Laser-absorption tomography beam arrangement optimization using resolution matrices

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.

Ammonia Distribution Measurement on a Hot Gas Test Bench Applying Tomographical Optical Methods

Measuring the distribution of gas concentration is a very common problem in a variety of technological fields. Depending on the detectability of the gas, as well as the technological progress of the sector, different methods are used. In this paper, we present a device and methods to detect the ammonia concentration distribution in the exhaust system of diesel engines in order to increase the performance of the exhaust aftertreatment system. The device has been designed for usage on a hot gas test bench simulating exhaust gas conditions. It consists of multiple optical beams measuring ammonia line concentrations by applying nondispersive absorption spectroscopy in the deep ultraviolet region. The detectors consist of photodiodes allowing high sampling rates up to 3 kHz while providing a high signal-to-noise ratio. A detection limit of only 1 ppm has been achieved despite the short path length of only eight centimeters. The obtained line concentrations form an inverse problem. The methodology of the tomographic techniques is described in detail in order to best solve the inverse problem and obtain the ammonia concentration distribution images for each time step.

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.

Improving chemical species tomography of turbulent flows using covariance estimation

Chemical species tomography (CST) experiments can be divided into limited-data and full-rank cases. Both require solving ill-posed inverse problems, and thus the measurement data must be supplemented with prior information to carry out reconstructions. The Bayesian framework formalizes the role of additive information, expressed as the mean and covariance of a joint-normal prior probability density function. We present techniques for estimating the spatial covariance of a flow under limited-data and full-rank conditions. Our results show that incorporating a covariance estimate into CST reconstruction via a Bayesian prior increases the accuracy of instantaneous estimates. Improvements are especially dramatic in real-time limited-data CST, which is directly applicable to many industrially relevant experiments.

Development of a beam optimization method for absorption-based tomography

Absorption tomography is an imaging technique that has been used simultaneously to image multiple scalar parameters, such as temperature and species concentration for combustion diagnostics. Practical combustors, such as internal combustion engines and gas turbine engines, only allow limited optical access, and typically a few (ca. 20-40) beams are available to probe the domain of interest. With such limited spatial sampling, it is non-trivial to optimize beam arrangement for a faithful reconstruction. Previous efforts on beam optimization rely on either heuristic/empirical methods lacking rigorous mathematical derivation or were derived by assuming certain prior information in the tomographic inversion. This paper aims to develop an approach that is expected to be especially useful when prior information is not easily available or intended to be included in the inversion processes. We demonstrate that the orthogonality between rows of the weight matrix directly correlates with reconstruction fidelity and can be used as an effective predictor for beam optimization. A systematic comparison between our method and the existing ones in the literature suggests the validity of our method. We expect this method to be valuable for not only the absorption tomography but also other tomographic modalities.

Bayesian approach to the design of chemical species tomography experiments

Reconstruction accuracy in chemical species tomography depends strongly on the arrangement of optical paths transecting the imaging domain. Optimizing the path arrangement requires a scheme that can predict the quality of a proposed arrangement prior to measurement. This paper presents a new Bayesian method for scoring path arrangements based on the estimated a posteriori covariance matrix. This technique focuses on defining an objective function that incorporates the same a priori information about the flow needed to carry out limited data tomography. Constrained and unconstrained path optimization studies verify the predictive capabilities of the objective function, and that superior reconstruction quality is obtained with optimized path arrangements.

An efficient approach for limited-data chemical species tomography and its error bounds

We present a computationally efficient reconstruction method for the limited-data chemical species tomography problem that incorporates projection of the unknown gas concentration function onto a low-dimensional subspace, and regularization using prior information obtained from a simple flow model. In this context, the contribution of this work is on the analysis of the projection-induced data errors and the calculation of bounds for the overall image error incorporating the impact of projection and regularization errors as well as measurement noise. As an extension to this methodology, we present a variant algorithm that preserves the positivity of the concentration image.

Demonstration of temperature imaging by H₂O absorption spectroscopy using compressed sensing tomography

This paper introduces temperature imaging by total-variation-based compressed sensing (CS) tomography of H2O vapor absorption spectroscopy. A controlled laboratory setup is used to generate a constant two-dimensional temperature distribution in air (a roughly Gaussian temperature profile with a central temperature of 677 K). A wavelength-tunable laser beam is directed through the known distribution; the beam is translated and rotated using motorized stages to acquire complete absorption spectra in the 1330-1365 nm range at each of 64 beam locations and 60 view angles. Temperature reconstructions are compared to independent thermocouple measurements. Although the distribution studied is approximately axisymmetric, axisymmetry is not assumed and simulations show similar performance for arbitrary temperature distributions. We study the measurement error as a function of number of beams and view angles used in reconstruction to gauge the potential for application of CS in practical test articles where optical access is limited.

Development of a fan-beam TDLAS-based tomographic sensor for rapid imaging of temperature and gas concentration

This work aims to develop a fan-beam tomographic sensor using tunable diode lasers that can simultaneously image temperature and gas concentration with both high spatial and temporal resolutions. The sensor features three key advantages. First, the sensor bases on a stationary fan-beam arrangement, by which a high spatial resolution is guaranteed because the distance between two neighboring detectors in a view is approximately reduced to the size of a photodiode. Second, fan-beam illumination from five views is simultaneously generated instead of rotating either the fanned beams or the target, which significantly enhances the temporal resolution. Third, a novel set of optics with the combination of anamorphic prism pair and cylindrical lens is designed, which greatly improves the uniformity of the planar beams, and hence improves the reconstruction fidelity. This paper reports the tomographic model, optics design, numerical simulation and experimental validation of the sensor. The sensor exhibits good applicability for flame monitoring and combustion diagnosis.

Spatially resolved and observer-free experimental quantification of spatial resolution in tomographic images

We present a novel framework and experimental method for the quantification of spatial resolution of a tomography system. The framework adopts the "black box" view of an imaging system, considering only its input and output. The tomography system is locally stimulated with a step input, viz., a sharp edge. The output, viz., the reconstructed images, is analysed by Fourier decomposition of their spatial frequency components, and the local limiting spatial resolution is determined using a cut-off threshold. At no point is an observer involved in the process. The framework also includes a means of translating the quantification region in the imaging space, thus creating a spatially resolved map of objectively quantified spatial resolution. As a case-study, the framework is experimentally applied using a gaseous propane phantom measured by a well-established chemical species tomography system. A spatial resolution map consisting of 28 regions is produced. In isolated regions, the indicated performance is 4-times better than that suggested in the literature and varies by 57% across the imaging space. A mechanism based on adjacent but non-interacting beams is hypothesised to explain the observed behaviour. The mechanism suggests that, as also independently concluded by other methods, a geometrically regular beam array maintains maximum objectivity in reconstructions. We believe that the proposed framework, methodology, and findings will be of value in the design and performance evaluation of tomographic imaging arrays and systems.