Rao C, Jiang W, Ling N
Appl Opt. 2001 Jul 20;40(21):3441-9. doi: 10.1364/ao.40.003441.
In optical propagation through atmospheric turbulence, the performance of compensation with adaptive optics depends on a beacon's spatial distribution. With distributed beacons, the inefficiency of the modal correction, which is defined as the ratio of the anisoplanatic error of the jth mode and the Zernike-coefficient variance, is derived by use of the wave-front expansion on the Zernike polynomials for non-Kolmogorov turbulence. Numerical results are presented for laser beam propagation through constant turbulence with an offset point beacon and an on-axis uniform circular beacon. The results show that compensation for an on-axis uniform circular beacon is much more effective than that for an offset point beacon. The low-order modes are much more correlated than the higher-order modes. The larger the power-law exponent of the refractive-index power spectrum beta, the smaller the propagation path length L and the larger the diameter D of the telescope aperture, the more effective the compensation is. For a specific extended degree of beacon for which there are a maximum number of modes N(max) to be corrected, only low-order-correction systems are useful.
在通过大气湍流进行光传播时，自适应光学补偿的性能取决于信标的空间分布。对于分布式信标，模态校正的低效性（定义为第j阶模式的非等晕误差与泽尼克系数方差之比）是通过对非柯尔莫哥洛夫湍流在泽尼克多项式上进行波前展开推导得出的。给出了激光束通过具有偏心点信标和轴上均匀圆形信标的恒定湍流传播的数值结果。结果表明，轴上均匀圆形信标的补偿比偏心点信标的补偿要有效得多。低阶模式的相关性比高阶模式强得多。折射率功率谱的幂律指数β越大、传播路径长度L越小以及望远镜孔径直径D越大，补偿效果就越有效。对于具有最大可校正模式数N(max)的特定信标扩展程度，只有低阶校正系统是有用的。
