## 3 Results and Discussion
### Analysis of Model Generalization Ability  
To investigate the impact of training set selection on detection accuracy and test the generalization of the Transfer OAM pattern classifier, we selected 500 test samples for each class under \(C_{n}^{2}=1\times 10^{-16}\) m\({}^{-2/3}\), \(5\times 10^{-16}\) m\({}^{-2/3}\), \(1\times 10^{-15}\) m\({}^{-2/3}\), \(5\times 10^{-15}\) m\({}^{-2/3}\), \(1\times 10^{-14}\) m\({}^{-2/3}\). Train using a training set under a certain turbulence condition to test the recognition accuracy of OAM patterns under different turbulence conditions. The detection  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Types** & **AT** & **Net1** & **Net2** & **Transfer-OAM** \\ \hline \multirow{3}{*}{Recognition accuracy} & Weak & 1.0000 & 1.0000 & 1.0000 \\  & Medium & 0.9562 & 1.0000 & 1.0000 \\ \cline{1-1}  & Strong & 0.7489 & 0.8134 & 0.9073 \\ \cline{1-1} \cline{2-5} Number of datasets per & / & 1000 & 1000 & 100 \\ \cline{1-1} \cline{2-5}  & \multicolumn{1}{c}{} & & & \\ \end{tabular}
\end{table}
Table 3: Recognition performance of different networks and required dataset quantity.  
Figure 7: Detection accuracy of classifier for 15 OAM states at different transmission distances.  
capability of the model under different turbulence intensities is shown in Figure 8. It can be clearly seen that the values in the main diagonal and adjacent areas are greater than those in the edge areas. This indicates that the classifier model trained on the dataset obtained under a certain AT can accurately detect modalities with small differences in intensity compared to that. In other words, the classifier model trained at a specific AT intensity has good generalization ability for situations where turbulence strengths are close, but there is still room for improvement for situations where turbulence strength differences are significant. It is worth mentioning that the classifier model trained with turbulence strengths \(C_{n}^{2}=1\times 10^{-15}\) m\({}^{-2/3}\) can achieve an average detection accuracy of 93.3% for these five types of ATs, proving that the model has good generalization ability.  
The following discusses the impact of mixed training sets on detection accuracy. Randomly select 20 training sets for each of these five different turbulence intensities of \(C_{n}^{2}=1\times 10^{-16}\) m\({}^{-2/3}\), \(5\times 10^{-16}\) m\({}^{-2/3}\), \(1\times 10^{-15}\) m\({}^{-2/3}\), \(5\times 10^{-15}\) m\({}^{-2/3}\), and \(1\times 10^{-14}\) m\({}^{-2/3}\) to create five AT mixed training sets, and train based on this 5 AT mixed training set. When the turbulence strength is within the range of \(C_{n}^{2}=1\times 10^{-16}\) m\({}^{-2/3}\) to \(C_{n}^{2}=3\times 10^{-14}\) m\({}^{-2/3}\), the detection accuracy is shown in Figure 9. It is evident that the Transfer OAM pattern classifier trained on a mixed training set has a stronger generalization ability than the Transfer OAM pattern classifier obtained on a single AT training set. The model can maintain high accuracy detection even when encountering turbulence strengths images that have not been seen before. This method can achieve OAM mode detection tasks for any AT intensity within turbulence strength in the range of \(C_{n}^{2}=1\times 10^{-16}\) m\({}^{-2/3}\) to \(C_{n}^{2}=3\times 10^{-14}\) m\({}^{-2/3}\), with an average detection accuracy of 97.36%. Compared with a single training set, the detection accuracy of the model obtained from the mixed training set is higher. This is because the intensity of atmospheric turbulence varies randomly, and the Transfer OAM mode classifier can learn more diverse features when trained on the mixed training set, thereby improving its performance on unknown turbulence data.  
Figure 8: Cross-test results of five types of AT.