Abstract

The smoothing effect of the rigid lap plays an important role in controlling midspatial frequency errors (MSFRs). At present, the pressure distribution between the polishing pad and processed surface is mainly calculated by Mehta’s bridging model. However, this classic model does not work for the irregular MSFR. In this paper, a generalized numerical model based on the finite element method (FEM) is proposed to solve this problem. First, the smoothing polishing (SP) process is transformed to a 3D elastic structural FEM model, and the governing matrix equation is gained. By virtue of the boundary conditions applied to the governing matrix equation, the nodal displacement vector and nodal force vector of the pad can be attained, from which the pressure distribution can be extracted. In the partial contact condition, the iterative method is needed. The algorithmic routine is shown, and the applicability of the generalized numerical model is discussed. The detailed simulation is given when the lap is in contact with the irregular surface of different morphologies. A well-designed SP experiment is conducted in our lab to verify the model. A small difference between the experimental data and simulated result shows that the model is totally practicable. The generalized numerical model is applied on a $\mathrm{\Phi }500\mathrm{mm}$ parabolic surface. The calculated result and measured data after the SP process have been compared, which indicates that the model established in this paper is an effective method to predict the SP process.

© 2014 Optical Society of America

Control of mid-spatial frequency errors considering the pad groove feature in smoothing polishing process

Xuqing Nie, Shengyi Li, Hao Hu, and Qi Li
Appl. Opt. 53(28) 6332-6339 (2014)

Correlation-based smoothing model for optical polishing

Yong Shu, Dae Wook Kim, Hubert M. Martin, and James H. Burge
Opt. Express 21(23) 28771-28782 (2013)

Theoretical and experimental comparisons of the smoothing effects for different multi-layer polishing tools during computer-controlled optical surfacing

Xuyu Li, Chaoyang Wei, Simin Zhang, Wendong Xu, and Jianda Shao
Appl. Opt. 58(16) 4406-4413 (2019)

Parametric smoothing model for visco-elastic polishing tools

Dae Wook Kim, Won Hyun Park, Hyun Kyoung An, and James H. Burge
Opt. Express 18(21) 22515-22526 (2010)

Modeling and in-depth analysis of the mid-spatial-frequency error influenced by actual contact pressure distribution in sub-aperture polishing

Lanya Zhang, Songlin Wan, Hanjie Li, Hao Guo, Chaoyang Wei, Dawei Zhang, and Jianda Shao
Opt. Express 31(9) 14414-14431 (2023)