Data-driven linearizing approach in inverse scattering.

Direct or forward wave scattering admits three classical regimes in which the map from scatterer properties or scattering potential to the data is linear, namely, the Born, Rytov, and physical optics approximations. In this paper we derive a new decomposition of the forward scattering map which reveals a previously unknown approximate bilinear forward scattering relation. The latter is data-driven, i.e., it involves exact scattering data, and has the useful property that the dependence on the data and the potential is bilinear. This fundamental result naturally leads to a new linear inverse scattering approach that generalizes and is more broadly applicable than the classical Born-approximation-based imaging. The developed scattering and inverse scattering theory are presented in both plane wave and multipole expansion representations, and the possibility of exploiting support information is also formally addressed in the multipole domain. The paper includes computer simulations illustrating the derived theory and algorithms.

Generalized likelihood ratio test change detection with optical theorem constraint.

We demonstrate a new application of the optical theorem to enhance the detection, from noisy scattering data, of an unknown scatterer embedded in an unknown background medium. The proposed methodology is based on a generalized likelihood ratio test detector with an additional constraint that must be obeyed by the scattered field data if the scatterer is known to be passive, lossless, or active. The constraint in question is based on the classical optical theorem, which is used throughout this paper in its most general form applicable to arbitrary probing fields and background media. It relies on background field information, which is accessible in many practical applications. This also reveals, from a fundamental wave physics point of view, that background information is highly relevant in extra ways beyond the basic background suppression operation. This "optical theorem constraint" is discussed in a general Hilbert space framework that applies to a broad class of scattering systems. Particular forms of the optical theorem constraint are presented for special cases, including spherical and cylindrical scanning systems for which it can be compactly expressed in the fundamental multipole representation. The pertinent change detection theory incorporating, via standard nonlinear programming, the physics-based optical theorem constraint is elaborated upon in detail, and the successful detection performance of this new change detection method is illustrated with examples.

Nonuniqueness of optical theorem detectors.

We demonstrate and discuss the multitude of ways in which the extinct power of a scatterer can be measured. To tie some of the developed results to the classical statement of the optical theorem involving the imaginary part of the forward-scattering amplitude, particular attention is given to plane wave excitation. On the other hand, the general results apply to more general probing fields including near fields carrying evanescent components. Novel optical theorem detectors are derived that are based on the Kirchhoff-Helmholtz and Rayleigh-Sommerfeld-based formulations of diffraction, backpropagation, and boundary-value problems as well as on the canonical multipole expansion. The derived detectors also lead to novel expressions for the extinct power in terms of the incident and scattered fields. Applications of the derived results to scattering power sensing with near-field data are also discussed.

Radiation enhancement due to metamaterial substrates from an inverse source theory.

In this paper the formalism of the electromagnetic inverse source theory is used to investigate radiation enhancement due to antenna substrates. Particular attention is given to sources that are confined within a spherical volume and are embedded within two nested spheres of arbitrary materials. Emphasis is given to the special case when the two nested spheres are made up of materials with oppositely signed constitutive parameters. The analysis comprises forward, or radiation, characterization for a given configuration as well as inverse-theoretic characterization. The forward characterization is focused on the singular-value spectrum of the linear source-to-field mapping relevant to each configuration while the inverse-theoretic characterization is performed via the so-called "minimum-energy" sources capable of generating a prescribed exterior field. The derived formulation is based on constrained optimization and multipole theory. Importantly, it is non-antenna-specific. Thus, this formulation enables fair comparison of different substrate configurations by comparing optimal radiation in each configuration (i.e., the "best" in each one), as governed by a formally tractable source-energy cost function that is physically motivated by Ohmic loss control. The derived theory is accompanied by numerical results illustrating the effects on radiation enhancement of particular substrate designs.

Illustration of the role of multiple scattering in subwavelength imaging from far-field measurements.

Recently it has been proposed that the classical diffraction limit could be overcome by taking into account multiple scattering effects to describe the interaction of a probing wave and the object to be imaged [Phys. Rev. E73, 036619 (2006)]. Here this idea is illustrated by considering two point scatterers spaced much less than a wavelength apart. It is observed that while under the Born approximation the scattered field pattern is similar to that of a monopole source centered between the scatterers, multiple scattering leads to a more complicated pattern. This additional complexity carries information about the subwavelength structure and can lead to superresolution in the presence of large noise levels. Moreover, it is pointed out that the additional information due to multiple scattering is interpreted as a form of coherent noise by inversion algorithms based on the Born approximation.

Intensity-only signal-subspace-based imaging.

