Standardization of methods for extracting statistics from surface profile measurements

Surface profilers and optical interferometers produce 2D maps of surface and wavefront topography. Traditional standards and methods for characterizing the properties of these surfaces use coordinate space representations of the surface topography. The computing power available today in modest personal computers makes it easy to transform into frequency space and apply well-known signal processing techniques to analyze the data. The Power Spectral Density (PSD) function of the surface height distribution is a powerful tool to assess the quality and characteristics of the surface in question. In order to extract useful information about the spectral distribution of surface roughness or mid-spatial frequency error over a particular spatial frequency band, it is necessary to pre-process the data by first detrending the surface figure terms and then applying a window function before computing the PSD. This process eliminates discontinuities at the borders of the profile that would otherwise produce large amounts of spurious power that would mask the true nature of the surface texture. This procedure is now part of a new draft standard that is being adopted by the US OEOSC for analysis of the statistics of optical surface, OP1.005.1 Illustrations of the usefulness of these procedures will be presented.