Spectral and angular covariance of scintillation for propagation in a randomly inhomogeneous medium

Based on a multiple transform approach, it is shown that it is possible to compute the statistics of propagation in a randomly inhomogeneous medium without invoking the small scattering angle approximation. This technique also makes it possible to compute the cross-statistics between two waves with different wavelengths or traveling in slightly different directions. The spectral covariance of log-amplitude and the spectral phase, and wave-structure functions are evaluated for horizontal propagation (i.e., for the statistics of turbulence not changing over the path). They are found to vary very slowly with separation of wavenumber. The angular covariance of log-amplitude and the angular-phase and wave-structure functions are formulated, but only the angular variance of log-amplitude is evaluated. It is found that the variance decreases very rapidly. Correlation only extends over an angular range of +/-0.2(4/zk)((1/2)), where z is the path length and k is the wavenumber. Comments concerning the application of these results to several problems are presented. These problems include: (1) the use of spectral diversity techniques in optical communications; (2) the possibility of turbulence garbling optical communications; (3) the cause of chromatic scintillation of stars; and (4) the scintillation and fading of laser illuminated targets, etc.