Inhomogeneous Random Media Research Articles

The acoustic inverse problem in the inhomogeneous medium by iterative Bayesian focusing algorithm

A random inhomogeneous sound propagation medium is considered in acoustic imaging, which is modeled by a random function of the spatial medium. The inhomogeneity of the sound propagation environment can cause large errors in the modeling and measurement of acoustic imaging. Since the wave equation contains random variables, Green’s function no longer has a specific analytical solution. The main work of this paper is as follows: (1) The acoustic inverse problem is considered in the inhomogeneous sound field, which is expressed according to predefined statistical information; (2) Karhunen-Loève expansion is used to simplify the proposed inhomogeneous propagation sound field, and the numerical solution of Green’s function is used instead of the original analytical solution; (3) A dual-driven (including data-driven and knowledge-driven) algorithm based on the Bayesian framework is developed to achieve acoustic imaging, which is implemented through the joint estimation of the aperture function and the sparse prior. Finally, the proposed model and algorithm are verified by a numerical simulation. The proposed algorithm is compared with conventional beamforming in terms of localization accuracy and sound power quantization. The simulation results show that the inhomogeneous sound field can be represented by a small number of random variables, and the proposed dual-drive algorithm can accurately achieve acoustic imaging in the inhomogeneous propagation environment.

A Survey of Structure of Atmospheric Turbulence in Atmosphere and Related Turbulent Effects

The Earth’s atmosphere is the living environment in which we live and cannot escape. Atmospheric turbulence is a typical random inhomogeneous medium, which causes random fluctuations of both the amplitude and phase of optical wave propagating through it. Currently, it is widely accepted that there exists two kinds of turbulence in the aerosphere: one is Kolmogorov turbulence, and the other is non-Kolmogorov turbulence, which have been confirmed by both increasing experimental evidence and theoretical investigations. The results of atmospheric measurements have shown that the structure of atmospheric turbulence in the Earth’s atmosphere is composed of Kolmogorov turbulence at lower levels and non-Kolmogorov turbulence at higher levels. Since the time of Newton, people began to study optical wave propagation in atmospheric turbulence. In the early stage, optical wave propagation in Kolmogorov atmospheric turbulence was mainly studied and then optical wave propagation in non-Kolmogorov atmospheric turbulence was also studied. After more than half a century of efforts, the study of optical wave propagation in atmospheric turbulence has made great progress, and the theoretical results are also used to guide practical applications. On this basis, we summarize the development status and latest progress of propagation theory in atmospheric turbulence, mainly including propagation theory in conventional Kolmogorov turbulence and one in non-Kolmogorov atmospheric turbulence. In addition, the combined influence of Kolmogorov and non-Kolmogorov turbulence in Earth’s atmosphere on optical wave propagation is also summarized. This timely summary is very necessary and is of great significance for various applications and development in the aerospace field, where the Earth’s atmosphere is one part of many links.

Two-Frequency Coherence Function for the Field of a Wave Propagating Through a Multiscale Randomly Inhomogeneous Medium

We study the possibilities of integral representation for the two-frequency mutual coherence function of the wave field in a randomly inhomogeneous ionosphere. The integral representation was obtained using the Double Weighted Fourier Transform (DWFT) method. We point out that the conditions of validity of the geometrical-optics approximation for frequency coherence are weaker than the same condition for individual samples. Examples of calculation of the frequency coherence functions for waves in the ionospheric plasma with the irregularities described by the Gaussian spectrum and Shkarofsky’s model are given. Simulation results show that diffraction effects reduce the width of the frequency coherence function. The capabilities of the methods for spatial processing of the wave field and its two-frequency mutual coherence function, which eliminate these effects through the Fresnel and DWFT inversions, are examined.

Turbulence effects on fluctuations of the aperture-averaged orbital angular momentum.

A complete asymptotic theory for the aperture-averaged orbital angular momentum (OAM) variance is developed for both weak and strong fluctuation conditions, based on the asymptotic expansions of the Feynman path-integral solution for the fourth-order coherence function of a spherical wave propagating through a random inhomogeneous medium. We show that the OAM fluctuation averaging is very different for circular-symmetric and non-circular-symmetric apertures. Aperture averaging of the OAM fluctuations does not obey the standard "square root" law, and the weak/strong fluctuation conditions for the aperture-averaged OAM are not defined solely by the values of the scintillation index of the incident wave.

