Light scattering by Gaussian random ellipsoid particles: First results with discrete-dipole approximation

We introduce the stochastic geometry of a Gaussian random ellipsoid (GE) and, with the discrete-dipole approximation, carry out preliminary computations for light scattering by wavelength-scale GE particles. In the GE geometry, we describe the base ellipsoid by the three semiaxes a?b?c. The axial ratios b:a and c:a appear as two shape parameters additional to those of the Gaussian random sphere geometry (GS). We compare the scattering characteristics of GE particles to those of ellipsoids. Introducing irregularities on ellipsoids smoothens the angular scattering characteristics, in a way analogous to the smoothening of spherical particle characteristics in the case of GS particles.     

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.     

Geometrical optics approximation for light scattering by absorbing spherical particles

By means of geometrical optics, an approximation method is presented to compute the light scattering intensity of absorbing spherical particles illuminated by a plane wave. For absorbing particles, the effective refractive index and the effective refractive angle are related to the complex refractive index and incident angle. The formulas for calculation of the break of phases of reflection and refraction, which are different from the case of transparent particles, are exactly derived. Verification of the geometrical optics approximation (GOA) was performed by case studies and comparison of the present results with the Mie scattering. It is found that agreement between the GOA and the Mie theory is excellent in forward directions for weakly/moderately absorbing particles. Differently, for strongly absorbing particles, good agreement between the calculation methods is in the forward directions and large scattering angles. The agreement between the GOA and the Mie theory is better for larger particles.     

Polarization of light backscattered by small particles

We study scattering of light by wavelength-scale spherical, cubic, and spheroidal particles as well as clusters of spherical particles for equal-volume-sphere size parameters 4≤x≤10 and refractive indices 1.1≤m≤2.0. Such particles exhibit three specific features in the regime of backscattering: first, the intensity shows a backscattering peak; second, the degree of linear polarization for unpolarized incident light is negative; and, third, the depolarization ratio is double-lobed. We find that the overall characteristics of the scattering-matrix elements can be explained by an internal field composed of waves propagating in opposite directions near the particle perimeter and forming standing waves, as well as a wave propagating forward with the wavelength of the internal medium. When moving from the central axis of the particle toward its perimeter, the internal field changes from a forward-propagating wave with a wavelength dictated by the particle refractive index toward a standing wave with an apparent wavelength of the surrounding medium. The mapping of the internal field to the scattered far field is like an interference dial where rotation of the dial by a quarter of a wavelength on the particle perimeter results in a change from a destructive to constructive interference feature in the angular patterns (or vice versa). The dial is a manifestation of a well-known rule of thumb: the number of maxima or minima in the scattering-matrix elements is given by the size parameter. We explain the backscattering peak as deriving from the backward-propagating internal wave near the particle perimeter. Negative polarization follows from the spatial asymmetry of the internal fields: inside the particle, the fields are amplified near the central plane perpendicular to the polarization state of incident light, resulting in more pronounced interference effects for the perpendicular polarization than for the parallel polarization. The double-lobe feature in the depolarization results from the same internal-field structure with leading cross-polarized fields located slightly different from the copolarized fields. We discuss practical implications of these findings for the retrieval of particle sizes, shapes, and refractive indices from observations and laboratory experiments.     

Arbitrary direction incident Gaussian beam scattering by multispheres

Based on spherical vector wave functions and their coordinate rotation theory,the field of a Gaussian beam in terms of the spherical vector wave functions in an arbitrary unparallel Cartesian coordinate system is expanded.The beam shape coefficient and its convergence property are discussed in detail.Scattering of an arbitrary direction Gaussian beam by multiple homogeneous isotropic spheres is investigated.The effects of beam waist width,sphere separation distance,sphere number,beam centre positioning,and incident angle for a Gaussian beam with two polarization modes incident on various shaped sphere clusters are numerically studied.Moreover,the scattering characteristics of two kinds of shaped red blood cells illuminated by an arbitrary direction incident Gaussian beam with two polarization modes are investigated.Our results are expected to provide useful insights into particle sizing and the measurement of the scattering characteristics of blood corpuscle particles with laser diagnostic techniques.     

Optimizing the discrete-dipole approximation for sequences of scatterers with identical shapes but differing sizes or refractive indices

We study scattering of light by small particles with identical shapes but either moderately differing sizes or refractive indices by utilizing the discrete-dipole approximation (DDA). Assuming that accurate DDA solutions are available for either a sequence of sizes or refractive indices, we initialize the iterative conjugate gradient solver for a new size or refractive index by making “educated guesses” of the electric field vectors using classical Lagrange, rational-function, and modified Adams–Bashforth–Moulton extrapolation schemes. In the present pilot study, we assess the initialization schemes for spherical and cubic particles. As compared to the common initialization using the incident electric field, we show that careful extrapolation can significantly reduce the number of iterations. At best, the computing time can decrease by an order of magnitude whereas, typically, the improvement is some tens of percent for sizes comparable to the wavelength. In solving large numbers of single-particle scattering problems, initialization via extrapolation can yield substantial savings in computing time. In particular, the present approach should prove useful when the precise scatterer sizes and refractive indices are unknown, e.g., when interpreting astronomical observations of atmosphereless solar-system objects and experimental measurements.     

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.     

