Imaging with eigenfunctions of a scattering operator

Abstract

An inverse scattering method using eigenfunctions of a scattering operator is reviewed. The framework of the method encompasses the use of eigenfunctions for focusing and quantitative image reconstruction in arbitrary media. Scattered acoustic fields are described using an operator. The eigenfunctions correspond to far-field patterns of an effective source distribution. Incident-wave patterns specified by the eigenfunctions focus on the distribution. The eigenfunction focusing properties are employed to reconstruct an unknown scattering medium by using products of numerically calculated fields defined in terms of eigenfunctions. A linearized version of the method is equivalent to the filtered-backprojection method for Born inversion. The full range of frequencies present in an incident pulse waveform can be used in the method. The method is examined by using both calculated and measured data. In the calculations, an exact solution for scattering from nonconcentric cylinders was employed to obtain the scattered field. In the measurements, a novel ring-transducer system was used to obtain the incident and total fields. The results of simulations and experiments show that the method is accurate for objects large compared to the incident pulse center-frequency wavelength and that the point resolution of the method is about one-half the center-frequency wavelength.