Invariant imbedding and radiation dosimetry: IX. inverse problem of determining a plane source in a finite isotropically scattering target slab

Abstract

Considering a homogeneous, isotropically scattering target slab of optical thickness x, containing an internal plane emitting source, the aim of the present paper is to determine the distribution of the internal emitting source by measuring the angular distribution of the intensity of radiation emergent from the slab. First, a system of differential recurrence relations for the intensity of finite order scattered radiation emergent from the top is deduced. In other words, a Cauchy system for determining the finite order emergent intensity is expressed in terms of a source function in the diffuse radiation field and the Fredholm resolvent that were computed in a preceding paper [cf. Bellman, Ueno, and Vasudevan, Math. Biosci. 15, 195–203 (1972)]. Then, the quasilinearization technique is used to solve the inverse problem of determining characteristics of the internal source by measuring the radiation field emergent from the top. This method will be employed in future computations relating to realistic situations in the radiation diagnosis and therapy.