Measurement of high-temperature absorption cross-sections using an optical cell with a non-uniform temperature distribution

A mathematical method to enable absorption cross-section measurements using an optical cell with a non-uniform temperature distribution is formulated, validated and experimentally demonstrated in this study. The motivation of the proposed method is to facilitate high-temperature spectroscopic studies in the long-wavelength mid-IR region, and to offer an alternative to highly engineered optical cells. The method is based on virtual segmentation of the non-uniform temperature field within an optical cell into bins, each having a sufficiently uniform temperature. By collecting a set of absorbance measurements corresponding to unique temperature profiles and expressing the temperature dependence of the absorption cross-section in terms of a model with limited number of unknowns, a closed-form system of equations is obtained which can be solved to evaluate absorption cross-sections. It is shown, through a set of simulated validation cases, that modeling the temperature dependence in terms of a third order polynomial results in accurate reconstruction of the cross-section spectra for a wide range of cases. Piece-wise polynomials and an alternative nonlinear model are proposed for improved accuracy and to model potentially complex temperature dependencies of the absorption cross-sections. To demonstrate the application of the proposed method, an optical cell with a non-uniform temperature profile was used to measure the cross-section spectra of methane over 1280 – 1330 cm^-1 at temperatures up to 523 K. The proposed method is expected to be highly useful in collecting spectroscopic data at high temperatures particularly in the mid-infrared region.