Describing small-scale structure in random media using pulse-echo ultrasound

A method for estimating structural properties of random media is described. The size, number density, and scattering strength of particles are estimated from an analysis of the radio frequency (rf) echo signal power spectrum. Simple correlation functions and the accurate scattering theory of Faran [J.J. Faran, J. Acoust. Soc. Am. 23, 405-418 (1951)], which includes the effects of shear waves, were used separately to model backscatter from spherical particles and thereby describe the structures of the medium. These methods were tested using both glass sphere-in-agar and polystyrene sphere-in-agar scattering media. With the appropriate correlation function, it was possible to measure glass sphere diameters with an accuracy of 20%. It was not possible to accurately estimate the size of polystyrene spheres with the simple spherical and Gaussian correlation models examined because of a significant shear wave contribution. Using the Faran scattering theory for spheres, however, the accuracy for estimating diameters was improved to 10% for both glass and polystyrene scattering media. It was possible to estimate the product of the average scattering particle number density and the average scattering strength per particle, but with lower accuracy than the size estimates. The dependence of the measurement accuracy on the inclusion of shear waves, the wavelength of sound, and medium attenuation are considered, and the implications for describing the structure of biological soft tissues are discussed.     

Scattering properties of aqueous suspensions with absorbing dispersed phase

Scattering matrices of aqueous suspensions of copper oxide and graphite the particles of which are characterized by strong absorption at a wavelength of 0.63 μm have been measured in the scattering angle range of 10°–155°. The results of the measurements are compared with calculation data for axially symmetric scatterers (ellipsoids of revolution and cylinders). It is shown that, if the size parameter equals 4–6, even under conditions of strong radiation absorption by particles of the dispersive medium, deviation of their shape from axial symmetry has an effect on the scattering properties of the medium.     

Microwave propagation and scattering in a dense distribution of non-tenuous spheres: experiment and theory

Controlled laboratory experimental results of coherent microwave propagation through a random medium are reported. The medium consisted of layers of styrofoam with spherical glass beads embedded at predetermined random positions generated by computer. The magnitude and phase of the transmitted field was measured over the frequency range 18-20.4 GHz for media with volume fractional densities ranging from 0.5% to 11%. The results are compared with independent scattering, Foldy's approximation, and the quasicrystalline approximation (QCA) using the solution of the Percus-Yevick (PY) equation for the pair distribution function. The effects of a size distribution are included. Experimental results indicate that at low densities, the measured extinction rate increases linearly with concentration in agreement with independent scattering. As concentration further increases, the extinction curve turns convex and is lower than independent scattering. However, it is higher than that predicted by QCA-PY. Using the known particle positions the authors have also computed the pair correlation function and good agreement is obtained with the Percus-Yevick approximation.     

Speckle diagnostics of multiple scattering media with the use of frequency-modulated laser radiation

A method for probing randomly inhomogeneous multiple scattering media with the use of frequency-modulated laser radiation is considered. The method is based on analysis of the dependence of the blinking index of time-averaged speckles formed upon scattering of the probing radiation in a medium on the frequency modulation depth of the probing radiation. In the case of a binary frequency modulation, the blinking index of the detected speckle-modulated radiation is determined by the cosine Fourier transform of the probability density of the optical path-length difference of partial components of the scattered field in the probed medium. The values of the probability density of the optical path-length difference reconstructed with the use of the proposed method from the measured blinking index of speckles for model scattering media (fluoroplastic layer and layer of TiO₂ particles on a glass substrate) are in a good agreement with the results of statistical simulation of the probing radiation transfer in multiple scattering media.     

二维随机介质中准态模的频谱时间演化特性

采用时域有限差分法数值求解Maxwell方程组，分析了平面随机介质中光波模式的频谱时间演化特性.随机介质的特征可以用散射颗粒的随机构形、介质参数（如颗粒的尺寸和填充率等）以及介质形态等因素来描述.这些因素决定了随机介质在准稳态下模式的频率特性与数量，但具有不同因素的随机介质中模式的产生、选择与演化，具有大致相同的特征与速度.平面随机介质的这些冷腔特性，与传统光腔中模式的产生、选择和演化的特征非常相似. 关键词： 激光物理 随机激光器 无序介质中的光学特性     

Microwave propagation and scattering in a dense distribution of non-tenuous spheres: experiment and theory

