Uniqueness and non-uniqueness in inverse radiative transfer

We characterize the non-uniqueness in the inverse problem for the stationary transport model, in which the absorption $a$ and the scattering coefficient $k$ of the media are to be recovered from the albedo operator. We show that ``gauge equivalent'' pairs $(a,k)$ yield the same albedo operator, and that we can recover uniquely the class of the gauge equivalent pairs. We apply this result to show unique determination of the media when the absorption $a$ depends on the line of travel through each point while the scattering $k$ obeys a symmetry property. Previously known results concerned the directional independent absorption $a$.