Random Scatterers Research Articles

Long Wavelength Scattering Approximations for the Effective Elastic Parameters of Spherical Inclusion Problems

The effective elastic properties of materials containing spherical inclusions were calculated by the elastic wave scattering theory. In the formulation additional scattering fields by the presence of random multiple scatterers that affects the effective properties were found by the single scattering approximation. In calculating the scattering fields the ensemble average on the displacements and strains inside the scatterer was found from the static approximation at long wavelength limit. The displacements were assumed to be equal to the incident field, while the strains were calculated by Eshelby's equivalent inclusion principle on the single inclusion problem. Four different models were considered and they reflected different degrees of multiple scattering effects based on the approximation introduced in the process of embedding the inclusion in the matrix. The expressions for the effective elastic constants were given in each model, and their relations to the results obtained from other scattering theory and elasticity theory were discussed. The theoretical predictions were compared with experimental results on the epoxy matrix composites containing tungsten particles of different sizes and volume fractions

Optical Coherence Imaging Method through Random Scattering Media.

Optical Coherence Imaging Method through Random Scattering Media.

Stochastic One-Dimensional Lorentz Gas on a Lattice

We stud ya one-dimensional stochastic Lorentz gas wher ea light particle moves i na fixed array of nonidentical random scatterers arranged i na lattice. Each scatterer is characterized b ya random transmissionreflection coefficient. We consider the case when the transmission coefficients of the scatterers are independent identically distributed random variables .A symbolic program is presented which generates the exact velocity autocorrelation functio n( VACF) in terms of the moments of the transmission coefficients. The VACF is found for different types of disorder for times up to 20 collision times. We then conside ra specific type of disorder :a two-state Lorentz gas in which two types of scatterers are arranged randomly i na lattice. The na lattice point is occupied b ya scatterer whose transmission coefficient is ' with probability p or '+= with probability 1&p .A perturbation expansion with respect to = is derived. The = 2 term in this expansion shows that the VACF oscillates with time, the period of oscillation being twice the time of flight from one scatterer to its nearest neighbor. The coarse-grained VACF decays for long times like t &32 , which is similar to the decay of the VACF of the random Lorentz gas wit ha single type of scatterer. The perturbation results and the exact one s( found up to 20 collision times) show good agreement.

Winding of a two-dimensional Brownian particle in a random environment

We study analytically the average probability for a Brownian particle to wind n times around a removed area of finite size in a 2D plane with randomly distributed traps. Such a model describes, for example, the Abrikosov vortex entanglement around a cylindrical cavity in a superconductor with repulsive columnar defects. The problem amounts to the quantum mechanics of a particle moving in a plane with point-like random scatterers pierced by a solenoid. It is shown that at large times t the asymptotic winding angle distribution, which is determined by a `Lifshitz tail' in the density of states of such a particle, is Gaussian with the scaling variable .

S-matrix network models for coherent waves in random media: construction and renormalization

Networks of random quantum scatterers (S-matrices) form paradigmatic models for the propagation of coherent waves in random S-matrix network models cover universal localization-delocalization properties and have some advantages over more traditional Hamiltonian models. In particular, a straightforward implementation of real space renormalization techniques is possible. Starting from a finite elementary cell of the S-matrix network, hierarchical network models can be constructed by recursion. The localization-delocalization properties are contained in the flow of the forward scattering strength ('conductance') under increasing system size. With the aid of 'small scale' numerics qualitative aspects of the localization-delocalization properties of S-matrix network models can be worked out.

S‐matrix network models for coherent waves in random media: construction and renormalization

AbstractNetworks of random quantum scatterers (S‐matrices) form paradigmatic models for the propagation of coherent waves in random media. S‐matrix network models cover universal localization‐delocalization properties and have some advantages over more traditional Hamiltonian models. In particular, a straightforward implementation of real space renormalization techniques is possible. Starting from a finite elementary cell of the S‐matrix network, hierarchical network models can be constructed by recursion. The localization‐delocalization properties are contained in the flow of the forward scattering strength (‘conductance’) under increasing system size. With the aid of ‘small scale’ numerics qualitative aspects of the localization‐delocalization properties of S‐matrix network models can be worked out.

Statistical properties of the cumulative phase of electromagnetic radiation transmitted through a waveguide with random scatterers

We calculate the probability distribution function and the average of the cumulative phase of electromagnetic radiation transmitted through the waveguide with randomly positioned dielectric scatterers. The average phase exhibits a crossover from linear to power-law behavior as a function of frequency. A detailed comparison with experimental results is made and a good agreement is found. Our results are consistent with the well-known observation that the scattering mean free path is of the order of the size of scatterers.

Photorefractive Image Amplification and Beam Fanning with Inclusion of Random Volume Scattering

Photorefractive effects, such as the image amplification and the beam fanning, can be described by a set of multivariable Langevin equations with inclusion of the random-phased volume scattering due to the inhomogeneities and/or defects in the crystal. The image amplification by two-wave-coupling configuration was studied analytically in the undepleted-pump approximation and numerically. It was found that the volume scattering can generate the beam fanning, as the surface scattering does.

