Scattering matrix of infrared radiation by ice finite circular cylinders

Scattering matrix characteristics of polydisperse, randomly oriented, small ice crystals modeled by finite circular cylinders with various ratios of the length to diameter (L/D) ratio are calculated by use of the exact T-matrix approach, with emphasis on the thermal infrared spectral region that extends from the atmospheric short-wave IR window to the far-IR wavelengths to as large as 30 microm. The observed ice crystal size distribution and the well-known power-law distribution are considered. The results of the extensive calculations show that the characteristics of scattering matrix elements of small ice circular cylinders depend strongly on wavelengths and refractive indices, particle size distributions, and the L/D ratios. The applicability of the power-law distribution and particle shapes for light scattering calculations for small ice crystals is discussed. The effects of the effective variance of size distribution on light scattering characteristics are addressed. It seems from the behavior of scattering matrix elements of small ice crystals that the combination of 25 and 3.979 microm has some advantages and potential applications for remote sensing of cirrus and other ice clouds.     

Limited possibility for quantifying mean particle size by logarithmic light-scattering spectroscopy

Recent studies have shown that the slope of logarithmic scattering spectroscopy of a turbid medium is related to the sizes of the scattering particles within the turbid medium. Mie theory can be used to generate a logarithmic plot of the reduced-scattering coefficient versus wavelength. According to Nilsson et al. [Appl. Opt. 37, 1256 (1998)], the slope value of a linear fit of the logarithmic scattering spectroscopy between 600 and 1050 nm can be used for direct determination of particle size. We performed similar calculations using the Rayleigh-Gans approximation and obtained an analogous overall shape with additional sinusoidal features. Our calculations indicate a possible relationship between the slope and the particle size when the size is used to calculate the slope, namely, in the forward calculation. However, because of the sinusoidal pattern, the inverse calculation to obtain the particle size from the slope may be applied only for particles with a radius of <0.13 microm in combination with 650-1050-nm light. Caution should be exercised when inverse calculation is performed to determine the scattering particle sizes in the range of radii >0.13 microm, with the slope of logarithmic scattering spectroscopy within 650-1050 nm.     

亚微米级扁椭球颗粒群的散射特性

采用T矩阵方法计算亚微米级扁椭球随机取向分布颗粒群的散射特性,研究消光截面、散射截面、吸光截面、单散射反照率、非对称因子以及散射矩阵元素与颗粒的大小、折射率、长短轴比之间的关系。结果表明,随颗粒粒径增大,消光截面、散射截面、吸光截面、非对称因子都单调增加,散射相函数F11的角分布曲线特征可以区分颗粒的大小;颗粒越偏离球形,颗粒对入射光的衰减效率越低,后向散射光强越强,在轴比不大时,前向50°内的F22/F11值可以区分颗粒的形状;折射率变化主要是对后向散射光的分布产生影响,实部、虚部的变化可分别通过F34/F11的角分布曲线、F12/F11的第一个峰值来体现。     

Mie理论在静态光散射粒度测量的应用下限研究

测量下限是光散射颗粒测试技术的关键问题。本文通过理论分析、比较归一化散射光强的分布图和构造方差函数F(d)对颗粒散射光的光强分布进行了定性和定量的讨论,对Mie散射向Rayleigh散射趋近的情况进行了分析,讨论了散射光光强大小的分布,分析了测量不同粒径的颗粒的可行性,最终得到在入射光源是波长为0.6328μm的He-Ne激光器的情况下,当粒径d取200nm以上时,不同粒径颗粒的M ie散射光强分布有较大差别,适合用静态光散射的方法来判断颗粒粒径。     

Scattering of light by polydisperse, randomly oriented, finite circular cylinders

