## 4 Conclusions  
This study demonstrates a high-precision OPD measurement system for the PAAM, combining an equal-arm heterodyne interferometer with multi-layer thermal shielding and HCB. The system achieves a background noise floor of 60 pm\(/\sqrt{\mathrm{Hz}}\) in the 1 mHz to 1 Hz frequency range, which represents a 6.5 times improvement over the prior UV-bonded designs [9], while extending the thermal time constant to 78.5 h. Three synergistic strategies were implemented: (1) a symmetric equal-arm configuration suppressing laser frequency noise via common-mode rejection, (2) HCB bonding of fused silica optics on an ULE substrate (\(\alpha_{\mathrm{ULE}}\)\(<\) 1 \(\times\) 10\({}^{-8}\)K\({}^{-1}\)) to minimize thermoelastic stress, and (3) a three-layer thermal shielding system attenuating external temperature fluctuations by 87% (from 286 mK\(/\sqrt{\mathrm{Hz}}\) to 37 mK\(/\sqrt{\mathrm{Hz}}\)).  
This study reveals the thermo-mechanical mechanisms of multi-layer thermal shielding, which provides theoretical guidance for thermally induced phase noise control in high-precision interferometers. The achieved system performance lays the technical foundations for space-based gravitational wave detection, particularly in advanced pointing tests. It also provides a practical reference for inter-satellite laser communication systems requiring sub-nanometer stability under extreme thermal environments. Collectively, these results advance precision measurement techniques that are applicable to fundamental physics research and space engineering.  
In future work, our priority will be to enhance the interferometer's sensitivity. The development of automated HCB alignment systems will reduce optical component positioning errors (\(<\) 1 \(\mu\)m). Given that thermal electron noise in photodetectors originates from the thermal effect of their resistive elements [33; 34; 35; 36], future work should explore suppressing this noise by implementing active thermal management for photodetectors (\(\Delta\)T \(<\) 1 mK\(/\sqrt{\mathrm{Hz}}\)). Additionally, suppressing the residual gas refractive index noise, which arises from pressure-related density fluctuations [37; 38; 39; 40], can be pursued through further optimization of the vacuum system. Collectively, these endeavors aim to bridge the gap between the current performance (60 pm\(/\sqrt{\mathrm{Hz}}\)) and the PAAM requirement (8 pm\(/\sqrt{\mathrm{Hz}}\)).  
**Author Contributions:** Conceptualization, Y.G., J.Y. and L.M.; methodology, Y.G. and L.M.; software, Y.G. and J.Y.; validation, Y.G. and J.Y.; formal analysis, Y.G.; investigation, Y.G.; resources, L.M.; data curation, Y.G.; writing--original draft preparation, Y.G.; writing--review and editing, Y.G., J.Y. and L.M.; visualization, Y.G.; supervision, L.M.; project administration, L.M. and J.J.; funding acquisition, H.Q. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key R&D Program of China (No. 2020 YFC2201300).  
**Infrared Consent Statement:** Not applicable.  
**Data Availability Statement:** The data that support the findings of this study are available from the corresponding author upon reasonable request.  
This work was completed at the Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences, and we would like to thank all the accommodating and helpful staff of this institute.  
The authors declare no conflicts of interest.