Abstract

Controlled laboratory experimental results of coherent microwave propagation through a random medium are reported. The medium consisted of layers of styrofoam with spherical glass beads embedded at predetermined random positions generated by computer. The magnitude and phase of the transmitted field was measured over the frequency range 18-20.4 GHz for media with volume fractional densities ranging from 0.5% to 11%. The results are compared with independent scattering, Foldy's approximation, and the quasicrystalline approximation (QCA) using the solution of the Percus-Yevick (PY) equation for the pair distribution function. The effects of a size distribution are included. Experimental results indicate that at low densities, the measured extinction rate increases linearly with concentration in agreement with independent scattering. As concentration further increases, the extinction curve turns convex and is lower than independent scattering. However, it is higher than that predicted by QCA-PY. Using the known particle positions the authors have also computed the pair correlation function and good agreement is obtained with the Percus-Yevick approximation.     

Compensation for receiver bandpass effects on ultrasonic backscatter power spectra using a random medium reference

A linear model of an ultrasonic pulse-echo system is used to express the measured power spectrum as the product of a scattering medium power spectrum and a transfer function accounting for system effects. Transfer functions are experimentally determined for multiple ranges using a random medium reference. Measured power spectra normalized by these functions are shown to be in close agreement with theoretical power spectra both in shape and absolute magnitude. The results indicate that the model allows scattering media to be distinguished when the media backscatter characteristics differ in the bandwidth of the measurement system.     

炸药爆轰法制备纳米石墨粉及其在高压合成金刚石中的应用

介绍了一种制备纳米石墨粉的新方法——负氧平衡炸药爆轰法. 对合成的黑粉产物进行x射线衍射分析，确认其为石墨结构，平均晶粒度为2.58 nm. 透射电子显微分析的结果表明，炸药爆轰法制备的黑粉为六方结构的纳米石墨粉，颗粒呈球形或椭球形. 用小角x射线散射法测定纳米石墨粉的粒度分布在1—50 nm，有92.6wt%的粉末粒度小于16 nm. 平均粒径为8.9 nm. 纳米石墨粉的比表面积约为500—650 m²/g. 在六面顶压机中用纳米石墨粉在Fe粉触媒的作用下进行金刚石的高压合成实验 关键词： 纳米石墨粉 爆轰 金刚石 合成     

Photoanisotropic properties of luminescence media for polarization holography based on new-type dyes

The size and shape distributions of particles of a dispersive medium are retrieved from measurements of the scattering matrix for aqueous suspensions of copper and zinc oxides by solving the optimization problem for the sum of the squared deviations of the experimental values of matrix elements and their values calculated using the model of spheroidal scatterers. It is shown that for dispersive media with particles of irregular shapes and with sizes corresponding to the size parameter of 0.1–2, the retrieved distribution has a distortion expressed in an increased fraction of smaller sized particles.     

Light scattering by Gaussian particles with internal inclusions and roughened surfaces using ray optics

We study light scattering by Gaussian-random-sphere particles that are large compared to the wavelength of the incident light using ray optics that, in addition to Fresnellian reflection and refraction, accounts for diffuse scattering. We consider two types of diffusely scattering media. One type of media constitutes a uniform medium inside the particle, i.e. a diffuse internal medium. The second type of media constitutes a layer on the surface of the particle that is thin compared to the particle dimensions and acts as a diffuse external medium mimicking the particle surface roughness. We illustrate the effects of the diffuse media on the scattering characteristics for both cases and show that incorporating diffuse scatterers allows us to explain the scattering matrices measured experimentally for Saharan sand particles large compared to the wavelength.     

Light scattering by diamond and graphite nanodisperse systems with their particles orientationally ordered in an electric field

We have presented the results of our investigations of relative changes in the intensity of light scattered by nanodisperse systems that are exposed to the action of an electric field. To orient particles of the systems under study, sinusoidal fields of variable amplitude and frequency from the radiofrequency range were used. We have examined aqueous polydisperse suspensions of diamond and graphite particles. The average sizes of particles in the two suspensions are close to each other and are comparable with the wavelength of the incident light. Graphite particles had the shape of disks, while polycrystalline diamond particles did not have a clearly pronounced shape. Investigations have been conducted not only in the regime of a stationary orientational order of particles in the field, but also in the course of forced and free relaxation of this order. For the graphite nanodisperse system, the normalized-in-amplitude dependences of observed electrooptical effects on the field strength almost do not depend on the scattering angle, whereas, for the diamond nanodisperse system, they considerably vary as this angle changes. Upon relaxation of the orientational order of particles, the time dependences of these effects in both systems change with varying scattering angle. We have compared field and time dependences of scattering-induced effects with analogous dependences of field-induced dichroism.     