We use the T-matrix method, as described by Mishchenko [Appl. Opt. 32, 4652 (1993)], to compute rigorously light scattering by finite circular cylinders in random orientation. First we discuss numerical aspects of T -matrix computations specific for finite cylinders and present results of benchmark computations for a simple cylinder model. Then we report results of extensive computations for polydisperse, randomly oriented cylinders with a refractive index of 1.53 + 0.008i, diameter-to-length ratios of 1/2, 1/1.4, 1, 1.4, and 2, and effective size parameters ranging from 0 to 25. These computations parallel our recent study of light scattering by polydisperse, randomly oriented spheroids and are used to compare scattering properties of the two classes of simple convex particles. Despite the significant difference in shape between the two particle types (entirely smooth surface for spheroids and sharp rectangular edges for cylinders), the comparison shows rather small differences in the integral photometric characteristics (total optical cross sections, single-scattering albedo, and asymmetry parameter of the phase function) and the phase function. The general patterns of the other elements of the scattering matrix for cylinders and aspect-ratio-equivalent spheroids are also qualitatively similar, although noticeable quantitative differences can be found in some particular cases. In general, cylinders demonstrate much less shape dependence of the elements of the scattering matrix than do spheroids. Our computations show that, like spheroids and bispheres, cylinders with surface-equivalent radii smaller than a wavelength can strongly depolarize backscattered light, thus suggesting that backscattering depolarization for nonspherical particles cannot be universally explained by using only geometric-optics considerations.     

Electromagnetic fields for a spheroidal particle with an arbitrary embedded source

A spheroidal coordinate separation-of-variables solution has been developed for the determination of the internal, near-surface, and scattered fields of a spheroid (either prolate or oblate) with an embedded source of arbitrary type, location, and orientation. Presented results for (1,0) and (1,1) electric multipoles embedded in 2:1 axis ratio prolate and oblate spheroids (equal volume sphere size parameter equal to 20) illustrate that the presence of the spheroid interface can have a profound effect on the corresponding far-field scattering pattern. The calculation procedure could be used, for example, to model the emission of inelastic scattered light (Raman, fluorescence, etc.) from biological particles of appreciably elongated (prolatelike) or appreciably flattened (oblatelike) geometries.     

Comparison of optically derived particle size distributions: scattering over the full angular range versus diffraction at near forward angles

The volume scattering function (VSF) of particles in water depends on the particles' size distribution and composition as well as their shape and internal structure. Inversion of the VSF thus provides information about the particle population. The commercially available LISST instrument measures the scattering at near forward angles to estimate the bulk size distribution of particles larger than about 1?μm. By using scattering over the full angular range (0°-180°), the recently improved VSF-inversion method [X. Zhang, M. Twardowski, and M. Lewis, Appl. Opt. 50, 1240 (2011).10.1364/AO.50.001240APOPAI0003-6935] can characterize particles in terms of particle subpopulations, which are described by their unique size distribution and composition. Concurrent deployments of the Multispectral Volume Scattering Meter and the LISST in three coastal waters (i.e., Chesapeake Bay, Mobile Bay, and Monterey Bay) allowed us to compare the size distributions derived from these two different methods. We also obtained indirect validation of the results for submicrometer particles and for the composition of particles provided by the VSF-inversion method. For particle sizes ranging from 1 to 100?μm, the concentration was shown to vary over 10 orders of magnitude, and excellent agreement was found between the two methods with a mean relative difference less than 10% for the total size distributions. The inversion results also reproduced spectral variations in the shape of the VSF, although these spectral variations were not frequently observed in our study. The increased backscattering towards the shorter wavelengths was explained by the stronger influence of submicrometer particles affecting the backscattering. Based on published measurements of cell sizes and intracellular chlorophyll-a [Chl] concentrations over a wide range of phytoplankton species and strains, [Chl] was estimated for the inverted subpopulations that were identified as phytoplankton based on their refractive index and mean sizes. The estimated [Chl] agreed well with the fluorescence-based estimates in both magnitude and trend, thus reproducing a bloom event observed at a time series station.     

