# Interferometric Wavefront Sensing System Based on Deep Learning
## 4 Conclusions  
In this work, we present a new deep learning wavefront sensing method. First, we designed an interference system to detect distorted wavefront and generated multiple interference fringe patterns  
Figure 10: Output results of the real experiments. (**a**) Wrapped phase obtained by the four-step phase-shifting method, (**b**) unwrapped phase calculated by net1, (**c**) unwrapped phase calculated by [PERSON]’s branch cut algorithm, (**d**) the difference of the two unwrapped phases, (**e**) Zernike coefficients fitted by net2, (**f**) reconstructed wavefront, (**g**) errors of the reconstructed wavefront.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \(\mathbf{a_{1}}\) & \(\mathbf{a_{2}}\) & \(\mathbf{a_{3}}\) & \(\mathbf{a_{4}}\) & \(\mathbf{a_{5}}\) & \(\mathbf{a_{6}}\) \\
1.7944 & 0.6126 & 0.27979 & \(-0.96737\) & \(-1.01558\) & \(-0.44856\) \\ \hline \(\mathbf{a_{7}}\) & \(\mathbf{a_{8}}\) & \(\mathbf{a_{9}}\) & \(\mathbf{a_{10}}\) & \(\mathbf{a_{11}}\) & \(\mathbf{a_{12}}\) \\ \(-0.00485\) & \(0.11478\) & \(-0.02006\) & \(-0.14852\) & \(-0.07189\) & \(-0.09368\) \\ \hline \(\mathbf{a_{13}}\) & \(\mathbf{a_{14}}\) & \(\mathbf{a_{15}}\) & \(\mathbf{a_{16}}\) & \(\mathbf{a_{17}}\) & \(\mathbf{a_{18}}\) \\ \(-0.11007\) & \(-0.07977\) & \(-0.06551\) & \(0.04326\) & \(-0.11056\) & \(-0.09216\) \\ \hline \(\mathbf{a_{19}}\) & \(\mathbf{a_{20}}\) & \(\mathbf{a_{21}}\) & \(\mathbf{a_{22}}\) & \(\mathbf{a_{23}}\) & \(\mathbf{a_{24}}\) \\ \(-0.14109\) & \(0.04773\) & \(0.09532\) & \(0.5545\) & \(0.06727\) & \(0.10555\) \\ \hline \(\mathbf{a_{25}}\) & \(\mathbf{a_{26}}\) & \(\mathbf{a_{27}}\) & \(\mathbf{a_{28}}\) & \(\mathbf{a_{29}}\) & \(\mathbf{a_{30}}\) \\ \(0.05787\) & \(-0.01177\) & \(-0.06569\) & \(-0.01927\) & \(0.05708\) & \(0.00327\) \\ \hline \(\mathbf{a_{31}}\) & \(\mathbf{a_{32}}\) & \(\mathbf{a_{33}}\) & \(\mathbf{a_{34}}\) & \(\mathbf{a_{35}}\) & \(\mathbf{a_{36}}\) \\ \(-0.03634\) & \(-0.04515\) & \(-0.04231\) & \(0.02874\) & \(0.05204\) & \(-0.0082\) \\ \hline \end{tabular}
\end{table}
Table 3: Zernike coefficients fitted by net2.  
Figure 9: Four-step phase-shifting fringe patterns recorded by camera.  
by phase-shifting method, which greatly improved the anti-noise ability and broke the dependence of the wavefront detection system to the dark environment. Second, we designed a neural network system to analyze the detected wavefront. The two neural network modules in the system were used to unwrap the phase and fit the Zernike coefficients. Compared with other traditional algorithms, the wavefront analysis neural network system not only has higher measurement accuracy but also greatly reduces the calculation time. Finally, simulation and experiments have proved the effectiveness of the system under different working conditions. In the future, we wish to apply the new wavefront detection system to radar research to achieve dynamic measurement and correction of the wavefront.  
Conceptualization, Y.N., Z.G. and X.W.; methodology, Y.N. and Z.G.; software, Y.N., validation, Y.N. and C.G.; formal analysis, Y.N. and J.Z.; investigation, J.Z.; resources, Z.G.; writing--original draft preparation, Y.N.; writing--review and editing, Y.N. and Z.G. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant number 51675038.  
The authors declare no conflict of interest.