## 3 Experimental Results and Discussion  
In our previous study [9], as shown in Figure 5a, to evaluate the background noise of the interferometer, we did not apply a voltage to the PAAM, keeping the steering mirror stationary, which acts as a reflector in this case. In this study, we used a reflector with a center height consistent with the PAAM instead of the PAAM for the system background noise test. In Figure 5b, the experimental system is shown, where key optical components such as fiber couplings and detectors were fixed to the surface of a ULE substrate (Corning\({}^{\circledR}\) ULE\({}^{\circledR}\)7973, \(\Phi\)280 \(\times\) 25 mm) using custom-made fused silica fixtures. The laser source was a custom-built 1064 nm laser. Two acousto-optic modulators (AOM, CETC SGTF150-1064-1P, CETC, Beijing, China) were used to apply frequency shifts of 150.8 MHz and 149.2 MHz, respectively, producing a 1.6 MHz heterodyne beat signal. A commercial phase meter (Liquid Instruments, Moku: Pro, Lyneham, Australia) was employed, along with a phase-locked loop (PLL) algorithm with a sampling frequency of 150 Hz. The entire optical path used polarization-maintaining fibers (PMF) to ensure polarization stability. To address the thermal noise in the low-frequency range (1 mHz to 1 Hz), this study differed from traditional approaches that utilized Invar steel as the substrate. Instead, it utilized a ULE substrate (\(\text{CTE}\ <\ 1\times 10^{-8}\text{K}^{-1}\)) and Hydroxide Catalysis Bonding (HCB) [30] technology to construct the optical path, as shown in Figure 5b. The bonding surfaces were super polished to achieve a surface form accuracy of \(\lambda/10\) (@633 nm), and in the HCB process, a bonding layer with a thickness of less than 10 nm was formed [31]. The experimental system was placed inside a vacuum chamber with a base vacuum level of \(10^{-5}\) Pa and an operational vacuum level of \(10^{-2}\) Pa, as shown in Figure 5b. It consisted of a composite thermal shielding system comprising three layers of copper  
Figure 5: Physical diagram of interferometer measurement system. (**a**) Previous study. (**b**) HCB interferometer. thermal shielding (P\({}_{1}\), P\({}_{2}\), P\({}_{3}\)) and PEEK brackets. The optical substrate was suspended within the shielding layers using PEEK brackets to minimize heat conduction. PT100 temperature sensors were installed in each layer (P\({}_{1}\), P\({}_{2}\), P\({}_{3}\)) and the optical substrate (P\({}_{4}\)) for real-time temperature monitoring, as depicted in Figure 6.  
The performance of the composite thermal shielding system in mitigating temperature fluctuations was assessed by monitoring the temperature variations across the vacuum chamber (P\({}_{0}\)), the three copper thermal shielding layers (P\({}_{1}\), P\({}_{2}\), P\({}_{3}\)), and the optical substrate (P\({}_{4}\)) over a 10 h period. The time sequence curves, illustrated in Figure 7a, depict the peak-to-valley (PV) temperature fluctuations for each layer. The recorded PV values were as follows: 428.73 mK for P\({}_{0}\), 152.92 mK for P\({}_{1}\), 88.25 mK for P\({}_{2}\), 67.66 mK for P\({}_{3}\), and 62.66 mK for P\({}_{4}\). The vacuum chamber (P\({}_{0}\)) exhibited pronounced temperature oscillations, with multiple peaks and troughs observed within the 10 h timeframe, reflecting its exposure to external thermal influences. In contrast, the thermal shielding layers progressively attenuated these fluctuations. Specifically, P\({}_{1}\) reduced the fluctuation amplitude by approximately 64.3% relative to P\({}_{0}\), with a noticeable slowing of the fluctuation trend. Further suppression was achieved by P\({}_{2}\) and P\({}_{3}\), which lowered the amplitudes by approximately 79.4% and 84.2%, respectively, compared to P\({}_{0}\). The optical substrate (P\({}_{4}\)) displayed a nearly linear temperature profile with no discernible fluctuations, demonstrating the shielding system's effectiveness in isolating the substrate from the external thermal disturbances.