## 3 Analysis and Design
### Semi-Physical Simulation Test for the Interferometry of Inter-Satellite Ranging  
As mentioned earlier, distance fluctuations caused by gravitational waves between two freely suspended test masses, which are located in adjacent spacecrafts, are measured using laser interferometry. As shown in Figure 7, the optical interference platform is mounted on the spacecraft. Although space is a microgravity environment, tiny vibrations still exist on the spacecraft. Inside the spacecraft, vibrations are treated as common mode noise, which can be suppressed [29]. For the interferometry of inter-satellite ranging, vibrations are treated as differential mode noise, which cannot be eliminated; therefore, two freely suspended test masses are adopted as displacement reference benchmarks for the interferometry of space gravitational waves. The optical measurement process for distance fluctuations between two test masses is divided into three segments. One segment involves the interferometry of inter-satellite ranging between two optical interference platforms located in adjacent spacecrafts, while the other two segments involve the interferometry of TM (test mass) ranging between the optical interference platform and TM in each spacecraft. The optical path design for the single-interference platform is depicted in Figure 8a. LASER1 (red line) is split into three parts by BS1 (beam splitter 1) and BS2. Two parts involve local laser beam 1, the first part of which is directly projected onto the center of the QPDs after splitting by BS3 of SCI. The second part is first transmitted to the TM. Both LPs (linear polarizers) and \(\frac{1}{4}\lambda\) wave plates are used to alter the polarization state of the laser. After passing through a \(\frac{1}{4}\lambda\) wave plate twice, the transmission direction of the laser through PBSs (polarized beam splitters) is changed. The laser beam (blue line) is reflected by the TM, MR2 (mirror reflector), and PBS2 in turn. Then, it is projected onto the center  
Figure 5: The 3D model of the customized piezo-driven hexapod. Figure 6: Technical solution for the semi-physical simulation test for the establishment of inter-satellite laser links. Figure 7: Interferometry of ranging between two test masses (side view). of the QPDs after splitting by BS4 of the TMI (test mass interferometer). The third part, which is split by BS2, is emitted out. LASER2 (pink line) is local laser beam 2 on the same platform. It is only projected onto the center of the TMI's QPDs. After being emitted by the remote spacecraft, the third part of LASER1 is received by the local interference platform. Then, the received laser beam (green line) is captured by the CCD and QPDs of SCI one-by-one. With the interference of the first part of LASER1 and the received laser beam, the interferometry of inter-satellite ranging is achieved using SCI. Meanwhile, with the interference of the second part of LASER1 reflected by the TM and LASER2, the interferometry of TM ranging is achieved using TMI. As described in Section 3.1, the SCI is also used to carry out high-precision angle measurements using DWS technology at the same time. The 3D model of a single interference platform with only SCI is also shown in Figure 8b. In order to achieve ranging noise of 100 pm/vHz, a series of technical specifications are proposed for the parameters of the optical interference platform, telescope, and lasers, as listed in Table 5. To obtain the ideal interference effect, the two interfering beams need to be of equal height and parallel to each other; therefore, the degree of spot coincidence and included angle of the interfering beams are two parameters that need to be considered for the optical interference platform. Their corresponding technical specifications are guaranteed by the accuracy of the optical manufacturing and assembly processes. A joining technology named HCB (hydroxide-catalyzed bonding) is used in assembly of the optical interference platform. Optical components are bonded on a substrate made of zerodur.