Visible Infra-red Double Extinction Measurements in Densely Laden Media,New Progress

This paper describes new progress obtained with an optical technique called V.I.D.E. (Visible Infra-red Double Extinction) which simultaneously measures mean particle size in the range of 10–120 μm and mean number density in densely laden media (up to 0.1% volume fraction). The underlying theory, taking account of multiple light scattering, is recalled. Simultaneous size and concentration measurements are obtained by simultaneously recording transmittances of the medium at two well chosen wavelengths. Experimental results for suspensions of glass particles in air, are described and discussed. The size of particles given by the technique agrees with that given by optical microscopy and Malvern diffractometry. The V.I.D.E. technique is shown to be very suitable to investigate dense media whose optical thickness is up to nine and for which other techniques fail.     

Singular value distribution of the propagation matrix in random scattering media

The distribution of singular values of the propagation operator in a random medium is investigated, in a backscattering configuration. Experiments are carried out with pulsed ultrasonic waves around 3 MHz, using an array of 64 programmable transducers placed in front of a random scattering medium. The impulse responses between each pair of transducers are measured and form the response matrix. The evolution of its singular values with time and frequency is computed by means of a short-time Fourier analysis. The mean distribution of singular values exhibits a very different behaviour in the single and multiple scattering regimes. The results are compared with random matrix theory. Once the experimental matrix coefficients are renormalized, experimental results and theoretical predictions are found to be in a very good agreement. Two kinds of random media have been investigated: a highly scattering medium in which multiple scattering predominates and a weakly scattering medium. In both cases, residual correlations that may exist between matrix elements are shown to be a key parameter. Finally, the possibility of detecting a target embedded in a random scattering medium based on the statistical properties of the strongest singular value is discussed.     

非均匀随机散射介质层的多次散射和热辐射的分层迭代解

为纳入矢量辐射传输方程的多次散射，将非均匀平行分层分布的随机散射介质划分成多个薄 层，利用各薄层的低阶Mueller矩阵解推导出整层的高阶散射迭代解.用这一方法计算了具有 占空比、粒子大小和温度廓线非均匀分布的平行分层随机密集球形粒子积雪层的极化热辐射 .数值结果与一层均匀随机散射层的离散坐标-特征值方法作了比较，讨论了多次散射和热辐 射与散射层各特征参数的关系，与积雪层微波遥感数据进行了对比. 关键词： VRT方程 平行分层 高阶散射解 迭代解     

Effect of electric field on light scattering by aqueous colloids of diamond and graphite

We present the results of our experimental investigation of light scattering by polydisperse colloids of diamond and graphite. The scattering is studied at a random orientation of particles and in an external radiofrequency electric field, which orients particles along the strength. The average dimensions of particles in both colloids are close to each other and comparable with the wavelength of the incident light. The shape of particles and the optical and electrooptical properties of diamond and graphite colloids are significantly different. We analyze the polarization components of scattered light energy when the light incident on the colloids is linearly polarized. We show that the quadrupole light scattering by isotropic diamond particles has the main effect on angular dependences of depolarization of scattered light. For light scattering by anisotropic graphite particles, the depolarization of scattered light is mainly determined by a particular feature of the dipole scattering of particles. It is shown that, in both colloids, the orientational order of particles considerably reduces the depolarization of light scattered by particles. We show that relative changes in the intensity and depolarization of scattered light, which depend on the scattering angle and polarization direction of light, as well as on the parameters of particles, can be used as a measure of electrooptical effects observed in colloids.     

