On uniqueness and linearization of an inverse electromagnetic scattering problem (Q814734)

The paper deals with the problem of recovering the shape of a two-dimensional cavity from the measurements of the wave field in the cavity aperture. The incident wave is assumed to be a time-harmonic electromagnetic plane wave impinging obliquely the plane containing the cavity aperture. The medium inside the cavity is assumed to be homogeneous, so that the scattering is determined by the shape of the cavity only. The direct scattering problem is reduced to a boundary-value problem with non-local boundary conditions. The paper is mainly aimed at showing that under some technical conditions, the cavity shape is uniquely determined by the wave field in the cavity apperture. The method is based on using the technique of domain derivative applied to a non-linear operator mapping a perturbation of the cavity to the solution of the direct scattering problem taken in the aperture. The author presents the construction of this derivative and describes a Newton-type iteration procedure for recovering the cavity shape.