中文摘要：

基于广义惠更斯-菲涅耳衍射积分公式和洛伦兹函数的厄米-高斯展开，导出了部分相干洛伦兹-高斯光束在湍流大气中经傍轴ABCD光学系统的峭度参数的解析表达式，对该峭度参数进行了数值计算。结果表明：空间相干长度和结构常数对峭度参数的影响与部分相干洛伦兹-高斯光束本身的光束参数有关；当空间相干长度小于光束参数时，其影响显著；当洛伦兹部分的光束参数较大或高斯部分的光束参数较小时，结构常数的影响较明显且随传输距离的增大而增强。

英文摘要：

Based on the generalized Huygens-Fresnel integral and the Hermite-Gaussian expansion of a Lorentz function, an analytical propagation expression for the kurtosis parameter of a partially coherent Lorentz-Gauss beam through a paraxial ABCD optical system has been derived in turbulent atmosphere, and the kurtosis parameter was numerically calculated. The results show that the influences of the spatial coherence length and the structure constant of the atmospheric turbulence on the kurtosis parame- ter are related to the beam parameters. When the spatial coherence length is smaller than the beam parameters, the influence of the spatial coherence length is remarkable. When the beam parameter of the Lorentzian part is relatively large or the beam parame- ter of the Gaussian part is relatively small, the influence of the structure constant is distinct. Moreover, the influence of the struc-