Electromagnetic characterization of rough-surface profile using conjugate gradient method

The paper presents an efficient inversion algorithm for reconstructing a one-dimensional perfectly conducting rough surface. The scattered far-field may be obtained with the Kirchhoff approximation and the stationary-phase formulation. The inverse scattering problem reduces to an optimization problem where the rough-surface profile is found by minimizing the norm of the difference between the measured scattering pattern and the calculated one for a reconstructed profile. Applying the conjugate gradient method to the optimization problem, one can derive an iterative formula for getting the surface profile. Computer simulations are performed for the surfaces consisting of a fundamental undulation and higher harmonics. Numerical results demonstrate that the iterative procedure provides high-quality reconstructions even for cases where the scattered field data contains the measurement error