Investigation into the error compensation method of the surface form based on feed rate optimization in deterministic polishing

As the final step to fabricate the optical parts, the deterministic polishing process is usually used to reduce the roughness and correct the surface form. In this article, a new compensation method of the surface form error was proposed by optimizing the feed rate of the polishing process. The local material removal was described as the polished depth orthogonal to the tool path, and the local material removal model was also developed. Then, the linear algebraic expression of the global polished profile was derived by convoluting the local removal depth at each dwell point of the polishing process. In this model, the global polished depth matrix equals to the product of influential matrix and feed rate matrix. On the basis of the above, the error compensation method for the polishing process can be seen as an optimization process of the feed rate in polishing. The non-negative least square method was used to solve this problem. The effectiveness of the model proposed is verified by the polishing experiments.