Applied Mathematics Seminar

Speaker: Peijun Li,  Department of Mathematics, Purdue University
 
Title: Near-Field Imaging of Rough Surfaces

Abstract: In this talk, we consider a class of inverse surface scattering problems in near-field optical imaging, which are to reconstruct the scattering surfaces with resolution beyond the diffraction limit. The scattering surfaces are assumed to be small and smooth deformations of a plane surface. Analytic solutions are derived for the direct scattering problems by using the transformed field expansion, and explicit reconstruction formulas are deduced for the inverse scattering problems. The methods require only a single incident field with a fixed frequency and are realized efficiently by the fast Fourier transform. An error estimate is derived with fully revealed dependence on such quantities as the surface deformation parameter, noise level of the scattering data, and the regularity of the exact scattering surfaces. Numerical results show that the methods are simple, stable, and effective to reconstruct scattering surfaces with subwavelength resolution. Some ongoing and future work will be highlighted along the research line of near-field imaging.