A heuristic model of irradiance fluctuations for a propagating optical wave in a weakly inhomogeneous medium is developed under the assumption that small-scale irradiance fluctuations are modulated by large-scale irradiance fluctuations of the wave. The upper bound for small turbulent cells is defined by the smallest cell size between the Fresnel zone and the transverse spatial coherence radius of the optical wave. A lower bound for large turbulent cells is defined by the largest cell size between the Fresnel zone and the scattering disk. In moderate-to-strong irradiance fluctuations, cell sizes between those defined by the spatial coherence radius and the scattering disk are eliminated through spatial-frequency filtering as a consequence of the propagation process. The resulting scintillation index from this theory has the form σ<sub>I</sub><sup>2</sup>=σ<sub>x</sub><sup>2</sup>+σ<sub>y</sub><sup>2</sup>+σ<sub>x</sub><sup>2</sup>σ<sub>y</sub><sup>2</sup>, where σ<sub>x</sub><sup>2</sup> denotes large-scale scintillation and σ<sub>y</sub><sup>2</sup> denotes small-scale scintillation. By means of 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 plane wave and a spherical wave that are valid under moderate-to-strong irradiance fluctuations. In many cases the models also compare well with conventional results in weak-fluctuation regimes. Inner-scale effects are taken into account by use of a modified atmospheric spectrum that exhibits a bump at large spatial frequencies. Quantitative values predicted by these models agree well with experimental and simulation data previously published. In addition to the scintillation index, expressions are also developed for the irradiance covariance function of a plane wave and a spherical wave, both of which have the form B<sub>I</sub>(ρ)=B<sub>x</sub>(ρ)+B<sub>y</sub>(ρ)+B<sub>x</sub>(ρ)B<sub>y</sub>(ρ), where B<sub>x</sub>(ρ) is the covariance function associated with large-scale fluctuations and B<sub>y</sub>(ρ) is the covariance function associated with small-scale fluctuations. In strong turbulence the derived covariance shows the characteristic two-scale behavior, in which the correlation length is determined by the spatial coherence radius of the field and the width of the long residual correlation tail is determined by the scattering disk.
© 1999 Optical Society of America
(010.0010) Atmospheric and oceanic optics : Atmospheric and oceanic optics
(010.1300) Atmospheric and oceanic optics : Atmospheric propagation
(030.0030) Coherence and statistical optics : Coherence and statistical optics
(030.7060) Coherence and statistical optics : Turbulence
L. C. Andrews, R. L. Phillips, C. Y. Hopen, and M. A. Al-Habash, "Theory of optical scintillation," J. Opt. Soc. Am. A 16, 1417-1429 (1999)