Fig. 1. Basic principle diagram of wavefront restoration based on CNN. (a) Diagram of optical path; (b) training and prediction data structure of CNN

Fig. 2. Diagram of CNN structure used for wavefront restoration

Fig. 3. Eight-layer CNN model for wavefront restoration

Fig. 4. Loss function curves in network training and testing processes. (a) D/r₀=5; (b) D/r₀=15; (c) D/r₀=1-15

Fig. 5. Single-frame aberration randomly generated at D/r₀=5 and its restoration results. (a) Wavefront to be restored; intensity images of (b1) focal plane and (b2) defocus plane; (c1) wavefront restored by CNNM1; (c2) residual aberration restored by CNNM1; (d1) wavefront restored by CNNM3; (d2) residual aberration restored by CNNM3

Fig. 6. Single-frame aberration randomly generated at D/r₀=15 and its restoration results. (a) Wavefront to be restored; intensity images of (b1) focal plane and (b2) defocus plane; (c1) wavefront restored by CNNM2; (c2) residual aberration restored by CNNM2; (d1) wavefront restored by CNNM3; (d2) residual aberration restored by CNNM3

Fig. 7. Comparison between actual Zernike coefficient and predicted Zernike coefficients by CNNM1,CNNM2, and CNNM3. (a) D/r₀=5; (b) D/r₀=15

Fig. 8. Strehl ratio of axial light intensity before and after distortion wavefront compensation. (a) D/r₀=5; (b) D/r₀=15; (c) D/r₀=1-15

Table 1. Description of training and testing data volumes

Table 2. Parameters of CNN network model for wavefront restoration