Exponentiated Weibull model for the irradiance probability density function of a laser beam propagating through atmospheric turbulence

Abstract

Many distributions have been proposed to model the probability density function of irradiance fluctuations. The most widespread models nowadays are the Lognormal (LN) and Gamma–Gamma (GG) distributions. Albeit these models comply with the actual PDF data most of the time, neither of them works in all scenarios and, depending on the conditions, one of the two have to be chosen. In this paper, a new model is presented resulting in the exponentiated Weibull (EW) distribution, along with a physical justification for the appearance of the model. Previously published data are used to compare the new model with the LN and GG distributions. Results suggest that the EW distribution is the better fit for data under all aperture averaging conditions and weak-to-strong turbulence regime.