Comparison of probability density functions for analyzing irradiance statistics due to atmospheric turbulence

Abstract

A large number of model probability density functions (PDFs) are used to analyze atmospheric scintillation statistics. We have analyzed scintillation data from two different experimental setups covering a range of scintillation strengths to determine which candidate model PDFs best describe the experimental data. The PDFs were fitted to the experimental data using the method of least squares. The root-mean-squared fitting error was used to monitor the goodness of fit. The results of the fitting were found to depend strongly on the scintillation strength. We find that the log normally modulated Rician and the log normal PDFs are the best fit to the experimental data over the range of scintillation strengths encountered.

Evaluating a linearized Euler equations model for strong turbulence effects on sound propagation

“…Most of these distributions can reproduce the known asymptotical distributions in the weak fluctuations regime (log-normal) and saturation regime (exponential). In this study only the GC distribution is evaluated because of its simple analytical expression (McLaren et al, 2012) and as the objective is to show the potential of the FDTD model in addressing this problem.…”

Probability density function estimation of laser light scintillation via Bayesian mixtures

“…A random variable that is inverse-gamma distributed is one whose reciprocal is gamma distributed. In this model, the base measure G 0 is defined as G 0 pϕ k pη k ; μ k ja; b; c pη k japμ k jb; c Expη k ; aInvGammaμ k ; b; c; (9) thus, the base measure G 0 is actually a product of two distributions Expη k ; aInvGammaμ k ; b; c. This construction casts the estimation of the PDF of the x n in a fully Bayesian context: only the x n are observed, the parameters fz n g n1∶N and fγ k ; V k ; η k ; μ k g k1∶K are all treated as latent random variables whose posterior distributions (and not simply an optimal value) are estimated during parameter inference. By estimating full posterior distributions on the model parameters, the Bayesian approach naturally quantifies uncertainty about the model parameters.…”

“…Traditionally, PDF estimates of laser light intensity in turbulent atmosphere are based on stochastic physics-driven models, heuristic concepts, or fitting via lower order moments of the data [9]. Several well-known and widely used examples of PDF estimation algorithms for laser light intensity include the gamma distribution [10], the gamma-gamma model [11], and the log-normal distribution [7].…”

“…Several well-known and widely used examples of PDF estimation algorithms for laser light intensity include the gamma distribution [10], the gamma-gamma model [11], and the log-normal distribution [7]. Significant ongoing research is devoted to the merits of the various approaches and is summarized well in a recent survey paper [9]. Physics-driven models and heuristic approaches are parametric in that they attempt to fit a distribution of known form to the observed scattered light, with goodness-of-fit assessed by computing the root mean square (RMS) error of the estimated PDF to a discrete histogram.…”

“…The primary approach to-date within the field of optics has been to compute the root mean square error between the estimated PDF at discrete points to a normalized frequency plot of the observations [6,9,29]. Such a metric is inherently dependent on and affected by the choice of bin widths used to construct the frequency plot.…”