Accurate depth-resolved temperature profiling via thermal-radiation spectroscopy: numerical methods vs machine learning

We present and compare three approaches for accurately retrieving depth-resolved temperature distributions within materials from their thermal-radiation spectra, based on: (1) a nonlinear equation solver implemented in commercial software, (2) a custom-built nonlinear equation solver, and (3) a deep neural network (DNN) model. These methods are first validated using synthetic datasets comprising randomly generated temperature profiles and corresponding noisy thermal-radiation spectra for three different structures: a fused-silica substrate, an indium antimonide substrate, and a thin-film gallium nitride layer on a sapphire substrate. We then assess the performance of each approach using experimental spectra collected from a fused-silica window heated on a temperature-controlled stage. Our results demonstrate that the DNN-based method consistently outperforms conventional numerical techniques on both synthetic and experimental data, providing a robust solution for accurate depth-resolved temperature profiling.