Rough surface reconstruction at grazing angles by an iterated marching method

An iterated marching method is presented for the reconstruction of rough perfectly reflecting one-dimensional (1D) surfaces from scattered data arising from a scalar wave at grazing incidence. This is based on coupled integral equations adapted from an earlier approach using the parabolic equation, relating the scattered field at a plane to the unknown surface. Taking the flat surface as an initial guess, these are solved here using at most three iterations. The method is applied to scattered field data generated from the full Helmholtz equations. This approach improves stability and self-consistency. The reconstructed surface profiles are found to be in good agreement with the exact forms. The sensitivity with respect to random noise is also investigated, and the algorithm is found to exhibit a type of self-regularization. (c) 2018 Optical Society of America