## 4 Inter-Satellite Link Angle Measurement Simulation Experiment
### Results and Discussion  
The Figure 9 illustrates the angle measurements depicted by the blue line (without imaging system) and the red line (with imaging system), in contrast to the ideal scenario represented by the gray dotted line, where no measurement error exists. As the perturbation angle expands, there is a corresponding amplification in the measurement inaccuracies relative to the ideal condition. Notably, the error magnitude is considerably more pronounced in the absence of the imaging system. This pattern underscores an escalating nonlinearity in the DWS signal's angle as the beam walk intensifies. Conversely, measurements employing the imaging system more closely mirror the actual perturbation angles, exhibiting enhanced linearity compared to the setup devoid of the imaging system.  
From the results, it can be observed in Figure 10 that when the piezoelectric-driven amplitude reaches 300 \(\upmu\)rad, the addition of the imaging system introduces an angular measurement error of approximately 50 \(\upmu\)rad, whereas the error without the imaging system is approximately 300 \(\upmu\)rad higher. The inclusion of the imaging system results in a relative reduction in measurement error by 83%. This deviation could potentially stem from optical alignment discrepancies, particularly the misalignment between the two interfering beams or the displacement of the beam center from the QPD's central point. Nonetheless, the integration of the imaging system distinctly amplifies the DWS technique's angle measurement capacity and mitigates measurement inaccuracies. These findings underscore the imaging system's efficacy in rectifying the beam walk.  
As shown in Figure 11, when the amplitude applied to the FSM is within 20 \(\upmu\)rad, the imaging system still significantly reduces the measurement error of the DWS.  
Figure 9: Comparative analysis of the DWS angle measurement error with and without imaging system correction for beam walk.  
During ground-based simulations, there is no magnification effect of telescope diagonal jitter. Narrowing the measurement angle range to 20 \(\upmu\)rad allows for a clearer assessment of the impact of the imaging system on the precision of QPD capture.  
For the entire link pointing control system, the stability of the DWS technique in reading out angles also constrains the stability of the link. Therefore, the next step was to test the inhibitory effect of the imaging system on pointing jitter when driving the FSM at different angular offsets.  
From Figure 12, it is evident that when the angular deviation of the measurement beam and the reference beam is constant, the root mean square value of jitter measured by the DWS technique is significantly smaller in the optical path with the imaging system compared to when the imaging system is removed. Therefore, the imaging system effectively reduces pointing jitter, and it can be anticipated that further suppression of pointing jitter will occur after closed-loop control by the control system.  
Figure 11: Comparative analysis of angular measurement errors in 20 \(\upmu\)rad: assessing performance with (red line) and without (blue line) the imaging system.  
Figure 10: Comparative analysis of angular measurement errors: assessing performance with (red line) and without (blue line) the imaging system.  
In summary, the integration of the imaging system notably enhances the angular measurement precision and stability of the DWS technique. These results demonstrate the effectiveness of the imaging system in correcting beam wander, making a significant contribution to improving laser pointing accuracy and suppressing inter-satellite link pointing jitter noise.