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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 obstacledoi:10.1088/0266-5611/25/1/015001 fatcat:ea2zljrjandsbeaezzfsel6lia