# Precision Analysis and Error Compensation of a Telescope Truss Structure Based on Robotics
## 3 Aberration-Compensation Method
### Adjustment Error Compensation Analysis of Simulated Assembly and Adjustment Errors  
A 2 m Ritchey-Chretien (RC) system is analyzed as an example for aberration compensation, and the initial RMS design value of the optical system is 0.021\(\lambda\). Setting the communication connection in Zemax and Matlab establishes the relationship between the misalignment of the SM and the aberration characteristics. Dynamic data exchange (DDE) interface is used in this paper to realize the real-time data exchange in Zemax and Matlab. First, a randomly distributed sample of misalignment is produced in a uniform distribution in the misalignment range, and each sample model corresponds to an actual misalignment state. Through Zemax ray tracing, the Zernike coefficients corresponding to each set of offsets, \(\Delta M\), can be obtained. The optical system produces predominantly primary aberrations in the misalignment state, with the result that fringe Zernike coefficients \(Z4\) to \(Z9\) are used for modeling and calculation. Considering factors such as sample size and calculation time, 10,000 samples were randomly generated in the interval of Table 5 according to a uniform distribution to fit the sensitivity matrix model. According to the calculation method of the quadratic and first-order coefficient matrices, a set of multivariate quadratic equations for the misalignment of the SM is established.  
The telescope adjustment was simulated using the optical software, 5000 sets of offset vectors were randomly generated in the interval of Table 5 and calculated in Equation (23) to take the ray-tracing result as the true value, and determine the calculation error of the compensation model after calculating the misalignment using the high-order sensitivity matrix. Figure 9 shows the histograms of the fitting error frequency, showing the root mean square error (RMSE) of the fitting of the corresponding Zernike coefficient. The horizontal axis in the figure represents the fitting error, while the vertical axis represents the frequency.  
For a two-mirror system, the rotation of the SM around the zero-coma point will introduce astigmatism that is linearly proportional to the field of view without introducing a coma. Therefore, the establishment and verification of the model also needs to consider multiple fields of view, with F (0, 0), F (0, -0.1), and F (0, 0.1) considered in Table 6. After the corresponding adjustment is calculated  
Figure 9: Calculation of model error. (**a**) The RMSE of Z4. (**b**) The RMSE of Z5. (**c**) The RMSE of Z6. (**d**) The RMSE of Z7. (**e**) The RMSE of Z8. (**f**) The RMSE of Z9.  
and applied through the method in Section 3.1, the RMSE of each Zernike coefficient in each field of view can be obtained.  
Combining the RMSE between the misalignment state wavefront calculated by the sensitivity matrix for multiple fields of view and the actual wavefront, it can be observed that the high-order sensitivity matrix method maintains high accuracy even when the system misalignment is large and demonstrates good compensation ability with respect to primary aberrations.