Effects of uncertainty on background permittivity in one-dimensional linear inverse scattering

We discuss the role of uncertainties in the knowledge of the background in inverse scattering for a buried object under the distorted Born approximation. In particular, we focus on the role played by inaccuracy in the knowledge of the dielectric permittivity of the host medium, with reference to both a lossless half-space and a lossless three-layered medium. This investigation allows us to show how reconstruction of an inhomogeneity in a three-layered medium is more critical than in the case of a half-space (two-layered) geometry.