Near-Field Imaging of Infinite Rough Surfaces

This paper is concerned with an inverse rough surface scattering problem in near-field optical imaging, which is to reconstruct the scattering surface with a resolution beyond the diffraction limit. The surface is assumed to be a small and smooth deformation of a plane surface. Based on a transformed field expansion, the boundary value problem with complex scattering surface is converted into a successive sequence of two-point boundary value problems in the frequency domain, where an analytic solution for the direct scattering problem is derived from the method of integrated solution. By neglecting the high order terms in the power series expansion, the nonlinear inverse problem is linearized and an explicit inversion formula is obtained. A spectral cut-off regularization is adopted to suppress the exponential growth of the noise in the evanescent wave components, which carry high spatial frequency of the scattering surface and contribute to the superresolution in the near-field regime. The method works for sound soft, sound hard, and impedance surfaces, requires only a single illumination at a fixed frequency, and is realized efficiently by the fast Fourier transform. Numerical results show that the method is simple, stable, and effective in reconstructing scattering surfaces with subwavelength resolution.