An effect of turbulent clustering on scattering of microwave radiation by small particles in the atmosphere

A coherent scattering of electromagnetic waves by clusters of inertial Rayleigh particles in atmospheric turbulence is considered. A preliminary estimate based on the Maxwell-Garnett theory and the Rayleigh approximation for single clusters demonstrates an importance of the coherent scattering contribution. It is confirmed by a general solution in a combination with theoretical estimates for the two-point probability density function for low-inertia spherical particles in isotropic turbulence. An approximate analytical expression for the coefficient characterizing effect of coherent scattering by the particle clusters is derived. The calculations for small Stokes numbers typical of water droplets in cumulus clouds yield an estimate of the coherent scattering effect on the microwave radar reflection. The model suggested allows solving the inverse problem to determine the pair correlation function for cloud particles. It is expected to be important for the investigations on particle–turbulence interaction in the atmosphere. The theoretical model developed is true not only in the limit of low-inertia particles and can be potentially used at arbitrary Stokes numbers in other applications.     

Spectral power determinations of compressibility and density variations in model media and calf liver using ultrasound

A model of scattering is used to relate average differential scattering cross section and power spectra of scattering medium variations. The model expresses the average differential scattering cross section as a sum of the power spectrum of medium compressibility variations, the power spectrum of density variations weighted by the square of the cosine of the scattering angle, and the cross-power spectrum of compressibility and density variations weighted by twice the cosine of the scattering angle. Known values of the average differential scattering cross section at a minimum of three different scattering angles and temporal frequencies corresponding to the same spatial frequency are used to calculate each of the three power spectra. Since noise and statistical fluctuations are present in actual measurements of average differential scattering cross section, the calculations of power spectra are obtained from an overdetermined set of equations to which a solution is found by using a singular value decomposition. Data derived from a model for scattering from a cloud of correlated particles are employed to show the influence of additive noise. Calculations are also made from measurements of scattering from three suspensions of particles that have a different average radius in each suspension but are similarly modeled by scattering from a cloud. Additionally, the calculations are applied to measurements of average differential scattering cross section of calf liver. The results show that determination of the power spectra of scattering medium variations can be made under practical conditions, and also imply that density variations contribute significantly to scattering by calf liver.     

Light scattering by large Saharan dust particles: Comparison of modeling and experimental data for two samples

Light scattering by large mineral-dust particles with small-scale surface roughness is investigated by comparing model simulations with laboratory-measured scattering matrices of two distinct dust samples collected from the Sahara desert. The samples have been chosen on the basis of their large effective radii, and the simulations are based on their measured size distributions. Size parameters larger than about 30 are modeled using a modified ray-optics model RODS (Ray optics with diffuse and specular interactions), while smaller particles are simulated with a T-matrix model. RODS allows us to mimic the surface roughness of large dust particles by covering the particle surface by a thin layer of external scatterers with specific single-scattering properties. The Gaussian-random-sphere geometry is used for the shapes of large dust particles. Small particles are modeled as an axial-ratio distribution of spheroids with smooth surfaces. One of the samples consists wholly of large particles and its scattering matrix can be reproduced very well by the RODS model, except for the phase function. The incorporation of wavelength-scale roughness is, however, necessary for good fits. The other sample, consisting of both small and large particles, proves more challenging to match with simulations. The analysis indicates, however, that the difficulties arise at least partially from the small-particle contribution, while RODS results are consistent with the measurements. Further, the results imply that the agreement with measurements would improve if roughness could also be accounted for in the small-particle simulations. Overall, the RODS method seems promising for modeling the optical properties of mineral-dust particles much larger than the wavelength.     

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.     

