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Most diffraction tomography (DT) algorithms use a homogeneous Green function (GF) regardless of the medium being imaged. This choice is usually motivated by practical considerations: analytic inversions in standard geometries (Cartesian, spherical, etc.) are significantly simplified by the use of a homogeneous GF, estimating a nonhomogeneous GF can be very difficult, as can incorporating a nonhomogeneous GF into standard DT algorithms. Devaney has circumvented these issues by developing a purely numerical DT inversion algorithm [A. J. Devaney and M. Dennison, Inverse Probl. 19, 855–870 (2003)] that is independent of measurement system geometry, number of frequencies used in the reconstruction, and GF. A planar multilayer GF has been developed for use in Devaney’s “Hilbert space” algorithm and used in a proof-of-principle nondestructive evaluation (NDE) experiment to image noninvasively a flaw in an aluminum/copper planar multilayer medium using data collected from an ultrasonic measurement system. The data were collected in a multistatic method with no beamforming: all focusing through the multilayer was performed mathematically “after-the-fact,” that is, after the data were collected.

We designed and built a phantom consisting of vertical wires maintained under tension to be used as an ultrasonic test, calibration, and reconstruction object for the Lawrence Livermore National Laboratory annular array scanner. We provide a description of the phantom, present example data sets, preliminary reconstructions, example metadata, and MATLAB codes to read the data.

A wave-based tomographic imaging method and apparatus based upon one or more rotating radially outward oriented transmitting and receiving elements have been developed for non-destructive evaluation. At successive angular locations at a fixed radius, a predetermined transmitting element can launch a primary field and one or more predetermined receiving elements can collect the backscattered field in a “pitch/catch” operation. A Hilbert space inverse wave (HSIW) algorithm can construct images of the received scattered energy waves using operating modes chosen for a particular application. Applications include, improved intravascular imaging, bore hole tomography, and non-destructive evaluation (NDE) of parts having existing access holes.

In previous ASA meetings and JASA papers, the extended and formalized theory of transmission mode time reversal in which the transceivers are noncoincident was presented. When combined with the subspace concepts of a generalized MUltiple SIgnal Classification (MUSIC) algorithm, this theory is used to form super‐resolution images of scatterers buried in a medium. These techniques are now applied to ultrasonic nondestructive evaluation (NDE) of parts, and shallow subsurface seismic imaging. Results are presented of NDE experiments on metal and epoxy blocks using data collected from an adaptive ultrasonic array, that is, a ‘‘time‐reversal machine,’’ at Lawrence Livermore National Laboratory. Also presented are the results of seismo‐acoustic subsurface probing of buried hazardous waste pits at the Idaho National Engineering and Environmental Laboratory. [Work performed under the auspices of the U.S. Department of Energy by University of California Lawrence Livermore National Laboratory under Contract No. W‐74...

We have formalized the theory of transmission mode time reversal imaging for arbitrary transducer geometry. Although it is not possible to implement such a system in practice, we have shown that transmission mode time reversal imaging is achievable a posteriori from the scattered field time series as measured at the receivers. We apply this theory to studying the singular value spectra of objects buried in the ground. We provide simulated finite‐difference time‐domain (FDTD) examples designed to model the case of geophysical vertical seismic profiling in which a series of sources are excited on the surface and the scattered fields are measured on a chain of receivers in a bore hole. A single, non‐point scatterer can have multiple singular values dependent upon the scatterer’s physical properties. We study the relationship between the singular value spectra and these physical properties.