Development of a beam optimization method for absorption-based tomography

Optimization Design of Laser Arrays Based on Absorption Spectroscopy Imaging for Detecting Temperature and Concentration Fields

Detecting temperature and concentration fields within engine combustors holds paramount significance in enhancing combustion efficiency and ensuring operational safety. Within the realm of engine combustors, the laminar absorption spectroscopy technique has garnered considerable attention. Particularly crucial is the optimization of the optical path configuration to enhance the efficacy of reconstruction. This study presents a flame parameter field reconstruction model founded on laminar absorption spectroscopy. Furthermore, an optimization approach for refining the optical path configuration is delineated. In addressing non-axisymmetric flames, the simulated annealing algorithm (SA) and Harris's Hawk algorithm (HHO) are employed to optimize the optical path layout across varying beam quantities. The findings underscore a marked reduction in imaging errors with the optimized optical path configuration compared to conventional setups, thereby elevating detection precision. Notably, the HHO algorithm demonstrates superior performance over the SA algorithm in terms of optimization outcomes and computational efficiency. Compared with the parallel optical path, the optimized optical path of the HHO algorithm reduces the temperature field error by 25.5% and the concentration field error by 26.5%.

Camera spatial arrangement influence on reconstruction accuracy of chemiluminescence tomography

Computed tomography of chemiluminescence (CTC) has been demonstrated to be a powerful tool for three-dimensional (3D) combustion visualization and measurement, in which the number of cameras and their spatial arrangement significantly impact the tomographic reconstruction quality. In this work, the relationship of the camera spatial arrangement and tomographic reconstruction accuracy is theoretically established based on two-dimensional (2D) and 3D Mojette transforms and their accurate reconstruction conditions. Numerical simulations and experiments were conducted to demonstrate the theories. The results suggest that the exact reconstruction conditions of the Mojette transforms can be used to determine the minimum number of cameras required for tomography reconstruction, and its achieved reliability can be used as an indicator to predict the reconstruction quality. Besides, the 2D coplanar semicircular configuration exhibits a better performance than that of the 3D non-coplanar arrangement. When the 3D non-coplanar arrangement is adopted, the cameras should be widely distributed in the hemispherical space. The related research provides a theoretical basis for the establishment of the CTC system and other tomography modalities.

Tomographic Absorption Spectroscopy for H2O Transport in a Laminar Jet with Inverse Concentration Gradient

We report a tomographic absorption spectroscopy (TAS) study of water vapor transport in a laminar jet issuing into the ambient. The jet was generated using compressed dry air that was straightened by a honeycomb and a smooth contraction nozzle. A TAS scheme using the water vapor in the ambient as absorbing species and the absorption line near 1368.598 nm was proposed to study the H₂O transport in the laminar jet with an inverse concentration gradient. One-dimensional tomography was conducted at various heights above the nozzle, and the results were validated by the predictions from computational fluid dynamics (CFD) simulations. Particularly, the variations in the concentration gradient in the shear layer at different heights were captured. The 2D distribution of water concentration in the dry laminar jet was obtained experimentally. The present study shows that TAS has great potential in the research of mass transfer and scalar field of gaseous flows.

Tomographic absorption spectroscopy based on dictionary learning

Tomographic absorption spectroscopy (TAS) has an advantage over other optical imaging methods for practical combustor diagnostics: optical access is needed in a single plane only, and the access can be limited. However, practical TAS often suffers from limited projection data. In these cases, priors such as smoothness and sparseness can be incorporated to mitigate the ill-posedness of the inversion problem. This work investigates use of dictionary learning (DL) to effectively extract useful a priori information from the existing dataset and incorporate it in the reconstruction process to improve accuracy. We developed two DL algorithms; our numerical results suggest that they can outperform classical Tikhonov reconstruction under moderate noise conditions. Further testing with experimental data indicates that they can effectively suppress reconstruction artifacts and obtain more physically plausible solutions compared with the inverse Radon transform.

Linear multispectral absorption tomography based on regularized iterative methods

A regularization approach of iterative algorithms was proposed to reconstruct the two-dimensional temperature and concentration distributions based on linear multispectral absorption tomography (MAT). This method introduces a secondary prior into a classical iterative algorithm via regularization to improve the reconstruction accuracy. Numerical studies revealed that the regularized iteration outperformed the classical and superiorized versions under various noisy conditions and with different number of spectral lines. The algorithms were also tested with the existing experimental data of a premixed flat flame produced by a McKenna burner. The comparison between the reconstructions and the measured temperature profile using thermocouples confirmed the superiority of our proposed regularized iterative method.

Influence of Line Pair Selection on Flame Tomography Using Infrared Absorption Spectroscopy

We report the influence of absorption line selection on the tomographic results for high-temperature flames by numerical and experimental methods. Different combinations of infrared H₂O absorption transitions are utilized with the Tikhonov-regularized Abel inversion to reconstruct the radial distribution of temperature and H₂O concentration in a flat flame. It is shown that besides using the mathematical algorithm such as regularization, selecting a line pair with a large Δ E″ (>1390 cm^-1) also reduces the reconstruction uncertainty at 300-2000 K. In this study, a proper selection of absorption line pairs reduces the reconstruction uncertainty by 25% at the same level of noise. The line pair of H₂O transitions at 4029.524 cm^-1 and 4030.729 cm^-1 is recommended for the tomography of high-temperature flames at 1000-3000 K, whereas the line pair of 7185.597 cm^-1 and 7444.352 cm^-1 can be used at 300-1000 K.

