Fig. 1. Schematic diagram of DLWFS

Fig. 2. DLWFS model structure, where x(x1,x2) is input double spots intensity data, G is the Generator, D is Discriminator, and y is input random wavefront data as “real” data to train Discriminator

Fig. 3. Loss function varying in training process of cGAN compared with CNN of encode-decode only

Fig. 4. Test data sets and wavefront recovery results comparison of DLWFS ( columns 1 and 2 are the intensity data of on-focus spots and defocus spots, columns 3 and 4 are the recovered wavefront G(x) by DLWFS and the input real wavefront y, column 5 is the residual between the recovered wavefront and the real wavefront)

Fig. 5. Synchronized acquisition setup of DLWFS and referencing SHWFS. The transmitted beam is collected by referencing SHWFS behind an telescope beam reducer, the reflected beam is reflected again into DLWFS, then the converged beam is split by another BS into focus camera to collect x1 and into defocus camera to collect x2. BS: 50/50 beam splitter prism

Fig. 6. Reconstructed wavefront by DLWFS and reference SHWFS. Three columns from left to right are wavefront G(x) retrieved by DLWFS, y' by reference SHWFS, and the residual error between two results

Fig. 7. An overview of the total experiment platform (DM1: disturbing deformable mirror; DM2: correcting deformable mirror)

Fig. 8. Control logic in wavefront correction(DM response function is collected by SHWFS, as shown by solid lines.While the AO closed-loop control corrected wavefront is detected by DLWFS, as shown by dashed lines)

Fig. 9. Comparison of wavefront correction result using DLWFS and SHWFS as WFS

Fig. 10. Results of AO closed-loop correction with DLWFS. The first two rows illustrate the comparison before and after correction for circular beams of 50 mm in diameter, and the last two rows are the comparison before and after correction for squared beam of 50 mm×50 mm. The intensity distribution of each spot is normalized for better view of the whole shape