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.     

Infrared extinction by homogeneous particle aggregates of SiC, FeO and : Comparison of different theoretical approaches

Particle shape and aggregation have a strong influence on the spectral profiles of infrared phonon bands of solid dust grains. Calculating these effects is difficult due to the often extreme refractive index values in these bands. In this paper, we use the discrete dipole approximation (DDA) and the T-matrix method to compute the absorption band profiles for simple clusters of touching spherical grains. We invest reasonable amounts of computation time in order to reach high dipole grid resolutions and take high multipolar orders into account, respectively. The infrared phonon bands of three different refractory materials of astrophysical relevance are considered—silicon carbide, wustite and silicon dioxide. We demonstrate that even though these materials display a range of material properties and therefore different strengths of the surface resonances, a complete convergence is obtained with none of the approaches. For the DDA, we find a strong dependence of the calculated band profiles on the exact dipole distribution within the aggregates, especially in the vicinity of the contact points between their spherical constituents. By applying a recently developed method to separate the material optical constants from the geometrical parameters in the DDA approach, we are able to demonstrate that the most critical material properties are those where the real part of the refractive index is much smaller than unity.     

Comparisons of the discrete-dipole approximation and modified double interaction model methods to predict light scattering from small features on surfaces

Two numerical methods to model light scattering from illuminated features on surfaces are presented. The discrete-dipole approximation (DDA) method is considered, as well as the modified double interaction method (MDIM). The DDA method models electromagnetic scattering of continuous features using discrete dipoles placed on a lattice structure. Sommerfeld integral terms are used to model dipole/surface interaction in the near-field. The MDIM method first computes scattering from the features based in free space using other methods such as Mie theory or other standard light scattering codes (including DDA). The surface interaction is modeled as a first approximation by means of a geometrical shadowing effect and the Fresnel coefficients. Comparisons of the methods will be shown for light scattering from spherical features. The material properties of dielectric and metallic materials will be considered and the feature sizes will be varied. The prediction accuracy and computational requirements of each method will be investigated. For most cases, the studies will show that the DDA method is more accurate than the MDIM method for dielectric materials since the modeling of the feature and surface electromagnetic interaction is more accurate; however, the modified double interaction method may be advantageous over the discrete-dipole approximation method for metallic features because of lesser computational times and memory requirements.     

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。     

Decompositioning method to compute scattering by complex shaped particles using a multiple scattering T-matrix approach

In a recent paper we proposed a decompositioning method to compute scattering by aggregated cylindrical fibres using a multiple scattering T-matrix approach. In this paper we extend this approach to scatterers lacking rotational symmetry. To investigate the capability of this method a square prism and a cube are decomposed into a number of subscatterers and scattering of the original particle shape is computed using multiple scattering. The results are validated using discrete dipole approximation (DDA).     

Extending the applicability of the discrete dipole approximation for multi-scale features on surface

Many problems in science and engineering involve significant physical entities and processes that span a substantial range of dimensions. In the case of characterization of bacteria on growth media using light scattering the length scales of interest can be classified as micro-scale (single bacterium), macro-scale (bacterial colonies of more than 10¹² bacterium that have passed through the exponential growth phase and reached mm size), and the intermediate or meso-scale of several tens of hundreds of bacteria. Light scattering approaches, to be effective in determining physical properties such as morphology and material composition, must comprehend this spectrum of length scales. The discrete dipole approximation (DDA), a powerful modeling tool for rigorous 3-D vector scattering, has shown its capability to predict the light scattering from micro-scale objects. To be able to accommodate meso-scale objects, we need to extend the computational limits of the DDA method such that it could compute object sizes of 10λ-30λ characteristic dimension (i.e. volumes of 10³-10⁴ cubic wavelengths). To accomplish this, an analysis of the DDA method was performed for meso-scale cases of interest especially in biological applications. Based on this study, we propose new Sommerfeld integration paths and a revised iterative algorithm that combine to provide substantial improvements in the size of the computational domain that can be modeled for a given convergence criterion.     

Amplitude and phase of light scattered by micro-scale aggregates of dielectric spheres: Comparison between theory and microwave analogy experiments

Light scattering is a useful diagnostic tool for characterization of particles. Direct scattering measurements for arbitrarily shaped micro-scale particles is difficult due to small-scale limitations. Microwave analogy is a convenient approach to realize such measurements as it enables realization of analogous experiments with larger model particles in a spectral domain where wavelengths are on centimeter scale. In the present study a test model analogous to light scattering by a micro-scale aggregate of dielectric spheres was constructed and experimentally characterized in the microwave regime. Measured amplitude and phase of the scattered field were compared with theoretical predictions obtained from quasi-exact multiple-scattering T-matrix method and discrete dipole approximation (DDA). Excellent agreement demonstrates the validities of both the experiment and the models.     

