Theoretical studies on particle shape classification based on simultaneous small forward angle light scattering and aerodynamic sizing

Particle shape contributes to understanding the physical and chemical processes of the atmosphere and better ascertaining the origins and chemical compositions of the particles. The particle shape can be classified by the aspect ratio,which can be estimated through the asymmetry factor measured with angularly resolved light scattering. An experimental method of obtaining the asymmetry factor based on simultaneous small forward angle light scattering and aerodynamic size measurements is described briefly. The near forward scattering intensity signals of three detectors in the azimuthal angles at 120?offset are calculated using the methods of T-matrix and discrete dipole approximation. Prolate spheroid particles with different aspect ratios are used as the shape models with the assumption that the symmetry axis is parallel to the flow axis and perpendicular to the incident light. The relations between the asymmetry factor and the optical size and aerodynamic size at various equivalent sizes, refractive indices, and mass densities are discussed in this paper. The numerically calculated results indicate that an elongated particle may be classified at diameter larger than 1.0 μm, and may not be distinguished from a sphere at diameter less than 0.5 μm. It is estimated that the lowest detected aspect ratio is around 1.5:1 in consideration of the experimental errors.     

Orientation dependence of broadband acoustic backscattering from live squid

A controlled laboratory experiment of broadband acoustic backscattering from live squid (Loligo pealeii) was conducted using linear chirp signals (60-103 kHz) with data collected over the full 360° of orientation in the lateral plane, in <1° increments. The acoustic measurements were compared with an analytical prolate spheroid model and a three-dimensional numerical model with randomized squid shape, both based on the distorted-wave Born approximation formulation. The data were consistent with the hypothesized fluid-like scattering properties of squid. The contributions from the front and back interfaces of the squid were found to dominate the scattering at normal incidence, while the arms had a significant effect at other angles. The three-dimensional numerical model predictions out-performed the prolate spheroid model over a wide range of orientations. The predictions were found to be sensitive to the shape parameters, including the arms and the fins. Accurate predictions require setting these shape parameters to best describe the most probable squid shape for different applications. The understanding developed here serves as a basis for the accurate interpretation of in situ acoustic scattering measurements of squid.     

Equivalent volume-averaged light scattering behavior of randomly inhomogeneous dielectric spheres in the resonant range

Finite-difference time-domain numerical experiments and supporting analyses demonstrate that the spectral dependence of the total scattering cross sections of randomly inhomogeneous dielectric spheres of sizes in the resonant range closely resemble those of their homogeneous counterparts that have a volume-averaged refractive index. This result holds even for the extreme case in which the refractive index within an inhomogeneous sphere varies randomly over the range 1.0-2.0.     

A study of light scattering of mononuclear blood cells with scanning flow cytometry

This study describes the measurement of light scattering of human mononuclear blood cells, the development of an appropriate optical model for those cells, and solution of the inverse light-scattering problem. The angular dependency of light-scattering intensity of mononuclear blood cells was experimentally measured by means of scanning flow cytometry. A sphere consisting of several concentric homogeneous layers with different refractive indices was tested as an optical model for mononuclear blood cells. A five-layer model has given the best agreement between experimental and theoretical light-scattering profiles. The inverse light-scattering problem was solved for a five-layer model with an optimization procedure that allows one to retrieve cell parameters: cell size relates to the outer diameter of the fifth layer; size of the nucleus relates to the outer diameter of the third layer. Mean values of cell size, nuclear size, refractive indices of nucleus and cellular cytoplasm were determined for blood monocytes and lymphocytes.     

Can particle shape information be retrieved from light-scattering observations using spheroidal model particles?

We address the question if and how observations of scattered intensity and polarisation can be employed for retrieving particle shape information beyond a simple classification into spherical and nonspherical particles. To this end, we perform several numerical experiments, in which we attempt to retrieve shape information of complex particles with a simple nonspherical particle model based on homogeneous spheroids. The discrete dipole approximation is used to compute reference phase matrices for a cube, a Gaussian random sphere, and a porous oblate and prolate spheroid as a function of size parameter. Phase matrices for the model particles, homogeneous spheroids, are computed with the T-matrix method. By assuming that the refractive index and the size distribution is known, an optimal shape distribution of model particles is sought that best matches the reference phase matrix. Both the goodness of fit and the optimal shape distribution are analysed. It is found that the phase matrices of cubes and Gaussian random spheres are well reproduced by the spheroidal particle model, while the porous spheroids prove to be challenging. The “retrieved” shape distributions, however, do not correlate well with the shape of the target particle even when the phase matrix is closely reproduced. Rather, they tend to exaggerate the aspect ratio and always include multiple spheroids. A most likely explanation why spheroids succeed in mimicking phase matrices of more irregularly shaped particles, even if their shape distributions display little similarity to those of the target particles, is that by varying the spheroids’ aspect ratio one covers a large range of different phase matrices. This often makes it possible to find a shape distribution of spheroids that matches the phase matrix of more complex particles.     

