Effective wavenumber coordinate correction and CO₂ concentration retrieval constrained by an absorption-band prior

Molecular absorption spectroscopy provides a species-selective basis for quantitative gas sensing and compact optical diagnostics in combustion, industrial processes, and emission monitoring. However, in scanned semiconductor laser spectrometers operating without an online frequency reference, residual tuning nonlinearities introduce deviations in the wavenumber coordinate that affect spectral registration, baseline variation, and concentration retrieval. Here, we report a joint inversion method for CO₂ direct absorption spectroscopy, in which the molecular absorption-band structure is used as an internal spectral constraint for effective wavenumber coordinate correction and concentration retrieval. Using the prior trajectory derived from the scan as the initial coordinate, the method estimates the residual wavenumber correction for each scan, a compact model of the non-absorbing intensity baseline, and the CO₂ mole fraction within a unified forward model, without requiring an online Fabry-Perot etalon, reference absorption cell, or wavemeter. In experiments with a DFB laser operating near 4990 cm^-1, a 45.0 cm effective path length, and standard CO₂/N₂ gas mixtures with concentrations ranging from 1000 to 4500 ppm, the absorption-band prior method reduced the absorbance residual RMSE from 2.01 × 10^-3 to 9.60 × 10^-4 compared with that of single-peak retrieval. For concentration retrieval, the mean absolute relative error and concentration standard deviation decreased from 4.08% to 1.63% and from 92.3 ppm to 38.9 ppm for single-scan retrieval and from 2.32% to 1.39% and from 60.8 ppm to 27.1 ppm after averaging over nine scan periods, respectively. These results show that spectroscopic constraints applied across the absorption band provide an effective approach for improving spectral registration, concentration accuracy, and retrieval stability over short measurement intervals in DAS systems operating without an online frequency reference.