The singular sources method for cracks

The singular sources method is given to detect the shape of a thin infinitely cylindrical obstacle from a knowledge of the TM-polarized scattered electromagnetic field in large distance. The basic idea is based on the singular behaviour of the scattered field of the incident point source on the cross-section of the cylinder. We assume that the scatterer is a perfect conductor which is possibly coated by a material and investigate two models with different boundary conditions. Also we give a uniqueness proof for the shape reconstruction.