Wolter-I structures based on X-ray grazing incidence optics are often used in extreme ultraviolet (EUV) collection optical systems, especially in the application of discharge plasma (DPP) sources. With the development of computer technology, the computerized surface forming (CCOS) method can significantly improve the surface accuracy and meet the optical requirements of high precision when processing Wolter-I grazing incident mirrors. In this paper, the nonlinear model predictive control (NMPC) system is innovatively introduced into the traditional CCOS method instead of the PID control system, and the application of NMPC in the rough grinding and fine grinding stages of Wolter-I grazing incident mirrors is studied, and it is found that the processing process and processing efficiency are effectively optimized through the system. Firstly, a detailed geometric model of the mirror was established for the special geometry of the inner surface of the cylindrical surface of the Wolter-I grazing incident mirror. Secondly, in view of the complex and nonlinear characteristics of the Wolter-I grazing incident mirror, a nonlinear model of the machining process is established, and the influence of spindle feed rate, removal pressure, abrasive particle size and other factors on the machining accuracy is considered, and the simulation results show that when the spindle feed rate is 25 mm/s, the removal pressure is 9 N, and the abrasive particle size is 10, the removal efficiency is the highest and the removal effect is the best. The experimental results show that the CCOS method combined with NMPC significantly improves the surface accuracy and effectively improves the processing efficiency and reduces the production cost when processing the Wolter-I grazing incident mirror.
Ding et al. (2026) studied this question.