Two-dimensional modelling of systematic surface height deviations in optical interference microscopy based on rigorous near field calculation

Optical interference microscopes are widespread in topography and roughness measurement on the micro- and nanoscale. In spite of a wide range of scientific and industrial applications, systematic deviations between the measured and the real surface topography occur in certain situations, e.g. at edges or steep flanks. We present a numerical model considering the properties of the measurement instrument as well as the surface structure to be measured in order to get new insights into the physical dependencies of these deviations. The computation is based on a rigorous simulation of the scattered near field combined with a Fourier optics treatment of the image formation in the measurement instrument. In this study, the near fields are calculated with an open-source finite element method (FEM) software and a commercial finite difference time domain method (FDTD) software. The numerical results are compared with an analytical Kirchhoff approach and measurements. The main intention of this paper is to introduce the modelling and point out possible fields of application. In further studies, this model could be extended to 3D and parameter dependencies of systematic deviations, such as the material of the measurement object and the NA of the measurement instrument, could be investigated.