Shape reconstruction of a penetrable homogeneous 3D scattering body via the ICBA

Abstract

This work deals with the inverse problem of the determination of the shape of a generally non-spherical penetrable 3D body from the way it scatters incident sonic plane waves. The measurements of the diffracted field are matched to a partial wave representation involving unknown coefficients. Rather than solve for these coefficients (i.e., forward problem) by invoking the transmission conditions, it is supposed that they are locally those of the penetrable sphere of the same composition (as that of the given body) which intersects the given body at its boundary (this is the so-called ICBA, i.e., Intersecting Canonical Body Approximation). These coefficients are known explicitly to within a single parameter which is none other than the length of the position vector joining the origin of the laboratory system to the given point on the boundary of the body. By varying the locations of the measurement point and corresponding boundary point, one generates a discrete form of the parametric equation of the boundary.