Characterisation of surface roughness for ultra-precision freeform surfaces

Ultra-precision freeform surfaces are widely used in many advanced optics applications which demand for having surface roughness down to nanometer range. Although a lot of research work has been reported on the study of surface generation, reconstruction and surface characterization such as MOTIF and fractal analysis, most of them are focused on axial symmetric surfaces such as aspheric surfaces. Relative little research work has been found in the characterization of surface roughness in ultra-precision freeform surfaces. In this paper, a novel Robust Gaussian Filtering (RGF) method is proposed for the characterisation of surface roughness for ultra-precision freeform surfaces with known mathematic model or a clould of discrete points. A series of computer simulation and measurement experiments were conducted to verify the capability of the proposed method. The experimental results were found to agree well with the theoretical results.