基于广义惠更斯菲涅耳原理，并利用Rytov相位结构函数二次近似的方法，推导出了受光阑限制的高斯谢尔模型(GSM)光束通过湍流大气传输的二阶矩宽度及扩展角解析表达式。以未受光阑限制的GSM光束为参照光束，分别利用扩展角和归一化远场平均光强分布研究了受光阑限制的GSM光通过湍流大气传输的方向性。研究表明，若以扩展角表征光束的方向性，则在一定条件下，截断参数δ不同的受光阑限制的GSM光束能够与相应的未受光阑限制的GSM光束在自由空间及湍流大气中具有相同的方向性；若以归一化远场平均光强分布表征光束的方向性，则即使扩展角一致，δ不同的受光阑限制的GSM光束与相应的未受光阑限制的GSM光束在自由空间中的方向性也并不相同，但在湍流中则一致。

Based on the extended Huygens-Fresnel principle, the expressions for the mean-squared width and the angular spread of apertured Gaussian Shell-model (GSM) beam propagating through atmospheric turbulent are derived by using the quadratic approximation of Rytov′s phase structure function. Compared with unapertured GSM beam, the directionality of apertured GSM beams propagating through atmospheric turbulence is studied by using angular spread and normalized far-field average intensity distribution. It is found that under a certain condition apertured GSM beams with different truncation parameter δ may have the same directionality as the corresponding unapertured GSM beam in free space and turbulence, if the angular spread in far-field is chosen as the characteristic parameter of beam directionality. On the other hand, if the beam directionality expressed in terms of the normalized far-field average intensity distribution, the directionality of different apertured GSM beams and the corresponding unapertured GSM beams in free space is not the same even if they have the same angular spreads, but the same in turbulence.