采用Rytov相位结构函数二次近似的方法和广义惠更斯-菲涅耳原理, 推导出了部分相干平顶光束通过大气湍流传输的空间相干度公式,研究了湍流对光 束空间相干特性的影响。研究表明:部分相干平顶光束的空间相干性由大气湍流 折射率结构常数、光束的相对空间相关长度、平顶光束的阶数、传输距离和观察点 位置坐标等因素共同确定。部分相干平顶光束通过湍流大气传输时,其空间相干度 会出现振荡和相位奇异现象,但随着湍流的增强,振荡减弱,直至振荡和相位奇异 现象消失。

Based on the quadratic approximation of the Rytov’s phase structure function and the Huygens-Fresnel principle, propagation equation for the spatial degree of coherence of partially coherent flat-topped beams propagating in turbulence atmosphere is derived, and the properties of the spatial degree of coherence in turbulence atmosphere are investigated numerically. The result shows that properties of spatial degree of coherence of partially coherent flat-topped beams are determined by the refractive index structure constant of atmospheric turbulence, the beams’ relative length of the space-related, the order of flat-topped beams, transmission distance and location of the observation point in common. It also shows that the oscillatory behavior and phase singularities of the spatial degree of coherence may occur when partially coherent flat-topped beams propagates through atmosphere turbulence. But the oscillatory behavior becomes sweaker with atmosphere turbulence increasing, and the phenomena of the oscillatory behavior and phase singularities will disappear in the end.