Experimental test of the Rayleigh-Debye-Gans theory for light scattering by fractal aggregates

Calibrated measurements of optical (lambda = 488-nm) scattering cross sections, in the form of Rayleigh ratios, are presented for two fractal aggregate aerosols. The aggregates have radii of gyration of approximately 280 nm, fractal dimensions of approximately 1.75, and monomer sizes of approximately 20 nm with approximately 150 monomers per cluster. One aerosol was composed of vitreous SiO2 with a refractive index of 1.46, the other of anatase TiO2 with a refractive index of 2.61. We found good agreement with the Rayleigh-Debye-Gans prediction for the scattering cross section of fractal aggregates.     

Finite-difference time-domain solution of light scattering by dielectric particles with large complex refractive indices

The finite-difference time-domain (FDTD) technique is examined for its suitability for studying light scattering by highly refractive dielectric particles. It is found that, for particles with large complex refractive indices, the FDTD solution of light scattering is sensitive to the numerical treatments associated with the particle boundaries. Herein, appropriate treatments of the particle boundaries and related electric fields in the frequency domain are introduced and examined to improve the accuracy of the FDTD solutions. As a result, it is shown that, for a large complex refractive index of 7.1499 + 2.914i for particles with size parameters smaller than 6, the errors in extinction and absorption efficiencies from the FDTD method are generally less than ~4%. The errors in the scattering phase function are less than ~5%. We conclude that the present FDTD scheme with appropriate boundary treatments can provide a reliable solution for light scattering by nonspherical particles with large complex refractive indices.     

Colors of transparent submicron suspensions on approaching the Rayleigh regime

The features of scattered and transmitted light by dilute suspensions of transparent submicron particles are investigated both in the spectral and in the perceived colorimetric domains, as a function of effective particle diameter D, particle-host refractive-index mismatch m, and scattering angle θ. Our results show that the wavelength λ-dependence of the scattering and extinction cross sections remains quite similar well beyond the Rayleigh regime up to particle sizes of a few hundreds nm, but only for specific scattering angles that depend on D and m, and tend to 90° on approaching the Rayleigh regime. Close to this limit (D/λ<1), a simple criterion that relates the perceived scattering color at θ=90° and the ratio of the sample extinction coefficients at two properly selected wavelengths is demonstrated. A comparison between computed and measured data is presented.     

Orientation-averaged light-extinction characteristics of compound particles including aggregate effects

Orientation-averaged light-extinction characteristics of compound sulfate-carbon-soot particles have been analyzed with a discrete-dipole algorithm (DDSCAT code) for r1/r2 (ratio of primary-particle radius to secondary-particle radius) in the range 7 to 1 and for wavelengths from 0.4 to 0.8 microm. It was found that compound particles above a particle radius of approximately 0.2 microm exhibit light-extinction characteristics that closely match those of a pure sulfate particle. The shielding of the carbon particle by the primary particle apparently reduces the absorption effect of the soot particle over the range of all possible orientations. In light of the fact that soot particles tend to be small in comparison with host sulfate particles, the light-extinction characteristics of compound particles are dictated by the optical properties of the host particles. This result has been applied for aerosol aggregates with log-normal size distributions. For r1/r2 > or = 2 the aggregate extinction coefficient of a group of compound particles remains within 12% of that of a group consisting only of sulfate particles. This allows for effective calculation of the overall aerosol light extinction on the basis of the optical and geometrical properties of the constituent particles without having to include a compound-geometry effect.     

Effects of polydispersity of chainlike aggregates on light-scattering properties and data inversion

A systematic evaluation of the effects of polydispersity of chainlike aggregates in terms of primary particle number density and size on the scattering quantities and data inversion is presented. For aggregates with refractive index in the range absolute value(m-1) = 0.8-1.2, average size parameter x < 0.40, and primary particle number Np < 20, it is shown that the effects of polydispersity of primary particle size on the light-scattering quantities are much stronger than the polydispersity of the number of primary particles per aggregate. For aggregates with polydisperse primary particle size, the assumption of monodispersity tends to underestimate the real and imaginary parts of the refractive index and the number of primary particles. Specifically, for values of the distribution width sigma greater than 0.10, the effect of polydispersity of the size of primary particles must be considered in the data inversion schemes. Furthermore, in the same range of values for the refractive index, particle size parameter, and primary particle number, the assumption of monodispersity for aggregates with polydisperse particle number tends to underestimate the value of the real part of the refractive index and overestimate the value of the imaginary part of the refractive index and primary particle size. However, for values of the distribution width sigma less than 0.60, the effects of polydispersity of primary particle number can be neglected. In addition, the suitable pairing sets of the measured scattering quantities for data inversion are presented and discussed.     

