Two-dimensional Scatterers Research Articles

An optimization method for acoustic inverse obstacle scattering problems with multiple incident waves

The inverse problem considered in this article is to determine the shape of a two-dimensional time-harmonic acoustic scatterer with Dirichlet boundary conditions from the knowledge of some far field patterns. Based on the optimization method due to Kirsch and Kress for the inverse scattering problem, we propose a new scheme by reformulating the cost functional via a technique of piecewise integration with respect to incident directions. Convergence analysis of this method is given. Numerical experiments show that our method accelerates the computations without losing the accuracy of the reconstructions for the full-aperture problems. The method is extended to the limited-aperture case by weighting the total fields with special factors. Numerical examples for limited-aperture problems are also presented which show that our method produces satisfactory results efficiently in the illuminated regions.

Modeling of the exact solution of the inverse scattering problem by functional methods

Relations between different functional algorithms for solving the inverse scattering problem are analyzed. It is shown that the Rose algorithm does not provide a unique solution, but can be used as a means to improve the interference resistance in reconstruction algorithms that provide unique restoration of scatterer characteristics. The possibility of unique reconstruction of refractive-absorbing scatterers by the modified Rose algorithm, which includes the Sokhotsky equation, is illustrated. Results of numeric simulation of the Novikov-Grinevich-Manakov algorithm, which is efficient in reconstructing two-dimensional acoustic refractive-absorbing scatterers of actually arbitrary shape and strength, are presented. The algorithm rigorously allows for multiple scattering effects. It is promising for tomography-like application problems and features a sufficiently high interference resistance.

Multifrequency generalization of the Novikov algorithm for the two-dimensional inverse scattering problem

The process of reconstruction of two-dimensional refractive-absorbing scatterers by the modified Novikov algorithm is considered. A generalization of this algorithm to the multifrequency mode is proposed. The scattering data obtained at different frequencies are combined in the process of the solution using the a priori known frequency dependence of the scatterer function, which yields the constraint equations that are absent in the single-frequency version. It is shown that the problem of reconstruction instability observed in strong scatterers in the single-frequency mode can be removed by the multifrequency mode. The quality of the scatterer estimate in the multifrequency mode is significantly higher than that of the estimate obtained by straightforwardly averaging the single-frequency solutions. Interference resistance of the algorithm is sufficiently high to allow its application in practice.

Scattering by acoustic boundary scatterers with small wave sizes and their reconstruction

The scattering efficiencies of hard and soft cylindrical scatterers are compared using the Novikov-Grinevich-Manakov functional algorithm designed to reconstruct two-dimensional scatterers. The existence of a rigid relationship between the amplitude and phase of the wave scattered by a quasi- point-like scatterer and by scatterers with small wave sizes in the form of a soft cylinder, a soft sphere, and an air bubble in a liquid is confirmed by numerical simulations.

Reconstruction of acoustic boundary scatterers using the Novikov-Grinevich-Manakov algorithm

Models of perfectly rigid and perfectly soft acoustic scatterers of different dimensions are used to study the applicability limits of the Novikov-Grinevich-Manakov functional algorithm intended for reconstructing two-dimensional scatterers. Particular scattering features intrinsic to boundary scatterers are revealed.

Green’s function surface integral equation method for theoretical analysis of scatterers close to a metal interface

A method for theoretical analysis of light scattering by arbitrary shaped two-dimensional scatterers placed near a planar surface between two media is presented. We show that light scattering by an object near a planar interface can be analyzed (exactly) using Green's function surface integral equations that are form invariant with those for a scatterer in free space. All effects of the planar interface structure are built into the Green's function. An approach for calculating the Green's function is presented along with far-field approximations that enable efficient evaluation of scattering into waves propagating out of the surface plane and, in the case of a planar metal-dielectric interface, evaluation of scattering into surface plasmon-polariton (SPP) waves propagating along the interface. Finally, the method is exemplified by analysis of light scattering by a nm-thin and sub-$\ensuremath{\mu}\text{m}$-wide gold strip (resonator) placed between 5 and 200 nm above a planar gold surface. We compare the amount of scattering going into the out-of-plane propagating waves and SPPs, respectively, and, for our configuration, scattering into out-of-plane propagating waves dominates. Scattering into SPP waves has a maximum if the strip is placed approximately 20 nm from the surface. We also find that when placing the gold strip more than 50 nm from the interface, the scattering resonance wavelength is practically independent of the distance, whereas changing the distance from 50 to 5 nm results in a $\ensuremath{\sim}400\text{ }\text{nm}$ redshift of the resonance wavelength.

