Optimal beam focusing through turbulence.

Beam spread and beam wandering are the most perceptible effects of atmospheric turbulence on propagating laser beams. The width of the mean irradiance profile is typically used to characterize the beam spread. This so-called long-term (LT) statistic allows for a relatively simple theoretical description. However, the LT beam size is not a very practical measure of the beam spread because its measurements are sensitive to the movements of the source and detector, and to the large-scale variations of the refractive index that are not associated with turbulence. The short-term (ST) beam spread is measured relative to the instantaneous position of the beam center and is free of these drawbacks, but has not been studied as thoroughly as the LT spread. We present a theoretical model for the ST beam irradiance that is based on the parabolic equation for the beam wave propagation in random media, and the Markov approximation for calculation of the statistics of the optical field, and discuss an approximation that allows introduction of the isoplanatic ST point spread function (PSF). Unlike the LT PSF, the ST PSF depends on the overall beam geometry. This allows optimization of the initial beam field in terms of minimizing the ST beam size at the observation plane. Calculations supporting this conjecture are presented for the simple case of the coherent Gaussian beam, and Kolmogorov turbulence.