Tomographic imaging of perfectly conducting objects

Abstract

In this paper, a new algorithm for tomographic imaging of perfectly conducting scatterers, with boundary conditions of the Dirichlet or Neumann type, is proposed. The boundary value problem is converted into a volume integral equation with a singular double-layer potential. Then, the resulting far-field pattern is expressed in the form of an impact parameter model, i.e., as a true Fourier transform of the profile function. No approximations are made in the construction of the forward model and derivation of the inversion algorithm. Instead, some elementary facts of the microlocal analysis, in particular the pseudo-locality of the corresponding operator, are used to recover the support of the scattering potential and, therefore, the shape of the obstacle. Mathematically, the problem is reduced to the Radon inversion of a classical computed tomography. It is shown that the algorithm is also capable of classifying the type (Dirichlet or Neumann) of the boundary condition imposed. A relation of the proposed algorithm to a previously known solution based on the physical optics approximation is discussed.