Deformable mirror tomography – An alternative imaging technique for inverse scattering applications

Several microwave tomography techniques have been developed to reconstruct the spatial distribution of the electrical property of penetrable objects. These techniques rely on solving the ill-posed nonlinear inverse scattering problem using field measurements acquired from multiple views at multiple frequencies and incorporate prior information during inversion to obtain a stable solution. Such techniques often employ a linear or circular antenna array with individual elements operating as a transceiver to acquire multiple field measurements for imaging. In this paper a tomographic inversion technique with single fixed transmitter and a deformable mirror is proposed as an alternative to the conventional tomography system. Limitations arising from the use of a single transmitter for acquiring multi-view data for the ill-posed problem are overcome by using a continuously deformable mirror with reflective coating. The continuously deformable mirror controlled by an underlying actuator circuit steers the incident field towards the scatterer for multi-view field measurements. A theoretical analysis of the proposed microwave tomography technique including system design, theory, operating principles and selection of optimal mirror shapes to obtain information rich field measurements are discussed in this paper. Computational feasibility of the proposed inverse scattering technique is investigated for two-dimensional penetrable dielectric scatterer in the presence of measurement noise.

Iterative image reconstruction of two-dimensional scatterers illuminated by TE waves

The iterative reconstruction of unknown objects from TE-measured scattered field data is presented. The paper investigates the performance of the iterative multiscaling approach (IMSA) in exploiting transverse electric (TE) illuminations. As a matter of fact, in these conditions, the problem turns out to be more complicated than the tranverse magnetic (TM) scalar one in terms of mathematical model as well as computational costs. However, it is expected that more information on the scenario under test can be drawn from scattered data. Therefore, this study is aimed at verifying whether the TE case can provide additional information on the scenario under test (compared to the TM illumination) and how such an enhancement can be suitably exploited by the IMSA for improving the reconstruction accuracy of the retrieval process. Such an analysis will be carried out by means of a set of numerical experiments concerned with dielectric and metallic targets in single- and multiple-objects configurations. Synthetic as well as experimental data will be dealt with.

On the robustness of space-time coding techniques based on a general space-time covariance model

The robustness of space-time coding techniques for wireless channels that exhibit both temporal and spatial correlation is investigated. A general space-time covariance model is developed and employed to evaluate the exact pairwise error probability for space-time block codes. The expressions developed for the pairwise error probability are used in conjunction with the union bound to determine an upper bound for the probability of a block error. The block error probability is evaluated for several space-time codes and for wireless channels that exhibit varying degrees of spatial and temporal correlation. Numerical results are presented for a two-dimensional Gaussian scatterer model which has been shown to be consistent with recent field measurements of wireless channels. The results demonstrate that the best-case wireless channel is uncorrelated in both space and time. Correlation between transmission paths, due to insufficient spacing of the transmit antennas or scatterers located in close proximity to the mobile, can result in a significant performance degradation. The conditions that result in uncorrelated transmission paths are quantified in terms of the effective scattering radius and the spacing of the transmit and receive antennas.

PECULIARITIES IN THE DIELECTRIC RESPONSE OF NEGATIVE-PERMITTIVITY SCATTERERS

This study analyzes polarizability properties of spherically layered small inclusions that possess negative permittivity. Conditions for invisibility to external electric fields are derived. The complementary principle for two-dimensional scatterers is used to derive special properties of self-complementary inclusions. A singular behavior between the limits of invisibility and infinite response is underlined for a hollow circular shell. A similar,although not as drastic,phenomenon is shown to take place for the three-dimensional hollow sphere.

