## 4 Implementation and Experimental Results
### Simulation Results  
Firstly, we examine the Zernike mode decomposition method by driving FSM-DM cascaded AO architecture and single DM architecture approaching our generated phase screen. The result presented in Figure 10 illustrates that when approaching a phase screen containing tilts aberrations, FSM-DM cascaded AO architecture can form a surface shape that is closer to the generated phase screen than the single-DM AO architecture. The PV of Figure 10a is 15.76 wavelength. As for Figure 10b,c, the PV values are 10.99 wavelength and 6.75 wavelength, respectively. Furthermore, due to the response rate of the FSM, the FSM-DM cascaded AO architecture is bound to have a swifter response towards tilts aberrations. Figure 8: (a) Digital calibration voltages for FSM constructing models in one period. (b) Normalized calibration voltages for FSM constructing models in one period. Figure 9: The fitting curve of both electrodes for the x coordinate of the 1 st spot. Secondly, to illustrate the merits of FSM-DM cascaded AO architecture against single DM AO architecture, we produced a single phase screen as the input wavefront according to the Kolmogorov theory [32]. Subsequently, generated phase screen is interpreted to spots offsets which is the direct information we can gain from the wavefront of our sensor. Finally, we observe the phase screen before compensation, phase screens compensated by FSM-DM cascaded AO architecture, and single DM architecture. The result is shown in Figure 11.  
Figure 11a shows the simulative input wavefront of the system where a peak phase value of 1.13 wavelength can be generated while the valley phase value is \(-0.953\) wavelength. After the compensation of FSM-DM cascaded AO architecture with the proposed algorithm, the convergent phase plane reaches a peak phase value of \(0.196\) wavelength and a valley phase value of \(-0.158\) compared to single DM AO architecture with the traditional algorithm whose reconstructed phase plane claims a peak phase value of \(0.360\) wavelength and a valley phase value of \(-0.302\) wavelength. In addition, although both the suggested and traditional architecture can compensate wavefront aberrations, the reconstructed phase planes demonstrate that the results produced by raised architecture with raised algorithms are more gentle which reflects the necessity of an FSM. In addition, by analysing the iterative procedure of compensating a single wavefront input, Figure 12 reveals that for a wavefront input of 0.53 wavelength, both FSM-DM cascaded architecture and single DM AO architecture converges using the iterative compensation algorithm within one iteration. Nevertheless, as for the convergence level, single DM architecture converges to 0.12 wavelengths after compensation compared to the results of our proposed architecture which is approaching 0.09 wavelengths. Figure 10: (**a**) A generated phase screen. (**b**) FSM-DM cascaded architecture approaching the generated phase screen. (**c**) Single DM architecture approaching the generated phase screen. Another verification for the consecutive compensating capability of our architecture with the algorithm is conducted. Firstly, a series of discrete phase screens according to Kolmogorov theory [32] are produced. Additionally, in order to simulate a dynamic atmospheric turbulence disturbed phase screen, we perform interpolation using a parallel temporal filter following [33] and produce 1000 distorted wavefront inputs in total. During the process, Zernike polynomials are also used to mathematically represent phase screens and change them to spots offsets. The results are shown in Figure 13.  
Figure 11: (**a**) Wavefront before compensation. (**b**) Wavefront compensated by proposed FSM-DM cascaded AO architecture with suggested algorithm. (**c**) Wavefront compensated by single DM AO architecture with traditional algorithm. Figure 12: The variation of the wavefront RMS value when compensating a single wavefront input with proposed AO architecture and single DM AO architecture.