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A tomographic laser absorption spectroscopy technique, using mid-wave infrared light sources, is presented as a quantitative method to spatially resolve the mole fraction and temperature in small-diameter reacting flows relevant to the combustion of nitrogen-based fuels and propellants, with particular applicability to the study of green propulsion concepts. Tunable quantum and interband cascade lasers are used to spectrally resolve multiple rovibrational transitions near 4.42 and 5.18 µm to measure N₂O, NO, and H₂O mole fractions, as well as gas temperature in an axially symmetric H₂-N₂O premixed jet flame. Signal processing methods for direct N₂O thermometry utilizing a Boltzmann regression are detailed for the experiment, including considerations for the tomographic reconstruction of axial and radial profiles of thermochemical structure for the flame. The tomographic absorption spectroscopy technique is demonstrated to recover radially resolved N₂O, NO, and H₂O mole fractions for multiple planes at different heights above the jet exit, revealing distinct reaction zones in the jet flame associated with the production of each H₂O and NO surrounding the relatively cool reactant core containing N₂O.