The inverse scattering problem for the soft ellipsoid Available to Purchase

A soft triaxial ellipsoid, of unknown semiaxes and orientation, is excited into secondary radiation by a plane acoustic wave of a fixed low frequency. It is proved that one measurement of the leading low‐frequency coefficient and exactly six measurements of the second low‐frequency coefficient of the real part of the forward or the backward scattering amplitude are enough to specify completely both the semiaxes, as well as the orientation of the ellipsoid. Therefore, only the first two low‐frequency coefficients of the real part of the scattering amplitude are needed in order to solve the inverse scattering problem for the soft ellipsoid. For the case of spheroids, the number of measurements is restricted to one for the first and three for the second coefficient. Finally, the sphere is specified by a single measurement of the leading coefficient. The special cases where the orientation or the semiaxes are known are also discussed.