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Rough surface reconstruction at grazing angles by an iterated marching method.

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    An iterated marching method reconstructs rough 1D surfaces from scattered wave data. This stable, self-consistent approach accurately models surface profiles, even with noise.

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    Area of Science:

    • Computational electromagnetics
    • Inverse scattering problems
    • Wave propagation and scattering

    Background:

    • Reconstructing surfaces from scattered wave data is crucial in various fields.
    • Previous methods often face challenges with rough surfaces and noise sensitivity.
    • Scalar wave scattering at grazing incidence presents unique reconstruction difficulties.

    Purpose of the Study:

    • To develop and present an iterated marching method for reconstructing rough 1D surfaces.
    • To adapt coupled integral equations based on the parabolic equation for surface reconstruction.
    • To assess the method's stability, self-consistency, and noise resilience.

    Main Methods:

    • Utilized an iterated marching method starting with a flat surface as an initial guess.
    • Employed coupled integral equations derived from the parabolic equation.
    • Solved the equations using a maximum of three iterations for scattered field data from Helmholtz equations.

    Main Results:

    • Achieved good agreement between reconstructed and exact surface profiles.
    • Demonstrated improved stability and self-consistency compared to previous approaches.
    • Investigated sensitivity to random noise, revealing a self-regularizing property of the algorithm.

    Conclusions:

    • The iterated marching method is effective for reconstructing rough 1D perfectly reflecting surfaces.
    • The method offers enhanced stability and self-consistency, even with noisy scattered data.
    • The algorithm exhibits inherent self-regularization, making it robust against random noise.