Quantitative subsurface imaging in strongly scattering media

We present a method to obtain quantitatively accurate images of small obstacles or inhomogeneities situated near the surface of a strongly scattering medium. The method uses time-resolved measurements of backscattered light to form the images. Using the asymptotic solution of the radiative transfer equation for this problem, we determine that the key information content in measurements is modeled by a diffusion approximation that is valid for small source-detector distances, and shallow penetration depths. We simplify this model further by linearizing the effect of the inhomogeneities about the known background optical properties using the Born approximation. The resulting model is used in a two-stage imaging algorithm. First, the spatial location of the inhomogeneities are determined using a modification of the multiple signal classification (MUSIC) method. Using those results, we then determine the quantitative values of the inhomogeneities through a least-squares approximation. We find that this two-stage method is most effective for reconstructing a sequence of one-dimensional images along the penetration depth corresponding to null source-detector separations rather than simultaneously using measurements over several source-detector distances. This method is limited to penetration depths and distances between boundary measurements on the order of the scattering mean-free path.