Inverse scattering for unbounded fractally corrugated surfaces

The phaseless inverse scattering of optical or electromagnetic waves from unbounded fractally corrugated surfaces are taken into account. The main characteristics of this inverse scattering problem are that only the phaseless scattered field is measured and the incident field is a tapered wave. In the previous recent works of the authors about the inverse scattering of rough surfaces, the cases of the Dirichlet boundary condition were considered [Inverse Prob. 32, 085002 (2016); Inverse Probl. Sci. Eng. 24, 1282 (2016)]. Here we consider the inverse rough surface problem with Neumann boundary conditions. The Frechet derivatives of the scattered field with respect to the parameters of the surfaces are derived. Then a numerical method to identify the rough surfaces from the phaseless measurements of the scattered field at a fixed frequency is developed. Numerical examples are presented to show the validity and efficiency of the proposed method. (C) 2016 Optical Society of America