在波数K为复数的情况下，对部分相干光强度二阶矩及M2因子的定义进行了修正。以部分相干高斯谢尔模型(GSM)光束为例，讨论了光束在介质中传输时M2因子的变化。研究结果表明，部分相干光束在增益或损耗介质中传输时的M2因子与光束在无增益无损耗介质传输时的M2因子具有不同变化特性，此时，M2因子不仅只与部分相干光的相干参量β有关，且随着传输距离B和表征介质增益(或损耗)特征Ki的增大而增大(或减小)；随着相干长度σ0的具体尺寸、波数实部Kr的减小而增大(或减小)。为控制光束质量提供几种有效的途径。

Considering of the complex wave number, the second-order intensity moments and the M2-factor of partially coherent beams have been modified. A partially coherent Gaussian Schell-model beam progating in media is taken as typical example to study the change of M2-factor. It can be shown that unlike in free-space, the M2-factor of partially coherent beams in the gain or absorbing media does not only depend on the coherent parameter β. In gain media, the M2-factor increases with the increase of the propagation distance B and the parameter characterizing the media Ki, and with the decrease of the coherent length σ0 and the wave number Kr, whereas in absorbing media, the M2-factor decreases with the increase of the propagation distance B and the parameter characterizing the media Ki, and with the decrease of the coherent length σ0 and the wave number Kr. The result can offer some effective methods of beam quality control.