Fig. 1. Random phase screen at each turbulence intensity: (a), (b) ; (c), (d) ; (e), (f) . 各湍流强度下的随机相位屏　(a), (b) ; (c), (d) ; (e), (f)

Fig. 2. The cross-section spot of transmission beam at each turbulence intensity: (a) Initial Gaussian beam; (b), (c) ; (d), (e) ; (f), (g) . 各湍流强度影响下传输光束截面光斑　(a)初始高斯光束; (b), (c) ; (d), (e) ; (f), (g)

Fig. 3. The CNN structure of extracting the turbulent phase.提取湍流相位的CNN结构

Fig. 4. The loss function curve of training process.训练过程损失函数曲线

Fig. 5. The turbulent phase during the training process: The number of iterations of (a) and (b), (c) and (d), (e) and (f), (g) and (h), (i) and (j), and (k) and (l) is 1, 100, 500, 4000, 8000, 14000.训练过程提取到的湍流相　(a)与(b), (c)与(d), (e)与(f), (g)与(h), (i)与(j)和(k)与(l)的迭代次数分别为1, 100, 500, 4000, 8000, 14000

Fig. 6. The loss function curve at each turbulence intensity.各湍流强度损失函数曲线

Fig. 7. The predicted turbulent phase based on CNN at each turbulence intensity: (a), (b), (c) Initial Gaussian beam; (d), (e), (f) Gaussian beam affected by atmospheric turbulence; (g), (h), (i) the actual turbulence phase; (j), (k), (l) the output phase of CNN.不同湍流强度下, 经过CNN提取到的湍流相位　(a), (b), (c)初始高斯光束; (d), (e), (f) 受大气湍流影响的高斯光束; (g), (h), (i)实际的大气湍流相位; (j), (k), (l) CNN输出的预测湍流相位

Fig. 8. The comparison of CNN and GS algorithm for extracting turbulence phase: (a), (b), (c) Gaussian beam affected by atmospheric turbulence with ; (d), (e), (f) the actual turbulence phase; (g), (h), (i) the predicted turbulent phase based on CNN; (j), (k), (l) the predicted turbulent phase based on GS algorithm. CNN与GS算法提取湍流相位效果对比　(a), (b), (c)受湍流强度为 影响的高斯光束; (d), (e), (f)实际湍流相位; (g), (h), (i)基于CNN模型提取的湍流相位; (j), (k), (l) GS算法提取的湍流相位

Fig. 9. Training and validation set test results: (a) The loss function curve of training process; (b) the predicted turbulence phase obtained by testing the validation set during training.训练及验证测试结果　(a)训练过程损失函数曲线; (b)训练过程中利用验证集测试得到的预测湍流相位

Table 2. The predicted time comparison of two methods.