Bayesian regression-based cross-scale characterization of random rough surfaces using multiple optical instruments

Engineering surfaces commonly exhibit multiscale topographical features that significantly influence contact, friction, and sealing behavior. Accurate characterization of surface topography across a wide range of spatial scales remains challenging due to the limited bandwidth and measurement uncertainties inherent to a single instrument system. This study meets this gap by introducing a Bayesian regression framework for integrating topographies obtained from multiple optical instruments. A wide-bandwidth power spectral density function is established from the fused data, and its associated uncertainty is quantitatively assessed using Gaussian process regression. The proposed method is validated through measurements on a finely ground sapphire wafer and comparison with scanning electron microscope images. The methodology provides a robust solution for surface characterization in contact mechanics and tribological analysis.