Highly filled particulate thermoplastic composites: Part I Packing density of irregularly shaped particles

The packing density of irregular shaped particles greatly affects the properties of highly filled particulate composite materials. The effects of particle size distribution parameters on the packing density of fused silica powder and cristobalite flour powder of different size ranges is reported. Various size distributions, according to the log-normal function, were prepared by sieving and characterized by light scattering, using a Malvern 2600 light scattering instrument. The apparent and tap density of the various powders was used to characterize the packing density. The size distribution width was found to have a major effect on the packing density. In addition, the particle size was found to affect the packing density however, its significance depends on the size range and shape of the particles. Mixtures of powders, each having a different size distribution, behave differently. This revised version was published online in November 2006 with corrections to the Cover Date.     

Particle shape as revealed by spectral depolarization

Through a series of numerical simulations we explore some scatter effects due to nonspherical particles. Specifically, we examine the link between the aspect ratio of randomly oriented, prolate spheroidal particles and the resulting linear depolarization of the scattered light in the forward and backscatter directions. The particular objective is to detect the presence of randomly oriented particles that have a systematic size and aspect ratio. Calculations show that the spectral behavior of the linear depolarization reveals the aspect ratio of the scattering particles. The concept is demonstrated using the size, shape, and refractive index of the spore form of Bacillus globigii (BG).     

Orientation dependence in near-field scattering from TiO(2) particles

This scattering of light by small particles embedded in a continuous transparent medium is influenced not only by the bulk optical properties of the particles and the medium but also by the size, shape, and spatial arrangement of the particles-that is, by the microstructure. If the particles are close together, as in agglomerated coatings or stereolithographic suspensions, interactions between the radiation fields of adjacent particles can lead to variations in the magnitude and spatial arrangement of the scattered light in the near and the far field, which can affect the color and hiding power of a coating, the cure depth and homogeneity in stereolithography, and the threshold intensity for stimulated emission in random lasers. Our calculations of the near- and the far-field scattering distribution for 200-nm TiO(2) spheres in pairs of various orientations and in an ordered array of five particles show that, depending on the orientation of the particles with respect to the incident light, these interactions can either increase or decrease the scattering efficiency, the isotropy of the scattering, and the magnitude of the electric field strength within the matrix and the particles. In the mid-visible range, two particles in line increase the backscattering fraction by 28% and the scattering strength by 38% over that of a single particle, whereas if the particles are in the diagonal configuration the backscattering fraction and scattering strength are actually reduced by addition of the second particle. At shorter or longer wavelengths the backscattering fraction is reduced regardless of the location of the second particle, by as much as 60% when five particles are arranged in the zigzag configuration. These results are surprising in that it is generally assumed that multiple scattering enhances backscattering. Simple models of multiple scattering or scattering of two particles as a single, larger particle are inadequate to explain these results.     

Application of dynamic light scattering to the study of small marine particles

Small particles ranging from approximately 0.1 μm to several micrometers in size, which include detrital material, bacteria, and other planktonic microorganisms, make a significant contribution to light scattering in the upper ocean. The scattering properties of these particles are strongly dependent on their size, which is difficult to measure in the submicrometer range with commonly used electronic resistive counters and microscopic techniques. We examined the size of small marine particles by application of the dynamic light scattering (DLS) method. In this method the time-dependent autocorrelation function of scattered intensity by particles undergoing Brownian motion provides information about the size of particles. The samples were collected in clear oceanic waters off the coast of Southern California. The mean hydrodynamic diameter of particles, determined from the DLS measurements at a scattering angle of 45°, was 0.54μ m. This indicates that the major contribution to scattering at this angle comes rom submicrometer particles. We also described an inverse method for estimating the general slope of the size distribution of small marine particles from the mean hydrodynamic diameter. This method is based on calculations of the size distribution weighted by distribution from Mie theory and assumes that a power-law approximation represents the actual particle scattered intensity. These calculations suggested that particulate assemblage in our seawater samples was best characterized by a differential size distribution with a slope of -4.35. This estimation was supported by independent measurements of particle size distribution and the spectral beam attenuation coefficient taken from the same samples as those used for the DLS measurements. We also demonstrated that multiangle DLS measurements may be used to determine the representative value of the refractive index of particles.     

