Scattering calculation and image reconstruction using elevation-focused beams

Abstract

Pressure scattered by cylindrical and spherical objects with elevation-focused illumination and reception has been analytically calculated, and corresponding cross sections have been reconstructed with a two-dimensional algorithm. Elevation focusing was used to elucidate constraints on quantitative imaging of three-dimensional objects with two-dimensional algorithms. Focused illumination and reception are represented by angular spectra of plane waves that were efficiently computed using a Fourier interpolation method to maintain the same angles for all temporal frequencies. Reconstructions were formed using an eigenfunction method with multiple frequencies, phase compensation, and iteration. The results show that the scattered pressure reduces to a two-dimensional expression, and two-dimensional algorithms are applicable when the region of a three-dimensional object within an elevation-focused beam is approximately constant in elevation. The results also show that energy scattered out of the reception aperture by objects contained within the focused beam can result in the reconstructed values of attenuation slope being greater than true values at the boundary of the object. Reconstructed sound speed images, however, appear to be relatively unaffected by the loss in scattered energy. The broad conclusion that can be drawn from these results is that two-dimensional reconstructions require compensation to account for uncaptured three-dimensional scattering.

3-D Nonlinear Acoustic Inverse Scattering: Algorithm and Quantitative Results

“…It is also certainly true that if the object is ‘cylindrical’ or cylindrical-like, that the 2D algorithm will give reasonable results and the 2D form factor can be partially compensated by the methods shown in[31],[32]. These elegant results however are validated using the Born approximation (weak scattering approximation), which is not applicable in our case.…”

Generalized theory of resonance excitation by sound scattering from an elastic spherical shell in a nonviscous fluid

“…nevertheless, theoretical and experimental advances depend on the ability to handle a more general problem than the scattering by plane (axisymmetric) waves, namely, the case in which the spherical target is illuminated by a gaussian or a flat-topped square profile (finite) beam [17]- [19], a zero-order [20], or a high-order Bessel vortex [21]- [24] or nonvortex beam [25], [26]. In those studies, however, the target was centered along the axis of propagation of the incident waves, so that only the axial acoustic scattering is investigated, though the analysis [17] based on a Fourier formalism allows for the arbitrary scattering (but this was not performed therein).…”

Acoustic scattering by arbitrary distributions of disjoint, homogeneous cylinders or spheres

“…A number of studies have previously investigated the effects of two-dimensional approximations to threedimensional, elevation-focused scattering in the context of linear 2,3 and nonlinear 4,5 inverse scattering involving electromagnetic or acoustic fields. The more thorough and recent studies [3][4][5] each considered a series of experiments involving scattering from and reconstructions of a single, radially symmetric, homogeneous scatterer.…”

“…The more thorough and recent studies [3][4][5] each considered a series of experiments involving scattering from and reconstructions of a single, radially symmetric, homogeneous scatterer. Quantitative evaluations of two-dimensional methods were made by computing the error of two-dimensional slice reconstructions relative to known scatterer profiles in the slice planes.…”

“…Finally, the efficient technique is used in two and three dimensions to conduct numerical experiments that assess the quality of two-dimensional approximations to three-dimensional scattering of elevation-focused beams by geometries that are more realistic and, hence, complicated than can be described with the analytic solutions of Ref. 5.…”