A New Algorithm for the Shape Reconstruction of Perfectly Conducting Objects

Abstract--A new and simple method for the reconstruction of shape and location of a perfectly conducting object illuminated by a single plane wave at a fixed frequency is addressed. By means of single-layer potential approach, the measured scattered field is analytically continued to a circle closely covering the object. Then, through the Taylor expansion of the total field in the radial direction around the circle and the use of the condition that the total field must vanish on the boundary of the unknown object, the problem is reduced to the solution of a non-linear equation containing the surface function of the object as an unknown. The non-linear equation is solved iteratively via Newton method. Numerical simulations show that the method yields satisfactory reconstructions for convex and concave surfaces.