# An Ultra-Precision Smoothing Polishing Model for Optical Surface Fabrication with Morphology Gradient Awareness

## TL;DR

This paper introduces a new model for polishing optical surfaces that improves quality by better controlling material removal and suppressing surface errors.

## Contribution

A novel spatiotemporal smoothing model with curvature-aware dwell time modulation for enhanced optical surface fabrication.

## Key findings

- The model significantly improves smoothing performance in optical surface fabrication.
- Mid-spatial frequency errors are effectively suppressed using the proposed method.
- Analytical expressions for PV, RMS, and PSD metrics enable quantitative performance evaluation.

## Abstract

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.