Consideration of a spread-out source in problems of near-infrared optical tomography

When the light propagates in media where absorption is not negligible and/or scattering is weak, a contribution to the energy density coming from ballistic photons cannot be neglected. A point source effectively spreads out over a scattering volume and its spatial distribution is described by the source function. We consider a boundary value problem of light propagation in half-space for such a source on the basis of the telegraph equation. A solution is found by convolution of Green's function with the source function. The final result shows a significant difference in the behavior of the radiant energy density between the solution obtained for a distributed source and the diffusion approximation. Our results agree well with the Monte Carlo simulations over a broad range of scattering and/or absorption conditions. The obtained results are of practical importance in luminescence optical tomography because an erroneous shape of the energy density function may lead to an incorrect estimate of the light source depth after image reconstruction. The range of applications of the diffusion approximation is also discussed.