## 3 Analysis and Design
### Semi-Physical Simulation Test for the Interferometry of Inter-Satellite Ranging
To ensure the scientific goals are achieved, high requirements are also placed on the telescope, including high wavefront quality, ultra-stable optical path stability, and extremely low stray light level. With a detailed design, high-precision optical manufacturing processes, and the use of an accurate alignment monitoring device, the corresponding technical specifications can be achieved. The frequency instability noise levels for LASER1 and LASER2 in Figure 8a are the major noise sources in laser interferometry, so high requirements are proposed for the laser frequency stability. These are met using the PDH (Pound-Drever-Hall) stabilization technique. In the semi-physical simulation test for interferometry of the inter-satellite ranging, the real working conditions in space should be simulated; however, when the simulation is conducted on the ground, gravity and ground vibration noise are two factors that cannot be ignored. Due to the existence of gravity, it is difficult to simulate a freely suspended test mass on the ground. According to previous studies [28; 29; 30; 31; 32; 33; 34], the specification test for interferometry ranging is conducted by measuring the system noise of the laser interference payload, in order to guarantee that the system noise is less than the specifications. The simulation of  
Figure 8: Schematic diagram of single interference platform: (**a**) the optical path design; (**b**) the 3D model of a single interference platform with only SCI. the freely suspended test mass is usually substituted by a fixed MR (mirror reflector) in a vacuum tank. As the common mode noise, the impact of the displacement fluctuation caused by various vibration noises on the interferometry ranging can be neglected. For the interferometry of inter-satellite ranging, two fixed MRs are needed. The noise caused by ground vibrations is differential mode noise. The relative displacement fluctuation between the two fixed MRs is much larger than the specifications, leading to test failure. To perform a real semi-physical simulation test, two freely suspended test masses must be simulated while isolating disturbances from ground vibration noise to ensure that the relative motion between two test masses can be ignored. For this, multistage suspension technology is used [46; 47; 48; 49], which was employed in LIGO. At the same time, an active control loop is imported. With the help of the millihertz-frequency and high-precision displacement sensor, the vibration noise in the low millihertz frequency band can be isolated through the active feedback control system. As a result, the freely suspended test mass can be simulated. A schematic diagram and block diagram of the multi-stage suspension vibration isolation based on active control are shown in Figure 9. A two-stage suspension is used. An active control system, which is achieved by utilizing technologies such as an inertial sensor, PID control, weak force driver, and precision machinery, is imported on TM 1. The control period for the active control is far less than the period for the ground vibration; thus, the ground vibration noise is isolated by the active control acting on TM 1 before it is transmitted to TM 2 and suspended at the second stage. As such, TM 2 can move freely in the horizontal direction. Through reasonable design of the suspension system and active control system, the displacement disturbance of TM2 in the low millihertz frequency band can be ensured to be in the order of the pm magnitude, so as to perform the semi-physical simulation of the freely suspended test mass. This challenging task is currently being tackled by another participating team from the Taiji program. The spacecraft simulation platform is also affected by the ground vibration noise. According to [50; 51], ground vibration noise is caused by natural phenomena and human activities.