David H. Chambers

Analysis of the time-reversal operator for a small spherical scatterer in an electromagnetic field

The time-reversal operator (TRO) for a planar array of crossed dipole elements illuminating a small conducting and/or dielectric sphere is investigated in order to determine the general properties of an electromagnetic time-reversing array system. The behavior of such a system for a given frequency is analyzed by studying the eigenvalues and eigenvectors of the TRO. Each eigenvector specifies a set of complex driving currents for the array elements that produce received voltages that are proportional to the conjugates of the drive currents. The proportionality constant is equal to the square root of the associated eigenvalue and is the same for all elements. The eigenvalues and eigenvectors can be determined by performing a singular value decomposition (SVD) on the multistatic data matrix of the array. The eigenvalues of the TRO are the squares of the singular values, and the eigenvectors are identical to the singular vectors. We have shown that the maximum number of singular vectors associated with the sphere is equal to the number of orthogonal orientations of the dipole moments induced in the sphere when irradiated by the array, so there is a maximum of six for a conducting sphere but only three are significant when the conductivity is small and the sphere may be considered being just a dielectric. Numerical results are presented for linear and circular arrays to show the general behavior of the system.

Time reversal for a single spherical scatterer

We show that the time reversal operator for a planar time reversal mirror (TRM) can have up to four distinct eigenvalues with a small spherical acoustic scatterer. Each eigenstate represents a resonance between the TRM and an induced scattering moment of the sphere. Their amplitude distributions on the TRM are orthogonal superpositions of the radiation patterns from a monopole and up to three orthogonal dipoles. The induced monopole moment is associated with the compressibility contrast between the sphere and the medium, while the dipole moments are associated with density contrast. The number of eigenstates is related to the number of orthogonal orientations of each induced multipole. For hard spheres (glass, metals) the contribution of the monopole moment to the eigenvalues is much greater than that of the dipole moments, leading to a single dominant eigenvalue. The other eigenvalues are much smaller, making it unlikely multiple eigenvalues could have been observed in previous experiments using hard materials. However, for soft materials such as wood, plastic, or air bubbles the eigenvalues are comparable in magnitude and should be observable. The presence of multiple eigenstates breaks the one-to-one correspondence between eigenstates and distinguishable scatterers discussed previously by Prada and Fink [Wave Motion 20, 151-163 (1994)]. However, eigenfunctions from separate scatterers would have different phases for their eigenfunctions, potentially restoring the ability to distinguish separate scatterers. Since relative magnitudes of the eigenvalues for a single scatterer are governed by the ratio of the compressibility contrast to the density contrast, measurement of the eigenvalue spectrum would provide information on the composition of the scatterer.

Comparison of ultrasound tomography methods in circular geometry

Extremely high quality data was acquired using an experimental ultrasound scanner developed at Lawrence Livermore National Laboratory using a 2D ring geometry with up to 720 transmitter/receiver transducer positions. This unique geometry allows reflection and transmission modes and transmission imaging and quantification of a 3D volume using 2D slice data. Standard image reconstruction methods were applied to the data including straight-ray filtered back projection, reflection tomography, and diffraction tomography. Newer approaches were also tested such as full wave, full wave adjoint method, bent-ray filtered backprojection, and full-aperture tomography. A variety of data sets were collected including a formalin-fixed human breast tissue sample, a commercial ultrasound complex breast phantom, and cylindrical objects with and without inclusions. The resulting reconstruction quality of the images ranges from poor to excellent. The method and results of this study are described including like-data reconstructions produced by different algorithms with side-by-side image comparisons. Comparisons to medical B-scan and x-ray CT scan images are also shown. Reconstruction methods with respect to image quality using resolution, noise, and quantitative accuracy, and computational efficiency metrics will also be discussed.

Time reversal and the spatio-temporal matched filter (L)

It is known that focusing of an acoustic field by a time-reversal mirror (TRM) is equivalent to a spatio-temporal matched filter under conditions where the Green’s function of the field satisfies reciprocity and is time invariant, i.e., the Green’s function is independent of the choice of time origin. In this letter, it is shown that both reciprocity and time invariance can be replaced by a more general constraint on the Green’s function that allows a TRM to implement the spatio-temporal matched filter even when conditions are time varying.

Imaging Modes for Ground Penetrating Radar and Their Relation to Detection Performance

The focus of this paper is an empirical study conducted to determine how imaging modes for ground penetrating radar (GPR) affect buried object detection performance. GPR data were collected repeatedly over lanes whose buried objects were mostly nonmetallic. This data were collected and processed with a GPR antenna array, system hardware, and processing software developed by the authors and their colleagues. The system enables GPR data to be collected, imaged, and processed in real-time on a moving vehicle. The images are focused by applying multistatic and synthetic aperture imaging techniques either separately or jointly to signal scans acquired by the GPR antenna array. An image-based detection statistic derived from the ratio of buried object energy in the foreground to energy of soil in the background is proposed. Detection-false alarm performance improved significantly when the detection algorithm was applied to focused multistatic synthetic aperture radar (SAR) images rather than to unfocused GPR signal scans.