Optical modeling of vesicular volcanic ash particles

We present a realistic shape model for nonspherical, vesicular particles and use the model to derive single-scattering properties of volcanic fine-ash particles. Light-scattering computations with discrete-dipole approximation reveal that, qualitatively, scattering by the model particles resembles that of the measured, real volcanic ash particles. Comparison of compact and vesicular ash shows that porosity promotes positive degree of linear polarization and decreases the depolarization ratio for both large and small vesicles. Yet, the single-scattering properties of ash particles with large vesicles are found to be surprisingly similar to those of compact ash particles. A comparison with Mie computations of equal-volume spheres indicates that for small size parameters, the spherical shape underestimates the asymmetry parameter of volcanic ash particles; whereas, for larger size parameters, it is overestimated.     

Light scattering by small feldspar particles simulated using the Gaussian random sphere geometry

The single-scattering properties of Gaussian random spheres are calculated using the discrete dipole approximation. The ensemble of model particles is assumed to be representative for a feldspar dust sample that is characteristic for weakly absorbing irregularly shaped mineral aerosol. The morphology of Gaussian random spheres is modeled based on a statistical shape analysis using microscope images of the dust sample. The size distribution of the dust sample is based on a particle sizing experiment. The refractive index of feldspar is estimated using literature values. All input parameters used in the light scattering simulations are thus obtained in an objective way based on the true properties of the mineral sample. The orientation-averaged and ensemble-averaged scattering matrices and cross sections of the Gaussian random spheres are compared with light scattering simulations using spheroidal shape models which have been shown to be applicable to the feldspar sample. The Gaussian random sphere model and the spheroidal shape model are assessed using the measured scattering matrix of the feldspar dust sample as a reference. Generally, the spheroidal model with strongly elongated prolate and strongly flattened oblate shapes agrees better with the measurement than the Gaussian random sphere model. In contrast, some features that are characteristic for light scattering by truly irregular mineral dust particles are rendered best by the Gaussian random sphere model; these features include the flat shape of the phase function and a minimum in the scattering matrix element F₂₂/F₁₁ as a function of the scattering angle.     

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.     

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。     

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。     

Spectral shifts produced by scattering of Rectangular Gaussian Schell Model sources from a deterministic medium

Within the accuracy of the first-order Born approximation, we investigate the scattering of Rectangular Gaussian Schell Model (RGSM) sources incident upon a deterministic medium. The analytical expression for the far-zone scattered spectrum is derived. Numerical results show that red shift or blue shift can be produced in the far-zone scattered spectrum, and the spectral shifts are mainly influenced by the scattering direction and the source parameters (i.e., the source width and the source correlation widths along the x and y directions).     

Monitoring of pathogen carrying air-borne tea dust particles by light scattering

In order to investigate whether tea (Camellia sinensis (L.) Kuntze) dust particles could be a possible carrier of the pathogen contaminated Mycobacterium a biotechnical procedure was used, and to verify the possibility of monitoring this dust, a laser based light scattering setup was designed and fabricated. Experiments were carried out using the strain Mycobacterium smegmatis mc² 155 as a model organism to study the effect on tea dust particles. Light scattering investigations on both M. smegmatis contaminated and uncontaminated tea dust particle samples were carried out as a function of scattering angle at 543.5, 594.5 and 632.5 nm wavelengths. The results have shown that the behavior of tea dust samples both with and without Mycobacterium varies significantly for all the three different incident laser wavelengths.     

Stability in Debye series calculation for light scattering by absorbing particles and bubbles

The Debye-series decomposition is of importance for understanding of light scattering features and for the validity of the geometrical optics approximation to light scattering. The numerical stability and accuracy for calculating light scattering with Debye series is studied and an improved algorithm is proposed in this work. The ratios of the Riccati-Bessel functions and the logarithmic derivatives of the Riccati-Bessel functions are employed and calculated with proper recurrences. Exemplifying results are provided to show the improvement of the algorithm.     

DDA simulations of light scattering by small irregular particles with various structure

We present DDA investigations of light scattering by irregular particles whose size is comparable with wavelength. We consider four types of randomly irregular particles: strongly damaged spheres, rough-surface spheres, pocked spheres, and agglomerated debris particles. Each type of particle is generated with a well defined algorithm producing an ensemble of stochastically different particles that have a common origin. The different types of irregular particles produce different angular dependencies of intensity and linear polarization degree. Transformation of phase curves of intensity and polarization with changing size parameter for irregular particles tends to be more monotonic, unlike spheres. We find that the magnitude of the negative polarization branch (NPB) tends to shrink as particle absorption increases; whereas, the maximal value and position of the positive polarization branch tends to increase. The most frequently observed shape of the negative polarization at small phase angles is asymmetric with a shift of the minimum position towards the angle of polarization sign inversion. All types of considered irregular particles reveal such asymmetry at x<10. Symmetric negative polarization branches occur seldom. The necessary conditions for their appearance are a relatively large size parameter x?10 to 12 and low absorption.     

Computer programs for light scattering by particles with inclusions

We present a comparison of computational results from light scattering by spherical particles with inclusions. The different simulation methods like the T-matrix method, multiple multipole method and the method of separation of variables are presented shortly. Exemplary numerical simulations involve scattering by particles with one or two spherical inclusions and scattering by particles with non-spherical inclusions.     

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.