The discrete-dipole-approximation code ADDA: Capabilities and known limitations

The open-source code ADDA is described, which implements the discrete dipole approximation (DDA), a method to simulate light scattering by finite 3D objects of arbitrary shape and composition. Besides standard sequential execution, ADDA can run on a multiprocessor distributed-memory system, parallelizing a single DDA calculation. Hence the size parameter of the scatterer is in principle limited only by total available memory and computational speed. ADDA is written in C99 and is highly portable. It provides full control over the scattering geometry (particle morphology and orientation, and incident beam) and allows one to calculate a wide variety of integral and angle-resolved scattering quantities (cross sections, the Mueller matrix, etc.). Moreover, ADDA incorporates a range of state-of-the-art DDA improvements, aimed at increasing the accuracy and computational speed of the method. We discuss both physical and computational aspects of the DDA simulations and provide a practical introduction into performing such simulations with the ADDA code. We also present several simulation results, in particular, for a sphere with size parameter 320 (100-wavelength diameter) and refractive index 1.05.     

煤烟聚集粒子的光散射特性研究(英文)

基于分形理论,用计算机模拟了由球形基本粒子构成的煤烟聚集粒子。利用离散偶极子近似方法(Discrete Dipole Approximation)研究了煤烟聚集粒子的散射特性,讨论了分形煤烟聚集粒子的散射强度随煤烟聚集粒子的分形结构、大小、相对折射率及入射波波长变化情况。     

Model of light scattering by dust particles in the solar system: Applications to cometary comae and planetary regoliths

We analyze both the intensity and linear polarization of cosmic dust particles by using the physically exact superposition T-matrix method in a fixed orientation for various aggregates of spheres and DDA for the aggregates of Gaussian random spheres. We study both the spherical geometry (in cometary comae) and cylindrical slabs (for regoliths) up to 2000 monomers with size parameters less than ∼3. It is straightforward to produce the observed linear polarization in both geometries while the typically convex and strong opposition spike seems to require wide regolith geometries. The dependence of various parameters on light scattering has also been studied in a rather detailed form. In applications to the cometary polarization we can fit the data in six colors from UV to the J band at a very good accuracy. We, however, emphasize that we do not claim our model to be unique. The most important parameters here are the refractive index and the size distribution of submicron particles. Rest of the parameters has only a minor role. We also found that it is critically important to use several realizations from any assumed particle geometry model because corresponding scattering characteristics can vary quite a lot.     

Light scattering from two component systems; an analysis of the dilution experiment

The intensity of depolarized light scattering, I _dep, is calculated as a function of concentration, X, of non-spherical scatterers in a solvent of spherical non-scatterers. The possibility of finding the second rank Kirkwood g-factor, g ⁽²⁾, from measurements of I _dep versus X is discussed.     

The effect of soot particle optical inhomogenity and agglomeration on the analysis of light scattering measurements in flames

Computations have been performed for homogeneous and radially inhomogeneous spheres plus agglomerated structures composed of spherical primary units. The ranges of refractive index and particle size considered are typical of soot in flames. The effects of uncertainty in the refractive index and neglect of its radial distribution on inferring spherical particle sizes and concentrations from in situ light-scattering measurements are delineated. A framework is established for computing various scattering characteristics of agglomerated particles in terms of the scattering functions for spherical particles. The results achieved for agglomerates indicate that mean values of the particle concentration, number of units in an agglomerate and overall agglomerate size may be inferred from light-scattering data.     

随机取向烟尘团簇粒子的光学截面的数值计算

采用蒙特卡罗方法根据团簇—团簇凝聚（CCA）模型对由球形原始微粒凝聚而成的烟尘团簇粒子进行了模拟,利用离散偶极子近似（DDA）方法数值计算了不同原始微粒粒径和数目组成的随机取向的烟尘团簇粒子的总消光截面、吸收截面及散射截面等光学特性参数,研究了原始微粒粒径及数目对随机取向烟尘团簇粒子光学特性的影响。结果表明：当入射波长一定时,随机取向烟尘団簇粒子的光学特性主要取决于原始微粒的粒径和数目;烟尘团簇粒子对不同波段激光的吸收和散射存在差别,这种差别随原始微粒粒径及数目变化而变化。这一工作为研究电磁波在烟尘中的传输特性提供重要参考数据。     

T-matrix calculation via discrete dipole approximation,point matching and exploiting symmetry

We present a method of incorporating the discrete dipole approximation (DDA) method with the point matching method to formulate the T-matrix for modelling arbitrarily shaped microsized objects. The T-matrix elements are calculated using point matching between fields calculated using vector spherical wave functions and DDA. When applied to microrotors, their discrete rotational and mirror symmetries can be exploited to reduce memory usage and calculation time by orders of magnitude; a number of optimization methods can be employed based on the knowledge of the relationship between the azimuthal mode and phase at each discrete rotational point, and mode redundancy from Floquet's theorem. A ‘reduced-mode’ T-matrix can also be calculated if the illumination conditions are known.     

Measurements of Optical Trapping Efficiency for Micron-Sized Dielectric Particles in Various Surrounding Media

The maximum axial trapping efficiency Q_max has been measured in water, ethanol, butanol and octanol for polystyrene latex spheres having a diameter of 2–15μm. The effects of the diameter of the particle as well as the refractive index and the viscosity of surrounding medium have been investigated. For particles of d≥7 μm, Q_max is almost independent of particle size, while it decreases as the diameters decrease to d≦5 μm. It is also noted that Q_max is affected by the viscosity rather than the refractive index of the surrounding medium.     

