Visualization of three-dimensional temperature distributions in a large-scale furnace via regularized reconstruction from radiative energy images: numerical studies

In this paper, the possibility of visualization of three-dimensional (3-D) temperature distributions in large-scale boiler furnaces from radiative energy images captured by multiple charge-coupled device (CCD) cameras mounted around the furnace is studied numerically. For the calculation of the radiative energy image formation, a fast algorithm proposed by the authors for pinhole imaging is used in this paper, which is based on the Monte Carlo method and combined with a concept of angular factor effective for image formation. This algorithm is applicable for the emitting, absorbing, and isotropic scattering medium. For the inversion of the 3-D temperature distributions which is an ill-posed problem, a modified Tikhonov regularization method is improved, where the finite difference regularizer is defined and can be used in 3-D cases, and the optimal regularization parameter is suggested to be selected by using a post-treatment method. For a 3-D unimodal temperature distribution, the numerical simulation results show that the reconstruction errors for the 3-D temperature distribution can be maintained at levels similar to the measurement error and the visualization quality of the temperature distribution is satisfactory. For a kind of bimodal temperature distribution, the reconstruction errors are higher than those for the unimodal distribution, but the bimodal feature of the temperature distribution can also be reproduced clearly.