On the feasibility of detecting thin conductive layers from field measurements on the surface of a medium

A two-dimensional environment in which the fields are described by the Helmholtz equation is considered. A linearized formulation of the problem of the recovery of medium parameters (an inverse problem for the Helmholtz equation) is studied. The conditions for the unique detection of thin conductive layers are established. Examples of nonuniqueness of the solution of the inverse problem from information that initially seemed redundant even for a unique solution are given.