Linearized T-matrix and Mie scattering computations

We present a new linearization of T-Matrix and Mie computations for light scattering by non-spherical and spherical particles, respectively. In addition to the usual extinction and scattering cross-sections and the scattering matrix outputs, the linearized models will generate analytical derivatives of these optical properties with respect to the real and imaginary parts of the particle refractive index, and (for non-spherical scatterers) with respect to the “shape” parameter (the spheroid aspect ratio, cylinder diameter/height ratio, Chebyshev particle deformation factor). These derivatives are based on the essential linearity of Maxwell's theory. Analytical derivatives are also available for polydisperse particle size distribution parameters such as the mode radius. The T-matrix formulation is based on the NASA Goddard Institute for Space Studies FORTRAN 77 code developed in the 1990s. The linearized scattering codes presented here are in FORTRAN 90 and will be made publicly available.     

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.     

Light scattering by needle-type and disk-type particles

A powerful tool to analyze light scattering by 3D arbitrary-shaped homogeneous or inhomogeneous obstacles located in free space is based on volume integral equation. In this paper we apply a weak form of volume integral equation to simulate light scattering by needle- and disk-type particles such as straight and curved cylinders, cylindrical plate and hexagonal prism with high aspect ratio and low and high values of refractive indexes. For problems where discrete sources method could be applied, we calculated differential scattering cross-section using both methods and got excellent agreement in results.     

Application of the pseudo-spectral time domain method to compute particle single-scattering properties for size parameters up to 200

The applicability, efficiency, and accuracy of the pseudo-spectral time domain (PSTD) method are investigated with specific emphasis on the computation of the single-scattering properties of homogeneous dielectric particles. By truncating the high spectral terms, the Gibbs phenomenon is eliminated, and, consequently, the applicability of the PSTD is enhanced. The PSTD simulations for ice spheres, with moderate refractive indices and size parameters up to 200, are compared with the exact Lorenz–Mie solutions at three wavelengths. In addition, the comparison is extended to a case with an extremely large refractive index (7.150+i2.914) and size parameters up to 40. Furthermore, the single-scattering properties of randomly oriented spheroids and circular cylinders for size parameters up to 150 and 75, respectively, are calculated with the PSTD in comparison with those computed from the T-matrix method. The aspect ratio of the spheroid and the diameter-to-length ratio of the circular cylinder are 0.5 and 1, respectively. The relative errors, given by the PSTD for these randomly oriented non-spherical particles, are smaller than 2% for the extinction efficiencies and asymmetry factors and less than 30% for the phase function. The PSTD is also employed to compute the phase matrices of randomly oriented hexagonal columns with size parameters of 50 and 100. The simulations show the PSTD to be a robust method for simulating the single-scattering properties of particles with small-to-medium size parameters and for a wide range of refractive indices.     

On the validity of modeling rayleigh scatterers by spheroids

For single homogeneous lossy dielectric Rayleigh particles, the manner in which the particle shape affects the absorption and scattering is examined by computing the polarizability tensor elements using a general purpose program valid for any rotationally symmetric body. The results for a number of generic shapes are compared with those for the corresponding spheroids. When the dielectric constant is real and negative, the resonances attributable to bulk and to shape-dependent or surface polariton modes are tracked as functions of the length-to-width ratio of the particle and the bulk dielectric constant. The adequacy of using spheroid approximations for individual particles in a dispersion is also discussed.     

Method for determining the asphericity and microphysical parameters of erythrocytes from the directional scattering coefficient

A method for determining the microphysical parameters and shape of human blood erythrocytes is proposed based on regression relations between them and the small-angle directional scattering coefficients β(Θ). It is shown that the use of β(Θ) for angles Θ = 5° and 12° in the transparency window allows one to determine not only the microphysical parameters and refractive index of erythrocytes, but also the shape parameters, such as the asphericity and the length of the major axis of the spheroid, with an accuracy of a few percent.     