分形结构对随机取向烟尘团簇粒子光散射特性的影响

利用蒙特卡罗方法对不同分形维数和分形前向因子的随机取向烟尘团簇粒子的分形结构进行了仿真,采用离散偶极子近似（DDA）方法对随机取向烟尘团簇粒子的缪勒矩阵元进行了数值计算,并与球形粒子模型进行了比较,深入探讨了烟尘团簇粒子的分形维数和分形前因子对其散射特性的影响。研究表明,等效球形粒子的光散射特性与随机取向烟尘团簇粒子的光散射特性存在很大差别,并且此差别随着团簇粒子的分形维数以及分形前向因子的增大而减小;分形维数对表征团簇粒子散射特性的缪勒矩阵元的影响在一定散射角范围内均比较明显,分形前向因子对团簇粒子的缪勒矩阵元角分布的影响与分形维数的影响类似,不过其影响相对分形维数较弱。     

随机分布烟尘团簇粒子辐射特性研究

基于分形理论,采用蒙特卡罗方法对随机分布的烟尘团簇粒子结构进行了仿真模拟,利用离散偶极子近似(discrete dipole approximation, DDA)方法研究了随机分布的烟尘团簇粒子的辐射特性,分析讨论了分形维数、原始微粒粒径和数量以及复折射率对随机分布烟尘团簇粒子辐射特性的影响.研究表明,在给定分形维数的情况下,烟尘团簇粒子的辐射特性取决于原始微粒粒径、数量及复折射率;原始微粒较小的团簇粒子,当分形维数较小时,吸收截面变化不明显,但当分形维数大于2时,吸收截面骤然增大,然而,对于具有比较大的原始微粒粒径、数量及复折射率的烟尘团簇粒子,吸收截面随着分形维数的增大而单调递减;随着分形维数的增大,团簇粒子的散射截面、消光截面及单次散射反照率均单调递增;从整体上来讲,团簇粒子的辐射特性与等效球形粒子的辐射特性存在着比较大的差别,并且这种差别随着分形维数的增大而减小.该工作对研究气溶胶粒子的辐射及气候效应具有重要的科学价值. 关键词： 烟尘团簇粒子 辐射特性 离散偶极子近似方法     

随机分布黑碳-硅酸盐混合凝聚粒子的消光特性研究

基于分形理论,采用蒙特卡罗方法对随机分布的混合凝聚粒子的空间结构进行了仿真模拟。利用Bruggeman有效介质理论得到了占有不同体积份额黑碳的内混合凝聚粒子的等效复折射率。采用离散偶极子近似方法对随机分布混合凝聚粒子在内外混合状态下的吸收、散射和消光效率因子等消光特性参量进行了数值计算,深入探讨了混合方式、容积含量、入射波长以及基本粒子粒径和数量对混合凝聚粒子消光特性的影响规律。通过将所得数值结果与T矩阵方法的数值结果进行比较发现,两种数值方法计算的结果非常相近。结果表明,随机分布混合凝聚粒子的散射效率因子对混合方式非常敏感,消光效率因子对混合方式较敏感,而吸收效率因子对混合方式不敏感。随着凝聚粒子尺度参数的增大,混合方式对散射和消光效率因子的影响逐渐显著。内外混合方式下,随着黑碳体积比的增大随机分布混合凝聚粒子的吸收、散射和消光效率因子均近似线性增大,并且增大的幅度随着粒子尺度参数的增大而增大。     

Studies on differential cross-sections of e–N2 scattering

The differential cross-sections (DCS) of the low-energy electron–N ₂ scattering are studied using the vibrational close-coupling (VCC) method and vibrational scattering potentials which include static, exchange and polarization contributions. The polarization is obtained based on the ‘better than adiabatic dipole’ (BTAD) and the ‘distributed spherical Gaussian’ (DSG) respectively. The converged (0 → 0, 0 → 1, 0 → 2, 0 → 3) DCS are obtained with the impact energies being the resonance's first two elastic scattering peaks?–?approximately 1.90 eV and 2.10 eV. Calculations from both polarization potentials agree with experimental results.     

随机取向群聚椭球粒子光散射特性研究

利用离散偶极子近似方法,考虑单元粒子之间的电磁相互作用,数值计算了随机取向的不同尺度参数、不同纵横比的群聚椭球粒子的缪勒矩阵元素,给出了各个缪勒矩阵元素的角分布曲线,探讨了随机取向的群聚椭球粒子的尺度参数、纵横比、基本粒子相对位置对其缪勒矩阵元素的影响。并将随机取向群聚椭球粒子的光散射特性与单个等效球形粒子的数值结果进行了比较。结果表明,随机取向群聚椭球粒子的光散射特性与等效球形粒子的光散射特性存在很大差别,基本粒子的形状越偏离球形,这种差别就越大; 随机取向群聚椭球粒子中椭球粒子的纵横比和相对位置对整个群聚粒子的缪勒矩阵元素存在不同程度的影响,并且此影响随着粒子尺度参数的增大而变得更加显著。