Subscale inversion of X-ray emission in electron probe microanalysis based on deterministic transport equations

Abstract The reconstruction methods (ZAF, ϕ(ρz) matrix correction) commonly applied in electron probe microanalysis (EPMA) make restrictive assumptions about the material structure. The model assumption that the material is homogeneous (or layered in depth) limits the spatial resolution of the reconstruction method to the interaction volume of electrons. Models based on Monte Carlo (MC) methods allow for arbitrary material structure, but suffer from statistical noise that prevents the use of MC in gradient-based reconstruction. We present a reconstruction framework for EPMA based on deterministic transport equations to model electron transport. Similar to MC, our model allows for an arbitrary material structure, but is also well-suited for application in gradient-based reconstruction. In this paper we discuss our model with a focus on inversion and discuss the necessity of regularisation (parametrisation of the material) for the reconstruction method. We conclude with reconstruction examples in 1D and 2D, that exemplarily show different parametrizations and, more importantly, the opportunity to resolve material structure smaller than the interaction volume.