P. Ola et E. Somersalo, ELECTROMAGNETIC INVERSE PROBLEMS AND GENERALIZED SOMMERFELD POTENTIALS, SIAM journal on applied mathematics, 56(4), 1996, pp. 1129-1145
In this article we study the inverse boundary value problem for Maxwel
l's equation; that is, we determine the scalar permeability, permissib
ility, and conductivity of a body from electromagnetic field measureme
nts outside the body. In this paper, the problem is approached by usin
g certain generalized Sommerfeld potentials that are shown to satisfy
a vector-valued Schrodinger equation. By using these potentials, the i
nverse boundary value problem is reduced to the problem of determining
the potential of this second-order operator. Further, it is shown tha
t the electromagnetic material parameters can be determined by using e
lectric or magnetic dipole point sources only.