Boosting numerical accuracy in calculation of polarizability of two-dimensional scatterers

This article presents an effective way to increase the accuracy of the numerical evaluation of the polarizability of two-dimensional scatterers. It is based on the numerical exploitation of the observation that the polarizabilities of complementary inclusions are closely related: if the permittivity is inverted, the polarizability changes sign. For anisotropic inclusions, the corresponding property cross-connects the orthogonal components, and can be used as well in the numerical calculations. The improvement of the numerical accuracy is several orders of magnitude. The method is also applied to evaluate the polarizability of split rings.

A new approximate solution for scattering by thin dielectric disks of arbitrary size and shape

In this paper, an approximate solution for electromagnetic scattering by a very thin planar homogeneous dielectric object is presented. This solution is obtained from a volumetric integral equation using Fourier transform and is shown to be uniformly valid from low to high frequencies at all incidence angles including edge-on incidence. Validity of the solution is demonstrated through a comparison with canonical objects such as an infinite dielectric slab, and a number of two-dimensional (2-D) and three-dimensional (3-D) dielectric scatterers. For 2-D, and 3-D scatterers, the approximate solution is compared with a method of moments solution. In all cases examined the approximate formulation provides very accurate results except for situations where the dielectric constant is very high.

Computational approach based on a particle swarm optimizer for microwave imaging of two-dimensional dielectric scatterers

A computational approach based on an innovative stochastic algorithm, namely, the particle swarm optimizer (PSO), is proposed for the solution of the inverse-scattering problem arising in microwave-imaging applications. The original inverse-scattering problem is reformulated in a global nonlinear optimization one by defining a suitable cost function, which is minimized through a customized PSO. In such a framework, this paper is aimed at assessing the effectiveness of the proposed approach in locating, shaping, and reconstructing the dielectric parameters of unknown two-dimensional scatterers. Such an analysis is carried out by comparing the performance of the PSO-based approach with other state-of-the-art methods (deterministic, as well as stochastic) in terms of retrieval accuracy, as well as from a computational point-of-view. Moreover, an integrated strategy (based on the combination of the PSO and the iterative multiscaling method) is proposed and analyzed to fully exploit complementary advantages of nonlinear optimization techniques and multiresolution approaches. Selected numerical experiments concerning dielectric scatterers different in shape, dimension, and dielectric profile, are performed starting from synthetic, as well as experimental inverse-scattering data.

A Novel Technique for Localizing the Scatterer in Inverse Profiling of Two Dimensional Circularly Symmetric Dielectric Scatterers Using Degree of Symmetry and Neural Networks

A novel technique for localizing the scatterer in microwave imaging of two-dimensional circularly symmetric dielectric scatterers using degree of symmetry and neural networks is presented. The degree of symmetry for a transmitter position is computed as a function of the difference between the first half and the spatially reflected second half of the measured scattered field vector. A Probabilistic Neural Network (PNN) classifier is trained with the degree of symmetry vectors for the different object configurations. It classifies the degree of symmetry vector of the unknown circularly symmetric scatterer presented to it into one of the classes that indicate the radius and location of the centre of the scatterer. Thus the scatterer is localized in the imaging domain. This not only reduces the degrees of freedom in the inversion for the unknown object, thereby aiding the global convergence of the solution, but also results in a reduction in computation time. The technique has been tested on synthetic data and the results are promising.

Microwave imaging from limited-angle scattered data using the iterative multiscaling approach

In this paper, with reference to limited-angle data configurations, the performance of the nonlinear multi-scaling inversion approach (IMSA) is analyzed. Such an assessment is carried out by considering synthetically-generated as well as laboratory-controlled experimental data ('Marseille data') concerning two-dimensional dielectric scatterers. The obtained results demonstrate a satisfactory robustness and the reliability of the approach.

LOCATION AND IMAGING OF TWO-DIMENSIONAL SCATTERERS BY USING A PARTICLE SWARM ALGORITHM

In this paper, a microwave imaging method for reconstructing two-dimensional dielectric scatterers is presented. Starting from an integral formulation of the electromagnetic scattering phenomena, the method is aimed at determining the dielectric profile of the scatterer under test by means of an innovative particle swarm algorithm. In order to preliminary assess the effectiveness of the proposed method, some numerical experiments are carried out in noiseless as well as in noisy conditions. The obtained results confirm the capabilities of the proposed method in term of reconstruction accuracy and robustness.

