  In this work, we study the instability of an inverse problem of radiative
transport equation with angularly averaged measurement near the diffusion
limit, i.e. the normalized mean free path (the Knudsen number) $0 < \eps \ll
1$. It is well-known that there is a transition of stability from H\"{o}lder
type to logarithmic type with $\eps\to 0$, the theory of this transition of
stability is still an open problem. In this study, we show the transition of
stability by establishing the balance of two different regimes depending on the
relative sizes of $\eps$ and the perturbation in measurements. When $\eps$ is
sufficiently small, we obtain exponential instability, which stands for the
diffusive regime, and otherwise we obtain H\"{o}lder instability instead, which
stands for the transport regime.
