Nonlinear relationship between signal and gas concentration in high-precision off-axis integrated cavity output spectroscopy

Abstract Off-axis integrated cavity output spectroscopy (OA-ICOS) is an extremely sensitive technique for measuring trace gas concentrations. Nevertheless, recent research has indicated that when the reflectivity of the mirrors forming the cavity is excessively high, it affects the linearity between the absorption signal and concentration. In this study, the causes and limitations of this phenomenon are discussed based on the Beer–Lambert law and the law of light propagation within the cavity. A new equation is derived to describe the nonlinear relationship between the integral area of absorption spectra and gas concentration. The absorption spectra of CO 2 and CH 4 , measured under different experimental conditions and concentrations, were fitted with Voigt functions to obtain parameters such as peak values and integral areas, which were used to verify the theoretical derivation process and results. The experimental results demonstrate that the relationship between the area of the measured absorption spectra and the gas concentration is consistent with the new formula, with an average fitting correlation coefficient of 0.9998. Meanwhile, the experimental results also demonstrate that the effective optical path length indeed decreases with increasing concentration. Furthermore, the cavity reflectances (99.99644% at 6242.6 cm −1 and 99.99833% at 6046.96 cm −1 ) derived from the fitting coefficient of the new concentration expression closely match the reflectances (99.99727% at 6242.6 cm −1 and 99.99868% at 6046.96 cm −1 ) obtained by applying the classical formula to the spectra of the lowest gas concentration. These experimental results validate the theoretical deduction process and expression. This research provides insights for the theoretical and practical advancements of OA-ICOS, which is significant for advancing high-precision trace gas detection technology.