Statistical generalizations of the optical cross-section theorem with application to inverse scattering

A fundamental result of scattering theory, the so-called optical theorem, applies to situations where the field incident on the scatterer is a monochromatic plane wave and the scatterer is deterministic. We present generalizations of the theorem to situations where either the incident field or the scatterer or both are spatially random. By using these generalizations we demonstrate the possibility of determining the structure of some random scatterers from the knowledge of the power absorbed from two plane waves incident on it.

Spectral Analysis of Demodulated Ultrasound Returns: Detection of Scatterer Periodicity and Application to Tissue Classification

Ultrasound returns from tissue display variations in amplitude on several spatial scales. Although large-scale variations result from factors such as attenuation, variations on smaller scales are caused by tissue characteristics such as variations in scatterer spacing and reflectance. These small scale variations cause a corresponding variation in the amplitude of the ultrasound return. A simple and direct method for detecting and quantifying periodicity in these variations in the presence of attenuation is described. The radiofrequency ultrasound return is first demodulated by full-wave rectification. The normalized power spectrum of the demodulated return then yields an index that we call the relative Fourier energy. Both computer simulations and in vitro experiments were performed in order to study how relative Fourier energy performed in discriminating between periodic and random scatterer distributions. Computer simulations demonstrated significant differences between the returns from periodic and random scatterer distributions. Ultrasound returns from aortic tissue yielded a relative Fourier energy index that was significantly different between normal vs. atherosclerotic tissue (normal: 0.868 +/- 0.076, mean +/- s.d., fibrofatty plaque: 0.705 +/- 0.109, p < 0.01 vs. normal, calcified plaque: 0.753 +/- 0.078, p < 0.01 vs. normal). In contrast, no difference was found in comparisons of overall reflectance.

Computer simulation of the scatter plate interferometer by scalar diffraction theory

Detailed computer simulations of the scatter plate interferometer with random scatterers in the scatter plate are performed, for the first time to our knowledge, by use of the scalar diffraction theory in the paraxial domain. It is shown that the computer simulations produce output image patterns of the expected qualitative characteristics. A qualitative comparison of the computed pattern with the experimentally observed pattern is presented. The effects of translation of the scatter plate and distortion and tilting of the test object are also successfully simulated by the computer.

Angular correlation function of wave scattering by a random rough surface and discrete scatterers and its application in the detection of a buried object

The scattering of waves by a buried object is often obscured by the clutter around it. Such clutter can be attributed to the scattering by random rough surfaces and random discrete scatterers. Recent studies show that, because of the memory effect, the angular correlation function can suppress the effects of clutter and make the scattering by the buried object more conspicuous. In this paper, we study the angular correlation function of wave scattering by a buried object underneath a layer of random discrete scatterers and a non-Gaussian random rough surface. Such problems are common when the target is buried below a rough surface that is underneath a layer of vegetation. Numerical results are illustrated for various parameters of rough surfaces and discrete scatterers. The angular correlation function is calculated by frequency and angular averaging. It is shown that the use of the angular correlation function can enhance target detection in the presence of clutter.

Microwave transmission through a periodic three-dimensional metal-wire network containing random scatterers

We have measured the transmission of microwave radiation through a nearly cubic metal-wire network with a lattice constant of 1 cm and a length of 8 cm on each side. We observe a sharp drop in the transmission below a cutoff frequency ${\ensuremath{\nu}}_{\mathrm{c}}$=9.33 GHz when the structure is empty. The gap persists when the network is filled with randomly positioned Teflon spheres, but ${\ensuremath{\nu}}_{\mathrm{c}}$ is reduced by the ratio of the phase velocities in air and in a random medium of Teflon spheres and air. When aluminum spheres are substituted for some of the Teflon spheres, transmission peaks appear within the gap. The average transmission in an ensemble of random configurations shows a broadening of the band edge associated with precursors to localized states in this small sample. This indicates that the statistics of the localization transition can be studied in larger samples.

The angular correlation function of wave scattering by a buried object embedded in random discrete scatterers under a random rough surface

Radar detection of a target embedded in geophysical media can be obscured by clutter. In this article the angular correlation function ( ) ACF is studied for wa! e scattering by an object embedded in random discrete scatterers under a rough surface. The ACF is calculated by using realization a! eraging, frequency a! eraging, and angular a! eraging. The results of the ACF for ! olume scattering, combined ! olume, and rough surface scattering and with a buried object are shown and compared. It is found that the ACF can be used to distinguish scattering by random discrete scatterers, random rough surface, and a deterministic buried object. The clutter return can be suppressed and the target becomes conspicuous. The ratio of ACF of the scattered wa! e with a target and that without a target can be 10 dB larger than the ratio of intensities. ! 1996 John Wiley & Sons, Inc. Microwave Opt Technol Lett 14, 144! 151, 1997.

