On the theory of refractive radio-wave scattering

We consider in detail the frequency correlation of radio-wave fluctuations in one or several thick layers with strong large-scale inhomogeneities of turbulent origin. General expressions are obtained for the space-frequency fluctuation correlation of the radio-waves received. We analyze particular cases of radio wave scattering in turbulent media with inhomogeneities described by power-law spectra with indices p2 and p3. It is shown, in particular, that the coherence band of signals propagated in media with strong large-scale inhomogeneities is critically dependent on the spectral type of thOse inhomogeneities. The occurrence of an additional strongly scattering layer, which has radically different properties compared to the first layer, on the radio-wave path can increase or decrease considerably the frequency correlation of the radio waves received.Radiophysical Research Institute, Nizhny Novgorod. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 10, pp. 1012–1022, October, 1995.     

Sound scattering by random fractal inhomogeneities in the ocean

Sound scattering by random volume inhomogeneities (fluctuations of the refraction index in a medium) with an arbitrary anisotropy is considered using the small perturbation method (Born’s approximation). Surfaces (boundaries) of the inhomogeneities are deemed to be fractal ones: the energy spectra of the refraction index fluctuations follow the power law with a nonintegral exponent. Formulas are obtained for the volume scattering coefficient. Frequency and angular dependences of the scattering coefficient and their relations to the fractal dimension of inhomogeneities with different kinds of anisotropy and different sizes (on the sound wavelength scale) are presented. The fractal dimension of the inhomogeneities is estimated.     

Laser excitation of flexural waves and their scattering by fractal inhomogeneities in a thin plate

The excitation of flexural waves in a thin plate (film) by harmonically modulated laser radiation and their scattering by small fractal inhomogeneities are considered. An expression for the mean fluctuation intensity for the scattered wave field is obtained. A relationship between the intensity, parameters of the laser radiation and the plate, and the fractal dimension of inhomogeneities is found. The expected frequency dependence of the flexural wave attenuation in the plate due to their scattering by fractal inhomogeneities is discussed.     

Multiple small-angle scattering—A review

Small-angle scattering (SAS) is a powerful experimental technique in condensed matter physics for studying structural features of inhomogeneities of colloidal dimensions. So far the technique has been largely exploited to study thin samples for which the single scattering approximation, for the radiation-matrix interaction, holds good. The single scattering approximation is invalid when the thickness of the sample exceeds the scattering mean free path. This situation calls for a guideline to analyse the scattering data having significant contribution from multiple scattering. Since multiple scattering broadens the scattering profile, the beam broadening nature of multiple scattering can also be exploited, by making the sample suitably thick, to study large size inhomogeneities which are otherwise inaccessible to a small-angle scattering set up because of its resolution constraints. The present article presents a review and extension of the theoretical basis for analysing multiple scattering data from the point of view of a recent formalism on multiple small-angle scattering. The formalism is valid for both monodisperse and polydisperse scattering media characterized by the presence of large size inhomogeneities in the matrix. It is shown that multiple scattering from a polydisperse sample can be described by a system of coupled integrodifferential equation. However, multiple scattering from a monodisperse sample can be described by a Fokker-Planck type of equation. These equations have been analysed with an emphasis laid on the nature of the structural information pertaining to the inhomogeneities which is extractable from the multiple scattering profile. When the linear dimension of inhomogeneities becomes comparable to the scattering mean free path of the radiation in the sample, the statistical nature of the medium becomes pronounced. The statistical nature of the medium modulates the scattering profile. The modulation effect could be broadening or narrowing of the profile depending upon the nature of the inhomogeneities and their population distribution. The limiting regimes of validity and the implications of various approximations, frequently used to analyse the scattering data, have been indicated.     

The angular dependence of the coefficient of sound reflection from anisotropic volume inhomogeneities of the ocean

The small perturbation method is used to consider the scattering of sound by random volume inhomogeneities of the ocean. The inhomogeneities are assumed to be horizontally anisotropic with their horizontal dimensions far exceeding the vertical ones. Expressions are obtained for the angular dependence of the scattering coefficient. Vertical and horizontal sections of the scattering pattern are presented, and the angular widths of its maxima are analytically estimated.     

Correlation functions and power spectra of Doppler response signals in ultrasonic medical applications

Ultrasound Doppler methods are widely used in clinical practice as prospective investigational tool to study the vascular system and soft biological tissues. Meanwhile, the most general relationship between the power Doppler spectra, spectral characteristics of the scattering fluctuations and the probing ultrasound field parameters for some clinical implementations are still unexplored. Based upon the continuum model of scattering inhomogeneities, a set of the closed-form expressions for the correlation functions and the spectra of Doppler response of soft tissues and blood have been derived. The influence of the correlation among inhomogeneities and the diffusion processes on the Doppler power spectra formed by stationary flows have been examined. Computer simulations of Doppler spectra were performed for different values of correlation radius and diffusion coefficient. With simulation results the effects of the correlation among inhomogeneities and the diffusion processes on the spectral width and mean frequency are established and discussed in respect to turbulent flows. Closed-form expressions for correlation functions and Doppler spectra for the vibrational sonoelastography technique for visualizing malignant tumors in tissues have been derived. Based on the peculiarities of the obtained Doppler spectra, it is shown that the differentiation of soft tissues with respect to the amplitude value of constrained oscillations is feasible. The expressions were derived for the cases of non-stationary accelerated blood movement. It has been found that the frequency dependence reveals solely at a finite time of observation and depends on the initial phase of the accelerated movement.     