Characterizing tissue with acoustic parameters derived from ultrasound data

In contrast to standard reflection ultrasound (US), transmission US holds the promise of more thorough tissue characterization by generating quantitative acoustic parameters. We compare results from a conventional US scanner with data acquired using an experimental circular scanner operating at frequencies of 0.3 - 1.5 MHz. Data were obtained on phantoms and a normal, formalin-fixed, excised breast. Both reflection and transmission-based algorithms were used to generate images of reflectivity, sound speed and attenuation.. Images of the phantoms demonstrate the ability to detect sub-mm features and quantify acoustic properties such as sound speed and attenuation. The human breast specimen showed full field evaluation, improved penetration and tissue definition. Comparison with conventional US indicates the potential for better margin definition and acoustic characterization of masses, particularly in the complex scattering environments of human breast tissue. The use of morphology, in the context of reflectivity, sound speed and attenuation, for characterizing tissue, is discussed.

Wideband multichannel time-reversal processing for acoustic communications in highly reverberant environments

The development of multichannel time-reversal (T/R) processing techniques continues to progress rapidly especially when the need to communicate in a reverberant environment is critical. The underlying T/R concept is based on time-reversing the Green’s function characterizing the uncertain communications channel mitigating the deleterious dispersion and multipath effects. In this paper, attention is focused on two major objectives: (1) wideband communications leading to a time-reference modulation technique; and (2) multichannel acoustic communications in two waveguides: a stairwell and building corridors with many obstructions, multipath returns, severe background noise, disturbances, and long propagation paths (∼180ft) including disruptions (bends). It is shown that T/R receivers are easily extended to wideband designs. Acoustic information signals are transmitted with an eight-element array to two receivers with a significant loss in signal levels due to the propagation environment. The results of the n...

Internal wave signal processing: a model-based approach

A model-based approach is proposed to solve the oceanic internal wave signal processing problem that is based on state-space representations of the normal-mode vertical velocity and plane wave horizontal velocity propagation models. It is shown that these representations can be utilized to spatially propagate the modal (depth) vertical velocity functions given the basic parameters (wave numbers, Brunt-Vaisala frequency profile, etc.) developed from the solution of the associated boundary value problem as well as the horizontal velocity components. These models are then generalized to the stochastic case where an approximate Gauss-Markov theory applies. The resulting Gauss-Markov representation, in principle, allows the inclusion of stochastic phenomena such as noise and modeling errors in a consistent manner. Based on this framework, investigations are made of model-based solutions to the signal enhancement problem for internal waves. In particular, a processor is designed that allows in situ recursive estimation of the required velocity functions. Finally, it is shown that the associated residual or so-called innovation sequence that ensues from the recursive nature of this formulation can be employed to monitor the models fit to the data.

Physics-Based Detection of Radioactive Contraband: A Sequential Bayesian Approach

The timely and accurate detection of nuclear contraband is an extremely important problem of national security. The development of a prototype sequential Bayesian processor that incorporates the underlying physics of ¿-ray emissions and the measurement of photon energies and their interarrival times that offers a physics-based approach to attack this challenging problem is described. A basic radionuclide representation in terms of its ¿-ray energies along with photon interarrival times is used to extract the physics information available from the uncertain measurements. It is shown that not only does this approach lead to a physics-based structure that can be used to develop an effective threat detection technique, but also motivates the implementation of this approach using advanced sequential Monte Carlo processors or particle filters to extract the required information. The resulting processor is applied to experimental data to demonstrate its feasibility.

Model-based dispersive wave processing: A recursive Bayesian solution

Wave propagation through dispersive media represents a significant problem in many acoustic applications, especially in ocean acoustics, seismology, and nondestructive evaluation. In this paper we propose a propagation model that can easily represent many classes of dispersive waves and proceed to develop the model-based solution to the wave processing problem. It is shown that the underlying wave system is nonlinear and time-variable requiring a recursive processor. Thus the general solution to the model-based dispersive wave enhancement problem is developed using a Bayesian maximum a posteriori (MAP) approach and shown to lead to the recursive, nonlinear extended Kalman filter (EKF) processor. The problem of internal wave estimation is cast within this framework. The specific processor is developed and applied to data synthesized by a sophisticated simulator demonstrating the feasibility of this approach.