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)].     

Finite-difference time-domain solution of light scattering by dielectric particles with a perfectly matched layer absorbing boundary condition

A three-dimensional finite-difference time-domain (FDTD) program has been developed to provide a numerical solution for light scattering by nonspherical dielectric particles. The perfectly matched layer (PML) absorbing boundary condition (ABC) is used to truncate the computational domain. As a result of using the PML ABC, the present FDTD program requires much less computer memory and CPU time than those that use traditional truncation techniques. For spheres with particle-size parameters as large as 40, the extinction and absorption efficiencies from the present FDTD program match the Mie results closely, with differences of less than ~1%. The difference in the scattering phase function is typically smaller than ~5%. The FDTD program has also been checked by use of the exact solution for light scattering by a pair of spheres in contact. Finally, applications of the PML FDTD to hexagonal particles and to spheres aggregated into tetrahedral structures are presented.     

Examination of surface roughness on light scattering by long ice columns by use of a two-dimensional finite-difference time-domain algorithm

Natural particles such as ice crystals in cirrus clouds generally are not pristine but have additional microroughness on their surfaces. A two-dimensional finite-difference time-domain (FDTD) program with a perfectly matched layer absorbing boundary condition is developed to calculate the effect of surface roughness on light scattering by long ice columns. When we use a spatial cell size of 1/120 incident wavelength for ice circular cylinders with size parameters of 6 and 24 at wavelengths of 0.55 and 10.8 microm, respectively, the errors in the FDTD results in the extinction, scattering, and absorption efficiencies are smaller than approximately 0.5%. The errors in the FDTD results in the asymmetry factor are smaller than approximately 0.05%. The errors in the FDTD results in the phase-matrix elements are smaller than approximately 5%. By adding a pseudorandom change as great as 10% of the radius of a cylinder, we calculate the scattering properties of randomly oriented rough-surfaced ice columns. We conclude that, although the effect of small surface roughness on light scattering is negligible, the scattering phase-matrix elements change significantly for particles with large surface roughness. The roughness on the particle surface can make the conventional phase function smooth. The most significant effect of the surface roughness is the decay of polarization of the scattered light.     

Efficient finite-difference time-domain scheme for light scattering by dielectric particles: application to aerosols

We have examined the Maxwell-Garnett, inverted Maxwell-Garnett, and Bruggeman rules for evaluation of the mean permittivity involving partially empty cells at particle surface in conjunction with the finite-difference time-domain (FDTD) computation. Sensitivity studies show that the inverted Maxwell-Garnett rule is the most effective in reducing the staircasing effect. The discontinuity of permittivity at the interface of free space and the particle medium can be minimized by use of an effective permittivity at the cell edges determined by the average of the permittivity values associated with adjacent cells. The efficiency of the FDTD computational program is further improved by use of a perfectly matched layer absorbing boundary condition and the appropriate coding technique. The accuracy of the FDTD method is assessed on the basis of a comparison of the FDTD and the Mie calculations for ice spheres. This program is then applied to light scattering by convex and concave aerosol particles. Comparisons of the scattering phase function for these types of aerosol with those for spheres and spheroids show substantial differences in backscattering directions. Finally, we illustrate that the FDTD method is robust and flexible in computing the scattering properties of particles with complex morphological configurations.     

Implementing the near- to far-field transformation in the finite-difference time-domain method

When the finite-difference time-domain (FDTD) method is applied to light-scattering computations, the far fields can be obtained by means of integrating the near fields either over the volume bounded by the particle's surface or on a regular surface encompassing the scatterer. For light scattering by a sphere, the accurate near-field components on the FDTD-staggered meshes can be computed from the rigorous Lorenz-Mie theory. We investigate the errors associated with these near- to far-field transform methods for a canonical scattering problem associated with spheres. For a scatterer with a small refractive index, the surface-integral approach is more accurate than its volume counterpart for computation of the phase functions and extinction efficiencies; however, the volume-integral approach is more accurate for computation of other scattering matrix elements, such as P12, P32, and P43, especially for backscattering. If a large refractive index is involved, the results computed from the volume-integration method become less accurate, whereas the surface method still retains the same order of accuracy as in the situation for the small refractive index.     

Development of an ice crystal scattering database for the global change observation mission/second generation global imager satellite mission: investigating the refractive index grid system and potential retrieval error

Computing time and retrieval error of the effective particle radius are important considerations when developing an ice crystal scattering database to be used in radiative transfer simulation and satellite remote sensing retrieval. Therefore, the light scattering database should be optimized based on the specifications of the satellite sensor. In this study, the grid system of the complex refractive index in the 1.6?μm (SW3) channel of the Global Change Observation Mission/Second Generation Global Imager satellite sensor is investigated for optimizing the ice crystal scattering database. This grid system is separated into twelve patterns according to the step size of the real and imaginary parts of the refractive index. Specifically, the LIght Scattering solver Applicable to particles of arbitrary Shape/Geometrical-Optics Approximation technique is used to simulate the scattering of light by randomly oriented large hexagonal ice crystals. The difference of radiance with different step size of the refractive index is calculated from the developed light scattering database using the radiative transfer (R-STAR) solver. The results indicated that the step size of the real part is a significant factor in difference of radiance.     

