基于广义惠更斯-菲涅耳原理和Wigner分布函数二阶矩的定义，推导出直角坐标系下大气湍流中部分相干光的M2因子传输公式。以厄米-高斯(H-G)光束为例，给出了H-G光束通过大气湍流传输后M2因子的解析表达式，并采用Tatarskii谱，详细讨论了M2因子的主要影响因素。结果表明，M2因子主要由光束的束腰宽度、波长、光束阶数、大气湍流的折射率起伏结构常数和在湍流中传输距离决定。随着光束阶数、折射率起伏结构常数及传输距离的增大，M2因子明显增大，光束阶数越高，湍流对M2因子变化的影响越小。对于给定的传输距离，存在最佳初始束宽，使M2因子最小。

Based on the extended Huygens-Fresnel principle and the definition of second-order moments of the Wigner distribution function, the propagation formula for the M2-factor of Hermite-Gaussian(H-G) beams propagating in turbulent atmosphere has been derived. Taking into account the Tatarskii spectrum, major factors affecting the M2-factor of H-G beams have been discussed. The results show that the M2-factor in turbulence depends mainly on the beam order, the waist size and wavelength of the beams, the structure constant of refractive-index fluctuations of turbulence and the propagation distance. The M2-factor of H-G beams in turbulent atmosphere increases obviously as the beam order, the structure constant of refractive-index fluctuations of turbulence and the propagation distance increase, but decreases with the increasing wavelength. However, for the H-G beams with higher beam order, the effect of turbulence is less. For a certain propagation distance, there is an optimal beam waist width, at which the minimum M2-factor appears.