Variational data-analysis method for combining laboratory-measured light-scattering phase functions and forward-scattering computations

A method is developed based on the variational data-analysis formalism to combine laboratory-measured scattering phase functions with forward-scattering phase function computations based on independent size distribution (SD) measurements. The algorithm yields an optimal estimate of the true phase function of the system that is not only based on the measurements and the computational results but also on all available information of the error variances and, if applicable, error covariances of the measured and computed phase functions. The high flexibility of the method is demonstrated by applying it to phase functions of feldspar and fly ash aerosols. Further, the algorithm is employed to determine the asymmetry parameter g of nine different mineral aerosol samples at two different optical wavelengths, and to assess the relative importance of different error sources in the determination of g. It is found that the use of spherical model particles in simulations of g can result in errors on the same order of magnitude as the uncertainty of the refractive index. The use of spherical model particles in computations of forward scattering, however, is found to be only a minor error source.     

Light-scattering methods for modelling algal particles as a collection of coated and/or nonspherical scatterers

Ocean reflectance or ocean colour measurements are an important tool for oceanographic studies of phytoplankton dynamics. Theoretical models based on homogeneous, spherical particles underestimate algal backscattering and thus reflectance values. It is our understanding that more advanced light-scattering methods must be employed, both for refractive index retrieval (Mie, Aden–Kerker) with inverse models, and for backscattering calculations (Extended Boundary Condition Method, EBCM). The measured optical properties of a monospecific bloom of the marine brown tide pelagophyte Aureococcus anophagefferens are used to compare the effects of assuming various simulated particle geometries. Computational results from polydisperse, coated spherical particles show results that compare better to experimental reflectance values than calculations based on homogeneous spheres. No noticeable change in simulated reflectance values is observed when a randomly oriented coated spheroidal (rather than spherical) geometry is assumed for the particle population. Our results suggest that a layered spherical geometry, based on Aden–Kerker theory, can adequately reproduce experimentally determined light-scattering properties even supposedly shape-sensitive properties such as the backscattering coefficient.     

Averaged Lagrangians and the mean effects of fluctuations in ideal fluid dynamics

We begin by placing the generalized Lagrangian mean (GLM) equations for a compressible adiabatic fluid into the Euler–Poincaré (EP) variational framework of fluid dynamics, for an averaged Lagrangian. We then state the EP Averaging Result—that GLM equations arise from GLM Hamilton’s principles in the EP framework. Next, we derive a new set of approximate small-amplitude GLM equations (gℓm equations) at second order in the fluctuating displacement of a Lagrangian trajectory from its mean position. These equations express the linear and nonlinear back-reaction effects on the Eulerian mean fluid quantities by the fluctuating displacements of the Lagrangian trajectories in terms of their Eulerian second moments. The derivation of the gℓm equations uses the linearized relations between Eulerian and Lagrangian fluctuations, in the tradition of Lagrangian stability analysis for fluids. The gℓm derivation also uses the method of averaged Lagrangians, in the tradition of wave, mean flow interaction (WMFI). The gℓm EP motion equations for compressible and incompressible ideal fluids are compared with the Euler-alpha turbulence closure equations. An alpha model is a GLM (or gℓm) fluid theory with a Taylor hypothesis closure (THC). Such closures are based on the linearized fluctuation relations that determine the dynamics of the Lagrangian statistical quantities in the Euler-alpha closure equations. We use the EP Averaging Result to bridge between the GLM equations and the Euler-alpha closure equations. Hence, combining the small-amplitude approximation with THC yields in new turbulence closure equations for compressible fluids in the EP variational framework.     

Geometrical optics approximation for light scattering by absorbing spherical particles

By means of geometrical optics, an approximation method is presented to compute the light scattering intensity of absorbing spherical particles illuminated by a plane wave. For absorbing particles, the effective refractive index and the effective refractive angle are related to the complex refractive index and incident angle. The formulas for calculation of the break of phases of reflection and refraction, which are different from the case of transparent particles, are exactly derived. Verification of the geometrical optics approximation (GOA) was performed by case studies and comparison of the present results with the Mie scattering. It is found that agreement between the GOA and the Mie theory is excellent in forward directions for weakly/moderately absorbing particles. Differently, for strongly absorbing particles, good agreement between the calculation methods is in the forward directions and large scattering angles. The agreement between the GOA and the Mie theory is better for larger particles.     

