Determination of the permittivity and conductivity in R 3 using wave splitting of Maxwell’s equations

Time domain wave‐splitting of Maxwell’s equations is applied to the inverse problem of determining the permittivity and conductivity in three dimensions (where the reflected field is produced by an impulse dipole, exterior to the scattering medium). The structure of the fundamental solution is analyzed, and the transport equation is used to derive a condition for the reconstruction. A numerical scheme to reconstruct the permittivity and conductivity simultaneously is given, using the tangential reflection fields due to a dipole with a fixed position and orientation.