Imaging of Local Surface Displacement on an Infinite Ground Plane: The Multiple Frequency Case

This paper is concerned with the inverse electromagnetic scattering from a perfectly conducting local surface displacement on an infinite ground plane. By using multiple frequency data to image the profile of the surface displacement, a stable and accurate reconstruction method is presented and investigated with numerical simulations. An integral equation approach is also introduced for the solution of the forward scattering problem. By recovering the main features at low frequencies and capturing the fine details at high frequencies, the proposed method yields a stable and convergent reconstruction of the general profile. In particular, for a multiple scale profile, the method resolves the fine scales with sufficiently high frequency information. Numerical examples are provided to illustrate the effectiveness of our approach.