Radiation force caused by scattering, absorption, and emission of light by nonspherical particles

General formulas for computing the radiation force exerted on arbitrarily oriented and arbitrarily shaped nonspherical particles due to scattering, absorption, and emission of electromagnetic radiation are derived. For randomly oriented particles with a plane of symmetry, the formula for the average radiation force caused by the particle response to external illumination reduces to the standard Debye formula derived from the Lorenz–Mie theory, whereas the average radiation force caused by emission vanishes.     

Direct simulation Monte Carlo ray tracing model of light scattering by a class of real particles and comparison with PROGRA experimental results

The Direct Simulation Monte Carlo (DSMC) model is presented for three-dimensional single scattering of natural light by suspended, randomly oriented, optically homogeneous and isotropic, rounded and stochastically rough cubic particles. The modelled particles have large size parameter that allows geometric optics approximation to be used. The proposed computational model is simple and flexible. It is tested by comparison with known geometric optics solution for a perfect cube and Lorenz–Mie solution for a sphere, as extreme cases of the class of rounded cubes. Scattering and polarization properties of particles with various geometrical and optical characteristics are examined. The experimental study of real NaCl crystals with new Progra² instrument in microgravity conditions is conducted. The experimental and computed polarization and brightness phase curves are compared.     

Theoretical comparison of optical traps created by standing wave and single beam

We used generalised Lorenz–Mie scattering theory (GLMT) to compare submicron-sized particle optical trapping in a single focused beam and a standing wave. We focus especially on the study of maximal axial trapping force, minimal laser power necessary for confinement, axial trap position, and axial trap stiffness in dependency on trapped sphere radius, refractive index, and Gaussian beam waist size. In the single beam trap (SBT), the range of refractive indices which enable stable trapping depends strongly on the beam waist size (it grows with decreasing waist). On the contrary to the SBT, there are certain sphere sizes (non-trapping radii) that disable sphere confinement in standing wave trap (SWT) for arbitrary value of refractive index. For other sphere radii we show that the SWT enables confinement of high refractive index particle in wider laser beams and provides axial trap stiffness and maximal axial trapping force at least by two orders and one order bigger than in SBT, respectively.     

随机取向非球形沙尘气溶胶粒子的光学特性

利用离散偶极子近似法分析了一种随机取向旋转椭球体沙尘气溶胶粒子模型在尺度参数变化范围为0.1~23时(波长0.55!m对应有效半径为0.01~2!m)的光学特性,研究了沙尘粒子非球形性程度对其光学特性的影响,并考察了非球形粒子的随机取向能否用等体积球体来代替。就随机取向单分散和多分散旋转椭球体沙尘气溶胶而言,粒子非球形特征越明显,消光效率因子、不对称因子和单次散射反照率基本上偏离其等体积球体越大;对于相同的非球形,不对称因子偏离其等体积球体的相对偏差要比消光效率因子和单次散射反照率要大。非球形粒子的随机取向并不能使其光学特性严格等效为其等体积球体的光学特性。如果粒子形状偏离球体较小,则非球形粒子的随机取向的平均效果能使其消光效率因子、不对称因子和单次散射反照率近似用等体积球体的对应光学参量来等效;而如果粒子形状偏离球形较大,仅有单次散射反照率可以近似用等体积球体的单次散射反照率来等效,例如,轴半径比为16的旋转椭球体沙尘粒子的单次散射反照率偏离其等体积球体仅在3%以内。     

沙尘大气电磁波多重散射及衰减

为了使干旱沙漠地区的电子系统能够全天候的工作, 必须开展沙尘大气的电磁波多重散射及衰减特性研究. 根据Mie理论、沙尘大气粒子尺寸分布和能见度的关系得到了电磁波沙尘大气传播衰减的计算方法, 计算了不同沙尘大气能见度的37 GHz电磁波的衰减, 与其他经验公式及文献中的实验结果进行比较, 文中方法得到的结果更接近于测量结果. 为了研究较低能见度沙尘暴中电磁波的传播特性, 需研究沙尘大气的多重散射效应. 应用Monte Carlo模拟方法, 在沙尘粒子为干燥和5%水含量时, 模拟了37 GHz和93 GHz电磁波在沙尘大气中传播时考虑多重散射效应的衰减, 并与基于Mie理论的计算结果进行比较, 结果显示, 在37 GHz时, 沙尘大气的多重散射对衰减的影响小, 在93 GHz时多重散射显著, 沙尘大气能见度越低, 多重散射的影响越显著. 粒子水含量增加使电磁波的衰减显著增大, 对多重散射的影响不明显. 因此, 在相同大气能见度下, 沙尘天气越干燥, 多重散射影响越大, 电磁波衰减减小越显著.     

