A NEW METHOD FOR SOLVING THE INVERSE SCATTERING PROBLEM FOR ACOUSTIC-WAVES IN AN INHOMOGENEOUS-MEDIUM .2.

In a previous paper in this journal, we presented a new method for solving the inverse acoustic scattering problem of determining the refractive index of an inhomogenous medium from a knowledge of the far-field data of the scattered field. This method was based on the idea of combining many incident plane waves such that the difference between the far-field pattern due to the inhomogeneous medium and the far-field pattern corresponding to a ball with non-vanishing surface impedance is equal to one. In this paper, we continue this investigation by combining the incident fields such that the modified far-field patterns are equal to Y(p)q(alpha) where Y(p)q is a spherical harmonic instead of being equal to a constant (i.e. the special case when p = q = 0). Numerical examples are given showing the increased accuracy in reconstruction that results from using this higher-order averaging process.