用单光束吸收光谱法解析非均匀温度分布。第一部分：理论能力和局限性
Resolving nonuniform temperature distributions with single-beam absorption spectroscopy. Part I: Theoretical capabilities and limitations
摘要：
吸收光谱学传统上用于通过测量具有不同温度依赖性的两个或更多个吸收跃迁的幅度来确定沿着激光视线的平均气体温度和物质浓度。先前的工作已经表明，每个跃迁的吸收强度的非线性温度依赖性，由较低状态的能量，E”设置，可以用来推断沿激光视线的温度变化。原则上，用更宽带宽的光源测量更多的吸收跃迁可以提高分辨温度变化的能力。在这里，我们引入了一个奇异值分解框架，以探索解决温度分布与单光束视线吸收测量的理论限制。我们表明，在没有测量噪声或误差的情况下，只有前14个精心选择的吸收功能提高了温度分辨率，和吉洪诺夫正则化方法提高了温度反演的准确性，特别是恢复沿激光束的最大气体温度。我们使用反演模拟来证明，可以解决选择的温度分布沿激光束的视线内的3%的样本情况下分析。在这项工作的第二部分中，我们探讨了测量噪声和误差的影响，并通过实验证明了该技术，以表明在真实条件下测量额外的吸收跃迁是有益的。
英文摘要：
Absorption spectroscopy is traditionally used to determine the average gas temperature and species concentration along the laser line-of-sight by measuring the magnitude of two or more absorption transitions with different temperature dependence. Previous work has shown that the nonlinear temperature dependence of the absorption strength of each transition, set by the lower-state energy, E", can be used to infer temperature variations along the laser line-of-sight. In principle, measuring more absorption transitions with broader bandwidth light sources improves the ability to resolve temperature variations. Here, we introduce a singular value decomposition framework in order to explore the theoretical limits to resolving temperature distributions with single-beam line-of-sight absorption measurements. We show that in the absence of measurement noise or error, only the first ~14 well-selected absorption features improve the temperature resolution, and a Tikhonov regularization method improves the accuracy of the temperature inversion, particularly for recovery of the maximum gas temperature along the laser beam. We use inversion simulations to demonstrate that one can resolve a selection of temperature distributions along a laser beam line-of-sight to within 3% for the sample cases analyzed. In part II of this work, we explore the influence of measurement noise and error, and experimentally demonstrate the technique to show that there is benefit to measuring additional absorption transitions under real conditions.
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