Gaussian beam weak scintillation: low-order turbulence effects and applicability of the Rytov method

A generally applicable and computationally efficient description of random irradiance fluctuations induced by single scattering from distributed low-order turbulence (LOT) phase fluctuations is developed for Gaussian beams in the weak scintillation regime. The LOT solution describes irradiance statistics resulting from coarse beam irradiance fluctuations such as beam wander and beam breathing and will generally underestimate the true scintillation owing to the neglect of higher orders. For a subset of beam and turbulence settings that naturally result in non-log-normal irradiance behavior in the weak regime, the LOT solution closely approaches the exact solution and accurately describes the irradiance statistics for any point on the observation plane. For the same settings, beam-wave scintillation theory derived from the Rytov perturbation method yields inaccurate predictions owing to an inherent confinement to log-normal behavior. Examples that naturally exhibit non-log-normal irradiance behavior include focused beams on horizontal paths and collimated beams on ground-to-space paths. The complementary nature of the two scintillation theories (LOT and Rytov) enables a hybrid combination that yields accurate and convenient scintillation predictions for any case exhibiting weak scintillation regardless of irradiance behavior. Comparison of hybrid model predictions with wave optics simulation data reveals excellent agreement.