Inverse Scattering Problem Of Infinite Rough Surface In Near-field Optical Imaging

This paper is concerned with an infinite 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 infinite rough surface is assumed to be a small and smooth deformation of a plan surface.Here we consider the order of disturbance at two different scales on the positive and negative half axes.For the direct scattering problem,we add the transparent boundary condition(TBC).The scattering problem on the unbounded domain is transformed into the boundary value problem in the long and narrow band domain,and the well posedness of the weak solution is obtained by using Lax-Milgram.Then,based on a transformed field expansion and perturbation expansion method,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 a convergent analytic solution for the direct scattering problem is derived from the method of integrated solution.In this paper,the near field data is used as the measurement data to reconstruct the scattering surface.Scattering surface evanescent wave is mainly composed of high spatial frequency components,which is contribute to the superresolution near field imaging,we mainly use the spectral cut-off regularization method to control the evanescent wave noise of exponential growth.The method works for sound soft,sound hard,and impedance surfaces.In addition,through the fast Fourier transform,we need only the single frequency incident wave in the reconstruction of two scale surface.And it can be demonstrated that the inverse scattering problem is locally unique in single frequency incident condition.