We seek to reconstruct an absorbing obstacle contained within the top layer of a two-layer halfspace from boundary measurements of backscattered light. This problem is a model for detecting early stages of cancer development in thin epithelial tissues that reside on top of thick stromal tissues. For the direct obstacle scattering problem, we use a combination of the discrete ordinate method with a pseudo-spectral/finite difference method to compute numerical solutions. For the inverse obstacle scattering problem, we use the first Born approximation to compute an explicit solution for a thin obstacle. Using that solution, we seek a numerical fit to the data to determine the depth of the obstacle. Using that recovered depth, we then seek a reconstruction of its transverse spatial distribution. © 2009 IOP Publishing Ltd.
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