Theory of optical scintillation: Gaussian-beam wave model

Abstract

Under the assumption that small-scale irradiance fluctuations are modulated by large-scale irradiance fluctuations, we developed a heuristic model of irradiance fluctuations for a propagating optical wave in a weakly inhomogeneous medium. This model takes into account the loss of spatial coherence as the optical wave propagates through atmospheric turbulence by eliminating effects of certain turbulent scale sizes that exist between two scale size, hereafter called the upper bound and the lower bound. These mid-range scale size effects are eliminated through the formal introduction of spatial frequency filters that continually adjust spatial cutoff frequencies as the optical wave propagates. By applying a modification of the Rytov method that incorporates an amplitude spatial frequency filter function under strong fluctuation conditions, tractable expressions are developed for the scintillation index of a Gaussian beam wave that are valid under moderate- to-strong irradiance fluctuations. Inner scale effects are taken into account by use of a modified atmospheric spectrum that exhibits a bump at large spatial frequencies. We also include the effect of a finite outer scale in addition to inner scale.