Inhomogeneous Random Media Research Articles

PECULIARITIES OF SPATIAL SPECTRUM OF SCATTERED ELECTROMAGNETIC WAVES IN ANISOTROPIC INHOMOGENEOUS MEDIUM

Features of spatial power spectrum (SPS) of scattered radiation in a randomly inhomogeneous medium with strongly prolated anisotropic inhomogeneities of dielectric permittivity are investigated. In single scattering approximation, it has been shown that a pronounced gap along a direction of prolate inhomogeneities appears in SPS. Features of SPS of multiple scattered waves at oblique illumination of a boundary of randomly-inhomogeneous medium with prolate irregularities have been analytically studied using smooth perturbation method taking into account diffraction effects. Numerical calculations have shown that with an increase of a distance passing by 192 Gavrilenko et al. the wave in random media, SPS has a double-peaked shape and a gap substantially increases. Its maximum is slightly changed and the width is broadening. The results have been obtained analytically for the first time and could find extensive practical application in optics and be useful in development of principles of remote sensing of random media.

Hybrid scattering method of finite multiplicity and diffusion approximation in optical visualization of biological tissues

We consider the problem of distribution of the intensity of diffusely reflected radiation along the surface of semibounded random inhomogeneous medium under the condition that a narrow monodirected light beam impinges upon the surface. Here, the starting point is the transfer equation for the light intensity in diffusing medium. Using a reciprocity to the canonical form of the integral equation for the Green function, the light intensity can be rewritten as the sum of two summands, namely, the contributions made by scatterings of multiplicities from 0 to N (N = 0, 1, 2, …), and the radiation of the efficient generator, in construction of which the radiation with scattering multiplicity N + 1 takes part. Practical realization of the proposed method consists in combining the usage of the diffusive asymptotic for the Green function in the term with the efficient source of radiation and the Monte Carlo method for computing the aforementioned contributions of scattering multiplicities. It is shown that, starting from some critical value of the scattering multiplicity, we have the asymptotic coincidence of computational results obtained by the hybrid method and by the standard Monte Carlo method for solving the problem formulated in its entirety. Moreover, this critical value of the scattering multiplicity depending on the elongation of the indicatrix and the albedo of the elementary act of radiation scattering is estimated.

Full Time-Domain DORT for Ultrawideband Electromagnetic Fields in Dispersive, Random Inhomogeneous Media

We investigate the decomposition of the time-reversal operator (DORT under its French language acronym) method applied to ultrawideband electromagnetic pulses propagating in dispersive and (continuous) inhomogeneous random media where volumetric scattering effects are important. We analyze the effects of random medium statistics on the time-reversal operator (TRO) eigenvalues and eigenvectors, and on subsequent selective focusing performance. We develop and employ a full time-domain DORT by tracking the excitation eigenvectors from a singular value decomposition of the TRO over the entire bandwidth of operation. We also study effects of frequency dispersion and conduction losses on the TRO and consider dispersion/loss compensation techniques to improve DORT operation in those cases

Parabolic approximation versus geometrical acoustics for describing nonlinear acoustic waves in inhomogeneous media

Propagation of intense periodic acoustic waves in inhomogeneous media is studied in the nonlinear geometrical acoustics (NGA) approximation and using nonlinear parabolic equation (NPE). Various types of 2-D inhomogeneities are considered, such as a phase screen, single Gaussian inhomogeneities, and random inhomogeneous media. Distributions of acoustic rays are obtained by numerical solution of the eikonal equation. Pressure field patterns are calculated numerically with account for nonlinear effects and diffraction using a frequency-domain algorithm for the NPE. The location of caustics and shadow zones in the ray patterns are compared with the results of the parabolic model for the areas of increased and decreased sound pressure. Both linear and nonlinear propagation is investigated in order to reveal the validity of NGA in predicting the acoustic field structure and to better understand how the combined effects of inhomogeneities, diffraction, and nonlinearity determine the overall peak and average parameters of the acoustic field. It is shown that NGA does not accurately represent all the locations of enhanced or reduced acoustic pressure even for single scattering inhomogeneities, and the discrepancies become larger for smaller size inhomogeneities and at longer distances in random inhomogeneous medium. [Work supported by CNRS, RFBR, and NIH Fogarty.]

