Open Access

ARTICLE

Solution of the Inverse Radiative Transfer Problem of Simultaneous Identification of the Optical Thickness and Space-Dependent Albedo Using Bayesian Inference

D. C. Knupp^1,2, A. J. Silva Neto³

1 Agência Nacional de Transportes Terrestres – ANTT, Av. Marechal Câmara 160, 11◦ andar – Ed. Le Bourget, 20020-080, Rio de Janeiro, RJ, Brazil.
2 corresponding author. Email: diego.knupp@antt.gov.br
3 Department of Mechanical Engineering and Energy, Instituto Politécnico – IPRJ Universidade do Estado do Rio de Janeiro, Rua Alberto Rangel s/n, Vila Nova 28630-050, Nova Friburgo, RJ, Brazil.

Computer Modeling in Engineering & Sciences 2013, 96(5), 339-360. https://doi.org/10.3970/cmes.2013.096.339

Abstract

Inverse radiative transfer problems in heterogeneous participating media applications include determining gas properties in combustion chambers, estimating environmental and atmospheric conditions, and remote sensing, among others. In recent papers the spatially variable single scattering albedo has been estimated by expanding this unknown function as a series of known functions, and then estimating the expansion coefficients with parameter estimation techniques. In the present work we assume that there is no prior information on the functional form of the unknown spatially variable albedo and, making use of the Bayesian approach, we propose the development of a posterior probability density, which is explored using the Markov Chain Monte Carlo method (MCMC) implemented with the Metropolis-Hastings algorithm. Moreover, since the scattering and the absorption coefficients, which are in fact the primary properties that produce the single scattering albedo, are considered unknown, then the optical thickness must also be considered unknown. Thus, in this work, the optical thickness is simultaneously estimated with the spatially variable single scattering albedo. Simulated experimental data have been used for the inverse problem solution considering different functional forms for the spatially variable albedo, and different optical thicknesses of the medium. The results are critically investigated, and the good performance observed demonstrates the feasibility of this approach.

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