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Influence of a waveguide on backscattered signals in the far field

The computation of the scattered field (acoustic, electromagnetic, and elastic) from a wide class of objects can be treated in a consistent manner using the extended boundary condition (EBC) or T-matrix method (originally derived by Waterman). A basic assumption for the objects using this technique is that it is located in free space i.e., volume void of boundaries. This method can still be used when the object is placed in a waveguide, however, it requires coupling the free space solution with the waveguide solution. In this paper the basic derivation for the far-field solution of the scattered field due to the scattering of a guided wave from an object in a waveguide is outlined. This method is then applied to a problem of physical interest which pertains to acoustical scattering from three-dimensional elongated impenetrable objects in an underwater acoustic waveguide.