## 3 Analysis and Design  
### Semi-Physical Simulation Test for the Establishment of Inter-Satellite Laser Links  
A three-stage acquisition strategy is adopted for the establishment of inter-satellite laser links in the Taiji program to suppress the pointing jitter of laser beams [39]. When the semi-physical simulation test is conducted in the laboratory, the distance between the two spacecraft simulation platforms is limited to a few meters. As a result, the procedure used for aligning the two spacecrafts with the STR (star tracker) cannot be simulated; therefore, only the two-stage acquisition strategy based on the CCD (charge-coupled device) and QPD can be studied using the proposed semi-physical simulation experimental platform. The main technical parameters involved in the two-stage acquisition strategy are listed in Table 1. The specification test for the pointing jitter value of 100 nrad\(/\surd\)Hz is needed within the uncertainty area range of \(\pm\)23.9 \(\upmu\)rad. Limited by the linearity range of DWS technology [40,41], the maximum detection FOV (field of view) of the QPD can only be set to 1.5 \(\upmu\)rad; thus, the two-stage acquisition strategy based on the CCD and QPD is necessary to achieve both a large dynamic range and high measurement accuracy. As depicted in Figure 4, the receiving optical axis passes through not only the reference position of the CCD, but also the center of the QPD. The received laser beam (green line) emitted by the remote spacecraft is first acquired by the CCD. The specification for the residual error for the acquisition phase based on the CCD is 1 \(\upmu\)rad. With an FOV of 1.5 \(\upmu\)rad, the received laser beam can be detected by the QPD. Due to the Doppler shift originating from the relative motion between spacecrafts, heterodyne interferometry is adopted; thus, the received laser beam interferes with the local laser beam, which is projected onto the center of the QPD. Then, the beat signal phase is calculated using DWS technology [41]. The two-dimensional angle of the pitch and yaw between the received laser beam and the local laser beam (also the receiving optical axis) is measured. Based on the measurement accuracy to the order of 1 nrad\(/\surd\)Hz, the pointing jitter can be suppressed to 100 nrad\(/\surd\)Hz; thus, precise pointing of laser is achieved. The DWS angle measurement is achieved using an SCI (science interferometer), which will be demonstrated in Section 3.2. The local laser beam will also bedepic \begin{table}
\begin{tabular}{c c c} \hline \hline
**Acquisition Procedures** & **Parameters** & **Technical Specifications** \\ \hline \multirow{2}{*}{Based on CCD} & Uncertainty area range & \(\pm\)23.9 \(\upmu\)rad \\  & Acquisition residual error & 1 \(\upmu\)rad \\ \hline \multirow{2}{*}{Based on QPD} & FOV (field of view) & 1.5 \(\upmu\)rad \\  & Pointing jitter & 100 nrad\(/\surd\)Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main technical parameters involved in the acquisition procedures based on the CCD and QPD [28]. Figure 3: Schematic diagram of the experimental platform for semi-physical simulations test of inter-satellite laser interference (side view). The acquisition process mentioned above should be simulated in the semi-physical simulation test to perform the specification test for a pointing jitter of 100 nrad/\(\surd\)Hz. The measurement accuracy of the test system must be 5-10 times higher than the targeted values; therefore, the semi-physical simulation system should have a test accuracy of at least 20 nrad/\(\surd\)Hz. This accuracy must be achieved in both the angle measurement and the simulation of the attitude adjustment. The value of 1\(\upmu\)rad is the designed residual error against the external FOV of the telescope. Since the magnification of telescope is 80X, the residual error at the CCD camera should be 80 \(\upmu\)rad. A CCD camera (SH640, TEKWIN, Xi'an, China) is chosen to meet the requirements.