Higher‐order time‐domain ultrasonic scattering

Abstract

To improve the reliability of diagnosis of tissue pathologies (e.g., cancers) based on ultrasonic imaging, quantitative images of physiological parameters, such as speed of sound and/or absorption coefficient, can, in theory, be obtained by inverse scattering procedures. Previous studies [T. J. Cavicchi, S. A. Johnson, and W. D. O'Brien, Jr., IEEE Trans. UFFC‐35, 22–33 (1988)] employed a moment method matrix formulation under a monofrequency assumption. Periodicities of the field phasors caused a nonuniqueness problem in the inverse scattering solution for scatterers with phase shift magnitudes greater than π, in practical medical imaging, the phase shift would be hundreds of π. A reformulation of the method in the time domain appears more promising because the phase shifts are now merely time delays. The time‐domain moment method formulation is presented for forward scattering. A preliminary numerical study has been undertaken using the moment method equations and the internal field calculated by the inverse discrete Fourier transform of the well‐known monofrequency solution solved at many frequencies. Using the exact field within the integral produces a resulting good approximation of the exact field. Current studies are aimed at inversion for the forward‐scattered field; future work will address inverse scattering.