Boundary determination of material parameters from electromagnetic boundary information

Abstract

Consider the following inverse problem. From electromagnetic information obtainable at the boundary of a body, can one determine material parameters, and their normal derivatives, at the boundary of the body? In this paper we answer this question in two physically distinct situations. The first is when the relationship between the electromagnetic fields depends on the conductivity, the electric permittivity and the magnetic permeability of the body, and these parameters together with their normal derivatives are shown to be recoverable at the boundary. The second is when the constitutive relations for the fields are altered so as to further take into account the chirality of the body. We also show how a layer-stripping algorithm may be derived to estimate the unknown parameters near the boundary in both situations. The approach is to calculate an explicit asymptotic expansion for the symbol of a boundary operator which is assumed to be known (from boundary measurements); this expansion is shown in each case to determine the unknown parameters at the boundary.