Determination of the Disperse Composition of a PbO Suspension Containing Aggregates of Particles of Lamellar Shape by the Laser-Polarimetry Method

The results of measurements of the scattering matrix at a wavelength of 0.63 μm in the range of scattering angles of 10°–155° are presented for an aqueous suspension of lead oxide containing particles of plate form and their aggregates of monomers with dimensions of ~5 nm. The results of the measurements are compared with the results of calculations for axially symmetric scatterers (ellipsoids of rotation, cylinders). It is shown that the presence of aggregates affects the scattering properties of such a medium. The results of reconstructing the distribution of particles of a disperse medium in sizes from the measurements data of the scattering matrix are presented. The reconstruction of the distributions was carried out by solving the problem of optimizing the sum of the squared deviations of the experimental and calculated values of matrix elements in the framework of the model of axially symmetric scatterers. It is shown that the distribution of particles by sizes is more accurately reconstructed by minimizing the sum of the squares of the deviations for the sum of the diagonal elements. The obtained distribution is compared with the distribution measured by the method of dynamic light scattering.     

Using the T‐Matrix Method for Light Scattering Computations by Non‐axisymmetric Particles: Superellipsoids and Realistically Shaped Particles

Light scattering by non‐axisymmetric particles is commonly needed in particle characterization and other fields. After much work devoted to volume discretization methods to compute scattering by such particles, there is renewed interest in the T‐matrix method. We extended the null‐field method with discrete sources for T‐matrix computation and implemented the superellipsoid shape using an implicit equation. Additionally, a triangular surface patch model of a realistically shaped particle can be used for scattering computations. In this paper some exemplary results of scattering by non‐axisymmetric particles are presented.     

Application of 30-MHz acoustic scattering to the study of human red blood cells

A technique for simultaneously measuring the scattering amplitude of individual particles at two angles is applied to human red blood cells. Using a Rayleigh scattering model, the density and compressibility of the cells may be determined given a priori knowledge of their volume. A calibration method relying on measurements of the bulk properties of particle suspensions is described. Red cell properties in hypotonic and hypertonic hosts are compared with a homogeneous mixture model, and a linear relation between hemoglobin content and scattering amplitude at a 90 deg scattering angle is established.     

Angle-resolved second-harmonic light scattering from colloidal particles

We report angle-resolved second-harmonic generation (SHG) measurements from suspensions of centrosymmetric micron-size polystyrene spheres with surface-adsorbed dye (malachite green). The second-harmonic scattering profiles differ qualitatively from linear light scattering profiles of the same particles. We investigated these radiation patterns using several polarization configurations and particle diameters. We introduce a simple Rayleigh-Gans-Debye model to account for the SHG scattering anisotropy. The model compares favorably with our experimental data. Our measurements suggest scattering anisotropy may be used to isolate particle nonlinear optics from other bulk nonlinear optical effects in suspension.     

A Pulsed Field Gradient NMR Technique for the Determination of the Structure of Suspensions of Non-Brownian Particles with Application to Packings of Spheres

The internal structure of systems of particles in a liquid is studied with a novel NMR technique based on the measurement of the squared modulus of the magnetization in presence of a pulsed field gradient. The formalism is analogous to the one used in classical scattering techniques (light, X-rays, neutrons); it allows similar information to be obtained about the structure (in particular, the structure factorS(q)). The main improvement is that the range of particles sizes is 10 μm to 1 mm, as compared with the range of the scattering techniques (<5 μm). The NMR technique was validated by studying packings of spherical particles of mean diameter 240 μm created by sedimentation. The profile of the experimental squared modulus of the magnetization versus the wave vector provides results for the mean size of particles and the compacity. The main feature is that it depends on the pair distribution function, and the present results are in good agreement with a model based on the Percus–Yevick approximation. This technique is then particularly adapted to systems such as non-Brownian suspensions, fluidized beds, porous media, and sediments.     

A simple new radiative transfer model for simulating the effect of cirrus clouds in the microwave spectral region

The upwelling atmospheric radiation in the millimeter wave spectral range is influenced by the presence of cirrus clouds. A plane parallel radiative transfer model which can take into account the effect of multiple scattering by ice particles in the cirrus has been developed and is used to simulate the brightness temperatures as they would be measured by a satellite instrument. The model uses an iterative procedure to solve the radiative transfer equation. The formulation of the model is such that it can easily be adapted to treat the full specific intensity vector instead of just the scalar total intensity. A convergence test for the model is explained and two cirrus cloud scenarios are simulated. The results illustrate the linearity of microwave radiative transfer for not too strong cirrus clouds in this frequency region.     

