Strong irradiance fluctuations in turbulent air, III Diffraction cutoff*

The theory of irradiance fluctuations of plane and spherical waves propagating through turbulent air is developed further to account for a saturation of the variance in the case where the Fresnel radius (L/k)1/2 exceeds the microscale l0. The crucial step is an expression for ray bending (excluding small eddies that cause diffraction effects) in the iterative solution of a set of nonlinear equations. Previous work was based upon a geometrical-optics expression, thus limiting the results to the case (L/k)1/2 < l0. The log-amplitude variance is found to be proportional to (Cn2k7/6L11/6)-1/6 in the saturation regime. The approximation also yields a log-amplitude covariance that appears to behave qualitatively as observed.