Unsupervised neural-implicit laser absorption tomography for quantitative imaging of unsteady flames

This paper presents a novel neural-implicit approach to laser absorption tomography (LAT) with an experimental demonstration. A coordinate neural network is used to represent thermochemical state variables as continuous functions of space and time. Unlike most existing neural methods for LAT, which rely on prior simulations and supervised training, our approach is based solely on LAT measurements, utilizing a differentiable observation operator with line parameters provided in a standard spectroscopy database format. Although reconstructing scalar fields from multi-beam absorbance data is an inherently ill-posed, nonlinear inverse problem, our continuous space-time parameterization supports physics-inspired regularization strategies and enables data assimilation. Synthetic and experimental tests are conducted to validate the method, demonstrating robust performance and reproducibility. We show that our neural-implicit approach to LAT can capture the dominant spatial modes of an unsteady flame from very sparse measurement data, indicating its potential to reveal combustion instabilities in measurement domains with minimal optical access.