Quantum manifestation of systems on the macro-scale — the concept of transition state and transition amplitude wave

Quantum effects which have usually been associated with micro-scale phenomena can also arise on the macro-scale in situations other than the well-known macro-quantum phenomena of superconductivity and superfluidity. Such situations have been shown here to arise in processes involving inelastic scattering with bound or partially bound systems (not bound in all degrees of freedom), and the macro-quantum behaviour is associated with the state of the total system in transition in the process of scattering. Such a state is designated as a ‘transition-state’. It is pointed out that we have already observed such manifestations for a particular system, the charged particles in a magnetic field where interference effects involving macro-scale matter waves along the magnetic field have been reported [R K Varma et al, Phys. Rev. E65, 026503 (2002)]      

The Measurement of Nanoparticles Using Photon Correlation Spectroscopy and Avalanche Photo Diodes

In many areas of particle research there is a growing requirement to measure small particles, dilute systems and poorly scattering materials. The laser based technique of photon correlation spectroscopy (PCS) is used to measure nanometer sized particles, but very high count rates are required to obtain repeatable sizing measurements with small, weakly scattering particles. Traditionally this has been achieved using high powered lasers. These have the disadvantage of themselves producing changes in the sample and being costly. This paper reports on the development of a new generation avalanche photo diode (APD) which enables the measurement of small, weakly scattering particles without the need for a powerful laser. Data are presented for a variety of sample types.     

Ultrasonic Measurement of Sub-Micron Particles

Based on technology described in a Du Pont patent for an offline system, we have developed a prototype in-line ultrasonic cell for measuring particle size distribution. We have used this cell to verify the Allegra-Hawley model of ultrasonic attenuation in dilute (< 5 % vol) slurries of sub-micron ceramic particles, and we are developing a model that can cope with the multiple scattering effects occuring at higher concentrations. In this paper we present the results of attenuation measurements for ultrasound (2–50 MHz) in slurries with concentrations ranging from 0.5 010 to 38 010 (vol). The attenuation is proportional to slurry concentration up to 5 010 (vol) and is predicted by single scattering models. Above approximately 100% concentration, the attenuation is actually lower than expected. For the dilute slurries we find excellent agreement between our measurements and the Allegra-Hawley calculations, and the effects of the particle size distribution are evident in the ultrasonic attenuation spectrum. These ultrasonic data can be inverted to determine the particle size and concentration in aqueous slurries of sub-micron particles.     

随机取向气溶胶凝聚粒子光学特性研究

利用Cluster-cluster aggregation (CCA)模型,模拟了由64个球形原始微粒凝聚而成的四种随机取向气溶胶凝聚粒子。结合离散偶极子近似方法,分别得到了不同入射角和不同尺寸参数情况下气溶胶凝聚粒子的吸收、散射、消光效率因子和不对称因子的数值结果,并比较分析了四种形状气溶胶凝聚粒子吸收、散射、消光效率因子和不对称因子的差异。结果显示：对于相同数目原始微粒的气溶胶凝聚粒子,其光学特性明显依赖于入射光的入射角度和气溶胶凝聚粒子的形状;对于不同尺寸参数的气溶胶凝聚粒子,当入射光波长给定时,吸收、散射和消光效率因子最初随尺寸参数增大而快速增大,随后又随尺寸参数增大缓慢变小,但在尺寸参数变化过程中存在一个极大值;不对称因子则随尺寸参数的增大一直呈增大趋势,且随尺寸参数的增大趋近于1。     

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.     

