The computer controlled optical surfacing (CCOS) technique provides superior fabrication performance for optical mirrors when compared to the conventional method, which relies heavily on the skill of the optician. The CCOS technique provides improvements in terms of mass production, low cost, and short polishing time, and are achieved by estimating and controlling the moving speed of the tool and toolpath through a numerical analysis of the tool influence function (TIF). Hence, the exact estimation of various TIFs is critical for high convergence rates and high form accuracy in the CCOS process. In this paper, we suggest a new model for TIFs, which can be applied for various tool shapes, different velocity distributions, and non-uniform tool pressure distributions. Our proposed TIFs were also verified by comparisons with experimental results. We anticipate that these new TIFs will have a major role in improving the form accuracy and shortening the polishing time by increasing the accuracy of the material removal rate.
