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.     

Light scattering modeling of small feldspar aerosol particles using polyhedral prisms and spheroids

The use of simplified particle shapes for modeling scattering by irregularly shaped mineral-dust particles is studied using polyhedral prisms and spheroids as model particles. Simulated phase matrices averaged over shape and size distributions at wavelength 633 nm are compared with a laboratory-measured phase matrix of feldspar particles with known size distribution with effective radius of . When an equi-probable shape distribution is assumed, prisms and oblate spheroids agree with measurements to a similar degree, whereas prolate spheroids perform markedly better. Both spheroids and prisms perform much better than spheres. When an automatic fitting method is applied for finding optimal shape distributions, it is found that the most elongated spheroids are most important for good fits, whereas nearly-spherical spheroids are generally of very little importance. The phase matrices for the different polyhedral prisms, on the other hand, are found to be similar, thus their shape-averaged phase matrices are insensitive to the shape distribution assumed. For spheroids, a simple parameterization for the shape distribution, where weights increase with increasing departure from spherical shape, is proposed and tested. This parameterization improves the fit of most phase matrix elements attained with an equi-probable shape distribution, and it performs particularly well for reproducing the measured phase function.     

具有各向异性的梯度颗粒复合材料的有效介电响应

本文研究了具有梯度壳层椭球颗粒复合体系的有效介电响应，在稀释条件下用准静态近似方法, 推导了颗粒壳层具有任意介电梯度形式的椭球颗粒复合体系的有效介电常数和部分共振条件的一般表达式。并以壳层的介电常数为主轴的幂函数形式为例，得出了通过调节壳层的介电梯度形式、颗粒的结构和形状,可以提高该体系的有效介电常数和实现部分共振的结论。     

Light-scattering by optically soft randomly oriented spheroids

In the framework of the Rayleigh–Gans–Debye approximation and anomalous diffraction approaches, the light scattering characteristics of randomly oriented spheroids have been investigated. It has been proved that the system of randomly oriented spheroids is equivalent to the system of polydisperse spherical particles that have the same values of volume and surface area as nonspherical particles. The power law size distribution meeting these requirements has been obtained.     

Evidence for particle size–shape correlations in the optical properties of silicate clay aerosol

Accurate modeling of the optical properties of atmospheric mineral dust is important for climate modeling calculations and remote sensing data retrievals. Atmospheric mineral dust in the accumulation mode size range is often rich in silicate clays including kaolinite and illite. This is important because dust optical properties depend on particle shape, and fundamental clay particles are known to consist of very thin flakes.In this combined laboratory and modeling study, we investigate the optical properties (IR extinction and visible light scattering) of two samples of silicate clay dust aerosol, kaolinite and illite. Particle size distributions are measured simultaneously with the optical properties. T-Matrix theory based simulations using a spheroidal particle approximation are compared with experimental data. We find that the full range of visible scattering and polarimetry data, and IR extinction profiles are not well fit by assuming a single size–shape distribution for the aerosol. In contrast, a simple bimodal distribution model that treats small particles (fundamental clay flakes) in the distribution as highly eccentric oblate spheroids with axial ratio parameters ≥5, but approximates larger particles by a more moderate shape distribution with axial ratio parameters <3, gives better agreement with the full range of experimental data. These conclusions are consistent with mineralogical data on the dimensions of fundamental clay particles.     

Using simple particle shapes to model the Stokes scattering matrix of ensembles of wavelength-sized particles with complex shapes: possibilities and limitations

We investigate to what extent the full Stokes scattering matrix of an ensemble of wavelength-sized particles with complex shapes can be modeled by employing an ensemble of simple model shapes, such as spheres, spheroids, and circular cylinders. We also examine to what extent such a simple-shape particle model can be used to retrieve meaningful shape information about the complex-shaped particle ensemble. More specifically, we compute the Stokes scattering matrix for ensembles of randomly oriented particles having several polyhedral prism geometries of different sizes and shape parameters. These ensembles serve as proxies for size-shape mixtures of particles containing several different shapes of higher geometrical complexity than the simple-shaped model particles we employ. We find that the phase function of the complex-shaped particle ensemble can be accurately modeled with a size distribution of volume-equivalent spheres. The diagonal elements of the scattering matrix are accurately reproduced with a size-shape mixture of spheroids. A model based on circular cylinders accurately fits the full scattering matrix including the off-diagonal elements. However, the modeling results provide us with only a rough estimate of the effective shape parameter of the complex-shaped particle ensemble to be modeled. They do not allow us to infer detailed information about the shape distribution of the complex-shaped particle ensemble.     