Application of the Model of Spheroidal Scatterers for Determination of Particles Sizes of Aqueous Suspensions by the Laser-Polarimetry and Dynamic-Light-Scattering Methods

Results of measurements of particle sizes of a dispersed medium by the methods of laser polarimetry and dynamic light scattering are presented for water suspensions of ZnO, CuO, TiO₂, and BaTiO₃ with particles of irregular shape. When using the laser-polarimetry method, the particle-size distributions within the framework of the spheroidal-scatterer model are reconstructed. The same model was used to correct data obtained by the method of dynamic light scattering. The data obtained are compared with results obtained by electron microscopy. It is shown that, at values of the size parameter of 2–5, correction of the results of measurements obtained by the dynamic-light-scattering method makes it possible to reduce the error in determining the average particle size by this method to no more than 11%.     

Identification of cloud phase from PICASSO-CENA lidar depolarization: a multiple scattering sensitivity study

A fast Monte Carlo simulation scheme is developed to assess the impact of multiple scattering on space-based lidar backscattering depolarization measurements. The specific application of our methodology is to determine cloud thermodynamic phase from satellite-based lidar depolarization measurements. Model results indicate that multiple scattering significantly depolarizes backscatter return from water clouds. Multiple scattering depolarization is less significant for non-spherical particles. There are sharp contrasts in the depolarization profile between a layer of spherical particles and a layer of non-spherical particles. Although it is not as obvious as ground-based lidar observations, it is likely that we can identify cloud phase not only for a uniform cloud layer, but also for overlapping cloud layers where one layer contains ice and the other water droplets.     

非独立散射对纳米颗粒介质光热效应的影响

本文采用有限元软件COMSOL结合双温度模型模拟了含金纳米颗粒复合介质的光热效应和温度分布,分析了金纳米颗粒非独立散射的影响,讨论了发生光热效应时复合介质内能量的传递方式。结果表明:将双温度模型与Fourier导热定律结合可以描述纳米颗粒及周围介质的温度变化;与独立散射的颗粒相比,非独立散射情况下光热效应与颗粒间的耦合现象有关,并且这种耦合效应与颗粒间的距离相关。     

海洋混合悬浮颗粒对蓝绿激光的散射特性研究

激光在水下的传输很大程度上会受到海水中悬浮颗粒物的影响,而目前对于海洋中悬浮颗粒物光散射的理论研究大多是针对单一成分的悬浮粒子而进行的,但是在真实海洋中悬浮颗粒物都是以多种成分混合的颗粒群形式而存在的,因此研究真实海洋中混合悬浮颗粒物对蓝绿激光的散射特性具有重要意义。该研究选取了对蓝绿激光传输产生较大影响的浮游藻类植物、悬浮泥沙、碎屑、悬浮气泡和矿物质这五种常见的悬浮颗粒物作为研究对象,充分考虑真实海况中这五种悬浮颗粒物的不同混合情况,构建了海水中混合球形悬浮颗粒物对蓝绿激光的散射特性模型。数值计算了海水中五种物质混合的球形悬浮颗粒物对532 nm蓝绿激光的统计平均光散射参量和平均散射相函数,分析不同混合悬浮颗粒物的混合比对平均散射、吸收和消光系数以及单次反照率随着粒子有效半径和粒子数浓度变化的影响,同时分析了不同粒子尺寸下的不同混合比对混合悬浮颗粒物的平均散射相函数随着角度变化的影响。数值结果表明,当悬浮泥沙在整个混合模型中占比越大时,平均散射系数越大,而当悬浮藻类粒子在整个混合模型中占比增大时,平均吸收系数增大,由此可知海洋中对光造成主要影响的五种常见悬浮颗粒物中,悬浮泥沙对光散射作用影响最大,悬浮藻类粒子对光吸收作用影响最大。随着悬浮颗粒物浓度的增大,混合粒子的单次反照率保持不变,由此可知混合悬浮颗粒物的平均光散射参量随着粒子浓度的增长速率是一致的。海洋中混合悬浮颗粒物的平均散射相函数随着粒子的有效半径的增大而增大,散射作用最大的混合比下的悬浮颗粒物其平均散射相函数最大,悬浮颗粒物的前向散射较强。该工作对蓝绿激光在海水中传输、信道建模,水下无线光通信的研究以及激光探测都具有重要的理论指导意义。