Recently Developed Formulations of the Inverse Problem in Acoustics and Electromagnetics

Abstract

Abstract : Recently developed formulations of the inverse problems in acoustics and electromagnetics are described. There are two types of formulations, one in the geometrical optics limit and the other, an exact formulation for the inverse source problem. Both basic formulations are extended to include the realistic problem of a 'limited aperture' of observations. It is also shown that the inverse source formulation can be applied to the problem of reconstruction of media inhomogeneities from remotely sensed field data. The basic physical optics result is that the characteristic function of the scattering obstacle and the phase and range normalized scattering amplitude are a Fourier transform pair. All other formulations lead to Fredholm integral equations of the first kind.