Lubricant homogeneity of industrial rough metallic substrates: a multivariate statistical analysis of spectroscopic ellipsometry data

In this paper, a non-destructive method is proposed for measuring the density of a very thin lubricant layer (weight and spatial) on an industrial surface. We considered spectroscopic ellipsometry measurements on rough tinplated steel substrates protected by a lubrication layer. The thickness of the coating was less than the roughness parameter characterizing the metallic surface. As the optical properties of the substrates could not be modelled in a conventional way due to the roughness and the complex structure of the metal, the variations of one of the ellipsometric angle (Δ) were evaluated as a function of the lubricant film surface density. After identification of the potential outliers using a multivariate analysis technique based on the Mahalanobis distance, we interpreted the data using the Drude’s approximation for thin dielectric films. The values of Δ linearly decrease with the lubricant surface density, allowing us to evaluate locally the lubricant surface density and its point-to-point variations.