Accurate reconstruction of the optical parameter distribution in participating medium based on the frequency-domain radiative transfer equation

Abstract

Reconstructing the distribution of optical parameters in the participating medium based on the frequency-domain radiative transfer equation (FD-RTE) to probe the internal structure of the medium is investigated in the present work. The forward model of FD-RTE is solved via the finite volume method (FVM). The regularization term formatted by the generalized Gaussian Markov random field model is used in the objective function to overcome the ill-posed nature of the inverse problem. The multi-start conjugate gradient (MCG) method is employed to search the minimum of the objective function and increase the efficiency of convergence. A modified adjoint differentiation technique using the collimated radiative intensity is developed to calculate the gradient of the objective function with respect to the optical parameters. All simulation results show that the proposed reconstruction algorithm based on FD-RTE can obtain the accurate distributions of absorption and scattering coefficients. The reconstructed images of the scattering coefficient have less errors than those of the absorption coefficient, which indicates the former are more suitable to probing the inner structure.

Model predictive inverse method for recovering boundary conditions of two-dimensional ablation*

“…The simulation experiment results given above (Figs. [18][19][20][21][22] illustrate that the inverse method established in this paper has little sensitivity to the number of the future time steps in the scope of above experiments.…”

“…[11][12][13][14][15] Thus, various optimization methods with anti-ill-posedness are developed. Heuristic algorithms [7,[16][17][18][19] and gradient algorithms, [20][21][22] as the typical inverse methods, are widely used to solve the inverse problems. For the IHTPs, Vakili and Gadala [23] used particle swarm optimization (PSO) algorithm to estimate the boundary conditions with different dimensions.…”

An efficient inverse approach for reconstructing time- and space-dependent heat flux of participating medium*

“…Determine methods are widely used to solve IHTPs for their high computational accuracy and strong stability. [29,30] Yang et al [31] applied conjugate gradient method (CGM) to determine the time-and space-dependent heat flux of brake system, in which the time-resolved temperature distribution measured within the disc was employed as measurement signals. Zhu et al [32] employed CGM to reconstruct the transient heat flux on the high-temperature wall of an engine, and the accuracy of reconstruction model was verified by experimental tests.…”