Reconstructing a thin absorbing obstacle in a half-space of tissue.

We solve direct and inverse obstacle-scattering problems in a half-space composed of a uniform absorbing and scattering medium. Scattering is sharply forward-peaked, so we use the modified Fokker-Planck approximation to the radiative transport equation. The obstacle is an absorbing inhomogeneity that is thin with respect to depth. Using the first Born approximation, we derive a method to recover the depth and shape of the absorbing obstacle. This method requires only plane-wave illumination at two incidence angles and a detector with a fixed numerical aperture. First we recover the depth of the obstacle through solution of a simple nonlinear least-squares problem. Using that depth, we compute a point-spread function explicitly. We use that point-spread function in a standard deconvolution algorithm to reconstruct the shape of the obstacle. Numerical results show the utility of this method even in the presence of measurement noise.