Intensity fluctuations of spherical acoustic waves propagating through thermal turbulence*

The intensity fluctuations of acoustic waves that propagate through thermal turbulence are investigated under well controlled laboratory conditions. Two heated grids in air are placed horizontally in a large anechoic room and the mixing of the free convection plumes above them generates a homogeneous isotropic random thermal field. The spectrum of refractive index fluctuations is accurately described by a modified von Karman model which takes into account the entire spectrum of turbulence. Experimental data are obtained by varying both the frequency of the spherical wave and the distance of propagation. In this paper we concentrate on the variance of the normalized intensity fluctuations and on their probability distributions. These measurements cover all the regimes from weak scattering to strong scattering including the peak of the intensity variance. Experimental values of the scintillation index are compared with classical theoretical predictions and also with the results of recent numerical simulations. The classical probability density functions (log-normal, exponential, I-K) are tested against the measured probability distributions. The generalized gamma distribution, which varies smoothly from log-normal to exponential as a function of two parameters, appears m represent the experimental data for a very large range of scattering conditions.     

Acoustic backscattering by Hawaiian lutjanid snappers. 1. Target strength and swimbladder characteristics

The target strengths and swimbladder morphology of six snapper species were investigated using broadband sonar, x rays, and swimbladder casts. Backscatter data were obtained using a frequency-modulated sweep (60-200 kHz) and a broadband, dolphinlike click (peak frequency 120 kHz) from live fish, mounted and rotated around each of their three axes. X rays revealed species-specific differences in the shape, size, and orientation of the swimbladders. The angle between the fish's dorsal aspect and the major axis of its swimbladder ranged from 3 degrees to 12 degrees and was consistent between individuals within a species. This angle had a one-to-one relationship with the angle at which the maximum dorsal aspect target strength was measured (r2 = 0.93), regardless of species. Maximum dorsal aspect target strength was correlated with length within species. However, the swimbladder modeled as an air-filled prolate spheroid with axes measured from the x rays of the swimbladder predicted maximum target strength significantly better than models based on fish length or swimbladder volume. For both the dorsal and lateral aspects, the prolate spheroid model's predictions were not significantly different from the measured target strengths (observed power >0.75) and were within 3 dB of the measured values. This model predicts the target strengths of all species equally well, unlike those based on length.     

随机取向非球形沙尘气溶胶粒子的光学特性

利用离散偶极子近似法分析了一种随机取向旋转椭球体沙尘气溶胶粒子模型在尺度参数变化范围为0.1~23时(波长0.55!m对应有效半径为0.01~2!m)的光学特性,研究了沙尘粒子非球形性程度对其光学特性的影响,并考察了非球形粒子的随机取向能否用等体积球体来代替。就随机取向单分散和多分散旋转椭球体沙尘气溶胶而言,粒子非球形特征越明显,消光效率因子、不对称因子和单次散射反照率基本上偏离其等体积球体越大;对于相同的非球形,不对称因子偏离其等体积球体的相对偏差要比消光效率因子和单次散射反照率要大。非球形粒子的随机取向并不能使其光学特性严格等效为其等体积球体的光学特性。如果粒子形状偏离球体较小,则非球形粒子的随机取向的平均效果能使其消光效率因子、不对称因子和单次散射反照率近似用等体积球体的对应光学参量来等效;而如果粒子形状偏离球形较大,仅有单次散射反照率可以近似用等体积球体的单次散射反照率来等效,例如,轴半径比为16的旋转椭球体沙尘粒子的单次散射反照率偏离其等体积球体仅在3%以内。     

