  We consider the inverse problem of reconstructing the optical parameters for
stationary radiative transfer equation (RTE) from velocity-averaged
measurement. The RTE often contains multiple scales characterized by the
magnitude of a dimensionless parameter---the Knudsen number ($K_n$). In the
diffusive scaling ($K_n \ll 1$), the stationary RTE is well approximated by an
elliptic equation in the forward setting. However, the inverse problem for the
elliptic equation is acknowledged to be severely ill-posed as compared to the
well-posedness of inverse transport equation, which raises the question of how
uniqueness being lost as $K_n \rightarrow 0$. We tackle this problem by
examining the stability of inverse problem with varying $K_n$. We show that,
the discrepancy in two measurements is amplified in the reconstructed
parameters at the order of $K_n^p~ (p = 1\text{ or} ~2)$, and as a result lead
to ill-posedness in the zero limit of $K_n$. Our results apply to both
continuous and discrete settings. Some numerical tests are performed in the end
to validate these theoretical findings.
