Comparison of the approximate Beckmann-Kirchhoff and a rigorous scattering model for coherence scanning interferometry modelling

Coherence scanning interferometry (CSI) is widely used in advanced manufacturing for high-accuracy surface topography measurement. Linear CSI modelling, based on approximate surface scattering models, fails to predict instrument responses for complex geometries (e.g., high slope angles, high aspect-ratio structures) that induce multiple scattering. Proper treatment of multiple scattering requires rigorous light-scattering simulations. This has been achieved in two dimensions using a boundary element method, enabling predictions of CSI optical responses for arbitrary geometries. In this work, we extend rigorous CSI signal simulations to three dimensions using the 3S BSM method and the SpeckleSim solver. Results are computed for various structures and compared with the Beckmann-Kirchhoff (B-K) model, highlighting cases where rigorous simulations significantly differ due to multiple scattering effects.