Inversion of the backscattering data and a problem of integral geometry

Abstract

The backscattered acoustic field from an inhomogeneity is known on a plane P for all frequencies. These data determine the inhomogeneity uniquely. An analytical formula for the inversion is given. The integral geometry problem which consists in finding a compactly supported function from the knowledge of its integrals over the spheres S( x 1, R) of various R centered at x 1, 0 < R < ∞, x 1 ϵ P, is solved analytically explicitly. The backscattered field known at any finite number of frequencie s does not determine the inhomogeneity uniquely.