# Optical Pupil Shift Correction Method for Large Ground-Based Optical Telescopes
## 4 Simulation Analysis and Experimental Verification
### Compensation of Optical-Axis Deviation Induced by Temperature Variations  
The thermal deformation analysis of the telescope system at different ambient temperatures (\(-\)20-50 \({}^{\circ}\)C) is illustrated in Figure 11. The variation in the angular deviation of the secondary mirror with temperature before and after compensation displays in Figure 17, obtained using the same analysis method as in Section 3.2. Figure 18 illustrates the variation in the position deviation with temperature.  
Figure 17: The angle deviations between primary and secondary mirror vs. the temperature variations. The data results were obtained through the deformation analysis of the telescope. (**a**) Before compensation; (**b**) after compensation.  
The same compensation method was used for the optical-axis deviation caused by temperature change. The variation in the optical-axis deviation of the telescope main system with temperature before and after the compensation is shown in Figure 19.  
Figure 19 leads to the conclusion that the optical-axis deviation after compensation reduces to within 5.5\({}^{\prime\prime}\). Additionally, the secondary mirror did not require to be rotated about the coma-free point for compensation.  
The following conclusions were drawn from the calculations of the secondary mirror deviations before and after compensation amid temperature variations (Figures 17 and 18) and those of the optical-axis deviations of the main system (Figure 19).  
Temperature variations induce relatively small angular and positional deviations in the telescope. In fact, the deviations of the secondary mirror with the compensation control of the Hexapod platform are close to zero.  
As the ambient temperature increases, the variation of the control input of the Hexapod platform is strictly linear. In application, the ambient temperature compensation can be considered linear.  
The maximum position and angular deviations of the primary and secondary mirrors before compensation were -30 \({}^{\circ}\)C each. The maximum angular deviation was approximately 24\({}^{\prime\prime}\), and the maximum position deviation was approximately 3.5 mm. After  
Figure 19: The variations in the optical-axis deviation of the main system vs. the temperature variation. The data results were obtained through the overall optical model of the telescope. (**a**) Before compensation; (**b**) after compensation.  
Figure 18: The position deviations between primary and secondary mirror vs. the temperature variation. The \(d_{z}\) refers to the axial position deviation between primary and secondary mirror. The data results were obtained through the deformation analysis of the telescope. (**a**) Before compensation; (**b**) after compensation.  
Hexapod platform compensation, the maximum angular deviation dwindled to 0.0058\({}^{\prime\prime}\) and the maximum position deviation was reduced to 0.015 mm. The maximum deviations of the optical axis before and after compensation were 21.3\({}^{\prime\prime}\) and 5.16\({}^{\prime\prime}\), respectively. The optical pupil shift caused by the deviation of the optical axis after compensation was within the acceptable range. Thus, the performance of the optical system was augmented.