## 3 Analysis and Discussion
### Experimental and Result Analysis  
As depicted in Figure 4, to test the effectiveness of the algorithm, a wavefront sensorless adaptive optics experimental system, based on a hyperparametric convolutional neural network, was created. First, 39 unit voltage data were obtained by SPGD algorithm to correct for random aberrations, where 0-27 V was represented by the numerical value of 0-4000 scaled Volt(sV), whose random data mean is 2000 scaled Volt(sV). Next, the corresponding far-field spot data and voltage data were obtained from the image sensor and stored as the training and testing datasets of the convolutional neural network, which received 128*128 pixel far-field spot data as input and produced 39 voltage data  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Types of Models** & **Test Set Optimal RMSE (V)** &
\begin{tabular}{c} **Number of Model** \\ **Parameters** \\ \end{tabular} \\ \hline Auto-U-net & 0.5476 V & 5,946,094 \\ Resnet18 & 3.1584 V & 58,430,240 \\ Inception v3 & 1.1312 V & 21,249,511 \\ U-net & 0.898 V & 40,492,546 \\ EfficientNet-B0 & 1.2569 V & 7,247,472 \\ DenseNet & 1.864 V & 12,687,072 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Model types and their performances.  
Figure 3: The proposed algorithm predicted four groups of 32-unit voltage data in the numerical simulation.  
as output. The testing dataset size was 1000, the training dataset size was 4000, and the hyperparameter optimization range was consistent with the information provided above.  
The optimized hyperparameters were as follows. The width of the convolutional network was 40, the number of convolutional layers was 9, the convolutional kernel size was 3, the convolutional step-size was 1, the pooling method is Max Pooling, the activation function type was tanh, the number of fully connected layer neurons was 3185, the optimization algorithm type was Adam, and the learning rate was 0.0063.  
Figure 5 shows the testing dataset comparison between the hyperparameter-optimized convolutional neural network Auto-U-net and the artificially designed convolutional neural network U-Net. As revealed by the above analysis, the testing set accuracy of the optimized network was significantly higher than that of the U-net network. Moreover, the root-mean-square-error (RMSE) of the predicted voltage of the algorithm in this paper was 41,246. The RMSE of the U-net network predicted voltage was 55,546, and the accuracy was increased by more than 26%. It demonstrated that the hyperparameter-optimized convolutional network outperformed the manually designed convolutional neural network in terms of accuracy.  
Figure 6 shows the comparison between the predicted value of 39 units of the deformable mirror as predicted by the hyperparameter- optimized convolutional neural network and the truevalue. The data on the horizontal axis represented the number of units of the deformable mirror, and the vertical axis represented the true value and predicted value of each unit of the deformable mirror. The overall prediction performance was good, and the error between the true value and predicted value of each unit of the deformable mirror was small. It showed that the model in this paper could accurately extract features from random distortion images and obtain random distortion correction data. The experiment in this paper was carried out on an GTX1070 graphics card, and it took approximately 0.32 ms to execute the model trained in this paper, and the frequency reached 3 kHz.  
Figure 4: Adaptive optics system verification platform. When the aberration is small, the SPGD algorithm is selected; in other cases, the CNN algorithm is selected.