Modeling and analysis of sub-aperture tool influence functions for polishing curved surfaces

Computer controlled optical surfacing requires accurate tool influence functions (TIFs) for deterministic fabrication of smooth curved surfaces. In the present paper, the three dimensional TIFs are investigated separately from their radial profiles, which can be simplified into circular arcs. TIFs are found significantly affected by the form deviation between the polishing pad and the workpiece, regardless of the specific shape of the workpiece. A new analytical TIF model is proposed as a function associated with the relative curvature difference. The condition to guarantee single-peak TIFs is then derived, which is of essence for stable planning of polishing paths. Thereby appropriate processing parameters can be selected accordingly. Practical experimental results demonstrate that the new model can reliably predict the TIFs in different situations, and the modelling error is greatly improved compared to the conventional methods.