Light scattering peak matrix and Bayesian inference: An effective methodology for characterizing rectangular surface defects in advanced optics with roughness interference

Optical components demand extremely high-level surface quality, which necessitates efficient and precise defect characterization. Light scattering measurement has emerged as a promising non-contact technique for quantitative evaluation of surface quality. However, the presence of surface roughness poses significant challenges in accurately characterizing surface defects. In this study, a customized light scattering measurement system was constructed to measure the spatial distribution of the scattered light intensity (SLI). A bi-directional reflectance distribution function (BRDF) model was established to describe the relationship between surface defects and the spatial distribution of SLI, providing a basis for the formulation of the inverse problem between parameters of a defect and its angular scattering behaviour. Subsequently, a roughness-integrated finite-difference time-domain (FDTD) model was developed to reveal how surface roughness influences defect-induced SLI. Validation of the FDTD model through the BRDF model and experiments demonstrated excellent agreement in angular distribution predictions, particularly in the peak positions of the SLI. Building on this, the light scattering peak matrix (LSPM) was introduced via a multi–incidence/scattering-angle measurement configuration. Additionally, a combined defect + roughness model was proposed which describes the statistical distribution of defect data for surfaces with varying roughness levels, providing the necessary information for defect detection and characterization in a Bayesian inversion framework. Using the proposed LSPM technique, experiments demonstrated that surface defects with actual widths of 3–5 μm can be accurately characterized. While depth measurement proved to be fundamentally more challenging, the characterization uncertainty can still be effectively quantified using the proposed Bayesian approach.