Reconstruction of the fine structure of an acoustic scatterer against the distorting influence of its large-scale inhomogeneities

In the ultrasonic diagnostics of small-size neoplasms of biological tissues at the earliest stage of their development, an efficient way to eliminate the distorting influence of high-contrast or large inhomogeneities of the biological medium is to apply the iterative technique. A simple approach is proposed, which makes it possible with only two iteration steps to achieve an efficient focusing of the tomograph array. At the first step, the unknown distribution of the large-scale inhomogeneities of sound velocity and absorption over the scatterer is reconstructed, where the large-scale inhomogeneities are those whose size exceeds several wavelengths. At the second step, the fine structure of the scatterer is reconstructed against the large-scale background, which can be performed with a high accuracy owing to the evaluation of the background at the first step. The possibility of simultaneous reconstruction of the large-scale and fine structures by the noniterative Grinevich-Novikov algorithm is considered as an alternative. This algorithm reconstructs in an explicit form two-dimensional refractive-absorbing acoustic scatterers of almost arbitrary shape and strength. Taking into account the effects of multiple scattering, this algorithm provides resolution of the fine structure almost as good as that achieved in reconstructing the same structure against an undistorting homogeneous background. The results of numerical simulations of both algorithms are presented.

Numerical method for the shape reconstruction of a hard target

A nonlinear optimization method was developed to solve the inverse problem of determining the shape of a hard target from the knowlegde of the far-field pattern of the acoustic scattering wave, it was achieved by solving independently an ill-posed linear system and a well-posed minimization problem. Such a separate numerical treatment for the illposedness and nonlinearity of the inverse problem makes the numerical implementation of the proposed method very easy and fast since there only involves the solution of a small scale minimization problem with one unknown function in the nonlinear optimization step for determining the shape of the sound-hard obstacle. Another particular feature of the method is that it can reproduce the shape of an unknown hard target efficiently from the knowledge of only one Fourier coefficient of the far-field pattern. Moreover, a two-step adaptive iteration algorithm was presented to implement numerically the nonlinear optimization scheme. Numerical experiments for several two-dimensional sound-hard scatterers having a variety of shapes provide an independent verification of the effectiveness and practicality of the inversion scheme.

TIME-DOMAIN INVERSE SCATTERING USING LAGRANGE MULTIPLIERS: AN ITERATIVE FDTD-BASED OPTIMIZATION TECHNIQUE

In this paper, we present an electromagnetic inverse scattering technique in the time domain, which is based on the minimization of an augmented cost functional. This functional is composed of an error term representing the discrepancy between the measured and the estimated values of the electromagnetic field, a regularization term related to the first-order Tikhonov's regularization scheme and, finally, an equality-constraints term associated with the fulfillment of the Maxwell's curl equations. These equality constraints are introduced by applying Lagrange multipliers. The minimization of the functional is carried out by applying the Polak-Ribière nonlinear conjugate-gradient algorithm. The required Fr´echet derivatives of the augmented cost functional with respect to the functions that describe the scatterer properties are derived by an analysis based on the calculus of variations. Actually, it is proven that the Lagrange multipliers are waves satisfying the Maxwell's curl equations. Consequently, during each iteration of the minimization procedure, we apply the finite-difference time-domain method and the perfectly-matched-layer absorber to calculate both the electromagnetic fields and the Lagrange multipliers. The presented technique is successfully applied to the reconstruction of multiple two-dimensional scatterers, which can be dielectric, lossy, and magnetic.

A new 2-D image reconstruction algorithm based on FDTD and design sensitivity analysis

This paper proposes a numerical algorithm that reconstructs the complex permittivity profile of unknown scatterers by the design sensitivity analysis (DSA) and topology optimization technique. By introducing the DSA and adjoint-variable method, the derivatives of the error function with respect to the complex permittivity variables can be calculated, and the material property in each cell can be changed simultaneously using sensitivity information. The steepest descent method is used as an optimization technique. The proposed method is validated by applying it to reconstructions of unknown two-dimensional scatterers that are illuminated by TM/sup z/ with a Gaussian-pulsed plane wave.