Small Spherical Scatterers Research Articles

Быстрый метод анализа возмущения электромагнитного поля малыми сферическими рассеивателями

Быстрый метод анализа возмущения электромагнитного поля малыми сферическими рассеивателями

Time-reversal Operator for a Small Sphere in Electromagnetic Fields

The paper investigates the time-reversal operator (TRO) for a planar array of crossed dipole antennas illuminating a small spherical scatterer in frequency domain. A simple approach making use of the reciprocal theorem is used to construct the TRO. The eigenvalues and eigenvectors of the TRO are obtained by transforming the original system into an equivalent system where a six-by-six governing matrix is built up, each singular vector of which specifies a set of electric current dipole moments and normalized magnetic current dipole moments induced in the small sphere. The results show that the polarization of the radiation from each crossed antenna driven by the currents specified by the eigenvectors depends on the composing material of the small sphere and the configuration of the antenna array. For some composing materials of the sphere, circularly polarized radiation is possible, depending on the positions and the lengths of the antennas of the array. For a nonmagnetic dielectric or perfectly conducting sphere, however, the eigenvectors produce only linearly polarized radiation from each crossed antenna, and no elliptically polarized wave can be radiated regardless of the configuration of the antenna array. This polarization property suggests its application for target classification.

Target characterization using decomposition of the time-reversal operator: electromagnetic scattering from small ellipsoids

Decomposition of the time-reversal operator for an array, or equivalently the singular value decomposition of the multistatic response matrix, has been used to improve imaging and localization of targets in complicated media. Typically, each singular value is associated with one scatterer even though it has been shown in several cases that a single scatterer can generate several singular values. In earlier papers Chambers and Berryman (2004 Phys. Rev. Lett. 92 0239021–4; 2004 IEEE Trans. Ant. Prop. 52 1729–38) showed that a small spherical scatterer can generate up to six singular values depending on the array geometry and sphere composition. It was shown that the existence and characteristics of multiple singular values for each scatterer can, in principle, be used to determine certain properties of the scatterers, e.g. conducting or non-conducting material. In this paper, we extend this analysis to non-spherical targets and show how orientation information about the target may be obtained from the spectrum of singular values. The general properties of the decomposition for small non-spherical dielectric (and possibly conductive) targets in an electromagnetic field are derived and detailed results are obtained for the specific cases of non-magnetic and perfectly conducting needles and discs. It is shown that scatterer orientation can be estimated by tracking the singular values of a linear array as it is rotated around its midpoint.

Characterization of subwavelength elastic cylinders with the decomposition of the time-reversal operator: Theory and experiment

The decomposition of the time-reversal operator provides information on the scattering medium. It has been shown [Chambers and Gautesen, J. Acoust. Soc. Am. 109, 2616-2624 (2001)] that a small spherical scatterer is in general associated with four eigenvalues and eigenvectors of the time-reversal operator. In this paper, the 2D problem of scattering by an elastic cylinder, imbedded in water, measured by a linear array of transducers is considered. In this case, the array response matrix has three nonzero singular values. Experimental results are obtained with linear arrays of transducers and for wires of different diameters smaller that the wavelength. It is shown how the singular value distribution and the singular vectors depend on the elastic velocities cL, cT, the density rho of each wire, and on the density rho0 and velocity c0 of the surrounding fluid. These results offer a new perspective towards solution of the inverse problem by determining more than scattering contrast using conventional array processing like that used in medical ultrasonic imaging.

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.

Characterization of scattering object with the decomposition of the time-reversal operator: Theory and experiment

The decomposition of the time-reversal operator provides information on the scattering medium. It has been shown [Chambers, J. Acoust. Soc. Am. 109, (2001)] that a small spherical scatterer is in general associated with four eigenvalues and eigenvectors of the time-reversal operator. In this paper, the 2D problem of scattering by a cylinder measured by a linear array of transducers is considered. Experimental results are obtained for wires of different diameters and different materials. It is shown how the singular-value distribution and the singular vectors depend on the elastic wave speeds cL, cT, the density and the radius of each wire. These results offer a new perspective towards solution of the inverse problem by determining more than scattering contrast using conventional array processing like that used in medical ultrasonic imaging.

Analysis of the time-reversal operator for scatterers of finite size.