Finite-difference time-domain solution of light scattering and absorption by particles in an absorbing medium

The three-dimensional (3-D) finite-difference time-domain (FDTD) technique has been extended to simulate light scattering and absorption by nonspherical particles embedded in an absorbing dielectric medium. A uniaxial perfectly matched layer (UPML) absorbing boundary condition is used to truncate the computational domain. When computing the single-scattering properties of a particle in an absorbing dielectric medium, we derive the single-scattering properties including scattering phase functions, extinction, and absorption efficiencies using a volume integration of the internal field. A Mie solution for light scattering and absorption by spherical particles in an absorbing medium is used to examine the accuracy of the 3-D UPML FDTD code. It is found that the errors in the extinction and absorption efficiencies from the 3-D UPML FDTD are less than approximately 2%. The errors in the scattering phase functions are typically less than approximately 5%. The errors in the asymmetry factors are less than approximately 0.1%. For light scattering by particles in free space, the accuracy of the 3-D UPML FDTD scheme is similar to a previous model [Appl. Opt. 38, 3141 (1999)].     

Range of validity of the Rayleigh-Debye-Gans theory for optics of fractal aggregates

The range of validity of the Rayleigh-Debye-Gans approximation for the optical cross sections of fractal aggregates (RDG-FA) that are formed by uniform small particles was evaluated in comparison with the integral equation formulation for scattering (IEFS), which accounts for the effects of multiple scattering and self-interaction. Numerical simulations were performed to create aggregates that exhibit mass fractallike characteristics with a wide range of particle and aggregate sizes and morphologies, including x(p) = 0.01-1.0, ‖m - 1‖ = 0.1-2.0, N = 16-256, and D(f) = 1.0-3.0. The percent differences between both scattering theories were presented as error contour charts in the ‖m - 1‖x(p) domains for various size aggregates, emphasizing fractal properties representative of diffusion-limited cluster-cluster aggregation. These charts conveniently identified the regions in which the differences were less than 10%, between 10% and 30%, and more than 30% for easy to use general guidelines for suitability of the RDG-FA theory in any scattering applications of interest, such as laser-based particulate diagnostics. Various types of aggregate geometry ranging from straight chains (D(f) ≈ 1.0) to compact clusters (D(f) ≈ 3.0) were also considered for generalization of the findings. For the present computational conditions, the RDG-FA theory yielded accurate predictions to within 10% for ‖m - 1‖ to approximately 1 or more as long as the primary particles in aggregates were within the Rayleigh scattering limit (x(p) ≤ 0.3). Additionally, the effect of fractal dimension on the performance of the RDG-FA was generally found to be insignificant. The results suggested that the RDG-FA theory is a reasonable approximation for optics of a wide range of fractal aggregates, considerably extending its domain of applicability.     

Mie theory for light scattering by a spherical particle in an absorbing medium

Analytic equations are developed for the single-scattering properties of a spherical particle embedded in an absorbing medium, which include absorption, scattering, extinction efficiencies, the scattering phase function, and the asymmetry factor. We derive absorption and scattering efficiencies by using the near field at the surface of the particle, which avoids difficulty in obtaining the extinction based on the optical theorem when the far field is used. Computational results demonstrate that an absorbing medium significantly affects the scattering of light by a sphere.     

Light-Scattering Cross Section of Hydrophilic and Hydrophobic Silica Aggregates

The aggregation dynamics of solid particles in liquid media is currently determined by optical-based particle sizing methods. Because it can be used in situ and applied to a wide particle size range, turbidimetry is acknowledged as one of the best methods for this characterization. Although much work has been done on aggregation, some aspects are less known and require additional experimental and theoretical research. This is particularly the case of aggregation of hydrophobic particles. Corresponding aggregates are three-phase objects (solid-liquid-gas) the morphology and optical properties of which are not known. The present work rests on the turbidimetric study of hydrophilic and hydrophobic silica samples in stirred aqueous solutions. Modeling involves different aspects: aggregate morphology, aggregate optical properties, and aggregation dynamics. This article particularly emphasizes the second aspect. Fractal-like models are proved to be representative of the aggregate morphology even at small size. Light-scattering cross section of the aggregates is calculated from their averaged projected area; effective refractive index is proved to be a good parameter for modeling the optical properties of both hydrophilic and hydrophobic aggregates. Classical models of porous aggregate formation (Kusters theory) are used for describing the aggregation dynamics.     

