# Equivalent Modeling and Verification of a High-Steepness and Lightweight Elliptical Aluminum Mirror
## 7 Conclusions and Future Work  
In order to solve the difficult challenge of achieving a very lightweight design of mirrors with a high steepness in an ultra-compact layout of space payload, an equivalent modeling method for the plate deformation of high-steepness elliptical mirrors is proposed in this paper. Guided by topology shape optimization, a lightweight mirror structure that can be quickly assembled is established. The error between the predicted results of the equivalent model and the finite element analysis results is within 10%. The experimental results show that the lightweight aluminum mirror with a high steepness shape accuracy is 1/10 \(\lambda\) (\(\lambda\) = 632.8 nm), and the surface roughness Ra is better than 3.342 nm. The vibration test shows that the dynamic stiffness of mirror is better than 192 Hz. This research provides a strong theoretical support and application prospect for the rapid manufacturing and application of a lightweight aluminum mirror with a high steepness.  
Future research should focus on three main aspects. First of all, due to limitations of the project cycle and schedule, the surface shape accuracy and surface roughness of the mirror still need to be improved. In the future, attempts will be made to further reduce the low-frequency and high-frequency surface shape errors. Secondly, with the improvement of the mirror shape accuracy, the print-through effect of a high lightweight mirror will also increase, and the mediated frequency error will be hard to correct for the mirror with a higher shape accuracy. Future studies should focus on reducing the influence of the mirror footprint effect. Finally, with the improvement and application of additive manufacturing and topology optimization design theory, future research should introduce a lattice structure suitable for high-steepness mirrors to further increase the local stiffness of mirrors and gradually promote the application of visible light.  
Conceptualization, S.T. and X.Z.; methodology, S.T.; software, S.T.; validation, H.W., L.Y. and M.H.; formal analysis, S.T.; investigation, S.T.; resources, X.Z.; data curation, S.T.; writing--original draft preparation, S.T.; writing--review and editing, S.T., L.Y., L.W. and Q.F.; visualization, S.T.; supervision, L.W.; project administration, M.H.; funding acquisition, Q.F. All authors have read and agreed to the published version of the manuscript.  
This work was supported by Funded by Youth Innovation Promotion Association of Chinese Academy of Sciences (2021221) and Jilin Province Science and Technology Development Project (No.20210508054 RQ).  
Not applicable.  
Figure 16: Vibration test of mirror: (**a**) installation of sensor measuring points; (**b**) test results.  
**Acknowledgments:** The authors thank the Key Laboratory of Manufacturing Technology, Chinese Academy of Sciences for the conditions. The authors also would like to thank the anonymous reviewers for their useful comments and critical remarks, which helped to improve this paper.  
**Conflicts of Interest:** The authors declare no conflict of interest. We purchased the genuine software license of UG and stated the company name in our article. The funders had no role in the design of the study.