Quantitative imaging using a time-domain eigenfunction method

An inverse scattering method that uses eigenfunctions of a scattering operator at a single frequency is extended to include the full range of frequencies present in the incident pulse waveform. The resulting so-called time-domain eigenfunction method is shown to yield a modulated version of the scattering potential. The potential is recovered by a demodulation process using cross correlation with a reference. Including an adaptive delay in the reference is shown to compensate partially for the linearization of the Born approximation and to extend its valid range. The k-space window of the time-domain solution is expressed in terms of the incident waveform and shown to be smoother than that of a single-frequency solution. The time-domain method is examined using both calculated and measured data. In the calculations, an exact solution for scattering from one or multiple nonconcentric cylinders is used to obtain the scattered field. In the measurements, a novel ring-transducer system was employed to obtain the incident and total fields. The results of simulations and experiments show that the method is robust and accurate for the size of objects considered and that the point resolution approaches one-half the wavelength at the pulse center frequency.