An Ellipsoidal Model for Small Multilayer Particles

This paper presents an ellipsoidal model that is constructed for small layered nonspherical particles and methods for constructing “effective” multilayer ellipsoids, the light-scattering properties of which would be close to the corresponding properties of original particles. In the case of axisymmetric particles, prolate or oblate spheroids (ellipsoids of revolution) are implied. Numerical calculations of the polarizability and scattering cross sections of small layered nonspherical particles, including nonconfocal (similar) spheroids, Chebyshev particles, and pseudospheroids, are performed by different approximate and rigorous methods. Approximate approaches involve the use of an ellipsoidal model, in which the polarizability of a layered particle is determined in two ways. In the first case, the polarizability is calculated in the approximation of confocal spheroids, while, in the second case, it is sought as a linear combination of the polarizabilities of embedded spheroids proportionally to the volumes of layers. Among rigorous methods, the extended boundary conditions method and the generalized separation of variables method are applied. On the basis of a comparison of the results obtained with rigorous and approximate approaches, their drawbacks and advantages are discussed.     

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%.     

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.     

Optical three-dimensional shape analysis of metallic nanoparticles after laser-induced deformation

The 3D shape of Ag nanoparticles in glass irradiated by fs laser pulses is investigated by optical spectroscopy. It is shown that in general spheroids are produced with their symmetry axis oriented along the direction of the linear laser polarization. Depending on the actual irradiation conditions, oblate or prolate spheroids are obtained. The halo of small Ag clusters and Ag ions around the reshaped particles causes a redshift of the surface plasmon resonances via refractive index increase.     

Modeling the radiative properties of nonspherical soil-derived mineral aerosols

Mineral dust aerosols have complex nonspherical shapes and varying composition. This study utilizes data on morphology (size and shape) and composition of dust particles to determine the extent to which the optical properties of real particles differ from those of spheres. A method for modeling the optical properties of complex particle mixtures is proposed. The method combines dust particle composition-shape-size (CSS) distributions reconstructed from the electron microscopy data, effective medium approximations and discrete dipole approximation. The method is used to compute optical characteristics of realistic dust mixtures representative of Saharan and Asian dust. We demonstrate that considered CSS distributions result in various differences in the extinction coefficient, single scattering albedo, asymmetry parameter and the scattering phase function relative to the volume-equivalent spheres and the mixtures of the randomly oriented oblate and prolate spheroids. Implications of these differences for radiation/climate modeling and remote sensing are discussed.     

Electrostatic solution and rayleigh approximation for small nonspherical particles in a spheroidal basis

The electrostatic problem for the case of axially symmetric particles is analyzed in a spheroidal basis. In this case, the wavenumber is zero and Maxwell’s equations are reduced to the Laplace equation for scalar potentials. An alternative approach involves solving integral equations that are similar to those obtained within the framework of the extended boundary conditions method. The scalar potentials are represented as expansions in terms of eigenfunctions of the Laplace equation in a spheroidal frame of reference, and unknown expansion coefficients are determined from an infinite set of linear algebraic equations (the separation of variables method). These two approaches yield exact solutions of the problem in the case of axially symmetric particles, which coincide with known solutions in particular cases. Investigation of infinite systems allowed finding the boundaries where these algorithms are valid. Numerical calculations showed that, for spheroidal Chebyshev particles (i.e., perturbed spheroids), the Rayleigh approximation based on the electrostatic solution is applicable in a wide range of the problem parameters and is in fair agreement with the results obtained using the discrete dipole approximation.     

Viscosity coefficients for nuclear fission

An expression for the energy dissipation during nuclear fission (or heavy-ion) processes has been derived in the first-order viscosity approximation. Irrotational flow and incompressibility have been assumed in order to calculate a quadratic form for the heat production, microscopically interpreted as particle-hole excitations. A modified algebraic parameterization of the nuclear shape has been found, which is more suitable than the usual ones to describe shapes close to spheroids (or spheres). Furthermore, it allows for analytical solutions of the fluid equations for one degree of freedom (and in special eases of the nuclear shapes, for all degrees).     

Effects of particle/matrix interface and strengthening mechanisms on the mechanical properties of metal matrix composites

A randomly distributed multi-particle model considering the effects of particle/matrix interface and strengthening mechanisms introduced by the particles has been constructed. Particle shape, distribution, volume fraction and the particles/matrix interface due to the factors including element diffusion were considered in the model. The effects of strengthening mechanisms, caused by the introduction of particles on the mechanical properties of the composites, including grain refinement strengthening, dislocation strengthening and Orowan strengthening, are incorporated. In the model, the particles are assumed to have spheroidal shape, with uniform distribution of the centre, long axis length and inclination angle. The axis ratio follows a right half-normal distribution. Using Monte Carlo method, the location and shape parameters of the spheroids are randomly selected. The particle volume fraction is calculated using the area ratio of the spheroids. Then, the effects of particle/matrix interface and strengthening mechanism on the distribution of Mises stress and equivalent strain and the flow behaviour for the composites are discussed.     