A signal-subspace method is derived for the localization and imaging of unknown scatterers using intensity-only wave field data (lacking field phase information). The method is an extension of the time-reversal multiple-signal-classification imaging approach to intensity-only data. Of importance, the derived methodology works within exact scattering theory including multiple scattering.

Time-reversal MUSIC imaging of extended targets.

This paper develops, within a general framework that is applicable to rather arbitrary electromagnetic and acoustic remote sensing systems, a theory of time-reversal "MUltiple Signal Classification" (MUSIC)-based imaging of extended (nonpoint-like) scatterers (targets). The general analysis applies to arbitrary remote sensing geometry and sheds light onto how the singular system of the scattering matrix relates to the geometrical and propagation characteristics of the entire transmitter-target-receiver system and how to use this effect for imaging. All the developments are derived within exact scattering theory which includes multiple scattering effects. The derived time-reversal MUSIC methods include both interior sampling, as well as exterior sampling (or enclosure) approaches. For presentation simplicity, particular attention is given to the time-harmonic case where the informational wave modes employed for target interrogation are purely spatial, but the corresponding generalization to broadband fields is also given. This paper includes computer simulations illustrating the derived theory and algorithms.

Generalized power-spectrum Larmor formula for an extended charged particle embedded in a harmonic oscillator.

The nonrelativistic Larmor radiation formula, giving the power radiated by an accelerated charged point particle, is generalized for a spatially extended particle in the context of the classical charged harmonic oscillator. The particle is modeled as a spherically symmetric rigid charge distribution that possesses both translational and spinning degrees of freedom. The power spectrum obtained exhibits a structure that depends on the form factor of the particle, but reduces, in the limit of an infinitesimally small particle and for the charge distributions considered, to Larmor's familiar result. It is found that for finite-duration small-enough accelerations as well as perpetual uniform accelerations the power spectrum of the spatially extended particle reduces to that of a point particle. It is also found that when the acceleration is violent or the size parameter of the particle is very large compared to the wavelength of the emitted radiation the power spectrum is highly suppressed. Possible applications are discussed.

Observations on "nonradiating surface sources": comment.

The proof, established in a recent paper [A. J. Devaney, "Nonradiating surface sources," J. Opt. Soc. Am. A 21, 2216 (2004)], of the existence of nonradiating surface sources formed by singlet-plus-doublet components whose generated fields vanish in either of the regions separated by a closed or infinite surface where the source resides is corroborated by means of an equivalent but slightly different formalism based on treatment of partial differential operators in a weak derivative or distributional sense. This approach yields a construction procedure applicable to a broad class of singular nonradiating sources. A fundamental question raised in that paper concerning the nonexistence of nontrivial nonradiating infinite planar sources that generate vanishing fields at both associated half-spaces is re-examined, with the conclusion that it is actually possible to mathematically construct such singular nonradiating sources as long as one allows for higher-order singularities such as certain combinations of singlet and triplet components.

Noniterative analytical formula for inverse scattering of multiply scattering point targets.

This paper derives, in the exact framework of multiple scattering theory for point targets, a noniterative analytical formula for the nonlinear inversion of the target scattering strengths from the scattering or response matrix that can be applied after the target positions have been estimated in a previous step via, e.g., time-reversal multiple signal classification or another approach. The new formula provides a noniterative analytical alternative to the iterative numerical solution approach for the same problem presented in a recent paper [A. J. Devaney, E. A. Marengo, and F. K. Gruber, "Time-reversal-based imaging and inverse scattering of multiply scattering point targets," J. Acoust. Soc. Am. 118, 3129-3138 (2005)]. The two methods (noniterative versus iterative) are comparatively investigated with two numerical examples.

Nonradiating sources with connections to the adjoint problem.

A general description of localized nonradiating (NR) sources whose generated fields are confined (nonzero only) within the source's support is developed that is applicable to any linear partial differential equation (PDE) including the usual PDEs of wave theory (e.g., the Helmholtz equation and the vector wave equation) as well as other PDEs arising in other disciplines. This description, which holds for both formally self-adjoint and non-self-adjoint linear partial differential operators (PDOs), is derived in the context of both the governing PDE and the corresponding adjoint PDE of the associated adjoint problem. It is shown that a necessary and sufficient condition for a source to be NR is that it obeys an orthogonality relation with respect to any solution in the source's support of the corresponding homogeneous adjoint PDE. For real linear PDOs, this description takes on a more relaxed form where, in addition to the previous necessary and sufficient condition, the obeying of a complementary orthogonality relation with respect to any solution in the source's support of the homogeneous form of the same governing PDE is also both necessary and sufficient for the source to be NR.