The stationary transport problem with angularly averaged measurements

We consider an inverse problem for the stationary linear (Boltzmann) transport equation on a bounded domain , with n ⩾ 2. In our measurement scheme we inject X with L 1 integrable flux having both positional and directional dependence. We then measure a weighted average of the outgoing flux. Taking measurements at every point on ∂ X , we are able to reconstruct the total extinction coefficient, σ. Once σ is known, measurements made at one point allow recovery of the scattering kernel under some additional assumptions. In particular, we assume that scattering is supported inside of X , the scattering phase function is known, and that the scattering kernel is small. The required smallness depends upon σ. We also require that σ and the phase function are 'close to' real analytic. Stability estimates are then obtained.