The scattering of electromagnetic waves in fractal media

The scattering of electromagnetic waves in fractal media is studied. The fractal dimension is naturally involved in the formulation of two physical problems studied in this paper. The general theory of multiple scattering of electromagnetic wave in fractal media is developed by modifying Twersky's theory. Statistical quantities, such as the average field and average intensity of the multiple scattered wave, are studied for a wave propagating in a fractal medium. The scattering cross section of the medium is deduced. The backscattering of electromagnetic waves is also studied. The results showing the range of dependence of the backscattered signals are in agreement with numerical simulations by Rastogi and Scheucher (1990). It also suggests a method of measuring the fractal dimension of the fractal embedded media using radar sounding. The theory developed in this paper can also be used for problems related to multiple scattering of other kinds of waves, such as acoustic waves, elastic waves etc, in fractal media.     

The scattering of electromagnetic waves in fractal media

Abstract

The scattering of electromagnetic waves in fractal media is studied. The fractal dimension is naturally involved in the formulation of two physical problems studied in this paper. The general theory of multiple scattering of electromagnetic wave in fractal media is developed by modifying Twersky's theory. Statistical quantities, such as the average field and average intensity of the multiple scattered wave, are studied for a wave propagating in a fractal medium. The scattering cross section of the medium is deduced. The backscattering of electromagnetic waves is also studied. The results showing the range of dependence of the backscattered signals are in agreement with numerical simulations by Rastogi and Scheucher (1990). It also suggests a method of measuring the fractal dimension of the fractal embedded media using radar sounding. The theory developed in this paper can also be used for problems related to multiple scattering of other kinds of waves, such as acoustic waves, elastic waves etc, in fractal media.     

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.     

Monte-Carlo simulation of light scattering in fractal porous media

Monte-Carlo simulation of light propagation in a porous medium with a mass fractal morphology was carried out. It was shown that the simulation results can be used to analyze experimental data on light scattering and to study the porous medium structure. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 2, pp. 193–196, March–April, 2008.     

改进的二维分形模型在海面电磁散射中的应用

提出了一种改进的二维分形海面模型，其表面谱函数在空间波数小于基波波数及大于基波波数时分别满足正幂率关系和负幂率关系.通过比较可以发现在不同风速时，改进模型的空间自相关函数及表面轮廓谱和有关文献结果有较好的吻合.在满足Kirchhoff近似条件下推导了改进分形模型的散射系数及散射强度系数的计算公式并进行了数值计算，比较了改进模型和经典模型的后向散射强度系数角分布并详细讨论了它们随入射频率、海上风速和风向的变化. 关键词： 改进分形模型 粗糙海面 电磁散射 Kirchhoff近似     

Multi-parameter ultrasound transmission tomography of biological media

Using a specially elaborated computer software and research setup, within the scope of this paper, projection and tomographic calculations (simulation) and real measurements of biological media by means of ultrasound were carried out, and the images of different parameters of the ultrasonic wave run through biological objects were obtained. The images were analyzed from the point of view of the precision of representation of the structures and visualization of different features of these structures. On the basis of the results obtained it can be said that such a complex multi-parameter ultrasound transmission tomography (MUTT) is best suited for diagnosing early stages of tumors in tissues, and especially women's breast tumors, because of the structure of this organ and its possible scanning in vivo from many directions.     

The IEM2M rough-surface scattering model for complex-permittivity scattering media

The integral equation model (IEM) was developed in the late 1980s and arguably became the most cited and implemented rough-surface scattering model in the field of radar remote sensing for Earth observation. It was derived by applying a second-order iteration in the incident electromagnetic field to the integral equations of the surface fields as given by Poggio and Miller. It is thus an extension of the first-order, Born approximation of these equations that produce the classical Kirchhoff approximation. The IEM has been subject to numerous amendments and variations over the last 20 years due to the imperfect introduction and handling of the Weyl representation of the spherical wave in its first version. The work presented here is a further development of the contribution made by the same author in 2001 (IEM2M), which was the first version of IEM able to blend analytically both the Kirchhoff and the small-perturbation approximations for the bistatic case. The improvement reported in this article is concerned with the inclusion of evanescent waves in the formulation of the model and the extension of the range of applicability of the second-order scattering terms to interfaces with complex-permittivity scattering media.     

