A group-theoretic analysis of symmetric target scattering with application to landmine detection

Landmines are generally constructed such that they possess a high level of geometric symmetry and are then buried in a manner that preserves this symmetry. The scattered response of such a symmetric target will likewise exhibit the symmetry of the target, as well as the electromagnetic reciprocity exhibited by all scatterers. Group theory provides a mathematic tool for describing geometric symmetry, and it can likewise be used to describe the symmetries inherent in the bistatic scattering from mines. Specifically, group theory can be used to determine specific forms of the dyadic Green's function of symmetric scatterers, such that multiple scattering solutions can be determined from a knowledge of a single bistatic geometry. Likewise, group theory can be used both to determine and analyze degenerate cases, wherein specific bistatic responses can be identified as zero regardless of target size, shape, or material. These results suggest a method for classifying subsurface targets as either symmetric or asymmetric. From the group-theoretic analysis, scattering features can be constructed that are indicative of target symmetry, but invariant with respect to other target parameters such as size, shape, or material. These features provide a physically based, target-independent value to aid in mine detection and/or clutter rejection. To test the efficacy of this idea, an extensive collection of bistatic ground-penetrating radar (GPR) measurements was taken for both a symmetric and an asymmetric target. The two targets were easily discernable using symmetry features only, a result that suggests symmetry features can be effective in identifying subsurface targets.