一种内混合气溶胶粒子模型光散射的等效性

以包含灰尘、黑碳和水三种成分的单分散内混合初次气溶胶为例,利用消光、吸收、散射效率因子和不对称因子,探讨了以等效折射率描述具有不同成分的内混合气溶胶粒子系统的适用性。结果表明,在尺度参数为0.1～25时不同半径比下,消光、吸收和散射效率因子的等效性较好,相对误差分别在3%、3%和4%以内;不对称因子的等效性相对稍差,相对误差在13%以内。当半径比a/b小于1/5,即内混合体中所含灰尘和黑碳较少时,等效折射率实部和虚部值基本可以确定,而不必考虑尺度参数的影响。用除散射相函数之外的其他光学量来等效时,较为容易找到等效的气溶胶粒子。     

散射相函数的高阶光学参量研究

漫反射光谱技术被广泛应用于无创测量生物组织光学性质。当光源与探测器很近时,仅仅依靠吸收系数μ_a和约化散射系数μ′_s不能准确描述光源附近光的传播状态。而二阶光学参量γ的引入改善了近光源光的传播状态的描述。本文将生物组织的散射等效成特定球形颗粒的散射,基于Mie散射理论,计算了与散射相函数p(θ)有关的单粒子和多分散系粒子的二阶光学参量γ,研究了γ随尺度参数α和相对折射率m的变化规律,描述了γ与组织结构参量之间的联系,并阐述了γ对粒子特征的表征能力。研究表明,参量γ对尺度参数α小于2的微粒尺寸的改变是敏感的,并呈二次函数关系,其系数与相对折射率呈线性关系;对于相对折射率和尺度参数都不相同的两个粒子,他们的各向异性因子g相同时,二阶光学参量γ却不同,粒子越大,γ表征粒子特征的能力越强。这对于无创探究组织微观形态具有深远的意义。     

颗粒系的可见消光光谱分析及最佳波长的选择

在光全散射法颗粒粒径测量中,被测颗粒系的消光光谱包含有颗粒粒径、折射率等信息。对常用的单峰及双峰R-R分布的可见消光光谱进行模拟,分析了可见消光光谱随粒径和相对折射率变化的规律。选取二阶微分可见消光光谱不连续点对应的波长作为测量波长,并将可见光边界波长同时作为测量波长,在非独立模式下,采用遗传优化算法反演粒径分布。仿真计算与实验验证结果表明,通过消光光谱分析,可以预先确定被测颗粒系的分布状况,缩小优化算法中反演参数的搜索范围。结合最佳波长选择方法,使测量的精度和可靠性明显提高。对测量光谱加入1%随机噪声时,单峰及多峰分布粒径反演均能得到满意的结果。     

Grouping and adding method for calculating light scattering by large fluffy aggregates

We present a method to derive the light scattering properties of very porous fractal aggregates composed of a large number of monomers where the size parameter of monomer is larger than unity. Our new method is based on the grouping of the aggregate: The aggregate is divided into groups, where each group is located along a line of the incident light, and the scattering properties of the group are calculated taking into account multiple scattering with monomers located inside the group, as well as those in a buffer region around the group. The scattering and absorption efficiencies are obtained by adding the resultant scattering properties for all the groups. We have shown that the method effectively works when the monomer scatters the incident lights predominantly in the forward direction, which is the case if the monomer size is large compared to the wavelength of the incident light.The errors in resulting scattering and absorption efficiencies for porous aggregates are investigated for various refractive indices and sizes of monomers. We found that the errors are larger for low absorbing materials and they can be reduced by expanding the buffer region. In the case of the buffer region for each group consisting of 1/8 of the total number of monomers, the results show errors less than 15% and 10% for absorption and scattering, respectively. It is also shown that the errors have a small standard deviation (i.e., 2%) for different directions of the incident light.     

气溶胶粒子散射和吸收特性对复折射率依赖性的数值研究

利用米散射理论数值计算分析了尺度参数为0.1~100时球形典型气溶胶粒子的散射和吸收特性对复折射率的依赖性关系。气溶胶粒子复折射率的实部和虚部是一个有机的整体,粒子复折射率的实部和虚部可以分别影响其散射和吸收特性。若实际大气气溶胶粒子大多是成核模态和积聚模态的小粒子,基于气溶胶的散射和吸收特性可以获得其复折射率的唯一解。但是,如果大气中存在大量的粗模态粒子时,气溶胶散射和吸收特性对其复折射率的依赖性较为复杂,只有选择有限的合适复折射率库区间,才有可能获得更合适的有效复折射率。     

Scattering behavior of nonabsorbing metallic nanoparticles

The optical property of nanosized metallic particles is unique and size-dependent, which cause color variation. In this work, the relationship between diameter and refractive index of nonabsorbing metallic nanoparticles and their scattering properties is studied by using Mie theory. Obtained results indicate that the optical scattering of metallic nanoparticle depends on their refractive index and diameter. The effect of refractive index on optical scattering depends on the nanoparticle diameter. So that, for very fine nanoparticle (10 nm diameter) the effect of refractive index on scattering is not significant. But the effect of refractive index of large size nanoparticle (700–900 nm diameter) on their optical scattering is higher than fine and medium size nanoparticles. The wavelength with maximum scattering depends on refractive index and nanoparticles diameter. In addition, the colorimetric study indicates that the color of nanoparticle depends on their size and refractive index. So that, the lightness, hue, and colorfulness of nanoparticles is changed by changing size and refractive index.     