Finite-difference time-domain solution of light scattering by an infinite dielectric column immersed in an absorbing medium

The two-dimensional (2-D) finite-difference time-domain (FDTD) method is applied to calculate light scattering and absorption by an arbitrarily shaped infinite column embedded in an absorbing dielectric medium. A uniaxial perfectly matched layer (UPML) absorbing boundary condition is used to truncate the computational domain. The single-scattering properties of the infinite column embedded in the absorbing medium, including scattering phase functions and extinction and absorption efficiencies, are derived by use of an area integration of the internal field. An exact solution for light scattering and absorption by a circular cylinder in an absorbing medium is used to examine the accuracy of the 2-D UPML FDTD code. With use of a cell size of 1/120 incident wavelength in the FDTD calculations, the errors in the extinction and absorption efficiencies and asymmetry factors from the 2-D UPML FDTD are generally smaller than approximately 0.1%. The errors in the scattering phase functions are typically smaller than approximately 4%. With the 2-D UPML FDTD technique, light scattering and absorption by long noncircular columns embedded in absorbing media can be accurately solved.     

多角度动态光散射法的纳米颗粒精确测量

基于动态光散射原理,采用自主研发的多角度动态光散射装置,对纳米及亚微米颗粒粒径准确测量方法进行了探究。自研装置采用带有光阑组的精密入射光路设计,以及匹配液池及Beam-stop设计,极大提高了信噪比;同时避免了测量角度的互补方向上,由于样品池与空气界面折射率不同导致的反射光信号对有效信号的干扰。在此基础上,对不同浓度、粒径的聚苯乙烯(PS)颗粒溶液进行了测定及不确定度分析。结果表明,对同一粒径的PS颗粒,增加颗粒浓度时,多重散射首先发生于大、小测量角度,越接近90°,发生多重散射的浓度越高;随着粒径增大,受不可忽略的颗粒间相互作用的影响,粒径测量结果表现出了强烈的角度依赖性,甚至波动性。     

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.     

Microphysical particle parameters from extinction and backscatter lidar data by inversion with regularization: experiment

We present effective radius, volume, surface-area, and number concentrations as well as mean complex refractive index of tropospheric particle size distributions based on lidar measurements at six wavelengths. The parameters are derived by means of an inversion algorithm that has been specifically designed for the inversion of available optical data sets. The data were taken on 20 June and on 20 July 1997 during the Aerosol Characterization Experiment ACE 2 (North Atlantic/Portugal) and on 9 August 1998 during the Lindenberg Aerosol Characterization Experiment LACE 98 (Lindenberg/Germany). Measurements on 20 June 1997 were taken in a clean-marine boundary layer, and a large value of 0.64 mum for the effective radius, a low value of 1.45 for the real part, and a negligible imaginary part of the complex refractive index were found. The single-scatter albedo was 0.98 at 532 nm. It was derived from the particle parameters with Mie-scattering calculations. In contrast, the particles were less than 0.2 mum in effective radius in a continental-polluted aerosol layer on 20 July 1997. The real part of the complex refractive index was ~1.6; the imaginary part showed values near 0.03i. The single-scatter albedo was 0.84. On 9 August 1998 an elevated particle layer located from 3000 to 6000 m was observed, which had originated from an area of biomass burning in northwestern Canada. Here the effective radius was ~0.24 mum, the real part of the complex refractive index was above 1.6, the imaginary part was ~0.04i, and the single-scatter albedo was 0.81. Excellent agreement has been found with results based on sunphotometer and in situ measurements that were performed during the field campaigns.     

Estimation of optical constants from multiple-scattered light using approximations for single particle scattering characteristics

The inversion of multiple-scattered light measurements to extract the optical constant (complex refractive index) is computationally intensive. A significant portion of this time is due to the effort required for computing the single particle characteristics (absorption and scattering cross sections, anisotropy factor, and the phase function). We investigate approximations for computing these characteristics so as to significantly speed up the calculations without introducing large inaccuracies. Two suspensions of spherical particles viz., polystyrene and poly(methyl methacrylate) were used for this investigation. It was found that using the exact Mie theory to compute the absorption and scattering cross sections and the anisotropy factor with the phase function computed using the Henyey-Greenstein approximation yielded the best results. Analysis suggests that errors in the phase functions and thus in the estimated optical constants depend mainly on how closely the approximations match the Mie phase function at small scattering angles.     

