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.
Predictions of scintillation for ground to space collimated Gaussian beams generated from a numerical wave optics simulation are compared with recent weak scintillation theory developed from the Rytov perturbation approach (L.Significant discrepancies are revealed for intermediate-sized beams, defined as beams whose initial diameters place the near ground turbulence in the transmitter near field and the remote space target in the transmitter far field. By adding wander tracking to the wave optics simulation, and by developing a separate analytic model of the beam wander scintillation mechanism, we show that the scintillation for intermediate-sized beams is dominated by turbulence-induced beam wander at the target, and that the results from the wave optics simulation are accurate. We conclude that the analytic theory's treatment of beam wander is incomplete, leading to the output of incorrect predictions for the second moment of irradiance. The error is most severe at the target point on the transmitter's optical axis.
Plane-wave scintillation is shown to impose multiconjugate adaptive optics (MCAO) correctability limitations that are independent of wavefront sensing and reconstruction. Residual phase and log-amplitude variances induced by scintillation in weak turbulence are derived using linear (diffraction-based) diffractive MCAO spatial filters or (diffraction-ignorant) geometric MCAO proportional gains as open-loop control parameters. In the case of Kolmogorov turbulence, expressions involving the Rytov variance and/or weighted C(2)(n) integrals apply. Differences in performance between diffractive MCAO and geometric MCAO resemble chromatic errors. Optimal corrections based on least squares imply irreducible performance limits that are validated by wave-optic simulations.
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