A two-step discrete method for reconstruction of temperature distribution in a three-dimensional participating medium

A new two-step discrete method is proposed in this paper for reconstruction of three-dimensional temperature distribution in an absorbing, emitting and isotropically scattering medium. With this new method, the temperature of the wall is also considered. The local radiative source term is reconstructed in the first step through the discrete transfer method from the directional, exit radiation intensities measured by CCD cameras. Then, the temperature of each discrete element is calculated in the second step by subtracting the scattering contribution from the retrieved radiative source term through the discrete ordinate method. The least squares minimum residual algorithm is employed to solve the ill-posed reconstruction equations and the calculation is improved to reduce the computational cost. The performance of the proposed method is examined by numerical test problems with unimodal and bimodal temperature distributions. The ill-conditioning of the reconstruction problem is checked by the Picard condition. The effects of the measurement noise and the radiative properties on the reconstruction accuracy are discussed. The results show that the method proposed in this paper is capable of reconstructing the temperature distribution accurately in large, confined, participating media, even with noisy input data. The computation time reduction of this new method is significant when compared with other methods.