Rapid tomographic reconstruction based on machine learning for time-resolved combustion diagnostics

Optical tomography has attracted surged research efforts recently due to the progress in both the imaging concepts and the sensor and laser technologies. The high spatial and temporal resolutions achievable by these methods provide unprecedented opportunity for diagnosis of complicated turbulent combustion. However, due to the high data throughput and the inefficiency of the prevailing iterative methods, the tomographic reconstructions which are typically conducted off-line are computationally formidable. In this work, we propose an efficient inversion method based on a machine learning algorithm, which can extract useful information from the previous reconstructions and build efficient neural networks to serve as a surrogate model to rapidly predict the reconstructions. Extreme learning machine is cited here as an example for demonstrative purpose simply due to its ease of implementation, fast learning speed, and good generalization performance. Extensive numerical studies were performed, and the results show that the new method can dramatically reduce the computational time compared with the classical iterative methods. This technique is expected to be an alternative to existing methods when sufficient training data are available. Although this work is discussed under the context of tomographic absorption spectroscopy, we expect it to be useful also to other high speed tomographic modalities such as volumetric laser-induced fluorescence and tomographic laser-induced incandescence which have been demonstrated for combustion diagnostics.

Toward real-time volumetric tomography for combustion diagnostics via dimension reduction

Volumetric tomography for combustion diagnostics is experiencing significant progress during the past few years due to its capability of imaging evolving turbulent flows. Such capability facilitates the understanding of the mechanisms behind complicated combustion phenomena such as lean blowout, acoustic oscillations, and formation of soot particles. However, these techniques are not flawless and suffer from high computational cost which prevents them from applications where real-time reconstructions and online monitoring are necessary. In this Letter, we propose a new reconstruction method that can effectively reduce the dimension of the inversion problem, which can then be solved with a minimum computational effort. This method and a classical iterative method were tested against each other using a proof-of-concept experiment in which endoscopic computed tomography of chemiluminescence (CTC) was implemented. The results show that the proposed method can dramatically reduce the computational time and, at the same time, maintain similar reconstruction accuracy, as opposed to the classical approach. Although this Letter was discussed under the context of CTC, it can be applied universally to other modalities of volumetric tomography such as volumetric laser-induced fluorescence.

Measurement-based meshing, basis selection, and prior assignment in chemical species tomography

Gas distributions imaged by chemical species tomography (CST) vary in quality due to the discretization scheme, arrangement of optical paths, errors in the measurement model, and prior information included in reconstruction. There is currently no mathematically-rigorous framework for comparing the finite bases available to discretize a CST domain. Following from the Bayesian formulation of tomographic inversion, we show that Bayesian model selection can identify the mesh density, mode of interpolation, and prior information best-suited to reconstruct a set of measurement data. We validate this procedure with a simulated CST experiment, and generate accurate reconstructions despite limited measurement information. The flow field is represented using the finite element method, and Bayesian model selection is used to choose between three forms of polynomial support for a range of mesh resolutions, as well as four priors. We show that the model likelihood of Bayesian model selection is a good predictor of reconstruction accuracy.

On the quantification of spatial resolution for three-dimensional computed tomography of chemiluminescence

Three-dimensional computed tomography of chemiluminescence (CTC) for combustion diagnostics is attracting a surged research interest due to recent progress in sensor technologies and reduced costs of high-speed cameras. For example, it has been applied to recover the 3D distributions of intermediate chemical species such as CH* and OH*, heat release rate, and flame topology. Although these applications were demonstrated to be successful, there are still a few drawbacks of this technique that have not be cured. For example, to the best of the authors' knowledge, all the imaging models that have been developed so far ignore the imperfections of cameras such as lens distortion and skewness. However, this will unavoidably introduce errors into the weight matrix. In addition, spatial resolution of a CTC system is a critical performance parameter. However, it has only been studied qualitatively and no quantitative quantification method is reported so far. This work aims to solve these problems by improving the imaging model and developing a method based on edge spread function for the quantification of spatial resolution. Although this work is conducted under the context of CTC for combustion diagnostics, it also provides useful insights for other tomographic modalities such as volumetric laser-induced fluorescence and tomographic laser-induced incandescence.

Demonstration of 3D computed tomography of chemiluminescence with a restricted field of view

Three-dimensional imaging techniques have experienced a surge in research interest during the past few years due to advancements in both hardware, i.e., the sensor arrays and data acquisition systems, and new imaging concepts, such as light field imaging and compressed sensing. Computed tomography of chemiluminescence (CTC) is an intriguing technique for combustion diagnostics due to its ease of implementation, as no excitation source is required in measurements. It has been applied extensively for the retrieval of intermediate species such as CH^*/OH^*, from which the flame topology can be obtained. However, all previous demonstrations or applications were performed under the assumption that a complete field of view is available for all projections. However, this prerequisite cannot be guaranteed for some practical scenarios, such as engine measurements, in which optical access is extremely limited and a portion of the field of view is unavoidably blocked, especially when a considerable number of projections are required. This work aims to develop an improved CTC modality that can handle projections with a restricted field of view, and to suggest the best strategy for tomographic reconstruction under such experimental conditions. Although this technique is discussed under the context of combustion diagnostics, it can also be useful and adapted for other tomographic areas, such as biomedical imaging.