A new algorithm for the shape reconstruction of perfectly conducting objects

In this paper, we describe a new and simple method for the reconstruction of the shape of a perfectly conducting object illuminated by a single plane wave at a fixed frequency. The basic idea of the method is to use the condition that the field must vanish on the (unknown) contour together with convenient representations of the scattered field. In particular, by means of a regularized single-layer potential approach, the measured data are first analytically continued to a circle closely covering the object, while a Taylor expansion in the radial direction is exploited to represent the field in the vicinity of the target. From the boundary condition, the problem is then recast as a polynomial equation containing the contour of the object as an unknown. This nonlinear equation is iteratively solved via the Newton method and it is regularized using the method of least squares. As shown by several numerical examples, the proposed method is computationally effective, it is robust against uncertainties on data and, despite the very limited number of data which are exploited, yields satisfactory reconstructions for convex and concave-shaped star-like scatterers of size comparable to the wavelength.