Liu Guohao, Deng Yonghong, Li Zhibin
Department of Mechanical and Electrical Engineering, Liaocheng University Dongchang College, Liaocheng 252000, China.
Sichuan Provincial Promotion Center of Digital Transformation, Chengdu 611730, China.
Micromachines (Basel). 2025 Jun 23;16(7):734. doi: 10.3390/mi16070734.
To improve the surface morphology quality of ultra-precision optical components, particularly in the suppression of mid-spatial frequency (MSF) errors, this paper proposes a morphology gradient-aware spatiotemporal coupled smoothing model based on convolutional material removal. By introducing the Laplacian curvature into the surface evolution framework, a curvature-sensitive "peak-priority" mechanism is established to dynamically guide the local dwell time. A nonlinear spatiotemporal coupling equation is constructed, in which the dwell time is adaptively modulated by surface gradient magnitude, local curvature, and periodic fluctuation terms. The material removal process is modeled as the convolution of a spatially invariant removal function with a locally varying dwell time distribution. Moreover, analytical evolution expressions of PV, RMS, and PSD metrics are derived, enabling a quantitative assessment of smoothing performance. Simulation results and experimental validations demonstrate that the proposed model can significantly improve smoothing performance and enhance MSF error suppression.
为了提高超精密光学元件的表面形貌质量，特别是在抑制中频空间（MSF）误差方面，本文提出了一种基于卷积材料去除的形貌梯度感知时空耦合平滑模型。通过将拉普拉斯曲率引入表面演化框架，建立了一种曲率敏感的“峰值优先”机制，以动态指导局部驻留时间。构建了一个非线性时空耦合方程，其中驻留时间由表面梯度大小、局部曲率和周期性波动项自适应调制。材料去除过程被建模为一个空间不变去除函数与局部变化的驻留时间分布的卷积。此外，推导了PV、RMS和PSD指标的解析演化表达式，能够对平滑性能进行定量评估。仿真结果和实验验证表明，所提出的模型能够显著提高平滑性能并增强MSF误差抑制。