Study of the sensitivity of size-averaged scattering matrix elements of nonspherical particles to changes in shape, porosity and refractive index

Studies of the physical parameters that influence the single scattering properties of a size distribution of small particles in random orientation are fundamental in understanding the origin of the observed dependence of the scattering matrix elements on the scattering angle. We present results of extensive calculations of the single scattering matrices of small nonspherical particles performed by a computational model based on the Discrete-Dipole Approximation. We have particularly studied the sensitivity of the size-averaged scattering properties at visible wavelengths of nonspherical, randomly oriented absorbing particles considering changes in shape, porosity and refractive index. These studies have importance regarding the inversion of physical properties of small particles as measured in the laboratory and the dust properties in various astrophysical and atmospherical environments. We have found that size distributions of randomly oriented irregular particles of different shape, including large aspect ratio particles, show similar scattering matrix elements as a function of the scattering angle, in contrast with the pattern found for regularly shaped particles of varying axis ratios, for which the scattering matrix elements as a function of the scattering angle show much larger differences among them. Regarding porosity, we have found a very different pattern in the scattering matrix elements for an ensemble of compact and porous particles. In particular, the linear polarization for incident unpolarized light produced by compact and absorbing particles of large size parameter tend to mimic the pattern found for large absorbing spheres. For porous particles, however, the linear polarization for incident unpolarized light tends to decrease as the size of the particle grows, with the maximum being displaced towards smaller and smaller scattering angles.     

The scattering matrix for size distributions of irregular particles: An application to an olivine sample

We have compared simulated and measured scattering matrices of a size distribution of olivine particles at wavelengths of 633 and 442 nm. The computations were carried out for size distributions of irregularly-shaped compact particles with different average projected areas using the discrete-dipole approximation (DDA). The results of the comparison show that the model of irregularly-shaped particles mimic the observations far better than the results given by spheres, spheroids or rectangular prisms having a wide range in aspect ratios. The computed scattering matrices for size distributions of irregularly-shaped particles do not depend very strongly on the precise particle shape assumed, providing a method to infer certain physical properties of an ensemble of natural dust particles, such as the refractive index, when some information on the sample, as the size distribution, is known a priori.     

Frequency bandwidth of light focused through turbid media

We study the effect of frequency detuning on light focused through turbid media. By shaping the wavefront of the incident beam light is focused through an opaque scattering layer. When detuning the laser we observe a gradual decrease of the focus intensity, while the position, size,and shape of the focus remain the same within experimental accuracy. The frequency dependence of the focus intensity follows a measured speckle correlation function. We support our experimental findings with calculations based on transport theory. Our results imply wavefront shaping methods can be generalized to allow focusing of optical pulses in turbid media.     

Effects of nondiffusive wave propagation upon coherent backscattering by turbid media

The nondiffusive contribution to the coherent backscattering intensity is calculated for the media with relatively large particles (size a is greater than wavelength λ). The results are in good agreement with the experimental data at the wings of the angular spectrum of the coherent backscattering. The shape of the backscattering peak is analyzed for strongly absorbing media. The correlation function of the intensity fluctuations is calculated for the scattering by Brownian particles at relatively large time shifts.     

Light scattering properties of sea-salt aerosol particles inferred from modeling studies and ground-based measurements

Direct climate radiative forcing depends on the aerosol optical depth τ, the single scattering albedo ?, and the up-scatter fraction β; these quantities are functions of the refractive index of the particles, their size relative to the incident wavelength, and their shape. Sea-salt aerosols crystallize into cubic shapes or in agglomerates of cubic particles under low relative humidity conditions. The present study investigates the effects of the shape of dried sea-salt particles on the detection of light scattering from the particles. Ground-based measurements of scattering and backscattering coefficients have been performed with an integrating nephelometer instrument for a wavelength . The measurements are compared to two models: the Mie theory assuming a spherical shape for the particles and the Discrete Dipole Approximation (DDA) model for the hypothesis of cubic shape of the sea-salt aerosols. The comparison is made accurately by taking into account the actual range of the scattering angles measured by the nephelometer in both models that is from 7° to 170° for the scattering coefficient and from 90° to 170° for the backscattering coefficient. Modeled scattering and backscattering coefficients increase for nonspherical particles compared to spherical shape of particles with diameter larger than about 1 μm. However, the comparison of the modeling results with the measurements gives best agreement for particles diameter less than about 1 μm. The size distribution of the particles is measured with two instruments with different size bins: an electrical low-pressure impactor (ELPI) and an aerodynamic particle sizer (APS). It is found that the size of the bins of the instruments to determine the number concentration of the particles in accordance with their diameter is critical in the comparison of measurements with modeling.