Spectropolarised ray-tracing simulations in densely packed particulate medium

Light scattering from particulate medium is simulated using the Monte Carlo ray-tracing technique. The medium is modelled as a randomly packed medium of ellipsoidal grains with stochastically rough surfaces, with an optional thin coating. Optical properties are modelled using a wavelength-dependent complex refractive index and taking Fresnelian reflections and refractions from the interfaces. The size and shape of the grains are assumed to be large and smooth enough for geometric optics to apply reasonably well.The ray-tracing technique uses parallel, weighted rays for computing simultaneously over a wide wavelength spectrum and a small roughness range, and scaling to obtain a large range of sizes and absorbities simultaneously. Polarisation is fully accounted for. The multiobservation technique is effectively used at each scattering point. The scattering from thinner sample layers is also received as a subresult.Simulations are run for a set of model samples to study the effects and sensitivities regarding the values of certain parameters. It has been found that the size and composition of the grains affect the scattering in a unique and invertible way. The shape of the grain causes similar significant effects that must certainly be taken into account if any accuracy is required, although inverting for the shape is difficult without further constraints. The packing density has a small but observable effect. Polarisation can be used to study the composition of low-albedo objects.     

Characteristics of light scattering by smoke particles based on spheroid models

Light scattering models of smoke particles play an important role on the development of photoelectric smoke detection. Aiming at the influence of morphology of smoke particles, spheroid models are introduced to analyze the Stokes scattering matrix of smoke particles, which are lognormal size distributions. Under the condition of random orientations, the effects of refractive indexes and mean size of smoke particles are considered. The results show that after averaging of the orientation and size, the nonsphericity of smoke particles has a considerable effect on their light scattering. Additionally, the nonsphericity of gray smoke particles generated from smoldering fires is more important than soot from flaming fires for analyzing the light scattering.     

鳀鱼(Engraulis japonicus)目标强度的模型法研究

采用声散射理论和目标强度近似模型评估法对黄海鲤鱼（Engraulis japonicus）的声散射特征和目标强度进行了数值计算与评估研究。散射模型由鱼鳔模型和鱼体模型两个部分构成，其中鱼鳔采用充满气体的椭球体模型，鳔除外的鱼体采用充满液体的椭球体模型。理论数值计算所需参数取自全长12．6cm的鲤鱼个体，其鱼鳔尺寸利用X光照片测得。平均目标强度利用模型算得的不同角度下的声散射强度与鲲鱼倾角分布函数的卷积计算，其中倾角（度）的分布函数设为N（-3．9，12．8^2）。结果显示，鲲鱼对声波的散射具有明显指向性；在38kHz和120kHz工作频率下，鲲鱼的最大背向目标强度分别为-41．2dB和-39．5dB，有效平均目标强度分别为-48．0dB和-51．5dB，与实测结果吻合较好。另外还对鲲鱼的反向散射指向性特征、目标强度的频率特征以及鱼鳔对鲲鱼整体目标强度的贡献等进行了分析与讨论。以上研究表明，模型法作为现场测定研究方法的重要补充和认知鱼类声学散射特性的有效途径，可在我国鱼类目标强度的研究中发挥重要作用。     

Analysis of 12C + 12C Elastic Scattering for Energy between 70 and 1440 MeV

Physics of Atomic Nuclei - In the present work, we reanalysis the 12C + 12C refractive scattering over a wide energy range. The analysis is performed in the framework of optical model with the...     

结合计算层析与光学相干层析测量折射率分布

通过将计算层析技术与光学相干层析技术相结合,测量散射介质非均匀折射率分布。该方法测量散射样品折射率分布时,通过光学相干层析技术测量散射样品折射率分布在多个方向上的投影,采用计算层析技术实现对样品折射率分布的层析重建,克服了传统折射率光学测量方法如单纯的基于光学相干层析原理的焦点追迹法和光程匹配法,不能测量散射介质非均匀折射率分布的缺点。采用该方法在实验中对梯度折射率棒的径向相对折射率分布进行层析重建,取得了较好的实验结果。     

Particle on surface: 3D-effects in dry laser cleaning

Previous analysis of dry laser cleaning within the frame of a one-dimensional (1D) model with homogeneous surface heating shows that this model disagrees with experiments by one–two orders of magnitude. The particle on the surface produces an inhomogeneous intensity distribution in its vicinity due to scattering and diffraction. This produces a nonstationary 3D distribution of the temperature and nonstationary 3D thermal deformations of the surface. If one uses the Mie theory for calculation of inhomogeneous intensity then in some region of the parameters, the 3D model predicts results close to the experimental ones. The next step was done when the scattering effects for radiation reflected from the surface was taken into account (so-called “particle on surface” problem). This approach yields results close to the experimental one within the wide range of parameters. PACS 42.25.Fx; 42.25.Hz; 81.65.CfAn erratum to this article can be found at .