Numerical Results for the Estimation of Source Distributions from External Radiation Field Measurements

by Richard Ernest Bellman, H. H. Natsuyama, Robert E. Kalaba, S. Ueno


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Consideration of a transport process in a slab bounded by two parallel planes. Radiation is both absorbed and scattered isotropically. The radiation is due to continuously distributed internal isotropic sources. The aim is to estimate the distribution of the internal sources based on experimental measurements of the angular dependence of the emergent radiation. First, a system of differential-integral equations for the emergent radiation is deduced. These are approximated by a system of ordinary differential equations, and some numerical results are given. Quasilinearization is then used to solve the inverse problem numerically. The results of some computational experiments are given which indicate the sensitivity of the estimates of the source distribution to the observational errors on the emergent radiation measurements. The methods can be generalized to the cases of anisotropic scattering and shell geometry.

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