## 5 Conclusions  
This study explores the complex relationship between the beam walk dimensions and DWS signal in inter-satellite laser communications. Through detailed theoretical analysis and simulations, it becomes evident that an increase in beam walk size leads to heightened nonlinearity in the DWS angle measurements. With a constant pointing jitter, the DWS measurement nonlinear errors caused by different degrees of beam walk will vary with changes in the axial propagation distance, worsening as the degree of beam walk increases. Next, a conjugate imaging system was constructed using two plano-convex lenses to verify the effectiveness of suppressing beam walk through conjugate position imaging. The imaging system can achieve conjugate imaging of the spot centroid within 0.8 mrad with minimal distortion and the introduction of only minor spherical aberration. Then, a ground simulation optical path for DWS angle measurement in inter-satellite links was designed, and the setup and measurements were conducted in the laboratory. By precisely aligning and locating the beam waist and the entrance and exit pupils of the imaging system, alignment errors and the zero-point offset of the DWS technique were suppressed. The experimental results show that with an angular offset of 300 \(\upmu\)rad, the measurement error can be reduced to 50 \(\upmu\)rad by adding the imaging system to the optical path, which reduces the error by 83% compared to the optical path without the imaging system. When the angular offset is constant, the root mean square value of the QPD measurement jitter is also smaller when the imaging system is added. This indicates that the experimental setup can effectively suppress the nonlinear errors in DWS caused by the beam walk, and the inclusion of the imaging system in the optical path helps to mitigate pointing jitter noise in inter-satellite links, thereby improving laser pointing control accuracy. This method will provide a valuable reference for the QPD interferometric measurement optical path and QPD precision acquisition measurement control on the optical platform in the future Taiji program.  
Figure 12: Comparative analysis of jitter RMS: assessing performance with (red line) and without (blue line) the imaging system.  
**Author Contributions:** Conceptualization, X.-G.Q., Y.-K.W. and R.-H.G.; methodology, X.-G.Q. and Z.C.; software, H.-Q.S. and W.-L.Y.; validation, X.-G.Q. and Z.C.; formal analysis, X.-G.Q., X.W., H.-Q.S. and R.-H.G.; investigation, Y.-K.W. and R.-H.G.; resources, Y.-K.W. and R.-H.G.; data curation, X.-G.Q.; writing--original draft preparation, X.-G.Q.; writing--review and editing, X.-G.Q.; visualization, X.-G.Q.; supervision, Y.-K.W.; project administration, Y.-K.W.; funding acquisition, Y.-K.W. All authors have read and agreed to the published version of the manuscript.  
This work was supported by National Key Research and Development Program of China (2022 YFC2203700), National Key Research and Development Program of China (2020 YFC2201300).  
**Institutional Review Board Statement:** Not applicable.  
**Infrared Consent Statement:** Not applicable.  
**Data Availability Statement:** The relevant data and code pertinent to this study are accessible via the provided link ([[https://pan.baidu.com/s/1](https://pan.baidu.com/s/1) FBbj/f92 GTSkfL_3 tb6 xg]([https://pan.baidu.com/s/1](https://pan.baidu.com/s/1) FBbj/f92 GTSkfL_3 tb6 xg)) (accessed on 26 May 2023). For access verification codes, please contact [EMAIL_ADDRESS] or the designated corresponding authors' email address. It is advisable to include your affiliation and the purpose of your inquiry in the communication.  
**Conflicts of Interest:** The authors declare no potential conflicts of interest.