DISCONTINUOUS MEDIA AND UNDERDETERMINED SCATTERING PROBLEMS

The problem of ambiguities in trying to determine a shape by means of scattering experiments, with one or a few illuminating angles and all directions of receivers, is discussed by means of numerical experiments. The model equation gives a good representation of scattering of scalar waves which can take into account impedance discontinuities inside the scatterer. Physical problems include, for instance, acoustical waves in media where the density rho and the Lame parameter-lambda may vary continuously everywhere except across a finite number of smooth surfaces through which they jump. For the sake of simplicity, results are illustrated here in the two-dimensional case, with one discontinuity curve. The input is a closed curve of arbitrary shape, with arbitrary boundary conditions, chosen in such a way that the quadratic approximation (Born term + second-order term) is valid. The scattering amplitude is calculated for one incident angle. Then a circular curve is calculated, with appropriate boundary conditions, which yields the same scattering amplitude within the approximation. Variations of incident angles, frequencies and shapes are discussed for the calculated examples. The relevance of these results in the theory of non-destructive sensing is obvious.