First-order intensity and log-intensity probability density functions of light scattered by the turbulent atmosphere in terms of lower-order moments

The probability density function (PDF) of the scattered intensity is expressed in terms of the corresponding lower-order moments, whether measured or derived theoretically, assuming that the probability density is unimodal. The sought-for PDP is given by a gamma PDF modulated by a series of generalized Laguerre polynomials; the expansion coefficients are expressed in terms of the scattered-intensity moments with the nth coefficient containing only the first n moments. The Laguerre PDF is not a statistical fit to the data; there are no free parameters in this expansion, and the answer depends directly on the first n moments. The log-intensity PDF is also obtained from the lower-order intensity moments. Laboratory scattering experiments that employed light scattering from a photorefractive crystal (a problem formally similar to the turbulent-atmosphere scattering problem) were performed. The first five scattered-intensity moments were measured as well as the intensity histogram; with the exception of the behavior in the immediate vicinity of the maximum, the Laguerre PDF is in good agreement with the experimental data. The Dashen-Flatte approach to the theoretically derived moments by means of path integrals is also discussed in the context of the Laguerre PDF. (C) 1999 Optical Society of America [S0740-3232(99)01709-3] OCIS codes: 010.1310, 010.1.330, 010.7060.