## 4 Conclusions  
The discrepancy in wavefront distortion aberrations within an adaptive optical system represents a systematic error stemming from the disparity in wavefront lengths between the system's signal and beacon lights. By adjusting system parameters and adopting advanced correction algorithms, the impact of turbulence on beam transmission can be  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Equipment Name** & **Type** & **Equipment Parameter** \\ \hline Liquid crystal spatial & & Target size: 0.78\({}^{\prime\prime}\) \\ light modulator & RL-SLM-R2 & Pixel size: 12.3 mm \\  & & Operating wavelength: 400–1620 nm \\  & & Phase modulation capability: 0–2\(\pi\)@532 nm \\ \hline \multirow{4}{*}{Deformable mirror} & & Number of actuators: 69 \\  & & Pupil diameter: 10.5 mm \\  & & Oblique wavefront modulation: 60 mm \\  & & Bandwidth: \(>\)750 Hz \\  & & Setting time: 800 \(\upmu\)s \\  & & Analog response time: \(<\)10 \(\upmu\)s \\ \hline \multirow{2}{*}{CCD} & \multirow{2}{*}{MW-GX-650} & Pixel Size: 5.5 mm \(\times\) 5.5 mm \\  & & Frame rate: 8 fps \\ \cline{1-1}  & & Exposure time: 300–1,000,000 ms \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of experimental equipment.  
Figure 8: The change in the light pattern in the picture correction experiment. (**a**) Before correction; (**b**) correction without the correction factor, and (**c**) after adding the correction factor correction.  
effectively reduced. In our study, theoretical and experimental results show that when the turbulence external scale is greater than 40 m, the speed of wavefront aberration change decreases. Wavelength matching optimization can reduce phase difference, that is, the closer the wavelengths of the beacon light and signal light are, the closer the wavefront aberration is to 0. In numerical simulation, the introduction of correction coefficients in the wavefront correction system increased the SR value from the basic 0.89 to 0.982, by about 11%, and accelerated the convergence speed. In the experiment, the SR value of the spot before and after the implementation of wavefront correction technology jumped from 0.112 to 0.74. After further adding the correction factor, the SR value reached 0.812, an increase of about 10% compared with the initial correction, clearly demonstrating the additional enhancement effect of secondary correction on system accuracy. The further improvement in spot energy and the SR value verifies that this method can effectively improve correction accuracy.  
Conceptualization, M.H. and X.K.; methodology, M.H. and X.K.; software, M.H.; validation, M.H., X.K. and J.L.; formal analysis, M.H.; investigation, M.H.; resources, J.L.; data curation, M.H., X.K. and J.L.; writing--original draft preparation, M.H.; writing--review and editing, M.H. and X.K.; supervision, X.K.; project administration, M.H. All authors have read and agreed to the published version of the manuscript.  
This study was funded by the Key Industrial Innovation Chain Project of Shaanxi Province [grant number 2017 ZDDXLGY-06-01] and the General Project of the National Natural Science Foundation of China [grant number 61377080].  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to the limitations of our patent work.  
The authors declare no conflicts of interest.