The resulting irradiance pdf takes the form of a generalized Kdistribution 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 Cn2 (or Rytov variance) and inner scale l0 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 turbulence conditions (weak to strong) that includes inner scale effects. The gamma-gamma pdf is found to generally provide a good fit to the simulation data in nearly all cases tested.
Ammar Al-Habash, Larry C. Andrews, R. L. Phillips, "Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media," Optical Engineering 40(8), (1 August 2001). https://doi.org/10.1117/1.1386641
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