Formation Mechanisms for the Spectral Characteristis of Low-Frequency Reverberations and Predictive Estimates

The paper considers the problem of monostatic scattering of low-frequency sound waves by nearsurface volumetric inhomogeneities under conditions of intense wind waves. We calculate the expected shape of the scattered signal spectrum taking into account the distribution of the volumetric inhomogeneities over the surface and their quasiperiodic motion in three-dimensional space under the action of wind waves. For deep-ocean conditions, a carrier frequency of 228 Hz, and a pulse duration longer than 100 s, we compare the experimental data on the shape of the reverberation spectrum with theoretical estimates. We compare the spectral levels of subsurface scattering with similar data on sound scattering directly on the wind-roughed surface.     

Computer modeling of sound propagation in the ocean with fractal inhomogeneities

The wave-field computer code based on the wide-angle parabolic equation is modified and adapted to the problems of sound scattering in a medium with anisotropic inhomogeneities of fractal type. To verify the computer code, a model numerical experiment on determining the angular dependence of the scattered sound field is performed for different anisotropy coefficients of the sound speed inhomogeneities. The comparison of the computed data with the theoretical dependences shows their rather good agreement and indicates that the computer code can be applied to calculations of sound propagation in the ocean with fine-structure inhomogeneities possessing fractal properties.     

Microwave scattering by tropospheric fluctuations in an evaporation duct

Numerical analysis of the centimeter wave propagation in an evaporation duct with allowance for scattering by correlated turbulent fluctuations of the tropospheric refraction index is carried out. It is shown that energy leakage from the duct leads to an additional decrease in the average wave power. The amplitude of random power variations above the duct turns out to be significantly higher compared with the variations inside the duct. An increase in the vertical correlation radius of refraction-index inhomogeneities leads to an increase in the vertical correlation radius of the radio-wave intensity. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 52, No. 4, pp. 307–317, April 2009.     

Detection of inhomogeneities in biological tissues by the methods of confocal microscopy

The model of detection of local inhomogeneities of scattering and absorbing types in biological tissues by the methods of reflection and transmission confocal microscopy has been developed on the basis of the theory of vision in scattering media. General equations for calculation of the image contrast of an inhomogeneity against the background of a scattering medium are derived. The influence of the object characteristics and observation-system parameters on the maximum detection depth of inhomogeneities is analyzed. Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 5, pp. 625–639, May, 1998.     

Investigation of multiple ultrasmall-angle neutron scattering with the aid of a double-crystal diffractometer

A method of multiple small-angle neutron scattering (MSANS), used to obtain information about inhomogeneities of substances, is considered. Experimental schemes and theory of a double-crystal diffractometer intended for measuring multiple small-angle neutron scattering are described. Methods used to approximate MSANS angular distributions at a low concentration of inhomogeneities and based on Moliére’s theory are reviewed. Their applicability is demonstrated for the examples ofMSANS spectra of samples from ferromagnetic iron-nickel alloys, aluminum powders, and high-T _c superconductor ceramic materials. Theoretical and experimental investigations of interference effects that manifest themselves in multiple small-angle neutron scattering on systems containing high concentrations of scatterers are reported.     

Studying the structural features of oxide nanoclusters of cerium and titanium in a silicate glass by means of the small-angle neutron scattering

The features of the formation of Ce-Ti-O complex oxide nanoclusters in a silicate glass are studied by means of the small-angle neutron scattering technique. It is found that bounded regions of density fluctuation of the glass material are formed in the initial glass matrix without the addition of titanium and cerium oxides. These regions could serve as nucleation centers for oxide clusters of cerium and titanium upon their introduction into the matrix. The calculated average size of these inhomogeneities does not exceed 30 ± 1 nm, and their surface volume equals 0.72 ± 3 nm³. A structural mechanism for Ce-Ti-O oxide formation in a silicate glass, in which the nanoclusters are formed within a bounded region of glass material inhomogeneities at low concentrations of the initial cerium oxide (CeO₂), is proposed. At high cerium oxide concentrations, oxide nanocluster growth occurs predominantly on the surface of these inhomogeneities. This leads to a sharp change in the nanocluster sizes and their fractal dimension.     

