  We consider the inverse problem of reconstructing the scattering and
absorption coefficients using boundary measurements for a time dependent
radiative transfer equation (RTE). As the measurement is mostly polluted by
errors, both experimental and computational, an important question is to
quantify how the error is amplified in the process of reconstruction. In the
forward setting, the solution to the RTE behaves differently in different
regimes, and the stability of the inverse problem vary accordingly. In
particular, we consider two scalings in this paper. The first one concerns with
a diffusive scaling whose macroscopic limit is a diffusion equation. In this
case, we showed, following the similar approach as in [Chen, Li and Wang,
arXiv:1703.00097], that the stability degrades when the limit is taken. The
second one considers a highly forward peaked scattering, wherein the scattering
operator is approximated by a Fokker-Planck operator as a limit. In this case,
we showed that a fully recover of the scattering coefficient is less possible
in the limit, whereas obtaining a rescaled version of the scattering
coefficient becomes more practice friendly.
