Inverse radiation problem of sources and emissivities in one-dimensional semitransparent media

An inverse analysis is presented for simultaneous estimation of the source term distribution and the boundary emissivity for an absorbing, emitting, anisotropic scattering, and gray plane–parallel medium with opaque and diffuse bounding surfaces from the knowledge of the exit radiation intensities and temperature at boundary surfaces. The inverse problem is formulated as an optimization problem that minimizes the errors between the exit radiation intensities calculated and the experimental data. The conjugate gradient method and the two-dimensional network searching method are used to solve the inverse problem. The effects of the measurement errors, anisotropic scattering, single-scattering albedo, optical thickness, and boundary emissivity on the accuracy of the inverse analysis are investigated. The results show that the source term and the boundary emissivity can be simultaneously estimated accurately for exact and noisy data, and the estimation of boundary emissivity is more sensitive to the measurement errors.