Propagation of the two-frequency coherence function in an inhomogeneous background random medium*

The spatial and temporal structures of time-dependent signals can be appreciably affected by random changes of the parameters of the medium characteristic of almost all geophysical environments. The dispersive properties of random media cause distortions in the propagating signal, particularly in pulse broadening and time delay. When there is also spatial variation of the background refractive index, the observer can be accessed by a number of background rays. In order to compute the pulse characteristics along each separate ray, there is a need to know the behaviour of the two-frequency mutual coherence function. In this work, we formulate the equation of the two-frequency mutual coherence function along a curved background ray trajectory. To solve this equation, a recently developed reference-wave method is applied. This method is based on embedding the problem into a higher dimensional space and is accompanied by the introduction of additional coordinates. Choosing a proper transform of the extended coordinate system allows us to emphasize ‘fast’ and ‘slow’ varying coordinates which are consequently normalized to the scales specific to a given type of problem. Such scaling usually reveals the important expansion parameters defined as ratios of the characteristic scales and allows us to present the proper ordering of terms in the desired equation. The performance of the main order solution is demonstrated for the homogeneous background case when the transverse structure function of the medium can be approximated by a quadratic term. This article is dedicated to the memory of Professor Reuven Mazar, a top notch scientist, whose creativity influenced many random media researchers. Professor Mazar passed away suddenly a few weeks before the publication of this paper.

Wave scattering in a multiscale random inhomogeneous medium

In this paper, using the Fock method of the fifth parameter and weighted Fourier-transform with respect to the coordinates of the source and observer, an integral representation is obtained for the wave field in a randomly inhomogeneous medium without invoking the assumption about small-angle propagation. Random trajectory variations to a first approximation are taken into account in calculating the partial wave phase (the expression under the integral sign). The expressions for the field in a medium with different-scale irregularities and for the scintillation index, obtained using this integral representation, are compared with known results. The good agreement with results from the theory of single scattering in a medium with background irregularities, and with investigations of the scintillation index made in terms of Rytov’s method and path integrals, indicates that it is possible to use the approach developed in this study to describe the effects of simultaneous influence of different-scale irregularities.

Systematic distortions of signal propagation times in random inhomogeneous media

Systematic distortions of signal propagation times in random inhomogeneous media

Estimation of nominal directions of arrival and angular spreads of distributed sources

In this paper, we consider the problem of estimating the nominal directions of arrival (DOA) and angular spreads of multiple distributed sources. Distributed sources arise due to the presence of local scattering and impairment in wave propagation. This problem is encountered in wireless communications due to the presence of scatterers in the vicinity of the mobile or when the signals propagate through a random inhomogeneous medium. Assuming a uniform linear array (ULA), a computationally efficient estimator based on auto-regressive (AR) modeling of the lags of the covariance function is derived. The estimates of nominal DOAs and angular spreads are obtained simply by rooting a polynomial. Numerical simulations are carried out to study the performance of the suggested estimator.

Temporal Mueller matrix solution for polarimetric scattering from inhomogeneous random media of nonspherical scatterers

Polarimetric scattering from inhomogeneous random media of nonspherical scatterers under a pulse incidence is studied. The time-dependent Mueller matrix solution of vector radiative transfer for layering random media is derived. Copolarized and cross-polarized bistatic and back- scattering are numerically calculated. The shape and intensity of polarized echoes well depict the inhomogeneous fraction profile of random scatterers. Its functional dependence upon the fraction profile, layering thickness, and other parameters are discussed. This technique is applicable to reconstruction of inhomogeneous fraction profile and inversion of the media thickness.

Atmosfernaya adaptivnaya optika

A study of atmospheric adaptive optics. It covers: adaptive phase correction of optical wave distortions in random inhomogeneous media; enhancement of images transmitted through the atmosphere by methods of adaptive optics; and equations for the moment of the corrected field.

Retrievals of underlying surface roughness and moisture from polarimetric pulse echoes in the specular direction through inhomogeneous vegetation canopy

The time-dependent Mueller matrix solution of vector radiative transfer for inhomogeneous random media of non-spherical scatterers is presented. Co-polarized and cross-polarized bistatic scatterings for a polarized pulse incidence are numerically simulated. Numerical results well demonstrate volumetric and surface scattering mechanism and depict the inhomogeneous fraction profile of random scatterers. The peak tails in polarized echoes due to wave reflections from the underlying surface can be identified. Its co-polarized peaks in the specular direction are applied to simultaneous retrievals of the underlying surface roughness and moisture in the presence of inhomogeneous vegetation canopy.