Characterizing string-of-pearls colloidal silica by multidetector hydrodynamic chromatography and comparison to multidetector size-exclusion chromatography, off-line multiangle static light scattering, and transmission electron microscopy

The string-of-pearls-type morphology is ubiquitous, manifesting itself variously in proteins, vesicles, bacteria, synthetic polymers, and biopolymers. Characterizing the size and shape of analytes with such morphology, however, presents a challenge, due chiefly to the ease with which the "strings" can be broken during chromatographic analysis or to the paucity of information obtained from the benchmark microscopy and off-line light scattering methods. Here, we address this challenge with multidetector hydrodynamic chromatography (HDC), which has the ability to determine, simultaneously, the size, shape, and compactness and their distributions of string-of-pearls samples. We present the quadruple-detector HDC analysis of colloidal string-of-pearls silica, employing static multiangle and quasielastic light scattering, differential viscometry, and differential refractometry as detection methods. The multidetector approach shows a sample that is broadly polydisperse in both molar mass and size, with strings ranging from two to five particles, but which also contains a high concentration of single, unattached "pearls". Synergistic combination of the various size parameters obtained from the multiplicity of detectors employed shows that the strings with higher degrees of polymerization have a shape similar to the theory-predicted shape of a Gaussian random coil chain of nonoverlapping beads, while the strings with lower degrees of polymerization have a prolate ellipsoidal shape. The HDC technique is contrasted experimentally with multidetector size-exclusion chromatography, where, even under extremely gentle conditions, the strings still degraded during analysis. Such degradation is shown to be absent in HDC, as evidenced by the fact that the molar mass and radius of gyration obtained by HDC with multiangle static light scattering detection (HDC/MALS) compare quite favorably to those determined by off-line MALS analysis under otherwise identical conditions. The multidetector HDC results were also comparable to those obtained by transmission electron microscopy (TEM). Unlike off-line MALS or TEM, however, multidetector HDC is able to provide complete particle analysis based on the molar mass, size, shape, and compactness and their distributions for the entire sample population in less than 20 min.     

Scattering of light by bispheres with touching and separated components

We use the T-matrix method as described by Mishchenko and Mackowski [Opt. Lett. 19, 1604 (1994)] to compute light scattering by bispheres in fixed and random orientations extensively. For all our computations the index of refraction is fixed at a value 1.5 + 0.005i, which is close to the refractive index of mineral tropospheric aerosols and was used in previous extensive studies of light scattering by spheroids and Chebyshev particles. For monodisperse bispheres with touching components in a fixed orientation, electromagnetic interactions between the constituent spheres result in a considerably more complicated interference structure in the scattering patterns than that for single monodisperse spheres. However, this increased structure is largely washed out by orientational averaging and results in scattering patterns for randomly oriented bispheres that are close to those for single spheres with size equal to the size of the bisphere components. Unlike other nonspherical particles such as cubes and spheroids, randomly oriented bispheres do not exhibit pronounced enhancement of side scattering and reduction of backscattering and positive polarization at side-scattering angles. Thus the dominant feature of light scattering by randomly oriented bispheres is the single scattering from the component spheres, whereas the effects of cooperative scattering and concavity of the bisphere shape play a minor role. The only distinct manifestations of nonsphericity and cooperative scattering effects for randomly oriented bispheres are the departure of the ratio F(22)/F(11) of the elements of the scattering matrix from unity, the inequality of the ratios F(33)/F(11) and F(44)/F(11), and nonzero linear and circular backscattering depolarization ratios. Our computations for randomly oriented bispheres with separated wavelengthsized components show that the component spheres become essentially independent scatterers at as small a distance between their centers as 4 times their radii.     