Simple algorithms for sonar imaging and bathymetry with a linear swept‐frequency (chirp) source

This article describes a digital implementation of time-delay sonar imaging for linear swept-frequency (chirp) sources. The technique, based on phase-shifting of match-filtered individual transducer echoes, is a direct equivalent of analog phased-array processing. Computing and sampling costs are minimized by sparse population of the receiver aperture, using a separate transmission array with controlled beamwidth to suppress grating lobes. Synthetic-aperture processing uses essentially the same computation, and is carried out for a chirp signal without frequency decomposition. When different arrays are used for transmission and reception, azimuthal resolution depends on transmission array length, but maximum movement between pings without aliasing is set by the length of the receiver array, so high resolution is compatible with fast survey. This article describes how a closely related algorithm can be used for swath bathymetric depth estimation, and presents simulation results using a random surface scatterer model. © 1997 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 8, 359–376, 1997

Simple algorithms for sonar imaging and bathymetry with a linear swept-frequency (chirp) source

This article describes a digital implementation of time-delay sonar imaging for linear swept-frequency (chirp) sources. The technique, based on phase-shifting of match-filtered individual transducer echoes, is a direct equivalent of analog phased-array processing. Computing and sampling costs are minimized by sparse population of the receiver aperture, using a separate transmission array with controlled beamwidth to suppress grating lobes. Synthetic-aperture processing uses essentially the same computation, and is carried out for a chirp signal without frequency decomposition. When different arrays are used for transmission and reception, azimuthal resolution depends on transmission array length, but maximum movement between pings without aliasing is set by the length of the receiver array, so high resolution is compatible with fast survey. This article describes how a closely related algorithm can be used for swath bathymetric depth estimation, and presents simulation results using a random surface scatterer model. © 1997 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 8, 359–376, 1997

Dynamical simulation of optical phonon transfer in the GaAs/AlxGa1-xAs/GaAs single-barrier structure.

Dynamical transfer of optical phonons in the GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As/GaAs single-barrier structure is simulated using a classical three-dimensional lattice-dynamics model, fully taking into account the random arrangement of Ga and Al atoms in the alloy barrier. The transmission coefficient of GaAs optical phonons through the alloy barrier exhibits, for given barrier thickness, an exponential decay with x in the small-x regime, and remains at a small constant value for x\ensuremath{\geqslant}0.3. The exponential decay is interpreted as incoherent scattering by random scatterers (Al atoms), and the small constant value presumably originates from the fluctuations induced by acoustic and localized modes. On the other hand, when the phonon lifetime and the clustering effect are considered, the transmission coefficient is enhanced, and the x dependence of the coefficient is significantly modified. In particular, the saturation of the transmission coefficient for x\ensuremath{\lesssim}0.3 reported in a recent experiment is shown to be explainable in terms of the clustering of like atoms in the alloy barrier. \textcopyright{} 1996 The American Physical Society.

Exact propagators for a two-dimensional electron in quadratic potentials and a transverse magnetic field.

The propagator for an electron moving in a two-dimensional (2D) saddle-point potential under the influence of a transverse magnetic field is evaluated exactly using the Feynmann path integrals. The applications of this result for the calculation of tunneling through a saddle point are discussed. We also investigate tunneling a 2D electron at finite temperature in the presence of a transverse magnetic field, dissipation, and random scatterers by the use of a nonlocal harmonic oscillator model and find a crossover temperature ${\mathit{T}}_{1}$. The application of the same model at zero temperature for a quantum Hall system is shown to be incorrect. \textcopyright{} 1996 The American Physical Society.

An FFT T‐matrix method for 3D microwave scattering solutions from random discrete scatterers

AbstractAn efficient method to solve the scattering by a cluster of randomly located discrete scatterers is described. The scatterers can have an arbitrary shape, and only their T matrices need be known. An iterative method is suggested to solve this problem. To expedite the matrix‐vector multiply, we first aggregate the random scattering centers of the scatterers into centers that reside on a regular array. Then, the FFT method is used to perform the matrix‐vector multiply in O(N log N) operations. This method can solve a problem with a large number of unknowns, involving thousands of discrete scatterers, on a workstation. © 1995 John Wiley &amp; Sons, Inc.

Modeling of backscattering by bottom volumetric inhomogeneities

It has been recognized that when a sound wave encounters the ocean bottom, part of the energy will be scattered by volumetric inhomogeneities in the bottom. To simplify the mathematics, previous efforts in modeling the volumetric scattering process invoke some forms of plane-wave approximation to either or both of the forward and backward propagating fields. Since the ocean bottom has different acoustic properties from that of the water column, particularly since it often has a more complicated structure, introduction of the plane-wave approximation casts clouds on the validity of the modeling results. Here an approach is presented that uses the exact forward and backward propagating fields and calculates the backscattering strength numerically in the spatial domain. The bottom is assumed to be generally layered with superimposed random scatterers which have given correlation functions. Finally the validity of this model and its range of applicability will be discussed.