Dan Youquan, Zeng Shuguang, Hao Bangyuan, Zhang Bin
College of Electronics Information, Sichuan University, ChengDu 610064, Sichuan, China.
J Opt Soc Am A Opt Image Sci Vis. 2010 Mar 1;27(3):426-34. doi: 10.1364/JOSAA.27.000426.
Two characteristic distances for partially coherent beams propagating in atmospheric turbulence have been proposed. The turbulent Rayleigh range is used for characterizing the range over which the beams propagate in turbulence without spreading appreciably; i.e., the concept of the well-known Rayleigh range in free space is extended to the case of turbulence. In this paper the range of turbulence-independent propagation of the beams, in contrast to similar characteristic distances in previous published works, is based on the formula of the beam propagation factor (M(2) factor) and is used for describing the range over which the spatial and angular spreading and the M(2) factor increase due to turbulence are sufficiently small and negligible. Several simple formulas used for calculating the approximate values of these distances are given, and the formulas are applied to Gaussian Schell-model (GSM) beams and illustrated by examples. Furthermore, as a typical example, the effect of the angular spread of GSM beams in turbulence on a thin-lens optical system is also discussed. We show that the turbulent Rayleigh range depends on the Rayleigh range in free space, the waist width, and the spatial power spectrum of the refractive-index fluctuations of the turbulent atmosphere, and that the range of turbulence-independent propagation depends on the waist width, the initial angular spread in the waist plane, and the spatial power spectrum.
已提出了部分相干光束在大气湍流中传播的两个特征距离。湍流瑞利范围用于表征光束在湍流中传播且不发生明显扩展的范围；也就是说，将自由空间中著名的瑞利范围概念扩展到了湍流情况。在本文中，与先前发表的工作中类似的特征距离不同，光束与湍流无关的传播范围是基于光束传播因子（M² 因子）的公式，用于描述由于湍流导致的空间和角向扩展以及 M² 因子增加足够小且可忽略不计的范围。给出了几个用于计算这些距离近似值的简单公式，并将这些公式应用于高斯谢尔模型（GSM）光束并举例说明。此外，作为一个典型例子，还讨论了湍流中 GSM 光束的角向扩展对薄透镜光学系统的影响。我们表明，湍流瑞利范围取决于自由空间中的瑞利范围、束腰宽度以及湍流大气折射率起伏的空间功率谱，并且与湍流无关的传播范围取决于束腰宽度、束腰平面内的初始角向扩展以及空间功率谱。
