Contrast source inversion of a buried object in TE-scattering

A method for reconstructing the complex permittivity of a bounded inhomogeneous object buried inside a half-space from measured scattered field data is presented. This article extends the contrast source method previously developed by Van den Berg and Kleinman (see Inverse Problems, vol.13, p.1607-20, 1997) to the more complicated TE-case with the object buried inside a half-space. In the TM-case, the electric field integral equation involves an integral operator whose integrand is simply a product of the background Green´s function, the contrast and the field. In the TE-case, the magnetic field is polarized along the axis of an inhomogeneous cylinder of arbitrary cross-section and the corresponding integral equation contain derivatives of both the background Green´s function for the half-space and the field. However, the integral equation can also be formulated as an electric field integral equation for the two transversal components of the electric field. The derivatives are operative outside the integral operator. These derivatives can efficiently be integrated by using rooftop functions in the discretization procedure. In this paper the electric field integral equation is taken as point of departure to develop a contrast source inversion scheme using the modified gradient method.