Advancements in astronomical telescopes and cutting-edge technologies, including deep ultraviolet (DUV) and extreme ultraviolet (EUV) lithography, have escalated demands and imposed stringent surface quality requirements on optical system components. Achieving near-ideal optical components requires ultra-smooth surfaces with sub-nanometer roughness, no sub-surface damage, minimal surface defects, low residual stresses, and intact lattice integrity. This necessity has driven the rapid development and diversification of ultra-smooth surface fabrication technologies. This paper summarizes recent advances in ultra-smooth surface processing technologies, categorized by their material removal mechanisms. A subsequent comparative analysis evaluates the roughness and polishing characteristics of ultra-smooth surfaces processed on various materials, including fused silica, monocrystalline silicon, silicon carbide, and sapphire. To maximize each process’s advantages and achieve higher-quality surfaces, the paper discusses tailored processing methods and iterations for different materials. Finally, the paper anticipates future development trends in response to current challenges in ultra-smooth surface processing technology, providing a systematic reference for the study of the production of large-sized freeform surfaces.

The precision of workpiece machining is critically influenced by the geometric errors in the kinematics of grind robots, which directly affect their absolute positioning accuracy. To tackle this challenge, this paper introduces a logistic-tent chaotic mapping Levenberg Marquardt algorithm designed to accurately identify and compensate for this geometric error. the approach begins with the construction of a forward kinematic model and an error model specific to the robot. Then the algorithm is adopted to identify and compensate for the geometric error. The method establishes a mapping interval around the initial candidate solutions derived from iterative applications of the Levenberg Marquardt algorithm. Within this interval, the logistic-tent chaotic mapping method generates a diverse set of candidate solutions. These candidates are evaluated based on their fitness values, with the optimal solution selected for subsequent iterations. Empirical compensation experiments have validated the proposed method's precision and effectiveness, demonstrating a 6% increase in compensation accuracy and a 47.68% improvement in efficiency compared to existing state-of-the-art approaches. This process not only minimizes the truncation error inherent in the Levenberg Marquardt algorithm but also significantly enhances solution efficiency. Moreover, simulation experiments on grind processes further validate the method's ability to significantly improve the quality of workpiece machining.

Path deviations caused by geometrical errors in machining equipment significantly affect the machining quality of optical components. To enhance the quality and efficiency of optical component processing, this paper presents a Chebyshev interpolated Levenberg-Marquardt algorithm (CILM) aimed at compensating for path deviations in a robotic smoothing system utilized for optical component processing. First, the positioning accuracy of the robotic smoothing system is measured using a laser tracker. Subsequently, an objective function is constructed based on robot kinematics and error models to optimize the geometric errors in the system. Then, the proposed method is adopted to identify the geometric parameters of the robotic smoothing system to compensate for the smoothing path deviations. The compensation results confirm the effectiveness of the proposed method in enhancing the absolute positioning accuracy of the robotic smoothing system. Additionally, experimental verification is conducted to validate the effectiveness of the proposed method in improving the surface quality of optical components through smoothing path compensation. The results of the three experiments indicate that the proposed CILM achieves optical components with peak-to-valley values 15.70%, 28.7%, and 4.01% lower than those obtained before compensation, along with root mean square of 33.67%, 21.57%, and 10.23% lower than before compensation values, respectively. Moreover, the power spectral density curves of CILM exhibit smoother characteristics in comparison to the curves before compensation.