Information content of the Born field scattered by an embedded slab: multifrequency, multiview, and multifrequency–multiview cases

Abstract

The information content of the scattered field in the framework of the linear Born and distorted Born approximations for a one-dimensional lossless dielectric permittivity profile embedded in a lossless homogeneous half-space is analyzed. The number of degrees of freedom of the scattered field and the class of the retrievable profiles from a multifrequency, a multiview, and a multifrequency–multiview configuration are evaluated by analytical considerations and validated by numerical singular-value decomposition. The analysis stresses the effects of the background permittivity value on the degrees of freedom and on the class of retrievable profiles within the distorted Born approximation. In particular, the results show that, for high values of the half-space permittivity, the information content in the multiview approach at a fixed frequency becomes too poor to yield effective reconstructions, whereas a suitable multifrequency or multifrequency–multiview approach can provide better results.