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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 generalized Huygens Fresnel principle and using the Rytov quadratic approximation of phase structure function, the second moment width and propagation angle of Gaussian Schell model (GSM) beams constrained by the aperture through the turbulent atmosphere are deduced. Analytical expression. Taking the GSM beam without aperture restriction as the reference beam, the directivity of GSM light propagating through the turbulent atmosphere restricted by the aperture was studied by using the spread angle and the normalized far-field average intensity distribution. The results show that under certain conditions, the GSM beam limited by the aperture with different cutoff parameter δ can be the same as the corresponding GSM beam without aperture limitation in free space and turbulent atmosphere If the normalized far-field average light intensity distribution is used to characterize the directionality of the beam, the GSM beam limited by the aperture and the corresponding GSM beam not limited by the aperture remain in free space even if the spreading angles are consistent The directionality is not the same, but the same in turbulence.