运用广义惠更斯-菲涅耳原理和相位结构函数的平方近似，研究了聚焦高斯空心涡旋光束通过湍流大气传输后在焦平面内的光强分布的理论模型，同时分析了不同大气折射率结构常数C2n、聚焦距离、光束拓扑荷和湍流外尺度对焦面光强分布特性的影响.结果表明：随着聚焦距离的增加，焦面光强分布由中央凹陷状向高斯分布转变.弱湍流对焦面光强分布的影响可以忽略；高拓扑荷光束在湍流大气中传输时光波奇异性的保持较低拓扑荷奇异光束要强；随着湍流外尺度增加，焦面光强分布的中央凹陷状变浅，光强分布变平滑.

Based on the extended Huygens-Fresnel principle and the quadratic approximation of phase structure function, the theoretical modal of optical intensity distribution on the focal plane for focused hollow vortex beams with a Gaussian background propagating in turbulent atmosphere was investigated and obtained.The effects of atmospheric index structure constant C2n, topological charge, focal length and beam wavelength on optical intensity distribution on the focal plane were analyzed. The results indicate that with the increase of focal length, the intensity distribution on the focal plane varies from central-dip form to Gaussian distribution. The effects of weak turbulence on intensity distribution are negligible. The maintenance of singularity of vortex beams with larger topological charge in turbulent atmosphere is better than that for vortex beams with smaller topological charge. The central-dip form of the intensity distribution becomes shallow and the intensity distribution becomes smooth with the turbulence outer scale increasing.