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.

中文翻译：

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使用温度分布不均匀的光学单元测量高温吸收截面


本研究制定、验证和实验演示了一种使用温度分布不均匀的光学单元进行吸收横截面测量的数学方法。所提出的方法的动机是促进长波长中红外区域的高温光谱研究，并提供一种高度工程化的光学单元的替代方案。该方法基于将光学单元内的非均匀温度场虚拟分割成多个 bin，每个 bins 都具有足够均匀的温度。通过收集一组对应于独特温度曲线的吸光度测量值，并以具有有限未知数的模型表示吸收截面的温度依赖性，可以得到一个封闭式方程组，可以求解该方程组以评估吸收截面。通过一组模拟验证案例，表明根据三阶多项式对温度依赖性进行建模，可以在各种情况下准确重建横截面光谱。提出了分段多项式和替代非线性模型，以提高精度并模拟吸收横截面的潜在复杂温度依赖性。为了证明所提出的方法的应用，使用具有非均匀温度分布的光学单元来测量在高达 523 K 的温度下超过 1280 – 1330 cm-1 的甲烷横截面光谱。预计所提出的方法在高温下收集光谱数据方面非常有用，尤其是在中红外区域。