Effects of dislocations on the energy loss of charged particles in hyperchanneling

A simple model to calculate the effects of dislocations on the energy loss of charged particles in proper axial channeling (hyperchanneling) is discussed. The cylindrically symmetric potential around the channel axis is obtained in the continuum approximation for 〈110〉 channel of diamond structure and 〈100〉 channels of fcc and bcc crystals. As in recent work planar case, the channel curvature due to dislocations is approximated by an arc of constant radius which is determined from the displacement equations for the dislocation. An analytical expression for the change in the energy loss of initially well channeled particles is obtained for channels with small curvature.     

Light Scattering by Small Multilayer Nonconfocal Spheroids Using Suitable Spheroidal Basis Sets

Optics and Spectroscopy - We construct a Rayleigh approximation for multilayer particles the layer boundaries of which are nonconfocal spheroids. The geometry of the problem is taken into account...     

Attenuation and scattering of light by a system of chaotically oriented axially symmetric particles: Analytical averaging in the modified <Emphasis Type="Italic">T</Emphasis>-matrix method

A procedure for analytical averaging of the attenuation and scattering cross sections for systems of chaotically oriented axially symmetric particles was developed for the first time within the framework of the modified T-matrix method and the method of separation of variables for spheroids. These approaches essentially complement each other: one is applicable to axially symmetric scatterers of different shape but is inefficient if the ratio of the maximum to the minimum size of the particles exceeds 3–5; the other is applicable only to spheroids, but the ratio of the major semiaxis to the minor one can be considerable, for example, 100 and larger.     

Inversion of visible optical extinction data for spheroid particle size distribution based on PCA

The problem of light scattering properties of spheroid particles is studied, and a general approach is presented for calculating the single particle light scattering of spheroids. In this approach, the extinction efficiency of spheroid particles can be calculated by combining the spline interpolation of T matrix method and ADA (anomalous diffraction approximation) theory. Furthermore, the retrieval of spheroid particle size distribution is performed in the dependent mode and a selection method about the optical extinction data is proposed based on PCA (principle component analysis) of first derivative corresponding to the raw optical extinction. By calculating the contribution rate of first derivative corresponding to the raw optical extinction, the optical extinction with more significant features can be selected as the inversion optical extinction data. In this way, the selected optical extinction has less information redundancy and higher capacity of resisting noise disturbance. Simulation experiments indicate that the spheroid particle size distributions obtained with the proposed method coincide fairly well with the given distributions, which provides a simple, reliable and efficient method to retrieve the spheroid particle size distribution using the optical extinction data.     

Preliminary results of a non-spherical aerosol method for the retrieval of the atmospheric aerosol optical properties

There is experimental evidence that the non-sphericity of certain atmospheric particles can cause scattering properties different from those predicted by standard Mie theory. Numerous studies indicate the need to consider the presence of non-spherical particles in modeling the optical properties of atmospheric aerosols. On the other hand, natural aerosols show a great variety of shapes, making difficult a realistic choice of a particle shape (or shape mixture) model. In this paper, we test a parameterization of the particle shape in the retrieval of size distribution, phase function, single scattering albedo and asymmetry parameter from direct and sky-radiance measurements. For this purpose we have substituted the Kernel based on the Mie theory included in the model SKYRAD.PACK by one derived for non-spherical particles. The method is applied under different atmospheric conditions, including Saharan dust outbreak, polluted and local mineral episodes. We compare the results with those obtained by the well known spheroids algorithm used in the AERONET network.     

Constraints on PSC particle microphysics derived from lidar observations

Based on extensive T-matrix computations of light scattering by polydispersions of randomly oriented, rotationally symmetric nonspherical particles, we analyze existing lidar observations of polar stratospheric clouds (PSCs) and derive several constraints on PSC particle microphysical properties. We show that sharp-edged nonspherical particles (finite circular cylinders) exhibit less variability of lidar backscattering characteristics with particle size and aspect ratio than particles with smooth surfaces (spheroids). For PSC particles significantly smaller than the wavelength, the backscatter color index and the depolarization color index β are essentially shape independent. Observations for type Ia PSCs can be reproduced by spheroids with aspect ratios larger than 1.2, oblate cylinders with diameter-to-length ratios greater than 1.6, and prolate cylinders with length-to-diameter ratios greater than 1.4. The effective equal-volume-sphere radius for type Ia PSCs is about 0.8 μm or larger. Type Ib PSCs are likely to be composed of spheres or nearly spherical particles with effective radii smaller than 0.8 μm. Observations for type II PSCs are consistent with large ice crystals (effective radius greater than 1 μm) modeled as cylinders or prolate spheroids.