An efficient regulation approach for tomographic reconstruction in combustion diagnostics based on TDLAS method

For tomographic reconstruction in combustion diagnostics, it is usually necessary to solve a rank-deficient problem, where the number of non-linear dependent equations is smaller than the number of unknowns. In some reconstructions, there are grids without rays passing through. This produces artifacts during the reconstruction. In this paper, the weight of the regulation equation is modified with the number of the rays crossing the grid cells. The effect of the neighboring grid values as well as the number of rays crossing the grid cells is considered in the new regulation method. Numerical simulation results show that the new regulation method suppresses the reconstruction error of the no rays crossing grid and successfully restrains the corner distortion in four projection angles. The effects of the weight coefficient and the smoothing factor on the reconstruction are examined through a numerical study. Finally, a combustion experiment demonstrates that the new regulation method can significantly reduce the reconstructed error, especially for the non-ray crossing condition, and the results are compared with thermocouple measurements and reconstructions without modified regulation.