Characterization of micro-scale surface features using Partial Differential Equations

Mass production of components with micro and nano scale surface features is known as micromoulding and is very sensitive to a number of variables that can cause important changes in the surface geometry of the components. The surface itself is regarded as a key element in determining the product's functionality and as such must be subject to thorough quality control procedures. To that end, a number of surface measurement techniques have been employed namely, White Light Interferometry (WLI) and Atomic Force Microscopy (AMF), whose resulting data is given in the form of large and rather unmanageable Cartesian point clouds. This work uses Partial Differential Equations (PDEs) as means for characterizing efficiently the surfaces associated with these data sets. This is carried out by solving the Biharmonic equation subject to a set of boundary conditions describing outer surface contours extracted from the raw measurement data. Design parameters are expressed as a function of the coefficients associated with the analytic solution of the Biharmonic equation and are then compared against the design parameters describing an ideal surface profile. Thus, the technique proposed here offers means for quality assessment using compressed data sets.