## 5 Conclusions  
Based on NAT, this paper studies the wave aberration compensation correction method of an unobscured off-axis TMA astronomical telescope. Firstly, third-order net astigmatism (C5/C6), third-order net coma (C7/C8), and third-order net spherical aberration (C9) induced by different perturbation parameters (misalignments and PM figure errors) in the unobscured off-axis TMA telescope are expressed analytically according to different field dependence. Furthermore, from the perspective of the compensation mechanism of aberration fields, the reason and feasibility that SM misalignments, TM misalignments, and PM figure errors can compensate each other are analyzed, and the aberration field compensation relationship shown in Equations (11)-(13) is constructed. It is worth noting that the misalignments include axial and lateral misalignments, and PM figure errors consist of third-order astigmatic figure errors, third-order coma figure errors, and third-order spherical aberration figure errors. On this basis, two aberration compensation correction models are constructed in this paper, one is to compensate for TM misalignments and PM figure errors simultaneously by adjusting SM, and the other is to compensate for SM misalignments and PM figure errors simultaneously by adjusting TM. Finally, the correctness of the two correction models was verified through a specific case simulation and Monte Carlo analyses. Our work not only contributes to a deep understanding of the coupling effect and compensation relationship of net aberration fields induced by different perturbation parameters but also provides a reference for an active optical compensation strategy of off-axis reflective telescopes. Conceptualization, [PERSON] and X.H. ; methodology, [PERSON] and X.H. ; software, [PERSON] and X.Z. ; validation, [PERSON], X.H. and M.M. ; formal analysis, [PERSON]; data curation, X.Z. and Z.C. ; writing--original draft preparation, [PERSON]; writing--review and editing, [PERSON] and X.Z. ; funding acquisition, X.H. and Z.C; supervision, [PERSON]; project administration, [PERSON]; visualization, [PERSON]; resources, Z.C. 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 No. 61875190 and 12003033), and the Natural Science Foundation of Jilin Province (Grant No. 20200201008 JC). **Institutional Review Board Statement:** Not applicable. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Case 1** & **Case 2** & **Case 3** & **Case 4** \\ \hline SMCM & \(9.672\times 10^{-4}\) & \(2.221\times 10^{-3}\) & \(3.466\times 10^{-3}\) & \(1.741\times 10^{-3}\) \\ \hline TMCM & \(7.400\times 10^{-3}\) & \(1.979\times 10^{-2}\) & \(4.024\times 10^{-2}\) & \(1.558\times 10^{-2}\) \\ \hline \hline \end{tabular}
\end{table} 
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