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

摘要

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. (c) 2007 Optical Society of America.