Optical modeling of mineral dust particles: A review

Dust particles are uniquely and irregularly shaped, they can be inhomogeneous, form agglomerates, be composed of anisotropic materials, and have a preferred orientation. As such, modeling their light scattering is very challenging. This review takes a look at the advances in dust optical modeling over the last decade. It is obvious that our ability to model the single-scattering properties of dust particles accurately depends on the size parameter. Unfortunately, our ability to account realistically for all the relevant physical properties in light-scattering modeling is the best for small particles; whereas, the realistic treatment of the particles would be most important for large size parameters. When particles are not much larger than the wavelength, even simple model shapes such as homogeneous spheroids appear to perform well; practically any reasonable shape distribution of non-spherical model particles seems superior compared to the Mie theory. Our ability to model scattering by dust particles much larger than the wavelength is very limited: no method presently exists to predict reliably and accurately the single-scattering properties of such particles, although there are models that can be tuned to agree well with the laboratory-measured reference scattering matrices. The intermediate size parameters between the resonance domain and the geometric-optics domain appear to be almost uncharted territory and, consequently, very little can be said about the impact of different physical properties on scattering in this region. Despite the challenges, the use of Mie theory should be avoided: contrary to the popular belief, the use of Mie spheres is a major source of error even in radiation-budget considerations.     

相对湿度对大气气溶胶消光系数的影响

消光系数是气溶胶颗粒物光学性质的关键参数之一。基于Mie散射理论和气溶胶颗粒粒径及折射率的湿度增长模型,本文详细研究了气溶胶吸湿性对其消光系数的影响。计算结果表明:当入射光波长为808nm、相对湿度在60%~95%之间增加时,因颗粒粒径的增长及折射率的减小,导致颗粒物消光系数曲线右移且其波动性更加明显;而对于同一球形颗粒,小粒径颗粒的消光系数随相对湿度的增加呈指数规律增大,较大粒径颗粒的则表现为波动减小趋势。此外,在不同入射光条件下,小颗粒消光系数与相对湿度之间的关系保持不变。本文的计算结果对气溶胶光学性质与大气环境质量的研究具有一定的参考价值。     

Optical modeling of vesicular volcanic ash particles

We present a realistic shape model for nonspherical, vesicular particles and use the model to derive single-scattering properties of volcanic fine-ash particles. Light-scattering computations with discrete-dipole approximation reveal that, qualitatively, scattering by the model particles resembles that of the measured, real volcanic ash particles. Comparison of compact and vesicular ash shows that porosity promotes positive degree of linear polarization and decreases the depolarization ratio for both large and small vesicles. Yet, the single-scattering properties of ash particles with large vesicles are found to be surprisingly similar to those of compact ash particles. A comparison with Mie computations of equal-volume spheres indicates that for small size parameters, the spherical shape underestimates the asymmetry parameter of volcanic ash particles; whereas, for larger size parameters, it is overestimated.     

散射相函数的高阶光学参量研究

漫反射光谱技术被广泛应用于无创测量生物组织光学性质。当光源与探测器很近时,仅仅依靠吸收系数μ_a和约化散射系数μ′_s不能准确描述光源附近光的传播状态。而二阶光学参量γ的引入改善了近光源光的传播状态的描述。本文将生物组织的散射等效成特定球形颗粒的散射,基于Mie散射理论,计算了与散射相函数p(θ)有关的单粒子和多分散系粒子的二阶光学参量γ,研究了γ随尺度参数α和相对折射率m的变化规律,描述了γ与组织结构参量之间的联系,并阐述了γ对粒子特征的表征能力。研究表明,参量γ对尺度参数α小于2的微粒尺寸的改变是敏感的,并呈二次函数关系,其系数与相对折射率呈线性关系;对于相对折射率和尺度参数都不相同的两个粒子,他们的各向异性因子g相同时,二阶光学参量γ却不同,粒子越大,γ表征粒子特征的能力越强。这对于无创探究组织微观形态具有深远的意义。     

一种内混合气溶胶粒子模型光散射的等效性

以包含灰尘、黑碳和水三种成分的单分散内混合初次气溶胶为例,利用消光、吸收、散射效率因子和不对称因子,探讨了以等效折射率描述具有不同成分的内混合气溶胶粒子系统的适用性。结果表明,在尺度参数为0.1～25时不同半径比下,消光、吸收和散射效率因子的等效性较好,相对误差分别在3%、3%和4%以内;不对称因子的等效性相对稍差,相对误差在13%以内。当半径比a/b小于1/5,即内混合体中所含灰尘和黑碳较少时,等效折射率实部和虚部值基本可以确定,而不必考虑尺度参数的影响。用除散射相函数之外的其他光学量来等效时,较为容易找到等效的气溶胶粒子。     

