基于广义惠更斯－菲涅耳原理，并采用光束的非相干合成方法，推导出了M×N双曲余弦高斯列阵光束在湍流中的三维光强传输方程.采用桶中功率、β参量和Strehl比作为光束质量的评价参量，研究了湍流大气对双曲余弦高斯列阵光束远场光束质量的影响.研究表明:在湍流大气中，双曲余弦高斯列阵光束的传输将经历三个阶段的变化，并且湍流使得光束传输经历三阶段的进程加快;湍流导致双曲余弦高斯列阵光束扩展、最大峰值光强下降,但是，β参量随光束数目M(N)、相邻子光束间距xd(yd)和光束参量δ的增加而减少，即光束扩展受湍流的影响减小;并且，存在最佳xd(yd)和δ值使得Strehl比取得极大值.因此，适当选取M(N)、xd(yd)和δ可以降低湍流对双曲余弦高斯列阵光束远场光束质量的影响.

Based on the extended Huygens-Fresnel principle,the propagation equation of three-dimensional intensity of M×N cosh-Gaussian (ChG) beams through atmospheric turbulence was derived by using incoherent combination.The power in the bucket (PIB),β-parameter and Strehl ratio (SR) were chosen as the parameters characterizing the beam quality in the far field,and the influence of turbulence on the far-field beam quality was studied.It is shown that the M×N ChG beams in turbulent undergo three stages of evolution with increasing propagation distance,and turbulence accelerates the evolution of three stages.The turbulence results in a spreading and degradation of the maximum intensity in the far field.But β-parameter decreases with increasing beam numbers M (N),separate distances xd (yd) and beam parameter δ.And there exists optimal values of xd (yd) and δ,and SR of the corresponding M×N ChG beams reaches its maximum.So a suitable choice of M (N),xd (yd) and δ may reduce the influence of turbulence on the beam quality in the far field.