由第一类零阶贝塞尔函数的级数展开推导出波结构函数在任意湍流条件下的近似表达式。由广义惠更斯菲涅耳原理、随高度变化的Hufnagel-Valley湍流廓线模型以及波结构函数在任意湍流条件下的近似表达式,导出了斜程传输时准单色高斯谢尔光束互相干函数的解析式。然后,利用表征光束时间相干性的纵向相干长度(可由互相干函数导出),研究了斜程传输时大气湍流对准单色高斯谢尔光束时间相干性的影响。研究结果表明,准单色高斯谢尔光束的时间相干性在整个斜程传输过程中保持不变。最后,对该结果在物理上给予了定性解释。

By use of the series representation of the Bessel function of the first kind and zero order, the approximate expression of the wave structure function under all conditions of atmospheric turbulence is derived. Based on the extended Huygens-Fresnel principle, the Hufnagel-Valley profile model of the turbulence which is dependent on altitude, and the wave structure function under all conditions of atmospheric turbulence, the mutual coherence function of quasi-monochromatic Gaussian Schell-model (GSM) beams propagating in the slant path through turbulent atmosphere is derived analytically. The longitudinal coherence length (that can be derived from the mutual coherence function) of quasi-monochromatic GSM beams is used to characterize the temporal coherence of them, and the effect of atmospheric turbulence on the temporal coherence of those beams is studied. The result shows that the temporal coherence keeps unchanging in the propagation. Lastly, a qualitative explanation is given to this result.