Single scattering of waves by random strong anisotropic inhomogeneities

Research is carried out into scattering of waves by random strong anisotropic inhomogeneities when the inhomogeneities are in the distant zone according to one (transverse) scale and at the same time they are in the near zone according to another (longitudinal) scale. To analyse the formulas of the single scattering the stationary phase method in the longitudinal coordinate integral is used. It is shown that the angle sensitivity of strong anisotropic scattering, unlike weak anisotropic scattering, strongly depends on the longitudinal statistical homogeneity of the medium.     

Vertical motions in the lower ionosphere and a sporadicE-layer

We propose a calculation technique for the main characteristics of a sporadic E-layer, including the effective recombination coefficient, the relative content of meteor and atmospheric ions in the layer, and the time of its evolution. This technique is based on measurements of vertical plasma velocities by the method of resonance scattering of radio waves by artificial periodic inhomogeneities of the electron density. The contribution of internal gravity waves and turbulent motions to the formation of sporadic layers is estimated. The characteristic values of the turbulent velocity measured by this method at the heights of the turbopause are presented. The possible mechanisms of mid-latitude sporadic E-layer formation at heights of 90 to 120 km are considered. Experimental studies confirmed the main statements of the wind shear theory concerning the determining role of the redistribution of ionization under the action of atmospheric winds with vertical gradient of velocity in the formation of E_s. Deceased. Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 1, pp. 26–35, January, 1999.     

A new method for determination of the electron number density in the e region of the ionosphere from relaxation times of artificial periodic inhomogeneities

We propose a new method for determination of the electron number density in the E region of the ionosphere on the basis of scattering of radio waves from artificial periodic inhomogeneities formed by the high-power radio emission at two frequencies and having different spatial periods. The ratio of relaxation times of the artificial periodic inhomogeneities at a given altitude is determined only by the ratio of their spatial periods, which makes it possible to determine electron number density. The paper presents the corresponding calculations and the estimates of possible measurement errors. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 9, pp. 744–750, September 2006.     

Interference of speckle fields in the diffraction zone of a focused spatially modulated laser beam by a random phase screen

The processes of formation of average-intensity interference fringes upon diffraction by a random-phase object of a laser beam having interference fringes and focused on the surface of the object are considered. The dependences of the fringe contrast on the parameters of scattering inhomogeneities of the object and the parameters of the focused laser beam are established in analytical form for various diffraction regimes. Practical possibilities of a method of probing of scattering objects in problems of measuring the parameters of inhomogeneities and problems of interference-pattern formation in optical systems with scattering media are discussed.     

The scattering of flexural waves by random fractal inhomogeneities in a thin plate

The scattering of flexural waves by small statistical fractal inhomogeneities in a thin plate is considered. An expression for the average intensity of the fluctuations of the scattered wave field is obtained. A relation of the intensity to the plate parameters and to the fractal dimension of the inhomogeneities is determined. An expected frequency dependence of the attenuation of flexural waves in a plate due to the scattering by fractal inhomogeneities is discussed.     

Amplitude fluctuations in the theory of radio-wave refraction scattering

We consider some aspects of the theory of radio-wave scattering with respect to studies of radiation intensity fluctuations behind a random phase screen. The expressions for a piecewise approximation of the function of distribution of intensity fluctuations in the near zone and in the region of random focusing behind the screen are found. The expressions obtained are used to calculate the radio-wave scintillation index in these regions. The corresponding calculations are performed with allowance for the finite dimensions of external and internal scales of turbulent inhomogeneities of the phase screen. It is shown that the radio-wave refraction scattering, as a rule, is characterized by a pronounced random focusing of the radiation intensity behind the phase screen. However, under strongly developed turbulence of the radio-wave propagation medium (phase screen) the above phenomenon may be absent.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 9, pp. 1114–1124, September, 1996.This paper was supported by the Russian Foundation for Fundamental Research under project 95-02-03716.     

Studies of the structure of defects in In4Se3 crystals by small-angle neutron scattering

Small-angle neutron scattering is used to study the layered semiconductor In₄Se₃. It is observed that the samples contain inhomogeneities of colloidal dimensions, which are attributed to the precipitation of indium. Annealing reduces the concentration of inhomogeneities. Modeling the system using an ensemble of primary spherical inhomogeneities showed that a single cluster of a rectangular superlattice (2-2-6) contains 24 primary inhomogeneities of radius 13.5±1,5 Å and the distance between them is 70.9±1.5 Å.     

Localization of inhomogeneities in diffuse optical tomography based on late arriving photons

An algorithm for localizing inhomogeneities in pulsed diffuse optical tomography is proposed and implemented. A distinctive feature of this technique is the formation of an initial approximation to the spatial distributions of the absorption and scattering coefficients in a biomedical object under study based on the angle-dependent homogeneity index, HI(a). The method allows one to determine the approximate optical structure of the object using late arriving photons and thus solve more rapidly the inverse problem. The suggestion that all absorbing and scattering inhomogeneities in an object under study are spherical also simplifies and enhances image reconstruction.