A numerical approach for inverse problems in photon transport inside an interstellar cloud (Q1827356)

The authors consider two inverse problems of stationary radiative transfer through a homogeneous medium with slab symmetry. Assuming the radiation intensity to be measured at a location far from the slab (and in a single, suitable direction), the two inverse problems are: \noindent 1. determination of the slab thickness \(L\), assuming that the constant parameters \(\sigma_a\) (absorption cross-section) and \(\sigma_s\) (scattering cross-section), as well as the sources \(q\), are known; \noindent 2. determination of \(\sigma_a\), assuming that \(L\), \(\sigma_s\) and \(q\) are known. A well-posedness analysis of the two problems, requiring elementary techniques of functional analysis, is carried out. Moreover, two different numerical schemes are proposed and discussed with examples.