Optimization of optical parameters for particle sizing in multiphase flows

Optimization of laser light scatter detection technique based on the geometrical optics method for measuring the size, velocity and refractive index of spherical particles was performed. A new optical orientation for extended phase-Doppler anemometry (EPDA) had been developed to improve the accuracy of particle material recognition in multiphase flow. The effects of both the intensity and phase factor of the reflected and refracted light were examined. The inverse sign of the phase factors from the refracted light and reflected light resulted in a (2π–φ) effect on phase determination. This was used for minimizing and validating the errors in the refractive index measurements of large particles. Furthermore, optimization results were compared with the results of simulation based on the generalized Lorenz–Mie theory (GLMT). A newly developed signal validation scheme was also described in detail. The scheme was used to reject the inaccurate data in order to further improve the accuracy of the recognition.     

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.     

阶矩阵及其在传统预处理方法中的应用

本文应用矩阵元素阶和阶矩阵概念,讨论了ICCG和MICCG这两种传统的预处理方法在实用中的一些问题。为什么ICCG(s,t)在s+t固定时取(s,t)=(1,1),(1,2),(1,3),(2,4),(3,5),…有较高的收敛速度?为什么MICCG(m)当m>3时迭代次数不变?ICCG和MICCG的填入方式如何系统化?MICCG是否总比ICCG收敛速度高?本文拟作一个初步的讨论。通过LU分解的阶矩阵,本文给出了按阶递增的填入原则,将ICCG和MICCG系统化为P阶ICCG和P阶MICCG,并讨论了MICCG原有填入方式存在的问题。应用误差阵的阶矩阵,本文讨沦了MICCG迭代参数选取中存在的问题,给出了合理的参数选取方法。通过不同算例,本文还比较了ICCG和MICCG的计算效率。     

Study on the local structure of (CrO6) complex in garnet crystals by optical and EPR spectrum

The local lattice structure distortions for YAG and YGG systems doped with Cr³⁺ have been investigated by the d³ configuration complete energy matrices which contain the Zeeman energy besides the electron–electron interaction, the trigonal crystal field as well as the spin–orbit coupling interaction. The local lattice structure parameters R and θ of (CrO₆)⁹⁻ complex are determined for Cr³⁺ in YAG and YGG systems, respectively. The calculated results show that the local lattice structures have expansion distortions, which almost tend to the same after distortions. Meanwhile, the EPR parameter D, g factors (g_||, g) and optical spectrum of these systems have been interpreted uniformly by quantitative calculation. It is shown that the effect of the orbit reduction factor k on g factors (g_||, g) cannot be ignored.     

球形雾霾粒子的紫外光散射偏振特性研究

在我国经济社会快速发展的同时,雾霾天气成为了突出的环境问题,雾霾粒子的测量非常重要。偏振紫外光与大气雾霾粒子发生散射后,散射光偏振状态(Stokes矢量以及偏振度)的改变能反映雾霾粒子的相关物理特性(粒径、复杂折射率等)。基于Mie散射理论建立了紫外光雾霾球形粒子直视和非直视单次散射模型,研究了单个球形粒子和链状结构球形粒子物理特性的改变对散射光偏振状态的影响,并用蒙特卡洛仿真分析已知粒径分布的雾霾粒子浓度对散射光偏振状态的影响。结果表明：针对单个球形粒子,随着粒子粒径的增大Stokes矢量中散射光光强(I_s)随之增强,粒子复折射率虚部为先增大后较小,偏振度也是在不断增大,且复折射率虚部较小时,偏振度增加趋势快;对于粒径分布不变的雾霾粒子,随着粒子的浓度增加,雾霾粒子的散射系数、消光系数和吸收系数均呈线性增加,但是I_s先增大后减小。针对链状球形粒子,随着粒子个数的增加,I_s均呈现增大的趋势,且偏振度可用于区分链状球形粒子是否由相同球形粒子组成; 相同球形粒子组成链状结构中,I_s随着粒子数量的增加而线性增大,偏振度不改变;不同球形粒子组成的链状结构,I_s以及偏振度的变化趋势可以区分粒子物理特性。