Estimation of the possibility of using dynamic spectroscopy to analyze biological scattering media

An attempt was made to extend the field of application of the methods of dynamic spectroscopy to analyze media with a large volume content of scatterers. It is shown that under conditions of multiple scattering the temporal spectrum S(w) depends not only on the dimensions of the scatterers, but also on their optical characteristics. A correlation dependence between the width of the temporal spectrum S(w) and the dimensions of aggregates of erythrocytes has been established. The existence of a correlation between the width of the temporal spectrum S(w) and important clinical characteristics of blood, such as the erythrocyte settling rate and the concentration of lipoproteins, has been found. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 1, pp. 97–102, January–February, 1997.     

Critical exponents of the Ising model on low-dimensional fractal media

The critical behavior of the Ising model on fractal substrates with noninteger Hausdorff dimension d_H<2 and infinite ramification order is studied by means of the short-time critical dynamic scaling approach. Our determinations of the critical temperatures and critical exponents β, γ, and ν are compared to the predictions of the Wilson-Fisher expansion, the Wallace-Zia expansion, the transfer matrix method, and more recent Monte Carlo simulations using finite-size scaling analysis. We also determined the effective dimension (d_ef), which plays the role of the Euclidean dimension in the formulation of the dynamic scaling and in the hyperscaling relationship d_ef=2β/ν+γ/ν. Furthermore, we obtained the dynamic exponent z of the nonequilibrium correlation length and the exponent θ that governs the initial increase of the magnetization. Our results are consistent with the convergence of the lower-critical dimension towards d=1 for fractal substrates and suggest that the Hausdorff dimension may be different from the effective dimension.     

Wave scattering on a fractal surface

A generalized Von Koch surface was constructed. On the basis of Freedman' s formulation for wave scattering and by applications of the Lipchitz transform under Holder conditions in fractals, a demonstration was given that the Hausdorff dimension of the solid-angle discontinuity on the scattering surface is the same as the one of the surface itself, and an expression of the scattering strength of the fractal surface has been given. A comparison with the Schulkin-Shaffer empirical formula for the sound scattering from sea surface proposes that, in this situation, the generalized (continuous) Koch surface seems to degenerate into the (discrete) four-two Cantor sets, only the latter make a contribution to the backscattering.     

Unified Mie and fractal scattering by biological cells and subcellular structures

Angle-resolved light scattering spectroscopy of biological cells is investigated in the visible wavelength range. A unified Mie and fractal model is shown to provide an accurate global agreement with light scattering spectra from 1.1 degrees to 165 degrees scattering angles. It is found that light scattering in forward directions (<8 degrees ) is dominated by Mie scattering by the bare cell and nucleus, whereas light scattering at large angles (>20 degrees ) is determined by fractal scattering by subcellular structures. The findings are consistent with the results of experimental investigation of the contributions of different cellular components to light scattering by cells.     

Time-resolved optical backscattering model in highly scattering media

A time-resolved backscattering model, which combines a single large-angle scattering with multiple small-angle scatterings, is used to produce a scattered-light profile about a medium. Inhomogeneity of the medium is included in the model. Some multidimensional integrals can be evaluated analytically.     

