Absorptivity contrast in transillumination imaging of tissue abnormalities

We calculate the time-resolved flux of photons transmitted across an optically turbid slab containing a partially absorbing inclusion. An analytical expression is obtained for the flux at a detector positioned opposite a point source (at a distance equal to the thickness of the slab) when the center of the inclusion lies on the line connecting those points. The calculation employs a discrete-time lattice random-walk model of photon transport. The resulting expression is used to assess the affects of time resolution on the detectability of the inclusion.