采用复高斯展开法和维格纳分布函数(WDF),推导出了截断光束的二阶矩矩阵通过大气湍流的传输公式。研究表明,将硬边光阑的复高斯展开函数引入z=0平面处的WDF中,能够避免截断光束二阶矩的积分发散问题,得到z=0平面处二阶矩的解析结果,并且保证了精度,从而方便地得到截断光束在大气湍流中传输的二阶矩矩阵。实验所得到的结果具有一般性,即无截断光束的二阶矩矩阵通过大气湍流传输和截断光束的二阶矩矩阵在自由空间的传输都可以分别作为特例给出。 Using the complex Gaussian expansion method and the Wiegand distribution function (WDF), the transfer formula of the second moment matrix of truncated beams through atmospheric turbulence is deduced. The results show that introducing the complex Gaussian expansion function of a hard-edged diaphragm into the WDF at the z = 0 plane can avoid the problem of integral divergence of the second moment of the cutoff beam and obtain the analytic result of the second moment at the z = 0 plane The accuracy allows for the easy derivation of a second-moment matrix of truncated beams transmitted in atmospheric turbulence. The experimental results are general, that is, the transmission of the second moment matrix of the truncated beam through the turbulent flow in the atmosphere and the transmission of the second moment matrix of the truncated beam in free space can be given as special cases respectively.