基于广义惠更斯-菲涅耳原理，并采用Rytov相位结构函数二次近似的方法，推导出了部分相干环状光束通过湍流大气传输时，其光谱相干度的解析公式，并研究了光束的空间相干特性。研究表明，部分相干环状光束通过自由空间传输时其光谱相干度会出现振荡和相位奇异现象，且光束遮拦比ε越大振荡越厉害。但是，随着湍流的增强，其振荡逐渐减弱直至消失，不同ε的光谱相干度曲线相接近，并呈类高斯分布。光束遮拦比ε越大的部分相干环状光束其空间相干性受湍流影响越小。此外，在自由空间中，若光束相干参数α较小，随ε的变化光谱相干度二阶矩宽度w_c可大于或小于其光谱强度二阶矩宽度w_i，且临界值ε₀随α的增大而增大；随着α的增大，则无论ε取何值都有w_c>w_i。然而，当湍流增强到一定程度，总是有w_ci。

Based on the extended Huygens-Fresnel principle, the analytical expression for the spectral degree of coherence of partially coherent annular beams propagating in atmospheric turbulence is derived by using the quadratic approximation of Rytov’s phase structure function, and the spatial correlation properties are studied. It is shown that the oscillatory behavior and phase singularities of the spectral degree of coherence may appear when partially coherent annular beams propagate in free space, and the oscillatory behavior becomes stronger with increasing the beam obscure ratio ε. However, the oscillatory behavior becomes weaker and even disappears as the strength of turbulence increases. The curves of the spectral degree of coherence of partially coherent annular beams with different values of ε are close to each other and turn into Gaussian-like profile with increasing turbulence. The larger ε is, the less the spatial correlation is affected by the turbulence. In addition, it is found that in free space for small α the mean-squared width of the spectral degree of coherence w_c can be either larger or smaller than that of the spectral density w_i depending on ε， and critical value ε₀ increases with increasing α. As α increases, there is w_c>w_i for different values of ε. However, there always exists w_ci when the turbulence is strong enough.