Light-Scattering Cross Section of Hydrophilic and Hydrophobic Silica Aggregates

The aggregation dynamics of solid particles in liquid media is currently determined by optical-based particle sizing methods. Because it can be used in situ and applied to a wide particle size range, turbidimetry is acknowledged as one of the best methods for this characterization. Although much work has been done on aggregation, some aspects are less known and require additional experimental and theoretical research. This is particularly the case of aggregation of hydrophobic particles. Corresponding aggregates are three-phase objects (solid-liquid-gas) the morphology and optical properties of which are not known. The present work rests on the turbidimetric study of hydrophilic and hydrophobic silica samples in stirred aqueous solutions. Modeling involves different aspects: aggregate morphology, aggregate optical properties, and aggregation dynamics. This article particularly emphasizes the second aspect. Fractal-like models are proved to be representative of the aggregate morphology even at small size. Light-scattering cross section of the aggregates is calculated from their averaged projected area; effective refractive index is proved to be a good parameter for modeling the optical properties of both hydrophilic and hydrophobic aggregates. Classical models of porous aggregate formation (Kusters theory) are used for describing the aggregation dynamics.     

Particle-sizing methods: a stationary-phase-based comparison

Stationary-phase approximation is used to examine and compare the reliability and interpretability of two main methods of particle sizing. The first method, differential light scattering, regards spherical objects having different refractive indices. Theoretical expressions are obtained, enabling the derivation of optical and geometrical properties of the object from its scattering pattern. The second method, automated microscope imaging, is considered with theoretical implications for the finite aperture of the objective lens. It is shown that, besides the well known Rayleigh resolution limit, finite aperture must affect size measurement due to optical properties of the particles. Simulation and experimental results for both differential light scattering and microscope imaging of polystyrene beads are in good agreement with theory.     

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。     

Error analysis of Raman differential absorption lidar ozone measurements in ice clouds

A formalism for the error treatment of lidar ozone measurements with the Raman differential absorption lidar technique is presented. In the presence of clouds wavelength-dependent multiple scattering and cloud-particle extinction are the main sources of systematic errors in ozone measurements and necessitate a correction of the measured ozone profiles. Model calculations are performed to describe the influence of cirrus and polar stratospheric clouds on the ozone. It is found that it is sufficient to account for cloud-particle scattering and Rayleigh scattering in and above the cloud; boundary-layer aerosols and the atmospheric column below the cloud can be neglected for the ozone correction. Furthermore, if the extinction coefficient of the cloud is ?0.1 km(-1), the effect in the cloud is proportional to the effective particle extinction and to a particle correction function determined in the limit of negligible molecular scattering. The particle correction function depends on the scattering behavior of the cloud particles, the cloud geometric structure, and the lidar system parameters. Because of the differential extinction of light that has undergone one or more small-angle scattering processes within the cloud, the cloud effect on ozone extends to altitudes above the cloud. The various influencing parameters imply that the particle-related ozone correction has to be calculated for each individual measurement. Examples of ozone measurements in cirrus clouds are discussed.     

Light scattering of ultrafine silica particles by VUV synchrotron radiation

Vacuum ultraviolet (VUV) light scattering from ultrafine silica particles is studied with an aerosol instrument recently established at the Advanced Light Source (ALS) in Berkeley. Silica particles, size-selected by a differential mobility analyzer, are introduced into vacuum through a set of aerodynamic lenses to form a particle beam. The scattered photons from the crossing area of the VUV synchrotron beam and particle beam are detected with a rotatable VUV photon detector. The angular distributions of scattered photons (ADSP) originating from 70, 100, 200 nm diameter silica particles are measured with 145.9 and 118.1 nm synchrotron radiation. These angular distributions show strong forward scattering. The measured ADSPs are consistent with simulation of Mie scattering. The refractive indices of silica particles, 2.6 + 1.1i and 1.6 + 0.0001i for 118.1 and 145.9 nm, respectively, are obtained by fitting the measured ADSPs; the least average percentage deviations are 18% and 6%, respectively. The scattered fluxes at widely different wavelengths (visible versus VUV) also exhibit clear size sensitivity. Under comparable experimental conditions of photon fluxes and detection efficiencies, limits of particle size detection of 70 and 250 nm are obtained, respectively, when using 118.1 and 532 nm illumination. As anticipated, VUV scattering is a more sensitive probe for ultrafine particles, which will find application in detection of these ubiquitous species beyond the confines of a laboratory.     

