A theoretical model of photon propagation in a scattering medium is presented, from which algebraic formulas for the
detector-readings perturbations (Δ*R*) produced by one or two localized perturbations in the macroscopic absorption
cross section Δ*μ*_{a} are derived. Examination of these shows that when
Δ*μ*_{a} is “titrated” from very small to large magnitudes in one voxel, the curve
traced by the corresponding Δ*R* values is a rectangular hyperbola. Furthermore,
while _{} is dependent on the
location of the detector with respect to the source and the voxel, the ratio
Δ*R*/Δ*R*^{∞} is *in*dependent of the
detector location. We also find that when Δ*μ*_{a} is varied in two voxels
simultaneously, the quantity Δ*R*(Δ*μ*_{a}_{,1}
∧ Δ*μ*_{a}_{,2}) is a bilinear rational
function of the Δ*μ*_{a}s. These results apply not only in the case of steady-state
illumination and detection but extend to time-harmonic measurements as well. The validity of the theoretical formulas is demonstrated by applying them
to the results of selected numerical diffusion computations. Potential applications of the derived expressions to image-reconstruction problems are
discussed.