Characteristics of exact retrieval of the structure of plane-stratified media using reflected and transmitted pulse signals

We consider the exact iterative algorithm for solution of the direct and inverse scattering problems in 1D inhomogeneous half-space using piecewise-constant approximation of the constitutive parameter profiles (e.g., refractive index). A novel modification of the Gelfand–Levitan equation is derived for solution of the inverse scattering problem. Numerical examples are given and the effects related to a finite frequency band of the sounding pulse are discussed.     

Correction factors for a total scatter/backscatter nephelometer

Total aerosol scattering and backscattering atmospheric values are typically obtained with an integrating nephelometer. Due to design limitations, measurements do not cover the full (0°–180°) angular range, and correction factors are necessary. The effect of angle cutoff is examined for a number of particle size distributions and refractive indices. Scattering data for sub-micron particles can be corrected by the use of a modified Anderson approximation, while data for larger particle distributions can be approximated by a function of the effective size parameter. Correction factors for the hemispheric backscatter ratio are found to be small if nonsphericity is assumed. Such approximations will help more accurate corrections for angle range, particularly at large size parameter values.     

Impact of particle shape on refractive-index dependence of scattering in resonance domain

The impact of particle shape on how scattering, in particular the asymmetry parameter g, depends on the refractive index m is studied. Light scattering simulations for spheres and 16 different spheroids with varying refractive indices and sizes are carried out using an exact T-matrix method to establish how m affects scattering for different shapes. In addition to single shapes, shape distributions of spheroids are used to mimic scattering properties of ensembles of irregularly shaped particles. The results show that Δg resulting from Δm are both size and shape dependent, and spheroids are not universally less or more sensitive to m than the corresponding spheres are. While shape distributions of spheroids show much weaker and much more consistent m-dependence of g than the spheres of the same size, an integration over a size distribution (SD) largely eliminates these differences. Thus, the use of spheres for estimating Δg resulting from Δm for a collection of nonspherical particles appears to be safe except for very narrow SDs. The actual g-values tend to be, however, considerably and consistently in error.     

Critical Angle Refractometry for Simultaneous Measurement of Particles in Flow: Size and Relative Refractive Index

The principle of the optical technique critical angle refractometry, used to determine the size and refractive index of spherical particles (with relative refractive index below unity) in liquid flows, was investigated. This technique is based on the observation of the particle scattering pattern around the critical angle. Similarly to the recent technique developed for rainbow scattering pattern analysis for droplet temperature and size measurements, it is shown that the relative particle refractive index (m_r<1) and size can be determined from the position of the primary diffraction fringe and from the angular spacing between two fringes. Explicit equations for refractive index and particle size measurement were derived from the first-order term of the physical optics approximation. An experimental validation test and numerical computations based on the Lorenz-Mie theory were used to validate the principle of the proposed technique and to estimate its sensitivity, which was shown to be of the same order as that of the rainbow technique. This technique is considered to be useful for various applications in liquid multiphase flows where the particles size and material are to be characterized.     

空间垂直方向气溶胶消光特性的研究

在已知大气气溶胶折射率和气溶胶谱分布的基础上,对空间垂直方向的气溶胶消光特性进行了研究。文章利用Mie散射理论计算讨论了气溶胶的消光、散射、吸收系数随各参数的变化,并在MATLAB中对变化情况进行了仿真。结果表明,粒子半径与入射波长大小相近时气溶胶的消光最强,并且随着能见度的增大,气溶胶衰减系数减小。这些结论可以为红外辐射的大气衰减计算和分析提供依据。     

切比雪夫雾霾粒子的紫外光散射偏振特性研究

雾霾天气已严重影响人们的日常生活,通过检测雾霾粒子的紫外光散射偏振特性可以有效分析雾霾成因。矿物粒子、灰尘粒子等雾霾颗粒均有小规模表面粗糙度的形态学特征,因此可用切比雪夫粒子作为模型分析。“日盲”紫外光与切比雪夫雾霾粒子相互作用发生散射,散射光偏振特性可反演切比雪夫雾霾颗粒物理性质(如粒子尺寸参数、复杂折射率、粒子形变、波纹参数)。采用紫外光单次散射模型和T矩阵方法,仿真分析切比雪夫雾霾粒子物理参数与散射光偏振特性(Stokes矢量和偏振度)之间的关系,结果表明：粒径对散射光Stokes矢量Is和Qs随散射角的变化趋势影响很大,粒子的粒径和复杂折射率虚部的变化会造成散射光偏振度随散射角的变化趋势的改变;具体分析散射角度为10°时,得到粒径对Is和Qs的数值影响最大,当粒径r<1 μm时,Is随粒径呈现抛物线趋势;切比雪夫粒子形变的增大,Is呈现先增大后减小的趋势。     

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.     

