Variance of irradiance for saturated scintillations*

A direct calculation of the normalized variance of irradiance for a beam wave of arbitrary aperture and focus in strong saturation employs a generalized function interpretation of the spherical-wave coherence function with the extended Huygens-Fresnel principle. The asymptotic limit is unity, and the limit of the probability distribution for the irradiance is exponential when the amplitude perturbation terms are neglected. Higher-order terms in the asymptotic series for a focused beam wave extend previously published results.