AN ASYMPTOTIC REPRESENTATION FORMULA FOR SCATTERING BY THIN TUBULAR STRUCTURES AND AN APPLICATION IN INVERSE SCATTERING.

We consider the scattering of time-harmonic electromagnetic waves by a penetrable thin tubular scattering object in three-dimensional free space. We establish an asymptotic representation formula for the scattered wave away from the thin tubular scatterer as the radius of its cross-section tends to zero. The shape, the relative electric permittivity, and the relative magnetic permeability of the scattering object enter this asymptotic representation formula by means of the center curve of the thin tubular scatterer and two electric and magnetic polarization tensors. We give an explicit characterization of these two three-dimensional polarization tensors in terms of the center curve and of the two two-dimensional polarization tensors for the cross-section of the scattering object. As an application we demonstrate how this formula may be used to approximate the residual and the shape derivative in an iterative reconstruction algorithm for an inverse scattering problem with thin tubular scattering objects. We present numerical results to illustrate our theoretical findings. [ABSTRACT FROM AUTHOR]