Two-dimensional vector flow inversion by diffraction tomography

Abstract

The reconstruction of a two-dimensional moving fluid from acoustic transmission measurements is considered. The fluid is described by both a scalar index of refraction and a vector velocity. If the measured data are assumed to be straight-ray geometric projections of the flow, it is known that inversion for the vector velocity is an underdetermined problem. In the present work, it is shown that if the measured data are assumed to satisfy a linearized time-harmonic wave equation, then a unique inversion for the vector velocity is possible. This result is a distinctly finite wavelength effect indicating why ray-based methods fail to produce a complete reconstruction. A filtered backpropagation algorithm for the tomographic reconstruction of the vector flow field is derived.