Concept of the equiphase sphere for light scattering by nonspherical dielectric particles

We introduce the concept of the equiphase sphere for light scattering by nonspherical dielectric particles. This concept facilitates the derivation of a simple analytical expression for the total scattering cross section of such particles. We tested this concept for spheroidal particles and obtained a bound on the minor-to-major axis ratio for the valid application of this technique. We show that this technique yields results that agree well with the rigorous numerical solution of Maxwell's equations obtained with the finite-difference time-domain method. The new technique has the potential to be extended to the study of light scattering by arbitrarily shaped convex dielectric particles.     

Computation of light scattering by axisymmetric nonspherical particles and comparison with experimental results

A laboratory prototype of a novel experimental apparatus for the analysis of spherical and axisymmetric nonspherical particles in liquid suspensions has been developed. This apparatus determines shape, volume, and refractive index, and this is the main difference of this apparatus from commercially available particle analyzers. Characterization is based on the scattering of a monochromatic laser beam by particles [which can be inorganic, organic, or biological (such as red blood cells and bacteria)] and on the strong relation between the light-scattering pattern and the morphology and the volume, shape, and refractive index of the particles. To keep things relatively simple, first we focus attention on axisymmetrical particles, in which case hydrodynamic alignment can be used to simplify signal gathering and processing. Fast and reliable characterization is achieved by comparison of certain properly selected characteristics of the scattered-light pattern with the corresponding theoretical values, which are readily derived from theoretical data and are stored in a look-up table. The data in this table were generated with a powerful boundary-element method, which can solve the direct scattering problem for virtually arbitrary shapes. A specially developed fast pattern-recognition technique makes possible the on-line characterization of axisymmetric particles. Successful results with red blood cells and bacteria are presented.     

Equiphase-sphere approximation for analysis of light scattering by arbitrarily shaped nonspherical particles

We extend the previously proposed concept of equiphase sphere (EPS) to analyze light-scattering properties of arbitrarily shaped particles. Our analyses based on the Wentzel-Kramers-Brillouin technique and numerical studies based on the finite-difference time-domain method demonstrate that a wide range of irregularly shaped particles can be approximated as their equivalent equiphase ellipsoids to determine their total scattering cross-section (TSCS) spectra. As a result, a simple expression given by the EPS approximation can be used to calculate the TSCS spectra of these particles. We find that the accuracy of the EPS approximation is influenced by both the magnitude and the geometric scale of the surface perturbation of the particle, and we derive validity conditions of the EPS approximation to guide the practical application of this method.     

Application of the pseudospectral time-domain method to the scattering of light by nonspherical particles

The pseudospectral time-domain (PSTD) method is a powerful approach for computing the single-scattering properties of arbitrarily shaped particles with small-to-moderate-sized parameters. In the PSTD method, the spatial derivative approximation based on the spectral method is more accurate than its counterpart based on the finite-difference technique. Additionally, the PSTD method can substantially diminish accumulated errors that increase with the spatial scale and temporal duration of simulation. We report on the application of the PSTD method to the scattering of light by nonspherical ice particles. The applicability of the PSTD method is validated against the Lorenz-Mie theory and the T-matrix method. The phase functions computed from the PSTD method and the Lorenz-Mie theory agree well for size parameters as large as 80. Furthermore, the PSTD code is also applied to the scattering of light by nonspherical ice crystals, namely, hollow hexagonal columns and aggregates, which are frequently observed in cirrus clouds. The phase functions computed from the PSTD method are compared with the counterparts computed from the finite-difference time-domain (FDTD) method for a size parameter of 20 and an incident wavelength of 3.7 microm. The comparisons show good agreement between the two methods.     

