Reconstruction of circularly distributed complex refractive-index using a boundary matching technique

The problem of reconstructing a medium parameter in an object from measurements of the field scattered when the object is illuminated by known sources has become of great interest in nondestructive testing, remote sensing, biomedical imaging and so on. In the inverse problem mentioned above, the relation between two unknowns, the field and the medium parameter in the object, is in general nonlinear and hence various reconstruction methods have been developed to give a high-resolution image in situations where the Born or Rytov approximation is not valid. To overcome such difficulties, we propose a novel reconstruction algorithm using a boundary matching technique. In our algorithm, on the assumption that the object may be divided into piecewise homogeneous regions, the field in the object is analytically expressed in terms of wave functions in each region and the mean square error between the measured and calculated fields on the boundary of the object is introduced to estimate the convergence of our procedure. We apply this algorithm to the reconstruction of circularly distributed complex refractive-index in the E-polarized plane wave.