Fig. 1. Typical closed-loop control system of deformable mirror. (a) Principle diagram of adaptive optics system; (b) block diagram of closed-loop control of deformable mirror

Fig. 2. Block diagram of closed-loop control of deformable mirror based on PI model

Fig. 3. Test platform of adaptive optics

Fig. 4. Hysteresis characteristic and fitting of typical actuator. (a) Deformation response of actuators; (b) hysteresis fitting curves

Fig. 5. Closed-loop correction of astigmatism Z3. (a) Target astigmatic profile; (b) astigmatism coefficient; (c) wavefront error RMS

Fig. 6. Closed-loop correction of initial wavefront

Fig. 7. 3D profiles of wavefronts before and after closed-loop correction. (a) Initial wavefront; (b) wavefront without hysteresis compensation after one correction; (c) wavefront with hysteresis compensation after one correction; (d) wavefront after 10 iterations in closed-loop

Fig. 8. Correction of dynamic aberrations

Fig. 9. 3D profiles of dynamic wavefronts before and after correction of aberrations. (a) Initial wavefront; (b) before hysteresis compensation; (c) after hysteresis compensation