## 4 Compensator Design and Simulation Verification  
The compensation capability of compensation devices is inherently limited. In order to effectively compensate for the image plane while maintaining appropriate image quality, it is crucial that the magnitude of the introduced aberrations remains within an acceptable range. The servo control performance of the image compensation system is closely related to the imaging quality. Therefore, it is necessary to use the adjustment capability of the compensation device as a strict criterion during its design to verify the effectiveness of image shift compensation. The design steps of compensation devices are as follows:  
1. Determine the adjustment range of compensation devices based on the control capability of the servo control system. 2. Preliminarily determine the structural parameters of the prism. 3. Perform compensation analysis and aberration analysis on image plane deformation. 4. Based on actual application requirements, taking into account the device structure and aberrations, determine the final structural form. Due to the errors in the above analysis and other factors, the required compensation may exceed the compensation range of the compensation device. To avoid exceeding the compensation range, an adjustment margin can be incorporated into the prism parameter design. Based on this, we use the 8.5 th generation glass substrate as an example and apply the designed compensating device for compensation. The design indicators are shown in Table 1.  
The mask template adopts a natural hanging deformation design, with dimensions of 1220 mm \(\times\) 1400 mm \(\times\) 13 mm. The long side is calculated based on simple fixation and simulated using COMSOL (all simulations were performed on personal computers \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Specification** \\ \hline Displacement resolution & 2 μm \\ Angular resolution & 5\({}^{\prime\prime}\) \\ PV of the surface deformation error & 10 μm \\ RMS of the surface deformation error & 1 μm \\ Max RMS WFE & 0.11\(\lambda\) \\ Average RMS WFE & 0.07\(\lambda\) \\ Telecentricity & \textless{}0.4 mrad \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Specifications of the doubly telecentric projection optical system. Figure 6: Comparison between theoretical calculation values of aberration coefficients in x and y directions and ray tracing values. (**a**) is the aberration coefficient in X direction, (**b**) is the aberration coefficient in Y direction. equipped with AMD R7-4800H CPU), and the deformation under its own weight is shown in Figure 7.  
As shown in Figure 8, there are 11 doubly telecentric projection optical systems distributed along the short side, each occupying approximately 100 mm of scanning exposure length. The reference wavelength is 0.365 \(\upmu\)m, and the NA is 0.1. Therefore, the depth of focus of the system is approximately \(\pm\)18 \(\upmu\)m. The maximum deformation of the mask template (123 \(\upmu\)m) far exceeds the depth of focus of the doubly telecentric projection optical system. The image plane deformation of each system is expected to be controlled within 10 \(\upmu\)m.  
Based on the above calculation, the doubly telecentric projection optical system at different positions needs to adjust the various parameters of the compensation device according to different image plane positions. The schematic diagram of the doubly telecentric projection optical system and compensation device is shown in Figure 9.  
Prisms have two parameters: wedge angle and center thickness, and are made of fused silica with high ultraviolet transmittance. The center thickness is set to 20 mm to ensure good deformation resistance. The influence of different wedge angles on the doubly telecentric projection optical system was compared using Zemax 2023 software. Figure 10a shows the initial RMS WFE of prisms with different wedge angles and the maximum RMS WFE during the adjustment process.