Transverse linear and orbital angular momenta of beam waves and propagation in random media

For paraxial propagation of scalar waves, the classic electromagnetic theory definition of transverse linear (TLM) and orbital angular (OAM) momenta of the beam wave are represented in terms of the coherence function. We show in examples that neither is the presence of optical vortices necessary for the intrinsic OAM, nor does the presence of optical vortices warrant the non-zero intrinsic OAM. The OAM is analyzed for homogeneously coherent and twisted partially coherent beam waves. A twisted Gaussian beam has an intrinsic OAM with a per-unit power value that can be continuously changed by varying the twist parameters. Using the parabolic propagation equation for the coherence function, we show that both the total TLM and OAM are conserved for the free-space propagation, but not for propagation in an inhomogeneous medium. In the presence of the random inhomogeneous medium, the total TLM and OAM are conserved in average, but the OAM fluctuations grow with the propagation path. This growth is slower for beams with rotation-symmetric irradiance.

Lensing effects in a random inhomogeneous medium

Curvature of the refractive index profile can cause the focusing or defocusing of a propagating beam. Such lensing can have detrimental effects on, for example, imaging through the atmosphere, where it can cause features to appear stretched or regions to appear artificially bright. We consider the problem of describing propagation in the presence of both curvature and stochastic fluctuations in the refractive index profile. For different scenarios motivated by atmospheric propagation data, we derive concise, robust formulas for the mean ray paths that include the effects of turbulence. In addition, for the case of a local maximum of the mean refractive index, we show that the focal length associated with the mean trajectories in the random medium is smaller than in the deterministic setting.

Features of the energy structure of acoustic fields in the ocean with two-dimensional random inhomogeneities

The paper is devoted to the analytic study and numerical simulation of mid-frequency acoustic signal propagation in a two-dimensional inhomogeneous random shallow-water medium. The study was carried out by the cross section method (local modes). We present original theoretical estimates for the behavior of the average acoustic field intensity and show that at different distances, the features of propagation loss behavior are determined by the intensity of fluctuations and their horizontal scale and depend on the initial regular parameters, such as the emission frequency and size of sound losses in the bottom. We establish analytically that for the considered waveguide and sound frequency parameters, mode coupling effect has a local character and weakly influences the statistics. We establish that the specific form of the spatial spectrum of sound velocity inhomogeneities for the statistical patterns of the field intensity is insignificant during observations in the range of shallow-water distances of practical interest.

Ultrawideband Time-Reversal Imaging With Frequency Domain Sampling

A new ultrawideband (UWB) time-reversal imaging method based on the unconventional utilization of UWB frequency data is introduced. First, a set of monostatic antennas is used to acquire the scattering data for a given scenario. Then, a corresponding multistatic data matrix is formed by casting the fine and coarse frequency samples of the scattering information into matrix form. The resulting frequency-frequency monostatic matrix is later fed into the adapted DORT (French acronym for decomposition of the time-reversal operator) and MUSIC (Multiple-Signal Classification) algorithms. The performance of the proposed method is investigated numerically by applying it to discrete scatterers embedded in homogeneous and continuously random inhomogeneous media. The effect of frequency bandwidth on image resolution is studied. It is observed that wider frequency bandwidths yield to better focusing resolutions.

Measurement of the transport-scattering coefficient in random inhomogeneous media using the method of low-coherence reflectometry

A method for determining a small magnitude of the transport-scattering coefficient in random inhomogeneous media is proposed. The method is based on analyzing the velocity of exponential decay of the signal of a low-scattering interferometer with a probing medium layer as the diffuse scatter in an object holder with increasing path-length difference in the reference and object holders. The results of experimental verification of the proposed method using a fluoroplastic film and filter paper as model scatterers are given.

Limits to the representation capacity of imaging in random media

The information capacity of an image in the atmosphere, ocean, or biological media does not grow indefinitely with increasing light power but has well defined limits. Here, the exact effects of the propagation of light in random inhomogeneous media are elucidated and upper bounds to the capacity of image pixels to represent a corresponding point in the object are described.