Information content of the scattering matrix for spheroidal particles

The T-matrix method is shown to be an efficient and accurate procedure for calculating the scattering matrix for randomly oriented nonspherical particles. Calculated scattering matrix elements for spheroidal particles are identical to those obtained by the spheroidal harmonic approach. T-matrix calculations for a randomly oriented finite length cylinder agree well with microwave scattering measurements. Analysis of the information content of the angular variation of the matrix elements for a set of moderately sized absorbing spheroidal particles is presented. It is found that the Fourier spectrum of the phase function and a parameter related to the depolarization ratio contain particle size and shape information, respectively.     

Light scattering by a multilayered spheroidal particle

The light scattering problem for a confocal multilayered spheroid has been solved by the extended boundary condition method with a corresponding spheroidal basis. The solution preserves the advantages of the approach applied previously to homogeneous and core-mantle spheroids, i.e., the separation of the radiation fields into two parts and a special choice of scalar potentials for each of the parts. The method is known to be useful in a wide range of the particle parameters. It is particularly efficient for strongly prolate and oblate spheroids. Numerical tests are described. Illustrative calculations have shown that the extinction factors converge to average values with a growing number of layers and how the extinction varies with a growth of particle porosity.     

Theoretical investigation on heat transfer to burning char of spheroidal particles

The combustion of biomass fuel provides efficient and inexpensive utilization of solid biomass. Biomass particles generally exhibit non-spherical shapes, which affect the heat and mass transfer and further the char surface reactions. The prolate and oblate spheroidal particles are considered presently. The energy balance is employed for the gas phase near the particle in spheroidal coordinate system. A theoretical study is conducted on the char combustion of the spheroidal particles under either static conditions or forced convection. The expressions for the Nusselt numbers of both prolate and oblate spheroids are obtained. The char combustion rates for the spheroidal particles are affected by the Nusselt number and the particle surface area.     

Light scattering from nonspherical airborne particles: experimental and theoretical comparisons

A laser light-scattering instrument has been designed to permit an investigation of the spatial intensity distribution of light scattered by individual airborne particles constrained within a laminar flow, with a view to providing a means of classifying the particles in terms of their shape and size. Ultimately, a means of detecting small concentrations of potentially hazardous particles, such as asbestos fiber, is sought. The instrument captures data relating to the spatial distribution of light scattered from individual particles in flow. As part of an investigation to optimize orientation control over particles within the sample airstream, the instrument has been challenged with nonspherical particles of defined shape and size, and a simple theoretical treatment based on the Rayleigh-Gans formalism has been used to model the spatial intensity distribution of light scattered from these particle types and hence derive particle orientation data. Both experimental and theoretical scattering data arepresented, showing good agreement for all particle types examined.     

Internal and near-surface electromagnetic fields for an absorbing spheroidal particle with arbitrary illumination

A previously developed [Appl. Opt. 34, 5542 (1995)] theoretical procedure for the calculation of the internal and the near-surface electromagnetic fields for nonabsorbing spheroidal particles with arbitrary monochromatic illumination has been generalized to permit solutions for absorbing (i.e., complex relative index of refraction) spheroidal particles. Calculations are presented that demonstrate the general effects of absorption on the internal and near-surface electromagnetic-field distributions for the particular case of a plane wave that is incident upon a 2:1-axis-ratio oblate spheroidal particle.     

Morphology-dependent resonances of nearly spherical particles in random orientation

We use precise T-matrix calculations for prolate and oblate spheroids, Chebyshev particles, and spheres cut by a plane to study the evolution of Lorenz-Mie morphology-dependent resonances (MDRs) with increasing asphericity of nearly spherical particles in random orientation. We show that, in the case of spheroids and Chebyshev particles, the deformation of a sphere by as little as one hundredth of a wavelength essentially annihilates supernarrow MDRs, whereas significantly larger asphericities are needed to suppress broader resonance features. The MDR position and profile are also affected when the deviation of the particle shape is increased from that of a perfect sphere. In the case of a sphere cut by a plane, the supernarrow MDRs are much more resistant to an increase in asphericity and do not change their position and profile. These findings are consistent with the widely accepted physical interpretation of the Lorenz-Mie MDRs.