Inversion of penetrable obstacles from far-field data on narrow angular apertures

Reported in this paper are reconstructions of shape and material parameters of two-dimensional, homogeneous, acoustic, penetrable obstacles of arbitrary cross-sections which are immersed in an infinite, homogeneous ambience. Reconstructions are based on the far-field scattering patterns of multiple incident plane acoustic waves. For remotely acquired data, practical necessities require not only that the entire data collection region be less than 2 pi, but also that each received "sees" the object over as narrow an angular aperture as possible. The inversions presented here were obtained under such conditions. Two types of data were used for each incidence namely, "near-monostatic" fields of narrow angular apertures (the narrowest aperture reported is 2 degrees), and a "duostatic" geometry consisting of backscatter plus one other receiver angle. These data sets were acquired for a series of incident angles. The theoretical formalism for inversion is algebraic in nature, requires no integral equation, and possesses a number of advantages for the implementation of a Gauss-Newton type of inversion that was used in this study. Moreover, the algorithm is shown to be inheritently parallelizable.