Geometric-optics-integral-equation method for light scattering by nonspherical ice crystals

A new geometric-optics model has been developed for the calculation of the single-scattering and polarization properties for arbitrarily oriented hexagonal ice crystals. The model uses the ray-tracing technique to solve the near field on the ice crystal surface, which is then transformed to the far field on the basis of the electromagnetic equivalence theorem. From comparisons with the results computed by the finite-difference time domain method, we show that the novel geometric-optics method can be applied to the computation of the extinction cross section and single-scattering albedo for ice crystals with size parameters along the minimum dimension as small as ~6. Overall agreement has also been obtained for the phase function when size parameters along the minimum dimension are larger than ~20. We demonstrate that the present model converges to the conventional ray-tracing method for large size parameters and produces single-scattering results close to those computed by the finite-difference time domain method for size parameters along the minimum dimension smaller than ~20. The present geometric-optics method can therefore bridge the gap between the conventional ray-tracing and the exact numerical methods that are applicable to large and small size parameters, respectively.     

Absorption and scattering properties of dense ensembles of nonspherical particles

The purpose of this work is to show that an appropriate multiple T-matrix formalism can be useful in performing qualitative studies of the optical properties of colloidal systems composed of nonspherical objects (despite limitations concerning nonspherical particle packing densities). In this work we have calculated the configuration averages of scattering and absorption cross sections of different clusters of dielectric particles. These clusters are characterized by their refraction index, particle shape, and filling fraction. Computations were performed with the recursive centered T-matrix algorithm (RCTMA), a previously established method for solving the multiple scattering equation of light from finite clusters of isotropic dielectric objects. Comparison of the average optical cross sections between the different systems highlights variations in the scattering and absorption properties due to the electromagnetic interactions, and we demonstrate that the magnitudes of these quantities are clearly modulated by the shape of the primary particles.     

On the integral characteristics of single scattering on nonspherical particles

Expressions are obtained for the integral characteristics of single scattering of polarized radiation on particles of arbitrary shape. Polarized radiation is described by Stokes parameters. The two known scattering characteristics are examined—the full scattering cross section and the scattering matrix normalization constant. A dimensionless scattering integral is analyzed that takes into account possible scattering of incident radiation in all directions and determines the two considered integral characteristics. The integral is expressed via the scattering matrix elements and Stokes parameters of incident radiation. In the case of a nonspherical particle, the matrix elements depend on the direction of radiation incident on the particle. In this connection, the total scattering is affected by the structure of the incident beam. The practically important cases of particle illumination by parallel and convergent beams are considered. Expressions are obtained for the integral characteristics, averaged over the directions of incident radiation. Simple relations between the two scattering characteristics under different particle illumination are derived.     

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.     

Absorption and scattering of light by pigment particles in solar-absorbing paints

The optical properties of black-pigmented solar absorbing paint were analyzed phenomenologically by use of the Kubelka-Munk theory, including correction for reflection on front and rear surfaces. The effective absorption and scattering coefficients and the efficiency curves for absorption and scattering were calculated for coatings with different pigment-to-volume concentration ratios. The dependence of absorption and scattering efficiency on the pigment-to-volume concentration ratio was analyzed by reference to theoretical data in the literature. It was concluded that, during drying and curing of coatings, spherical primary pigment particles most likely collect in elongated groups oriented perpendicularly to the coating surface. Formation of such groups helps in understanding the independent measurements of solar absorptance.     

Effective suppression of multiply scattered light in static and dynamic light scattering

The evaluation of conventional light-scattering experiments in turbid media is often highly complicated because of the presence of multiple scattering contributions. The three-dimensional (3-D) cross-correlation method presented provides an effective and handy method to suppress the influence of multiply scattered light. As the time dependence of the 3-D cross-correlation function is determined solely by the singly scattered light, the evaluation of the decay constant yields reliable values for the effective diffusion coefficient and the hydrodynamic particle size of the suspended particles. Furthermore, analysis of the amplitude of the 3-D cross-correlation function permits the determination of the differential scattering cross section even for highly turbid suspensions.     

Peculiarities in light scattering by spherical particles with radial anisotropy

Light scattering by a spherical particle with radial anisotropy is discussed by extending Mie theory to diffraction by an anisotropic sphere, including both the electric and the magnetic anisotropy ratio. It is shown that radial anisotropy may lead to great modifications in scattering efficiencies and field enhancement, elucidating the importance of anisotropies in the control of scattering. The capacity for nondissipating damping is demonstrated for anisotropic spheres with different signs in radial and transversal permittivities.     

