A LINEARIZED INVERSE BOUNDARY-VALUE PROBLEM FOR MAXWELL EQUATIONS

In this paper, we consider the problem of determining the electromagnetic state of a body from measurements made on the surface of the body. We study the full set of Maxwell's equations that govern time-harmonic electric and magnetic fields. We seek to reconstruct the magnetic permeability-mu, the electric permittivity-epsilon and the electric conductivity-sigma in the interior of the body from measurements made on the surface. We exhibit appropriate boundary measurements in the form of a boundary mapping, specifically the mapping from the tangential components of the electric field to the tangential components of the magnetic field. This data can be used to reconstruct mu, epsilon and sigma approximately, provided they deviate only slightly from known constants. We also estimate the reconstruction errors.