Near-field imaging of obstacles

Abstract

A novel method is developed for solving the inverse obstacle scatteringproblem in near-field imaging. The obstacle surface is assumed to be a small andsmooth deformation of a circle. Using the transformed field expansion, thedirect obstacle scattering problem is reduced to a successive sequence oftwo-point boundary value problems. Analytical solutions of these problems arederived by a Green's function method. The nonlinear inverse problem islinearized by dropping the higher order terms in the power series expansion.Based on the linear model and analytical solutions, an explicit reconstructionformula is obtained. In addition, a nonlinear correction scheme is devised toimprove the results dramatically when the deformation is large. The methodrequires only a single incident wave at a fixed frequency. Numerical tests showthat the method is stable and effective for near-field imaging ofobstacles with subwavelength resolution.