Fig. 1. The actuator arrangement of a 37-channel DM.

Fig. 2. The residual wavefront error varies with the iteration number in the SPGD correction.

Fig. 3. The residual wavefront error varies with the iteration number in the DM-modal-based correction.

Fig. 4. The residual wavefront error varies with the mode bias amplitude. SNR=50.

Fig. 5. The PV value of each DM mode with the unit amplitude.

Fig. 6. The experimental system layout.

Fig. 7. The initial wavefront error (PV=19.2  rad and RMS=4.3  rad) and the corresponding image.

Fig. 8. The residual wavefront error after a one-cycle correction of the DM-modal-based algorithm, where PV=9.12  rad, and RMS=1.48  rad. Image after correction (right).

Fig. 9. The residual wavefront error after the SPGD correction, where PV=2.87  rad and RMS=0.26  rad. Image after correction (right).

Fig. 10. The metric function-changing curve. (a) The hybrid correction. (b) The only SPGD correction. (c) The only modal correction with a different bias amplitude (unit: rad).