Anisotropic model for RF Tomography

Summary form only given. RF Tomography is an application of ground penetrating radar which uses distributed multiple sensors to detect deeply buried objects. In order to overcome the difficulty posed by dispersion, low frequency and very narrow bandwidth are preferred. Previous work showed very clear reconstructed images of buried targets inside a box filled with sand or gravel (Negishi et al., “Buried objects and void detection using RF Tomography,” National Radio Science Meeting, Boulder, Co, Jan. 2014). The results presented showed that buried Styrofoam (used to simulate cavities inside denser materials) was reconstructed more clearly than buried copper cylinders.The forward model of RF Tomography is based on a volume integral equation which would involve a nonlinear inversion to find the unknown permittivity distribution. The forward model could be linearized using the Born approximation. However, the approximation is valid only if the contrast between an object and the background is small, and the wave numbers are similar between the two regions. While this is a reasonable assumption for some dielectric targets, it is not for metallic targets. A well-known method to overcome this problem is the distorted Born iterative method which involves nonlinear inversion and updating the Green´s function as a part of the iteration. In previous work, we observed that the induced currents on an elongated thin scatterer are different depending on the material. For dielectric objects they are polarized in the same direction as the incidence, while the induced currents on metallic objects are polarized toward the main axis of the elongated object itself. We propose that this phenomenon could be taken into account by modeling the unknown contrast function as a dyad, similarly to what is done in the study of crystals in optics. The unknown dyadic contrast function allows each point scatterer to affect the polarization of the scattered field and can explain depo- arization effects.