# Interferometric Wavefront Sensing System Based on Deep Learning
## 3 Experiment  
To validate the effectiveness of this deep learning wavefront detection method we proposed, we successively conducted simulation experiments and real experiments in general environment. First, we conducted a simulation experiment. We extracted two sets of wrapped phases with a signal-to-noise ratio (SNR) of 9 and a signal-to-noise ratio (SNR) of 3 from the test dataset of net1. Then, we input these data separately to the net1, branch cut algorithm, and quality-guided phase unwrapping algorithm to get the unwrapped phases. We compared these results with the real phase and observed the net1 performance with the two other methods according to the errors. The output results are shown in Figures 5 and 6. From Figure 5, we can see that there are some errors between the output calculated by each method and the true phase. These errors are mainly caused by incorrect estimation of the wrap counts of the points on the wrapped phase so that there are differences of 2\(\pi\)k between the calculated wavefronts and the real wavefront at these points. These errors are represented as spikes in the difference maps. The more spikes and the greater its value in the difference map, the greater the error of the output result, which also indicates the poor performance of the method. According to Figure 5 and Table 1, we can see that these methods all have good performance when dealing with a wrapped phase with less noise (SNR = 9). Among them, the output result of [PERSON]'s branch cut algorithm has the highest accuracy, with the root mean square error (RMSE) of 0.06 and calculation time of 1.94 s. The net1 uses the least computation time. It only takes 1.04 s to complete the work, and the error is comparable to [PERSON]'s branch cut algorithm, with an RMSE of 0.07. Compared with the other two algorithms, the quality-guided algorithm performs poorly. Not only the calculation time is long (12.48 s), the accuracy of its output results is also relatively low, with an RMSE of 0.22. Figure 4: Samples of the training dataset. (**a**) true phase, (**b**) wrapped phase, (**c**) wrap count, (**d**) reconstructed wavefront using Zernike polynomials. When dealing with a noisy wrapped phase map (SNR = 3), as shown in Figure 6, the accuracy of the output results of the three methods are all reduced. As the noise becomes denser, more spikes appear in the difference maps, and their value may become larger. [PERSON]'s branch cut algorithm, which performed well before, was a bit disappointing this time. From Table 2, we found the accuracy of the output result is greatly reduced, the RMSE is 1.48. As to the quality-guided algorithm, due to the increased noise, the calculation error is transmitted and amplified, which caused the error to occur in regions. The performance of the deep learning method is still stable enough; it has an excellent performance in the face of a noisy image, with an RMSE of 0.37. \begin{table}
\begin{tabular}{c c c c} \hline  & **Net1** & **Branch Cut** & **Quality-Guided** \\ \hline RMSE & 0.07 & 0.06 & 0.22 \\ Time & 1.04 s & 1.94 s & 12.48 s \\ \hline \end{tabular}
\end{table} 
Table 1: Accuracies (RMSEs) and time consumption of different phase-unwrapping algorithms (SNR = 9). Figure 5: The output results of the wrapped phase with signal-to-noise ratio (SNR) = 9. Figure 6: The output results of the wrapped phase with SNR = 3. After that, we selected two sets of distorted wavefronts from the test dataset and used net2 and the least-squares method to fit their first 36 Zernike coefficients, as shown in Figure 7. It can be seen that the fitting speed of the least-squares method is faster; it only takes 0.5 s to complete the calculation. However, the fitting accuracy of the least-squares method is poor, and there is a large deviation between the fitting result and the true value; the RMSE is 1.94 and 1.13, respectively.