Charnotskii Mikhail
J Opt Soc Am A Opt Image Sci Vis. 2015 Nov 1;32(11):1943-51. doi: 10.1364/JOSAA.32.001943.
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.
光束扩展和光束漂移是大气湍流对激光束传播最显著的影响。平均辐照度分布的宽度通常用于表征光束扩展。这种所谓的长期（LT）统计量允许进行相对简单的理论描述。然而，长期光束尺寸并不是光束扩展的一个非常实用的度量，因为其测量对光源和探测器的移动以及与湍流无关的折射率的大规模变化很敏感。短期（ST）光束扩展是相对于光束中心的瞬时位置进行测量的，并且没有这些缺点，但尚未像长期扩展那样得到充分研究。我们提出了一个基于随机介质中光束波传播的抛物方程以及用于计算光场统计量的马尔可夫近似的短期光束辐照度理论模型，并讨论了一种允许引入等晕短期点扩散函数（PSF）的近似方法。与长期PSF不同，短期PSF取决于整个光束几何形状。这允许在最小化观测平面处的短期光束尺寸方面优化初始光束场。针对相干高斯光束和柯尔莫哥洛夫湍流的简单情况给出了支持这一推测的计算结果。
