Chris Evans and Angela Davies recently published a paper with co-author Liangu He in Annals of the CIRP. The title of the paper is ‘Optical surface characterization with the area structure function,’ (Annals of the CIRP, 62, 539–542, 2013.).
Abstract: The structure function (SF) represents the average height difference squared as a function of separation and, like power spectral density (PSD), can be used to describe the spatial content of optical surfaces. The linear SF has been applied in astronomy and captures data of all spatial content. However, it loses anisotropic information. The recently introduced two-quadrant area SF (ASF) characterizes surfaces of any arbitrary aperture over all spatial content, while retaining information on anisotropy. This paper relates SF to alternative representations of spatial content, and shows interpretation and combination of the SFs based on multi-instrument data.