Iterative approach of high-order scattering solution for vector radiative transfer of inhomogeneous random media

By stratifying a random scatter media into multiple thin layers in the vertical z direction, the first-order scattering solution of each thin layer is employed to derive high-order scattering solution of whole random media. Using the Fourier transform and Mueller matrices in discrete ordinates, an iterative approach to solve high-order scattering solution of vector radiative transfer (VRT) equation is newly developed. Numerical results are well compared with the Mueller matrix solutions of the first order for a single layer medium, second order for a half-space, and the results of the discrete ordinate and eigen analysis method. It demonstrates our approach as feasible, effective and especially applicable to high-order solution of VRT for both bistatic scattering and thermal emission of inhomogeneous non-spherical scatter media.

Estimation of directions of arrival of multiple scattered sources

We consider the problem of estimating the directions of arrival (DOA) of multiple sources in the presence of local scattering. This problem is encountered in wireless communications due to the presence of scatterers in the vicinity of the mobile or when the signals propagate through a random inhomogeneous medium. Assuming a uniform linear array (ULA), we develop DOA estimation algorithms based on covariance matching applied to a reduced-size statistic obtained from the sample covariance matrix after redundancy averaging. Next, a computationally efficient estimator based on AR modelling of the coherence loss function is derived. A theoretical expression for the asymptotic covariance matrix of this estimator is derived. Finally, the corresponding Cramer-Rao bounds (CRBs) are derived. Despite its simplicity, the AR-based estimator is shown to possess performance that is nearly as good as that of the covariance matching method.

ボルン近似による地震波散乱特性の評価とそのコーダ波解析への適用

Scattering of elastic waves including mode conversions between P- and S-waves is quite nonisotropic compared to that of acoustic waves. Thus, it is important to the analysis of coda waves of local earthquakes to use a fully realistic scattering model of seismic waves. In this paper, we summarize briefly a theory (Born approximation) on the scattering of elastic waves due to local spatial fluctuations of elastic parameters. The directional dependence of scattering amplitude for all scattering modes is evaluated for a random inhomogeneous medium characterized stochastically by using an autocorrelation function. We also review past seismological studies to confirm the usefulness and limitation of single scattering models (approximations), which have been used for the analysis of coda waves to investigate short-wavelength random heterogeneities of the lithosphere. It is shown that three-component seismogram envelope including both P- and S-coda waves is successfully modeled by using a single scattering model adopting the Born approximation for the evaluation of seismic scattering.

Representation of a wave field in a randomly inhomogeneous medium in the form of the double‐weighted Fourier transform

New integral representation of a wave field dn a continuously inhomogeneous random medium is suggested in the form of double‐weighted Fourier transformation, performed simultaneously with respect to coordinates of the source and the observer. The integral representation under consideration takes into account both the diffraction effects and the multiray effects. It incorporates many results of known techniques of wave propagation description in continuously inhomogeneous media: the methods of geometrical optics, smooth perturbations, phase screen, and two‐scale expansions. The method delivers new opportunities to retrieve small‐scale inhomogeneous structure of ionosphere plasma from radio‐sounding data and can serve as the basis for diffraction tomography of the ionosphere.

Direction finding in random inhomogeneous media in the presence of multiplicative noise

The performances of high resolution array processing methods are known to degrade in random inhomogeneous media. Such a degradation is caused by random amplitude and phase variations of source wavefronts. In this letter, the popular covariance matching approach to direction finding in the presence of multiplicative noise is extended to the multiple source case. Using a few unrestrictive physics-based assumptions on the environment, we derive a generic multiplicative noise data model. Based on this model, new direction finding techniques are proposed.

