## 2 FSM-DM Cascaded AO Architecture
### Theoretical Compensation Ability of FSM and DM Compensating Tilts Aberrations  
For MMDM, the reflective surface is a static electricity controlled membrane shown in Figure 2a. Configured by the wavefront reconstructor, controlling voltages are passed to the electrodes which produce electrostatic force pulling and pushing the reflective film to form a desired shape. The advantages of MMDM lie in its cabinet size allowing it to work in a narrow environment. However, due to the absence of a physical connection between the flexible membrane and electrodes, the maximum deflection of a membrane varies from electrode to electrode. Meanwhile an inhomogeneous distribution of the tension  
Figure 1: Proposed AO architecture. on the mirror surface thwarts the stablization of deviation caused by marginal electrodes. Hence, the mirror could scarcely form an inclined plane to compensate tilts aberrations with the whole area. Generally the most suitable use scenario for MMDM is high-frequency compensation. As for the PDM, a brief schematic is displayed in Figure 2b. Unlike MMDM, the flexible surface is physically linked with piezoelectric ceramics. Consequently, even marginal electrodes share nearly the same rigorous mapping relationship between digital voltages configured to the electrode and stretching the measurement of the corresponding piezoelectric ceramics with the centre electrodes. Nevertheless, the physical characteristics of piezoelectric ceramics demand a hysteresis model for better precision depicting the influence of the reflective surface for the spots offsets. Owing to the balanced performance in terms of stroke and spatial resolution, it is widely used in single DM AO systems as the only wavefront corrector. For FSM, a schematic of it supported by piezoelectric ceramics is depicted in Figure 2c. It consists of a rigid non-deformable mirror. Correspondingly, the FSM cannot express any other aberrations except tilts aberrations with two controlling signals which determine the tipping and tilting angle of the mirror. Commonly, FSMs are used to either process low-order aberrations or fine tracing. On our testbed, the diameter of MMDM is 15 mm and the number of electrodes is 37. As for the PDM, the diameter of it is 30 mm with same 37 electrodes. In addition, the FSM has two electrodes controlling a circular area with a diameter of 19 mm. According to the literature, the maximum deflection of the mirror center is 9.4 \(\upmu\)m. Therefore, by assuming MMDM could form an ideal tilting surface within a 90-degree sector when the center electrode is configured to the maximum stroke, \(\frac{1}{4}\) of the mirror reaches the extreme compensation scope. Represented in Figure 3a, MMDM could compensate a tilts aberrations of 4.23 wavelength at the cost of sacrificing \(\frac{3}{4}\) correction area. When electrodes are configured by the same digital voltages, the deformation of the panel shares the same magnitude. This leads to the feasibility of using the whole area to frame an inclined plane to compensate tilts aberrations. The technique documents indicate that the maximum stroke of PDM is 8 \(\upmu\)m. According to the simulation results shown in Figure 3b, the compensation scope of PDM is 1.8 wavelength. Similarly, the FSM can also use the whole surface to compensate tilts aberrations. Due to the non-deformable reflective surface, a  
Figure 2: (**a**) Schematic section of the micromachined membrane deformable mirror. (**b**) Schematic section of the piezoelectric deformable mirror. (**c**) Schematic section of the fast steering mirror. literal depiction of its technical parameters focuses on inclination generation capability. According to the literature, the maximum deflection angle of FSM is 5 mrad, as shown in Figure 3c. This means a capability of 33.75 wavelength when compensating tilts aberrations. As shown in Figure 3, the FSM has a desirable compensation ability for tipping and tilting as well as a swift response rate of 8 mrad within 1 ms which is faster than higher spatial resolution wavefront correctors.