Anthony J. Devaney

Time reversal imaging of obscured targets from multistatic data

The methods employed in time-reversal imaging are applied to radar imaging problems using multistatic data collected from sparse and unstructured phased array antenna systems. The theory is especially suitable to problems involving the detection and tracking (locating) of moving ground targets (MGT) from satellite based phased array antenna systems and locating buried or obscured targets from multistatic data collected from phased array antenna systems mounted on unmanned aerial vehicles (UAV). The theory is based on the singular value decomposition (SVD) of the multistatic data matrix K and applies to general phased array antenna systems whose elements are arbitrarily located in space. It is shown that the singular vectors of the K matrix together with knowledge of the Green function of the background medium in which the targets are embedded lead directly to classical time-reversal based images of the target locations as well as super-resolution images based on a generalized Multiple-Signal-Classification algorithm recently developed for use with the K matrix. The theory is applied in a computer simulation study of the TechSat project whose goal is the location of MGTs from an unstructured and sparse phased array of freely orbiting antennas located above the ionosphere.

Time-reversal imaging with multiple signal classification considering multiple scattering between the targets

The time-reversal imaging with multiple signal classification method for the location of point targets developed within the framework of the Born approximation in Lehman and Devaney [“Transmission mode time-reversal super-resolution imaging,” J. Acoust. Soc. Am. 113, 2742–2753 (2003)] is generalized to incorporate multiple scattering between the targets. It is shown how the same method can be used in the location of point targets even if there is multiple scattering between them. On the other hand, both the conventional images and the calculated values of the target scattering amplitudes are scattering model-dependent.

Wavefront sensing by phase retrieval

Phase retrieval implies extraction of a wavefront θ(f) at one spatial plane based on the intensity p(x) in a conjugate plane. For example, θ(f) might be the phase distortion at the entrance pupil of an imaging system when a distant point source is imaged through a turbulent atmosphere; p(x) is the real, non-negative point spread function measured in the image plane. In this paper we describe the mathematics of the technique and show computer simulations.

Time-reversal-based imaging and inverse scattering of multiply scattering point targets

The treatment of time-reversal imaging of multiply scattering point targets developed by the present authors in Gruber et al. [“Time-reversal imaging with multiple signal classification considering multiple scattering between the targets,” J. Acoust. Soc. Am., 115, 3042–3047 (2004)] is reformulated and extended to the estimation of the target scattering strengths using the Foldy–Lax multiple scattering model. It is shown that the time-reversal multiple signal classification (MUSIC) pseudospectrum computed using the background Green function as the steering vector yields accurate estimates of the target locations, even in the presence of strong multiple scattering between the targets, and that the target scattering strengths are readily computed from the so-determined target locations using a nonlinear iterative algorithm. The paper includes computer simulations illustrating the theory and algorithms presented in the paper.

Three-dimensional images generated by quadrature interferometry

Quadrature detection techniques have been applied to images obtained from a Mach-Zehnder interferometer with differently polarized beams to yield the real and the imaginary parts of the diffracted fields simultaneously. This approach eliminates the need for phase retrieval by providing complete information on the complex amplitude of the diffracted signal. We present results in which we demonstrate our ability to reconstruct two- and three-dimensional microscopic objects from their complex diffraction patterns.

Diffraction tomography for multi-monostatic ground penetrating radar imaging

A generalized diffraction tomographic (DT) algorithm is derived for subsurface imaging from multifrequency multi-monostatic ground penetrating radar (GPR) data. The algorithm is based on the Born approximation for vector electromagnetic scattering and incorporates realistic nearfield models for the receiving and transmitting antennas. The forward scattering model is inverted analytically using the regularized pseudoinverse operator to yield an algorithm for imaging the underground region based on scattered field measurements at a set of receiving antennas. Whereas the usual inversion algorithms of DT require a lossless background medium and ideal point sources and receivers, the algorithm described here allows an attenuating background and arbitrary transmitting and receiving antennas. The algorithm places no restrictions on the radar frequency, and can thus include shallow imaging applications where the wavelengths are on the same order as the depth of buried objects of interest. Versions of the algorithm are given for both the three dimensional and the 2.5-dimensional cases. Results are given of computer simulations designed to test the algorithm.

Tomographic reconstruction from optical scattered intensities

A generalized tomographic reconstruction procedure is described for determining the complex-valuedindex-of-refraction distribution of a semitransparent, three-dimensional inhomogeneous object from observations of the far-field intensity patterns generated by the object in a sequence of scattering experiments. The inversion procedure is based on the wave equation governing the scattered optical field and fully accounts for the diffraction and propagation effects associated with the interaction of the incident wave with the object and the subsequent free-space propagation of the scattered wave to the wave zone (far field). The reconstruction of the object’s index-of-refraction distribution is performed digitally directly from the far-field intensity of the scattered wave and does not require direct measurement or retrieval of the phase of the scattered field. An optical scattering experiment is reported in which the cross-sectional profile of the index-of-refraction distribution of an optical fiber is reconstructed from the measured intensity of the diffraction pattern of the fiber by using the described inversion procedure.

Maximum likelihood estimation of object location in diffraction tomography

The problem is formulated within the context of diffraction tomography, where the complex phase of the diffracted wavefield is modeled using the Rytov approximation and the measurements consist of noisy renditions of this complex phase at a single frequency. The log likelihood function is computed for the case of additive zero mean Gaussian white noise and shown to be expressible in the form of the filtered backpropagation algorithm of diffraction tomography. In this form however, the filter function is no longer the rho filter appropriate to least square reconstruction but is now the generalized projection (propagation) of the object (centered at the origin) onto the line(s) parallel to the measurement line(s), but passing through the origin. This result allows the estimation problem to be solved via a diffraction tomographic imaging procedure where the noisy data is filtered and backpropagated in a first step, and the point of maximum value of the resulting image is then the maximum likelihood (ML) estimate of the objects location. The authors include a calculation of the Cramer-Rao bound for the estimation error and a computer simulation study illustrating the estimation procedure. >

Digital microscopy using phase-shifting digital holography with two reference waves

A lensless, coherent optical microscope is described that uses a version of phase-shifting digital holography (PSDH) in conjunction with a field backpropagation algorithm to form coherent images of transmission-type objects. The PSDH is implemented by use of only two reference waves, in contrast with the usual implementation that requires four quadrature phase-shifting reference waves. Therefore only two digital holograms need to be recorded, and the complexity of the microscopic system is reduced. Experimental results are presented that compare images generated from conventional Gabor digital holography, two-reference-wave PSDH, and conventional white-light microscopy.

The inverse source problem of electromagnetics: linear inversion formulation and minimum energy solution

We address the inverse source problem of finding the time-harmonic current distribution (source) with minimum L/sup 2/ norm (minimum energy) that generates a prescribed electromagnetic field outside the sources region of support. Using the well-known multipole expansion of the electromagnetic field we compute (via a linear operator formalism) the sought-after minimum L/sup 2/ norm-current distribution consistent with the data.