Determination of the characteristics of a suspension of particles from the spectrum of low-angle light scattering

A method is suggested for determining the concentration and properties of particles suspended in liquids based on combined analysis of low-angle light scattering spectra and absorption spectra in the 200–900 nm range. __________ Translated from Izmeritel'naya Tekhnika, No. 1, pp. 57–60, January, 2006.     

Simultaneous determination of refractive index and size of spherical dielectric particles from light scattering data

The diameter and refractive index of micrometer sized spherical dielectric particles are simultaneously deduced using the wavelength dependence of backscattering data from optically levitated particles. The accuracy of the results is set by experimental errors in the determination of the wavelength of backscatter resonance peaks and the ratio of slopes of specified peaks. At present the refractive index and diameter can be deduced with relative errors of 5 x 10(-5). This represents the most accurate determination of absolute size and refractive index yet made by light scattering. A reduction of these errors by an order of magnitude is possible. We assume a priori knowledge of diameter and refractive index with accuracy of 10(-1) and 5 x 10(-3), respectively.     

Vesicle sizing by static light scattering: a Fourier cosine transform approach

A Fourier cosine transform method, based on the Rayleigh-Gans-Debye thin-shell approximation, was developed to retrieve vesicle size distribution directly from the angular dependence of scattered light intensity. Its feasibility for real vesicles was partially tested on scattering data generated by the exact Mie solutions for isotropic vesicles. The noise tolerance of the method in recovering unimodal and biomodal distributions was studied with the simulated data. Applicability of this approach to vesicles with weak anisotropy was examined using Mie theory for anisotropic hollow spheres. Aprimitive theory about the first four moments of the radius distribution about the origin, excluding the mean radius, was obtained as an alternative to the direct retrieval of size distributions.     

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)].     

Two software tools for plane-wave scattering on nonspherical particles in the German Aerospace Center's Virtual Laboratory

We present the methodological background, the range of applicability, and the on-line usage of two software packages, MIESCHKA and CYL, which we have developed for light-scattering analysis on nonspherical particles. MIESCHKA solves Maxwell's equations in a rigorous way but is restricted to axisymmetric geometries, whereas CYL is an approximation for finite columns with nonspherical cross sections. We have established an easy on-line access to both of these programs through the Virtual Laboratory. Its generic software infrastructure was designed to simplify the web-based usage and to support the intercomparability of scientific software.     

激光光散射法测定聚乳酸分子量及其分子量分布

介绍了一种用于测定聚乳酸分子量及其分布的多角度激光光散射法；给出了该方法的实验步骤及结果。该法以四氢呋喃为溶剂和流动相，凝胶渗透色谱柱为分离体系，结合十八角激光散射仪和示差折光仪等检测器进行联机测量。实验测得合成聚乳酸重均分子量在30000-150000g／mol之间，分子量分布（Mw／Mn）为1.3～1．8。     

Comparison of near-forward light scattering on oceanic turbulence and particles

We examine and compare near-forward light scattering that is caused by turbulence and typical particulate assemblages in the ocean. The near-forward scattering by particles was calculated using Mie theory for homogeneous spheres and particle size distributions representative of natural assemblages in the ocean. Direct numerical simulations of a passive scalar with Prandtl number 7 mixed by homogeneous turbulence were used to represent temperature fluctuations and resulting inhomogeneities in the refractive index of water. Light scattering on the simulated turbulent flow was calculated using the geometrical-optics approximation. We found that the smallest temperature scales contribute the most to scattering, and that scattering on turbulence typically dominates over scattering on particles for small angles as large as 0.1 degrees . The scattering angle deviation that is due to turbulence for a light beam propagating over a 0.25-m path length in the oceanic water can be as large as 0.1 degrees . In addition, we carried out a preliminary laboratory experiment that illustrates the differences in the near-forward scattering on refractive-index inhomogeneities and particles.