Approximate maximum likelihood estimators for array processing in multiplicative noise environments

We consider the problem of localizing a source by means of a sensor array when the received signal is corrupted by multiplicative noise. This scenario is encountered, for example, in communications, owing to the presence of local scatterers in the vicinity of the mobile or due to wavefronts that propagate through random inhomogeneous media. Since the exact maximum likelihood (ML) estimator is computationally intensive, two approximate solutions are proposed, originating from the analysis of the high and low signal to-noise ratio (SNR) cases, respectively. First, starting with the no additive noise case, a very simple approximate ML (AML/sub 1/) estimator is derived. The performance of the AML/sub 1/ estimator in the presence of additive noise is studied, and a theoretical expression for its asymptotic variance is derived. Its performance is shown to be close to the Cramer-Rao bound (CRB) for moderate to high SNR. Next, the low SNR case is considered, and the corresponding AML/sub 2/ solution is derived. It is shown that the approximate ML criterion can be concentrated with respect to both the multiplicative and additive noise powers, leaving out a two-dimensional (2-D) minimization problem instead of a four-dimensional (4-D) problem required by the exact ML. Numerical results illustrate the performance of the estimators and confirm the validity of the theoretical analysis.

A theory of optical coherence tomography

Analytical models of optical coherence tomography (OCT) of strongly turbid media of the type of biological tissues are developed on the basis of the theory of wave scattering in random inhomogeneous media. Similarity relations for signals of coherent and pulsed sounding are established, and general expressions for random realizations and statistical characteristics of tomograms are obtained. It is shown that after the appropriate modification the theory of image transfer in turbid media can be used for analysis of their informative properties. Simple formulas for estimating the visibility depth into the internal structure of biological tissues are proposed.

Theory of transfer with delay for trapping of nonstationary acoustic radiation in a resonant randomly inhomogeneous medium

The propagation of a quasimonochromatic wave packet of acoustic radiation in a discrete randomly-inhomogeneous medium under the condition that the carrier frequency of the packet is close to the resonance frequency of Mie scattering by an isolated scatterer is studied. The two-frequency Bethe-Salpeter equation in the form of an exact kinetic equation that takes account of the accumulation of the acoustic energy of the radiation inside the scatterers is taken as the initial equation. This kinetic equation is simplified by using the model of resonant point scatterers, the approximation of low scatterer density, and the Fraunhofer approximation in the theory of multiple scattering of waves. This leads to a new transport equation for nonstationary radiation with three Lorentzian delay kernels. In contrast to the well-known Sobolev radiative transfer equation with one Lorentzian delay kernel, the new transfer equation takes account of the accumulation of radiation energy inside the scatterers and is consistent with the Poynting theorem for nonstationary acoustic radiation. The transfer equation obtained with three Lorentzian delay kernels is used to study the Compton-Milne effect—trapping of a pulse of acoustic radiation diffusely reflected from a semi-infinite resonant randomly-inhomogeneous medium, when the pulse can spend most of its propagation time in the medium being “trapped” inside the scatterers. This specific albedo problem for the transfer equation obtained is solved by applying a generalized nonstationary invariance principle. As a result, the function describing the scattering of a diffusely reflected pulse can be expressed in terms of a generalized nonstationary Chandrasekhar H-function, satisfying a nonlinear integral equation. Simple analytical asymptotic expressions are found for the scattering function for the leading and trailing edges of a diffusely reflected δ-pulse as functions of time, the reflection angle, the mean scattering time of the radiation, the elementary delay time, and the parameter describing the accumulation of radiation energy inside the scatterers. These asymptotic expressions demonstrate quantitatively the retardation of the growth of the leading edge and the retardation of the decay of the trailing edge of a diffusely reflected δ-pulse when the conventional radiative transfer regime goes over to a regime of radiation trapping in a resonant randomly-inhomogeneous medium.

Solidification and melting of succinonitrile within the porous network of an aerogel

As a model for a three-dimensional nanostructured material, molten succinonitrile (SCN) is infiltrated into aerogels, directionally solidified and remelted with various temperature gradients and solidification front velocities. Static light scattering was used to study the phase transformation. We observe that solidification occurs over a wide temperature range beginning from the equilibrium freezing temperature to undercoolings of up to 20 K below it. The wide freezing range is explained by pure capillary undercooling due to the spectrum of pore sizes ranging from a few nanometers to a few \ensuremath{\mu}m. A model is developed to calculate the capillary undercooling in a cylindrical pore. It is shown by repeated solidification and remelting that the fragile aerogels are not destroyed by the infiltration process, since the light scattering pattern is unaltered. The scattered light intensity profile is described with the Debye model of light scattering in a random inhomogeneous medium, assuming a certain pore size distribution in the aerogel. During remelting a hysteresis of several degrees in the melting temperature is observed, whose origin is explained by dynamic wetting.