Development of beam arrangement design for tunable diode laser absorption tomography reconstruction based on Tikhonov regularization parameter matrix

Abstract

Beam arrangement with limited projections is a critical part of research on tunable diode laser absorption tomography reconstruction for combustion diagnosis. Based on the efforts to regularize this rank-deficient and ill-posed problem with Tikhonov regularization, a novel approach to using the regularization parameter matrix is developed for designing optical component layout and predicting the reconstruction accuracy. Objective function of beam arrangement is established by the rigorous mathematical derivation, and genetic algorithm is adopted to realize the optimization of function to overcome the difficulty associated with the multimodal nature of the problem. Nonuniform distribution properties of matrix elements in physical space relate to location and alignment of the laser/detector pairs, and form a basis for adjusting the weight between measurement and regularization to improve the reconstruction performance. A mathematical model of double Gauss distributions is established in a 10 × 10 element discrete tomography domain, and typically 20 measurement beams scanning the H<sub>2</sub>O transition at 7185.6 cm<sup>–1</sup> are available to probe the domain of interest. The systematic comparison between optimized beam array here and four existing beam arrangements in the literature is analyzed to validate the method. The reconstruction with Tikhonov regularization parameter matrix shows obvious advantages of reducing errors especially under the condition of fewer projections. The validation of reconstruction performance of the optimized beam array is also examined by simulating the laser absorption measurement which is carried out on phantoms generated using a simulation of external flow field of an air-gasoline pulsed detonation engine. The result shows that the optimized beam array consistently outperforms other arrangements reported in complicated fluid field. A demonstration reconstruction experiment is performed on the distribution from small gas burners. Both locations and amplitudes are in good agreement with those in the actual case. This proposed design method will be valuable in broadening the scope of applications of tunable diode laser absorption tomography reconstruction for engine diagnosis and combustion efficiency improvement.