部分相干光在斜程和水平大气湍流中的光强与扩展

基于广义惠更斯-菲涅尔原理、交叉谱密度函数，利用修正von Karmon 谱模型以及
ITU-R 颁布的大气折射率结构模型，首先推导出部分相干高斯-谢尔光束在大气湍流中斜程和
水平传输时的光强分布以及光束扩展解析式，然后分别从归一化光强分布和相对束宽的角度
讨论并对比了斜程和水平传输时天顶角、湍流强度、光束相干长度等参数对光束光强分布和
扩展的影响，并给予相应的物理解释. 研究表明：1) 部分相干高斯-谢尔光束在自由空间中水
平传输时的归一化光强与斜程传输时的光强分布相同；2) 天顶角越小，光束的归一化强度分
布越集中，峰值光强越强，同时所受湍流的影响也越小. 3) 在斜程传输情况下，天顶角、湍流
强度、光束相干长度等参数对光束扩展的影响与水平传输几乎一致.

Intensity and Expansion of Partially Coherent Beam Propagating in Slant and Horizontal Atmospheric Turbulence

Based on the generalized Huygens-Fresnel principle, we derive the cross-spectral
density function using the modified von Karmon spectrum and atmospheric refractive-index
structure constant issued by ITU-R. We also derive analytic expressions of intensity distribution
and beam width of partially coherent Gaussian-Schell beam propagating in the
atmosphere along slant and horizontal paths. The impact on the beam propagating in
the two ways due to turbulence intensity, zenith, coherence length of the beam and other
parameters are discussed. They are compared respectively from the perspective of normalized
intensity distribution and relative expansion. The results show that the normalized
intensity distribution of the beam in a free space along a horizontal path is the same as
that along a slant path. The normalized intensity distribution is more concentrated, with
the peak much stronger when zenith is smaller, while the effects of the turbulence become
weaker. Impact on the zenith expansion, turbulence, coherence of the beam is almost consistent
with the slant path.