A Newton method for the reconstruction of perfectly conducting slightly rough surface profiles

A new method for the reconstruction of a one-dimensional profile of a perfectly conducting rough surface illuminated by a plane wave at a fixed frequency is addressed. By a special representation of the scattered electric field, the total field in the half-space over the surface is obtained from the measured data, which leads to a nonlinear equation with a surface function as unknown. The nonlinear equation is solved iteratively via the Newton method and a regularization in the least square sense. Numerical simulations show that the method yields satisfactory reconstructions for slightly rough surface profiles.