Determining the shape of defects in non-absorbing inhomogeneous media from far-field measurements

We consider non-absorbing inhomogeneous media represented by some refraction index. We have developed a method to reconstruct, from far-field measurements, the shape of the areas where the actual index differs from a reference index. Following the principle of the factorization method, we present a fast reconstruction algorithm relying on far-field measurements and near-field values, easily computed from the reference index. Our reconstruction result is illustrated by several numerical test cases.