Recently, it was shown that the time-reversal operator for a single, small spherical scatterer could have up to four distinguishable eigenstates [Chambers and Gautesen, J. Acoust. Soc. Am. 109, 2616-2624 (2001)]. In this paper, that analysis is generalized for scatterers of arbitrary shape and larger size. It is shown that the time-reversal operator may have an indefinitely large number of distinguishable eigenstates, with the exact number depending on the nature of the scatterer and the geometry of the time-reversal mirror. In addition, the case of a multiple number of well-separated scatterers is investigated, with the result that the total spectrum is the direct combination of the eigenstates associated with each scatterer. As an example, the singular value spectrum of the time-reversal operator for a linear array is calculated explicitly for bubbles and hard rubber spheres of finite size. Both resonance peaks and apparent crossing points can be observed in the spectrum as the size of the scatterer increases.

Multiple eigenvalues of the time reversal operator for a small spherical scatterer

Time reverse mirrors have been used to discriminate and focus energy on individual scatterers embedded in difficult media. A time reverse mirror consists of an array of transceivers, each of which records the incident pressure field then re-emits a time reversed image of it. Prada [J. Acoust. Soc. Am. 97(1) (1995)] described this operation in terms of a time reverse operator whose eigenvalues are associated with individual scatterers in the medium. In particular, it was shown that there was a one-to-one correspondence between the eigenvalues and scatterers for the case of well separated scatterers whose density is identical to the medium. In this talk, Prada’s approached is generalized to scatterers of arbitrary densities where the scattered wave is no longer spherical. It is shown that the one-to-one correspondence between scatterers and eigenvalues of the time reversal operator is broken. For the specific case of a small spherical scatterer, there are three eigenvalues. Physical interpretations of the three eigenvalues and the implications for applications of the time reverse method will be discussed. [Work performed under the auspices of the Department of Energy by the Lawrence Livermore National Laboratory under Contract No. W-7405-Eng-48.]

Some results from the radiative wave equation for a slab of random, densely-distributed scatterers

Using the ladder-approximated Bethe-Salpeter equation, the radiative wave equation for a slab of random, densely-distributed small spherical scatterers is constructed. The quasicrystalline approximation with coherent potential method is used for calculation of the effective propagation constant. The coherence of random scatterers is taken into account. The first and second-order bistatic scattering and transmission coefficients through the slab are obtained by iteration. Constructive interferences due to the boundaries are computed. The radiative wave equation for thermal emission from this slab is solved by a discrete ordinate method. Comparison with the independent scattering assumption in the conventional radiative transfer equation is discussed.

Radiative Wave Equations for Vector Electromagnetic Propagation in Dense Nontenuous Media

A set of radiative wave equations including all four Stokes parameters is derived for vector electromagnetic wave propagation in dense nontenuous media. The derivation is based on the quasi-crystalline approximation with coherent potential on the first moment of the field, and the modified ladder approximation on the second moment of the field. These two approximations are shown to be energetically consistent for dense nontenuous media. To simplify the derivation of the radiative wave equations, the model of small spherical scatterers is used. The derived radiative wave equations assume the same form as the classical radiative transfer equations. However, the relations of the extinction rate, the albedo and the phase matrix to the physical parameters of the media include the effects of dense media and can be different from the classical relations of independent scattering.

Acoustic backscatter from highly dense scattering arrays

Acoustic backscatter signals from several specimens containing high number densities of small spherical scatterers were measured in order to compare the signals obtained with those calculated from the independent scatterer model for the case of high scatterer concentration and long wavelengths. The scatterers were prepared by precipitation of less dense second-phase spherical particles from a glass host by controlling the melt chemistry and cooling rate. Statistics on the size, number, and distribution of the scatterers were obtained from microscopic observation. The results show that the backscatter signal energy measured is directly related to the mean interparticle spacing between scatterers. The reason for this relationship is shown, from the independent scatterer model, to come from the fact that the distribution of interparticle spacings can be represented by a Gaussian probability with a specified mean. Results of the calculation and comparison with experimental results illustrating the effect of the spacing distribution on the scattering structure factor are presented. [Work supported by the Interior Department's Bureau of Mines through Department of Energy.]

Effect of flow disturbance on ultrasonic backscatter from blood.

Due to the better resolution and performance provided by the new generation of real-time high resolution ultrasonic scanners, blood now becomes a tissue which can also be visualized ultrasonically. There is strong experimental evidence indicating that the echogenicity of blood is increased as a result of erythrocyte aggregation. In this paper, we will show that flow disturbance may also play a significant role in influencing blood ultrasonic backscatter or echogenicity. Our results indicate that the introduction of turbulent flow can cause ultrasonic backscatter from erythrocyte suspensions to increase appreciably for hematocrits greater than 10%. We will also show that this increase may be correlated to the turbulent intensity. Moreover, the scattering peak is observed to shift to lower hematocrits when turbulence is eliminated. Experimental results obtained for uniform flow are in excellent agreement with theoretical models for small spherical scatterers which predict a scattering maximum at a hematocrit of 13%.