## 4 Inter-Satellite Link Angle Measurement Simulation Experiment
### Design of Pointing Angle Measurement System  
In 2022, [PERSON] et al. [19] proposed that zero-offset analysis on the DWS technique would affect the absolute angle measurement error and designed an experimental system to verify the hypothesis. The zero-offset is theoretically eliminated at the beam waist position. To reduce the impact of zero-offset on the experiment, we refer to his optical path design. The pointing jitter noise verification system proposed by [PERSON] et al. [23] in 2022 is regarded as another reference for the following design. Figure 8 illustrates the experimental setup where a laser undergoes division and frequency alteration through two Acousto-Optic Modulators (AOMs), generating two Gaussian beams with a frequency discrepancy denoted as \(\Delta f\). In space interference, this  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Offset/mrad** & **Center of X/mm** & **Center of Y/mm** & **x-Axis Radius/mm** & **y-Axis Radius/mm** \\ \hline
0 & \(-\)0.00005638 & \(-\)0.00006197 & 0.24985080 & 0.25016640 \\
0.1 & \(-\)0.00007094 & \(-\)0.00006395 & 0.24985112 & 0.25009686 \\
0.2 & \(-\)  
frequency difference is caused by the Doppler frequency shift [6,24]. The \(\Delta f\) is set to 1.6 MHz, which is a value consistent with the Doppler frequency shift of the Taiji program and the detector bandwidth. The blue line depicts the reference beam, emulating the local Gaussian beam, which traverses a linear polarizer (LP2) before reflection by a beam splitter (BS). Following this path, the beam navigates through an imaging system and is precisely directed into the QPD's center. During optical path alignment, meticulous care ensures the Gaussian beam's propagation along the optical axis, injecting perpendicularly into the QPD. The QPD's placement on the conjugate plane relative to the waist position aims to negate zero-offset. Conversely, the measurement beam, signified by the red line, proceeds through a distinct linear polarizer (LP1) and a beam expander. This expansion endows the beam with Gaussian flat-top characteristics, mimicking the beam relayed from a distant satellite. A subsequent aperture trims the beam spot to align with the reference spot's dimensions. This beam then reflects off a Fast Steering Mirror (FSM), sequentially moves through BS and the imaging system, and eventually intersects with the reference beam on the QPD, thereby replicating the actual interference conditions of an inter-satellite laser link. In the experiment, optical beam angular deviations induced by pointing jitter are simulated by driving the Fast Steering Mirror (FSM) to generate beam deflections, mimicking the beam walk phenomenon. To ensure conjugate imaging, the QPD needs to be positioned at the rear focal point of the imaging system, while the FSM should be positioned at the front focal point of the imaging system. To suppress zero-offset and minimize its impact on actual measurements, a reference beam is utilized. By moving the imaging system, a beam quality analyzer is used to find two points with equal beam sizes in the vicinity and far from the rear end of the imaging system. The central position of these two points is considered as the beam waist position. This method effectively locates the beam waist of the reference beam, and iterative adjustments of the imaging system ensure that this point coincides with the rear focal point of the imaging system. The FSM is positioned at the front focal point of the imaging system, which can be determined by the focal length of the lens. In the Taiji program, the exit pupil position of the measurement beam after four off-axis reflections from the telescope is also the entrance pupil of the optical system. Pointing jitter will couple at this position, affecting interferometric measurements. After completion of the alignment, the entrance pupil position of the optical system is designated as FSM, and using FSM to simulate disturbances aims to achieve results as consistent as possible with actual conditions.