• DOI:10.1137/130944485
• Corpus ID: 15143742

Near-Field Imaging of Infinite Rough Surfaces in Dielectric Media

@article{Bao2014NearFieldIO,
  title={Near-Field Imaging of Infinite Rough Surfaces in Dielectric Media},
  author={Gang Bao and Peijun Li},
  journal={SIAM J. Imaging Sci.},
  year={2014},
  volume={7},
  pages={867-899}
}

• G. Bao, Peijun Li
• Published 1 May 2014
• Mathematics
• SIAM J. Imaging Sci.

This paper is concerned with an inverse surface scattering problem in near-field optical imaging, which is to reconstruct the scattering surface of a dielectric medium with a resolution beyond the diffraction limit. It is a nontrivial extension of the authors' work on near-field imaging of infinite rough surfaces from impenetrable to penetrable media [G. Bao and P. Li, SIAM J. Appl. Math., 73 (2013), pp. 2162--2187], where a more sophisticated transmission problem needs to be considered. The scattering surface is modeled as a small and smooth deformation of a plan surface. Based on a transformed field expansion, an analytic solution, which is given as a power series, is derived for the direct scattering problem. By neglecting high order terms in the power series, the original nonlinear inverse problem is linearized; explicit and unified reconstruction formulas are deduced for both reflection and transmission configurations. A spectral cut-off regularization is adopted to suppress the exponential growth of...