  We consider in a two dimensional absorbing and scattering medium, an inverse
source problem in the stationary radiative transport, where the source is
linearly anisotropic. The medium has an anisotropic scattering property that is
neither negligible nor large enough for the diffusion approximation to hold.
The attenuating and scattering properties of the medium are assumed known. For
scattering kernels of finite Fourier content in the angular variable, we show
how to recover the anisotropic radiative sources from boundary measurements.
The approach is based on the Cauchy problem for a Beltrami-like equation
associated with $A$-analytic maps. As an application, we determine necessary
and sufficient conditions for the data coming from two different sources to be
mistaken for each other.
