Multiparameter gas sensing with linear hyperspectral absorption tomography

Abstract

Hyperspectral absorption tomography (HAT) reconstructs the distribution of key gas parameters, including composition, pressure, and temperature, from multi-beam absorbance data with numerous spectral resolution elements. There is a nonlinear relationship between the parameters of interest and the spectral absorption coefficient, which must be incorporated into the tomography algorithm. Nonlinear HAT simultaneously reconstructs the composition and temperature of a gas by minimizing a single nonconvex objective function, which combines the light attenuation and spectroscopy models, using a metaheuristic technique. The time required for this computation depends, strongly, on the assumed heuristics, but the high computational cost limits the problem size and, hence, the obtainable spatial resolution. Conversely, linear HAT reconstructs the absorption coefficient for each measurement wavenumber, individually, exploiting the linear structure of the underlying tomography problem. Local spectra are then post-processed with a spectroscopic model to recover multiple parameters. The linear technique enables accurate reconstructions on a high-resolution grid by way of an established statistical imaging algorithm. Moreover, local spectra can be employed to gauge phenomena such as multi-species broadening and line mixing with a calibrated regression model. We simulate linear and nonlinear HAT and reconstruct experimental absorbance data using the former approach to demonstrate its superior performance. Nonlinear reconstructions required a 100-fold computational effort compared to linear HAT. In our experimental test, we reconstructed the mole fraction, pressure, and temperature of water vapor in a stagnation flow, which represents the first three-parameter laser absorption tomography experiment. Simulated and experimental results in our paper make a comprehensive case for linear HAT compared to the nonlinear method.

Relative Entropy Regularized TDLAS Tomography for Robust Temperature Imaging

“…The constrained optimisation problem in Eqn. ( 11) can be reformulated into the following unconstrained problem using Lagrange's multipliers, (12) where μ represents the two-line absorbance ratio regularisation parameter. Unlike the smoothness regularisation parameter γ for single-line absorbance, the selection of μ has a direct impact on the reconstruction of line strength ratio and thus the temperature.…”

“…The widely adopted method in TDLAS tomography for temperature imaging is the so-called two-line strategy [11], where the absorbance distributions for two spectral transitions with different temperature-dependent line strengths are individually reconstructed, then the temperature image is retrieved from the ratio of the absorbances in each pixel of the Region of Interest (RoI). Alternatively, temperature images can be reconstructed by using spectra for multiple transitions, the so-called hyperspectral tomography (HT) [12,13]. Although better accuracy and noise resistance can be achieved by HT, measurement of the necessary spectra requires expensive hardware, e.g.…”

Axisymmetric Linear Hyperspectral Absorption Spectroscopy and Residuum-Based Parameter Selection on a Counter Flow Burner

“…We employ the LHAT algorithm as presented in [8] and hence give only a short overview of the algorithm. The goal of tomography is to reconstruct a spatial distribution in a reconstruction domain from M integrating measurements along beams through this reconstruction domain.…”

“…The reconstruction is defined by the point of maximum likelihood x MAP of the posterior distribution in Equation (5). It can be shown in [8] that this maximum a posteriori is given by the least-squares problem…”

“…In spite of yielding good results, this method requires computationally expensive preprocessing of the absorbance data by fitting Voigt line profiles to absorption features which are only an approximate solution to the complex superposition of line profiles of different width in the beam path. The method of linear hyperspectral absorption tomography (LHAT), initially presented by Wood et al [7] and summarized and benchmarked by Grauer et al [8], performs the tomographic reconstruction on the absorbance spectra themselves, yielding local absorption coefficient spectra for each location and thus does not require spectroscopic models (e.g., Voigt line shapes), greatly reducing the computational effort. The availability of full local spectra also allows for giving local signal-to-noise ratios (SNR) for measuring the trustworthiness of the results.…”