Shape-based ultrasound tomography using a Born model with application to high intensity focused ultrasound therapy

A shaped-based ultrasound tomography method is proposed to reconstruct ellipsoidal objects using a linearized scattering model. The method is motivated by the desire to detect the presence of lesions created by high intensity focused ultrasound (HIFU) in applications of cancer therapy. The computational size and limited view nature of the relevant three-dimensional inverse problem renders impractical the use of traditional pixel-based reconstruction methods. However, by employing a shape-based parametrization it is only necessary to estimate a small number of unknowns describing the geometry of the lesion, in this paper assumed to be ellipsoidal. The details of the shape-based nonlinear inversion method are provided. Results obtained from a commercial ultrasound scanner and a tissue phantom containing a HIFU-like lesion demonstrate the feasibility of the approach where a 20 mm x 5 mm x 6 mm ellipsoidal inclusion was detected with an accuracy of around 5%.     

The cantor distribution and fractal transition scattering

A new distribution is introduced for the elaboration of a theory of fractal electrodynamics. The construction of the new distribution is based on the Cantor set structure and Cantor measures. The basic properties of this Cantor distribution are discussed. The semigroup of operators defined in terms of Cantor measures is examined. As an example, the theory of transition scattering of a dissipative permittivity burst by a stationary charge is considered.     

Absence of biological damage from prolonged exposure to intravascular ultrasound: a swine model

Ultrasound (US) has been used in IMS II (intravascular US) and CLOTBUST (transcranial US) clinical trials for thrombolysis. During the treatment, in addition to the targeted thrombus, other biological components, such as blood and vessel walls are subjected to long durations of US exposure. In this study we explored evidence of biological damage due to mechanical forces or thermal effects of US exposure at the frequency, intensity and duration employed for thrombolysis treatment. Biological effects were investigated by exposing swine ilio-femoral arteries bilaterally to an intravascular US generating catheter and a conventional catheter. A total of 12 animals each underwent 8h of exposure to intravascular pulsed US with a frequency of 2.2MHz and spatial peak time average intensity (I(SPTA)) of 6W/cm(2) per transducer (a total of six transducers per catheter) while the ultrasonic device surface temperature was maintained at 43 degrees C. The animals were euthanized either 24+/-3h or 28+/-3 days post treatment. A range of physiological and hematological parameters were evaluated pre-, post-, and during US exposure. The vascular diameter was determined pre- and post-US exposure using angiograms. Following euthanasia, each animal underwent a gross pathological examination, and the treated vessels and an unexposed vessel were excised for comparative histopathological evaluation. No evidence of biological damage was found at the end of 8h exposure to intravascular US.     

基于超声散射回波功率谱的热疗无损测温模型

在随机起伏介质超声散射理论下,基于组织超声散射问波功率谱,提出一种无损获取组织温度信息的新方法。组织中声速及密度的随机起伏引起超声散射,散射回波声压谱的均方值与组织中声速c、声速对温度的梯度dc/dt和组织的平均温度T等有关。分析组织散射超声回波信号平均归一化功率谱与组织温度的关系,可以从超声散射回波中有效提取组织温度信息。理论分析和模拟实验为医学上肿瘤热疗提供了一种新的无损测温的方法和思路。     

The fractal interpretation of the weak scattering of elastic waves

Nondestructive methods, in particular the measurement of elastic waves, have become increasingly important in determining the microstructure of many materials in recent years. One of these methods is observing the attenuation of ultrasonic waves of known amplitude and direction, e.g., in granular metals. The waves are exponentially attenuated with distance with a frequency-dependent attenuation fractor. The attenuation factor can be decomposed into two parts: absorption and scattering. Experimentally, the absorption part varies linearly with frequency, while the scattering part has a noninteger power law behavior, the exponent of which is related to the strength of the material. Theoretically, at long wavelengths the exponent is 4 (Rayleigh scattering) while for grain-sized wavelengths it is 2 (diffusive scattering). We relate the attenuation factor to the forward scattering amplitude which is related to the frequency dependence of the scatterers and their cross sections. We attribute the noninteger attenuation exponent to a fractal distribution of grain shapes and sizes.Supported by the Defense Advanced Research Projects Agency.