Resolving nonuniform temperature distributions with single-beam absorption spectroscopy. Part I: Theoretical capabilities and limitations

Absorption spectroscopy is traditionally used to determine the average gas temperature and species concentration along laser line-of-sight by measuring magnitude of two or more absorption transitions with different dependence. Previous work has shown that nonlinear dependence strength each transition, set lower-state energy, E", can be infer variations line-of-sight. In principle, broader bandwidth light sources improves ability resolve variations. Here, we introduce a singular value decomposition framework in order explore theoretical limits resolving distributions single-beam measurements. We show absence measurement noise error, only first ~14 well-selected features improve resolution, Tikhonov regularization method accuracy inversion, particularly for recovery maximum beam. use inversion simulations demonstrate one selection beam within 3% sample cases analyzed. part II this work, influence experimentally technique there benefit additional under real conditions.