Optimization of beam arrangement for tunable diode laser absorption tomography reconstruction based on fractional Tikhonov regularization

Abstract

Beam arrangement with limited projections based on tunable diode laser absorption spectroscopy is the key to achieving a more accurate two-dimensional reconstruction of the combustion. Using fractional calculus theory, a beam optimization method based on fractional Tikhonov regularization is proposed. The beam arrangement function based on fractional Tikhonov regularization is established by extending the standard Tikhonov regularization to fractional modes. The genetic algorithm is used to analyze the calculation results of different orders in a range of (0, 1), and the beam arrangement is obtained. Using 20 laser beams to scan the characteristic absorption spectrum of H₂O in the near-infrared band 7185.6 cm^–1, modeling the calculations in a 10×10 element discrete tomography domain, and comparing the reconstruction results of the five beam arrangements for different Gaussian distribution models, the beam arrangement based on fractional Tikhonov regularization shows more obvious advantages. This design method proposed in this work is valuable for the theoretical study of the optimal design of two-dimensional measurement beams based on the tunable diode laser absorption spectroscopy technique, which can promote the application of this technique in the two-dimensional reconstruction of complex engine combustion and combustion efficiency improvement.