## 3 Analysis and Design
### Semi-Physical Simulation Test for the Establishment of Inter-Satellite Laser Links
The main technical parameters of the CCD camera are listed in Table 2. The focal length of the imaging system is designed to be 150 mm. With the chosen CCD camera and spot centroid algorithm, the positioning accuracy can reach 0.1 pixels; thus, the two-dimensional angle measurement accuracy of the pitch and yaw between the real position of the received laser beam and the reference position (also the receiving optical axis) is calculated. With an accuracy of 10 \(\upmu\)rad, the specification of the residual error can be met. Additionally, converting the FOV of the CCD to the external FOV of the telescope, a detection range of 800 \(\upmu\)rad \(\times\) 640 \(\upmu\)rad can be obtained. The pointing uncertainty area range of \(\pm\) 23.9 \(\upmu\)rad can be completely covered. With the CCD and spot centroid algorithm, the laser can be acquired in the FOV of the QPD. In the Taiji program, the diameter of the laser spot is designed to be 1 mm and the power is designed to be ca. 100 pW; thus, the QPD is required to have low NEP (noise equivalent power). To meet these requirements, a GD4542-20M QPD is chosen (China Electronic Technology Corporation, Chongqing, China), the technical parameters for which are listed in Table 3. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Technical Specifications** \\ \hline Number of pixels & 640 \(\times\) 512 \\ Pixel size & 15 \(\upmu\)m \\ Focal length of imaging system & 150 mm \\ Photoelectric conversion efficiency (n) & 0.7 A/W @ 1064 nm \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Main technical parameters of the SH640 camera. Figure 4: The two-stage acquisition strategy based on the CCD and QPD. As mentioned in the literature [42], the two acquisition procedures based on CCD and QPD have strong coupling; therefore, by utilizing the DWS technology, not only can the effect of the acquisition phase based on the CCD be verified, but the specification test for the pointing jitter can also be performed. With testing accuracy in the region of 1 nrad/\(\surd\)Hz, the high-precision angle measurement requirements for the semi-physical simulation test system can also be met. Another problem that needs to be solved is the simulation of high-resolution attitude adjustments. The attitude adjustment of the spacecraft is achieved through micro-thrusters. With minimum thrust in the order of \(\mu\)N magnitude, the resolution of the attitude adjustment can be achieved up to nrad magnitude. This is far beyond the limits of conventional mechanical motion. Piezoceramics technologies based on solid-state physics effects have infinite resolution potential in principle [43]; thus, the simulation of high-resolution attitude adjustment can be achieved using a piezo-driven hexapod. Considering the weight of the optical interference platform (ca. 30 kg), a customized piezo-driven hexapod with the ability for both large load and high resolution is used. According to the analysis above, the specification test for the pointing jitter can be performed using DWS technology. To achieve accurate measurements, the angle measured by the DWS should be calibrated before the test [44]; therefore, only a motion capability of 100 nrad/\(\surd\)Hz needs to be satisfied for the customized piezo-driven hexapod, rather than 20 nrad/\(\surd\)Hz. To achieve a motion capability of 100 nrad/\(\surd\)Hz in the low millihertz frequency band, the corresponding specification requirement in the time domain cannot be met. It is well known that during conversion to the frequency domain, the signal in the time domain will be broken into components with different frequencies.