Time-reversal imaging of objects near rough surfaces based on surface flattening transform

This paper considers the imaging of objects located close to rough surfaces such as ocean or terrain. If transmitters and receivers are also located close to rough surfaces, incident wave is no longer a plane wave nor a spherical wave in free space and it is necessary to consider Green’s functions with the point source located close to the surface, similar to the Sommerfeld dipole problem. This paper considers the near-surface imaging by making use of time-reversal imaging and surface flattening transform. Surface flattening transform converts the rough surface problem into flat surface with inhomogeneous random medium. Mutual coherence function is obtained and used to obtain imaging of point target near rough surface, making use of the multi-static data matrix, time-reversal matrix, the eigenvectors, and the steering matrix. Numerical examples are given. An important point is that integration of stochastic wave propagation and signal processing is necessary to obtain imaging through complex clutter environment. Surface flattening transform is related to the transformation electromagnetics which attracted much interest because of cloaking possibilities. This paper includes some discussions on the relations between surface flattening and transformation electromagnetics.

Vector Monte Carlo simulations on atmospheric scattering of polarization qubits

In this paper, a vector Monte Carlo (MC) method is proposed to study the influence of atmospheric scattering on polarization qubits for satellite-based quantum communication. The vector MC method utilizes a transmittance method to solve the photon free path for an inhomogeneous atmosphere and random number sampling to determine whether the type of scattering is aerosol scattering or molecule scattering. Simulations are performed for downlink and uplink. The degrees and the rotations of polarization are qualitatively and quantitatively obtained, which agree well with the measured results in the previous experiments. The results show that polarization qubits are well preserved in the downlink and uplink, while the number of received single photons is less than half of the total transmitted single photons for both links. Moreover, our vector MC method can be applied for the scattering of polarized light in other inhomogeneous random media.

SOLUTION OF THE ELECTROMAGNETIC SCATTERING PROBLEM FROM AN ELECTRICALLY LARGE RANDOM DIELECTRIC MEDIUM

The time-harmonic electromagnetic scattering problem from a random inhomogeneous dielectric medium (here a turbulent plasma wake created by the atmospheric reentry of a vehicle) is considered. The electronic density of the plasma, that gives rise to its dielectric permittivity, has a ∞uctuating part †f(r), the variance and correlation function of which are known a priori. Because the electrical dimensions of the wake can be very large, the numerical solution of Maxwell's equations via a full-wave calculation performed with a boundary element and flnite element method is prohibitive when statistical quantities such as the mean Radar Cross Section (RCS) and its variance are required, that necessitate a large number of random realizations. To remedy this di-culty, two approximations are considered and illustrated for a 2D scattering problem. First, a Mie series approach is adopted where the medium is discretized with small disks, thus reducing considerably the number of unknowns for a given random realization of †f(r), and a domain decomposition method is proposed to further reduce the complexity of the numerical solution of the corresponding system. Second, the statistical mean and the variance of the RCS are derived in closed-form from the Born approximation and yield accurate results when, as expected, the statistical mean of the relative dielectric permittivity is close to unity and j†f(r)j is small. Conversely, it is shown how these expressions can be used to validate the results obtained with the Mie series approximation. Numerical examples are presented that illustrate the potentialities of these techniques.

Coherent light scattering of heterogeneous randomly rough films and effective medium in the theory of electromagnetic wave multiple scattering

We have developed a general formalism based on Green's functions to calculate the coherent electromagnetic field scattered by a random medium with rough boundaries. The approximate expression derived makes it possible to determine the effective permittivity, which is generalised for a layer of an inhomogeneous random medium with different types of particles and bounded with randomly rough interfaces. This effective permittivity describes the coherent propagation of an electromagnetic wave in a random medium with randomly rough boundaries. We have obtained an expression, which contains the Maxwell – Garnett formula at the low-frequency limit, and the Keller formula; the latter has been proved to be in good agreement with experiments for particles whose dimensions are larger than a wavelength.

Imaging and tracking of targets in clutter using differential time-reversal techniques

Two time-reversal algorithms for identifying, imaging, and tracking moving targets in clutter are introduced. The first algorithm classifies existing scatterers into stationary versus moving targets. Multistatic data matrices (MDMs) corresponding to successive radar acquisitions (snapshots) of the scene are recorded. Singular value decomposition of the (time-)averaged MDM provides information on stationary targets, whereas singular value decomposition of the differential MDM provides information on moving targets. The second algorithm yields real-time selective tracking of each moving target by means of differential time-reversal. It requires minimal processing and memory resources, and exploits distinctive features of time-reversal such as statistical stability and super-resolution. Numerical simulations are used to illustrate the capabilities of the proposed algorithms in different scenarios involving clutter from discrete secondary scatterers and from inhomogeneous random medium backgrounds.