中红外区二氧化钛反蛋白石光子晶体的光子定域化研究

为了得到二氧化钛反蛋白石光子晶体中影响光子定域化的规律,基于Mie散射理论和低浓度近似,对光子定域化参量进行了数值计算与理论分析,发现在该氧化物的剩余射线区内,入射波长和散射体大小对光子定域化有明显的影响.结果表明,在散射体浓度为10%,相对折射率大于3.8时,在中红外区13.3~15.3 μm范围内出现了光子定域化现象,并随着散射体半径的增大,定域化区向长波方向移动;同时,定域化参量先增大后减小.研究结果为实验上在该类光子晶体中实现光子定域化现象提供了理论参考.     

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.     

Mie光散射理论的数值计算方法

Mie散射级数的计算速度和精度对颗粒测量结果有着重要的影响。针对不同颗粒直径和相对折射率，一般采用前向递推，后向递推，连分式法等计算Mie散射级数。在这3种方法的基础上提出一种改进算法，即首先通过连分式法计算Mie散射级数的初始值，然后后向递推其余各值。该算法在Matlab中实现时，数据以数组的数据类型存储和调用，程序采用递归算法。通过比较计算结果发现，该算法耗时短且结果不易溢出，具有快速、稳定、不受颗粒直径和折射率范围影响等优点。     

团簇自然气溶胶散射相函数的数值分析

针对不同比例的灰尘和海盐团簇自然气溶胶,利用离散偶极子近似(DDA)法,通过考察成分的影响,使用波长为0.55 m,尺度参数变化范围为0.1~25时,研究了散射相函数和激光雷达比的影响,结果表明二者的变化趋势大体相同。尺度参数为13~24时,团簇自然气溶胶散射相函数有明显的后向散射加强,其中尺度参数为18附近,后向散射加强效应最明显。灰尘比海盐对散射相函数影响更大,二者的影响主要集中在尺度参数为15~25范围内,但除了散射角为180附近的后向外,影响的散射角方向略有不同。不同比例下的团簇自然气溶胶激光雷达比在尺度参数为3左右有最大值,其值约为180。在尺度参数为0.2~25范围内,成分对激光雷达比的影响不大,相对偏差小于10%,特别是尺度参数为0.5~2时的影响可以忽略,相对偏差小于1%。     

Performance of discrete dipole approximation for prediction of amplitude and phase of electromagnetic scattering by particles

Electromagnetic scattering provides useful signatures for nonintrusive particle characterization. Scattered wave which carries characteristic information about particles is identified completely by its intensity, polarization state and phase. Recent developments in measurement techniques have enabled measurement of phase of the scattered wave which is a source of additional information about particles. In the present study, accuracy of discrete dipole approximation (DDA) in predicting amplitude and phase of scattered wave is investigated via publicly available DDSCAT code by Draine and Flatau, which is a well-established tool for DDA and has found wide range of applications in the literature due to its flexibility. DDSCAT routine is modified to enable accurate computation of phase of complex amplitude scattering matrix (ASM) elements as well as their magnitude. DDA method was implemented by using lattice dispersion relation for dipole polarizabilities, generalized prime factor algorithm for fast-Fourier transformation and pre-conditioned bi-conjugate gradient method with stabilization for the solution of the complex linear system of equations. Accuracy of ASM elements predicted by DDA is assessed on single sphere problems with various size parameters and refractive indices by validation against Mie theory solutions. Excellent agreement between predictions and exact solutions proves the reliability of the modified DDSCAT code for prediction of amplitude and phase of scattered electromagnetic wave. Applicability conditions and requirements of the present DDA application to ensure accurate prediction of complete set of scattering parameters are mapped for single spheres, on an extensive domain of size parameters and refractive indices. A correlation is presented to estimate the magnitude and phase errors associated with given size parameter, refractive index and cubic lattice subdivision. Assessment of computational time requirements for different optical constants shows that implementation of DDA with the present specifications is unfeasible for size parameters larger than 4 when Re(m)>2 and Im(m)<0.1 at the same time, due to slow convergence rate.     

一种描述散射体系中散射颗粒消光能力的新方法

提出了一种新的衡量散射体系中散射颗粒消光能力、散射能力和吸收能力的方法并与传统方法进行了比较。在此基础上 ,讨论了散射颗粒折射率和颗粒大小对其散射能力的影响。运用此方法可以为各种散射体系 ,尤其是强散射体系选择恰当的散射颗粒 ,其结果优于用传统方法所得的结果     

Applicability of quasi-static and Rayleigh approximations for spheroidal particles

Expressions are obtained for the efficiency of absorption and scattering of radiation by uniform spheroids in the quasi-static approximation and the region of their applicability is studied. The prolate and oblate nonabsorbing particles with refractive indices 1.1≤n≤10 and axial ratios 1.1≤a/b≤100 were studied. The approximation expressions are found for the particle size at which the efficiency factors are calculated in the quasi-static approximation with an accuracy of 1%.