Accuracy of internal fields in volume integral equation simulations of light scattering

We studied the accuracy of volume integral equation simulations of internal fields in small particles illuminated by a monochromatic plane wave as well as the accuracy of the scattered fields. We obtained this accuracy by considering scattering by spheres and comparing the simulated internal and scattered fields with those obtained by Mie theory. The accuracy was measured in several error norms (e.g., mean and root mean square). Furthermore, the distribution of the errors within the particle was obtained. The accuracy was measured as a function of the size parameter and the refractive index of the sphere and as a function of the cube size used in the simulations. The size parameter of the sphere was as large as 10, and three refractive indices were considered. The errors in the internal field are located mostly on the surface of the sphere, and even for fine discretizations they remain relatively large. The errors depend strongly on the refractive index of the particle. If the discretization is kept constant, the errors depend only weakly on the size parameter. We also examined the case of sharp internal field resonances in the sphere. We show that the simulation is able to reproduce the resonances in the internal field, although at a slightly larger refractive index.     

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。     

基于Mie散射理论的微球体颗粒数值模拟计算和实验研究

应用Mie散射理论,在散射角0～π范围内,模拟微球体颗粒的散射光强度与粒径大小的变化关系,分析了相对折射率的大小对散射光强度的影响;在实验装置条件下,分别模拟了散射光强度与粒径大小的变化关系及2um、5um、10um三种粒子的散射光强度与波长的变化关系。实验验证了数值模拟与实验结果基本一致,也证明实验中粒子散射遵从Mie散射理论模型。     

An Approximation Method for the Backward Scattering of Light by a Soft Spherical Obstacle

Abstract

The optical analogue of a formula by Reading and Bassichis for the backscattering of a high-energy scalar wave by a square-well potential has been examined. In optical scattering, this corresponds to the problem of the back-scattering of light by a homogeneous spherical particle. Numerical checks with the Mie theory are presented for various values of the refractive index and size parameter. The formula is found to reproduce some scattering features extremely well for intermediate-size soft particles.     

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.     

Analytical light-scattering solution for Chebyshev particles

We develop a modification of the T-matrix method that allows for fast calculations of scattering properties of particles with irregular shapes. This modification uses the so-called Sh matrices, the elements of which depend on the shape of particles and do not depend on the particle size or optical constants; i.e., the introduction of Sh matrices makes possible the separation of these parameters within the T-matrix algorithm. For a given shape of a scattering object we calculate the Sh matrices only once and then can quickly calculate the T-matrix elements for a number of sizes and refractive indices. This, in particular, can provide rapid particle-size and refractive index averaging in a particle ensemble. This separation is useful for the derivation of an analytical light-scattering solution for Chebyshev particles.     

Light scattering by a core-mantle spheroidal particle

A solution of the electromagnetic scattering problem for confocal coated spheroids has been obtained by the method of separation of variables in a spheroidal coordinate system. The main features of the solution are (i) the incident, scattered, and internal radiation fields are divided into two parts: an axisymmetric part independent of the azimuthal angle ? and a nonaxisymmetric part that with integration over ? gives zero; the diffraction problems for each part are solved separately; (ii) the scalar potentials of the solution are chosen in a special way: Abraham's potentials (for the axisymmetric part) and a superposition of the potentials used for spheres and infinitely long cylinders (for the nonaxisymmetric part). Such a procedure has been applied to homogeneous spheroids [Differential Equations 19, 1765 (1983); Astrophys. Space Sci. 204, 19, (1993)] and allows us to solve the light scattering problem for confocal spheroids with an arbitrary refractive index, size, and shape of the core or mantle. Numerical tests are described in detail. The efficiency factors have been calculated for prolate and oblate spheroids with refractive indices of 1.5 + 0.0 i, 1.5 + 0.05 i for the core and refractive indices of 1.3 + 0.0 i, 1.3 + 0.05i for the mantle. The effects of the core size and particle shape as well as those of absorption in the core or mantle are examined. It is found that the efficiency factors of the coated and homogeneous spheroids with the volume-averaged refractive index are similar to first maximum.     

Geometrical-optics approximation of forward scattering by gradient-index spheres

By means of geometrical optics we present an approximation method for acceleration of the computation of the scattering intensity distribution within a forward angular range (0-60 degrees ) for gradient-index spheres illuminated by a plane wave. The incident angle of reflected light is determined by the scattering angle, thus improving the approximation accuracy. The scattering angle and the optical path length are numerically integrated by a general-purpose integrator. With some special index models, the scattering angle and the optical path length can be expressed by a unique function and the calculation is faster. This method is proved effective for transparent particles with size parameters greater than 50. It fails to give good approximation results at scattering angles whose refractive rays are in the backward direction. For different index models, the geometrical-optics approximation is effective only for forward angles, typically those less than 60 degrees or when the refractive-index difference of a particle is less than a certain value.