Scalar quantum field theory in disordered media

A free massive scalar field in inhomogeneous random media is investigated. The coefficients of the Klein-Gordon equation are taken to be random functions of the spatial coordinates. The case of an annealed-like disordered medium, modeled by centered stationary and Gaussian processes, is analyzed. After performing the averages over the random functions, we obtain the two-point causal Green's function of the model up to one-loop. The disordered scalar quantum field theory becomes qualitatively similar to a $\lambda\phi^{4}$ self-interacting theory with a frequency-dependent coupling.

Multiple scattering of ultrasound in weakly inhomogeneous media: Application to human soft tissues

Waves scattered by a weakly inhomogeneous random medium contain a predominant single-scattering contribution as well as a multiple-scattering contribution which is usually neglected, especially for imaging purposes. A method based on random matrix theory is proposed to separate the single- and multiple-scattering contributions. The experimental setup uses an array of sources/receivers placed in front of the medium. The impulse responses between every couple of transducers are measured and form a matrix. Single-scattering contributions are shown to exhibit a deterministic coherence along the antidiagonals of the array response matrix, whatever the distribution of inhomogeneities. This property is taken advantage of to discriminate single- from multiple-scattered waves. This allows one to evaluate the absorption losses and the scattering losses separately, by comparing the multiple-scattering intensity with a radiative transfer model. Moreover, the relative contribution of multiple scattering in the backscattered wave can be estimated, which serves as a validity test for the Born approximation. Experimental results are presented with ultrasonic waves in the megahertz range, on a synthetic sample (agar-gelatine gel) as well as on breast tissues. Interestingly, the multiple-scattering contribution is found to be far from negligible in the breast around 4.3 MHz.

Cherenkov radiation threshold in random inhomogeneous media

Cherenkov radiation in media with random inhomogeneities like aerogel or Earth atmosphere is discussed. The spectral-angular distribution of Cherenkov photons emitted by relativistic charged particle and averaged over the dielectric permittivity fluctuations shows angular broadening similarly to the case of media with the photon absorption. The broadening results in the smoothing of Cherenkov threshold, and therefore media with strong photon scattering have more extended dependence of Cherenkov light output on the particle speed. It can be potentially used for the particle identification.

Theoretical Analysis of Bit Error Rate for Satellite Communications in Ka-Band Under Atmospheric Turbulence Given by Kolmogorov Model

We study the influence of atmospheric turbulence on satellite communications by the theoretical analysis of propagation characteristics of electromagnetic waves through inhomogeneous random media. The analysis is done by using the moment of wave fields given on the basis of a multiple scattering method. We analyze the bit error rate (BER) using the average received intensity or power for the Geostationary Earth Orbit (GEO) satellite communications in Ka-band at low elevation angles under atmospheric turbulence whose statistical characteristics are given by the Kolmogorov model. From the analysis, the degradation in BER for the uplink is found to be caused by the decrease in the average received intensity due to spot dancing and wave form distortion of wave beams; on the other hand, for the downlink, the degradation in BER is caused by the decrease in the spatial coherence of received waves.

A Method for the Direction-of-Arrival Estimation of Incoherently Distributed Sources

We consider the problem of estimating the nominal direction of arrival (DOA) of an incoherently distributed source. This problem is encountered due to the presence of local scatterers in the vicinity of a transmitter or due to signals propagating through a random inhomogeneous medium. Since the spatial covariance matrix has full rank for an incoherently distributed source, the performance of most high-resolution DOA estimation algorithms conceived under coherently distributed sources, as well as point source models, degrades when scattering is present. In addition, several DOA estimation techniques devised under a distributed source model require a high-dimensional nonlinear optimization problem. In this paper, we propose a novel method based on the conventional beamforming approach, which estimates the nominal DOA from a spatial maximum peak of the output power. The proposed method is computationally more attractive than the maximum likelihood (ML) estimator, although the performance degrades in comparison with the ML estimator, whose asymptotic performance is equivalent to the Cramer-Rao bound (CRB). We derive and compare the asymptotic performances of the proposed method and the redundancy-averaged covariance matching (RACM) method in the single-source case. The simulation results illustrate that the asymptotic performance of the proposed method is better than that of the RACM method.