Modeling the optical properties of mineral particles suspended in seawater and their influence on ocean reflectance and chlorophyll estimation from remote sensing algorithms

The optical properties of mineral particles suspended in seawater were calculated from the Mie scattering theory for different size distributions and complex refractive indices of the particles. The ratio of the spectral backscattering coefficient to the sum of the spectral absorption and backscattering coefficients of seawater, b(b)(lambda)/[a(lambda) + b(b)(lambda)], was analyzed as a proxy for ocean reflectance for varying properties and concentrations of mineral particles. Given the plausible range of variability in the particle size distribution and the refractive index, the general parameterizations of the absorption and scattering properties of mineral particles and their effects on ocean reflectance in terms of particle mass concentration alone are inadequate. The variations in the particle size distribution and the refractive index must be taken into account. The errors in chlorophyll estimation obtained from the remote sensing algorithms that are due to the presence of mineral particles can be very large. For example, when the mineral concentration is 1 g m(-3) and the chlorophyll a concentration is low (0.05 mg m(-3)), current global algorithms based on a blue-to-green reflectance ratio can produce a chlorophyll overestimation ranging from approximately 50% to as much as 20-fold.     

两种方法测量大气气溶胶折射率的对比分析

针对气溶胶折射率在分析大气气溶胶光学特性中的重要性,介绍两种综合利用黑碳仪、浊度计、光学粒子计数器和微脉冲激光雷达测量大气气溶胶折射率的新方法。两种方法都是根据球形粒子的Mie散射理论计算大气气溶胶的折射率,使用以上两种方法对厦门地区气溶胶折射率进行了计算和对比分析,证明了它们的合理性,分析了它们的测量精度和误差来源。     

Blood platelet aggregometer: predicted effects of aggregation, photometer geometry, and multiple scattering

The in vitro aggregation of blood platelets is usually monitored with a visible light transmittance photometer (aggregometer). These cells in plasma are large (alpha = 2pi a/lambda approximately = 16) soft (m = 1.04) particles. The factors which significantly influence transmittance include the inherent scattering properties, multiple scattering, and photometer design. Now scattering theory and numerical methods for radiative transfer are used to survey how aggregation should influence transmittance as measured with various photometers. The results should help expand the analytical power of the transmittance photometer as a tool for monitoring aggregation. Evidence is also presented that scattering by aggregates of aerosol particles, which are of a higher relative refractive index, should also be adequately predicted by these approximate methods.     

Unified inversion scheme that uses light scattering for morphological parameters and optical properties of aggregated aerosols

A robust scheme for characterizing chainlike aggregated aerosols by use of nonintrusive light-scattering measurements is presented. This scheme entails the selection of suitable scattering quantities and their optimal measurement angles; the development of an inversion algorithm to yield the complex refractive index of agglomerates m = n + ik, the primary particle diameter d(p), the number of primary particles per agglomerate N(p), the number density of agglomerates n(A), and the volume fraction of agglomerates f(v); and evaluation of the uncertainties of the inferred parameters that correspond to measuring uncertainties. The data-inversion algorithm is based on the exact formulation of light scattering for agglomerates that consist of primary particles in the Rayleigh limit and therefore has solid theoretical foundations. In addition, this approach yields all the desired parameters of the aggregated aerosols by using in situ light-scattering measurements with a minimum of possible uncertainties. Furthermore, the methodology developed here can be extended to aerosols with other types of morphology and optical property.     

Light scattering by a coated infinite cylinder in an absorbing medium

The scattering formulation for a coated infinite cylinder in an absorbing medium is presented in this paper. The cylinder is subjected to an arbitrarily polarized plane wave propagating in a general direction at the cylinder. The refractive index and magnetic permeability of the host medium, as well as those for the core and coating of the cylinder, can be real or complex. The scattering and extinction efficiencies and the scattering amplitudes are derived for both the near field and the far field. As the medium is absorbing, the "true" extinction and scattering efficiencies are derived based on the radiative energy outflow at the surface of the cylinder. The radiative efficiencies in the far field are denoted as "apparent" properties because they include absorption by the intervening medium. The influence of the refractive index and permeability of the host medium on the scattering properties of a coated cylinder is illustrated by numerical examples.     

Retrieval of aerosol refractive index from extinction spectra with a damped harmonic-oscillator band model

A new method for the retrieval of the spectral refractive indices of micrometer-sized particles from infrared aerosol extinction spectra has been developed. With this method we use a classical damped harmonic-oscillator model of molecular absorption in conjunction with Mie scattering to model extinction spectra, which we then fit to the measurements using a numerical optimal estimation algorithm. The main advantage of this method over the more traditional Kramers-Kronig approach is that it allows the full complex refractive-index spectra, along with the parameters of the particle size distribution, to be retrieved from a single extinction spectrum. The retrieval scheme has been extensively characterized and has been found to provide refractive indices with a maximum uncertainty of approximately 10% (with a minimum of approximately 0.1%). Comparison of refractive indices calculated from measurements of a ternary solution of HNO3, H2SO4, and H2O with those published in J. Phys. Chem. A 104, 783 (2000) show similar differences as found by other authors.