Characterizing inclusions in optical tomography

In optical tomography, one tries to determine the spatial absorption and scattering distributions inside a body by using measured pairs of inward and outward fluxes of near-infrared light on the object boundary. In many practically important situations, the scatter and the absorption inside the object are smooth apart from inclusions where at least one of the two optical parameters jumps to a higher or lower value. In this work, we investigate the possibility of characterizing these inhomogeneities in the framework of the diffusion approximation of the radiative transfer equation using the factorization method: for purely scattering inclusions, or if the scattering and absorption coefficients interplay in a correct way, the outcoming flux corresponding to a point source belongs to the range of an operator, determined through boundary measurements, if and only if the point source lies inside one of the inclusions.