The use of two angle elastic and Raman scattering to obtain molecular density and aerosol scattering profiles

The method of dual angle, multiple wavelength lidar interrogation to effect a radiative separation of the scattering produced by aerosols and molecules is extended. A given wavelength is transmitted, and the Raman shifted return from nitrogen as well as the elastically scattered transmitted wavelength are both interrogated. This procedure is carried out in the backscatter mode at the zenith and one other slant path at some angle from the zenith. The methodology is developed for obtaining molecular density, temperature, pressure, and aerosol scattering profiles.     

Multiple scattering and the structure of a finite thickness of scatterer

The transport equation is solved for a scattering medium of finite thickness. A method is given for approximate derivation of the size distribution for the particles on the basis of multiple scattering. An appendix deals with the particular case of particles that are small in relation to the wavelength.     

Light scattering by a spherical particle with multiple densely packed inclusions

This paper calculates light scattering by a spherical water particle containing densely packed inclusions at a visible wavelength 0.55 \mum by a combination of ray-tracing and Monte Carlo techniques. While the individual reflection and refraction events at the outer boundary of a sphere particle are considered by a ray-tracing program, the Monte Carlo routine simulates internal scattering processes. The main advantage of this method is that the shape of the particle can be arbitrary, and multiple scattering can be considered in the internal scattering processes. A dense-medium light-scattering theory based on the introduction of the static structure factor is used to calculate the phase function and asymmetry parameters for densely packed inclusions. Numerical results of the single scattering characteristics for a sphere containing multiple densely packed inclusions are given.     

Characterization of porous materials by small-angle scattering

Characterization of porous materials by small-angle scattering has been extensively pursued for several years now as the pores are often of mesoscopic size and compatible with the length scale accessible by the technique using both neutrons and X-rays as probing radiation. With the availability of ultra small-angle scattering instruments, one can investigate porous materials in the sub-micron length scale. Because of the increased accessible length scale vis-a-vis the multiple scattering effect, conventional data analysis procedures based on single scattering approximation quite often fail. The limitation of conventional data analysis procedures is also pronounced in the case of thick samples and long wavelength of the probing radiation. Effect of multiple scattering is manifested by broadening the scattering profile. Sample thickness for some technologically important materials is often significantly high, as the experimental samples have to replicate all its essential properties in the bulk material. Larger wavelength of the probing radiation is used in some cases to access large length scale and also to minimize the effect of double Bragg reflections.     

Average intensity of multiply scattered waves

The methods of the theory of multiple wave scattering are applied to a calculation of the mean intensity of radiation above a jagged rough surface under conditions such that shadowing and scattering form an intricate multipath structure on the part of the scalar field. The multiple wave scattering is described in the Twersky approximation, and a relationship of the given problem to the radiative transfer problem in an infinite plane-parallel layer is indicated. Expressions are derived for the coherent and incoherent components of the intensity at interior points of the layer, and the dependence of the mean value of the total intensity on the distance, radiation wavelength, and other parameters of the problem is analyzed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 85–90, May, 1984.     

Limits of time-reversal focusing through multiple scattering: long-range correlation

Experimental results of time-reversal focusing in a high-order multiple scattering medium are presented and compared to theoretical predictions based on a statistical model. The medium consists of a random collection of parallel steel rods. An ultrasonic source (3.2 MHz) transmits a pulse that undergoes multiple scattering and is recorded on an array. The time-reversed waves are sent by the array back to the source through the scattering medium. The quality of temporal focusing is very well predicted by a simple statistical model. However, for thicker samples, persistent temporal side-lobes appear. We interpret these side-lobes as a consequence of the growing number of crossing paths in the sample due to high-order multiple scattering. As to spatial focusing, the resolution is practically independent from the array's aperture. With a 16-element array, the resolution was found to be 30 times finer than in a homogeneous medium. Resolutions of the order of the wavelength (0.5 mm) were attained. These results are discussed in relation with the statistical properties of time-reversal mirrors in a random medium.     

Multiple scattering of light transmission in a smoke layer

The visibility in a fire scene decreases because of the existence of smoke produced by the flammable materials. With the growth of smoke concentration, the relationship between light and smoke becomes complicated due to the multiple scattering. In this paper, the radiative transfer equation (RTE) that considers the multiple scattering was applied to calculate the light transmission in a smoke layer. As input parameters of RTE, the single scattering albedo, asymmetry parameter and extinction cross section of single smoke agglomerate were calculated by the discrete dipole approximation (DDA) method. The effects of smoke agglomerate diameter, number density of smoke layer, and the incident light wavelength were considered. The results show that the light transmitted flux decreases with the growth of smoke diameter and number density, and increases with the growth of wavelength. The smoke diameter is dominant among the three parameters, and the light transmitted flux tends to be stable when the wavelength reaches a certain value.     

Modeling of Multiple Scattering Effects in Fraunhofer Diffraction Particle Size Analysis

A model for the direct problem of calculating the forward scattering signature of a multiple scattering medium is presented. The new formulation is optimized for integration into schemes for reconstructing the particle size distribution from laser diffraction (forward scattering) signatures obtained from optically thick media. The analysis is valid for media where the particle sizes and interparticle spacings are large (relative to the wavelength and the particle size, respectively) such that Fraunhofer diffraction theory adequately describes the properties of the forward scattered light from individual scattering events. The simulated performance of laser diffraction particle sizing instruments was then studied using predictions of the scattered light signatures which would be measured by laser diffraction instrument under multiple scattering conditions. The results were compared with experimental data and theoretical calculations based on other models.     

0.5 mm金刚石X射线相位延迟板及偏振度的标定

在利用步辐射光源的偏振特性进行自旋相关X射线散射及吸收谱实验来研究材料的磁学性质时，需要应用圆偏振光，这就提出了对具有高通量、高偏振度' 长连续可调的圆偏振X射线的需求；另一方面标定实验所用X射线的圆偏振度也成为这一研究领域的关键技术。由于X射线多光束衍射强度与σ场和π场的光程差δ相关，通过测量圆偏振分析晶体的多光束衍射的强度分布，可以获得入射X射线的圆偏振度。实验在美国国家同步辐射光源实验室X25光束线实验站进行，光子能量为7．1keV的圆偏振X射线由线偏振X射线经过一厚度为0．5mm、晶面为[111]的金刚石晶体产生。通过测量多光束衍射强度，确定了斯托克斯参量。实验值与X射线动力学理论计算结果能较好地吻合。     

Characterizing extended changes in multiple scattering media using coda wave decorrelation: numerical simulations

In multiple scattering media, the coda wave decorrelation relates linearly to the scattering cross-section of structural change when the change is small compared to the wavelength. In practical applications, we assume that the total decorrelation induced by changes in the medium is the sum of the decorrelation induced by each elementary change. In this article, we investigate the validity of this linear approximation for extended changes larger than the wavelength, and the possible signature of the change orientation. Coda waves are simulated using a 2-D finite-difference model in multiple scattering media. We perform a parametric analysis of the decorrelation induced by extended structural changes of various length and orientation, as well as the mutual influence between two identical changes separated by a varying distance. Our findings are: (1) we underestimate the length of the change when it exceeds one wavelength. (2) the decorrelation value is sensitive to the orientation of extended changes at distances smaller than four mean free paths between the source and the receiver. (3) two simultaneous changes are interacting within a distance of the order of the mean free path, but can be considered independent at a separation distance larger than a few mean free paths.     

金复合纳米微粒的消光特性

基于Mie光散射理论,研究了金壳介质芯的金复合纳米球壳微粒在光散射与吸收中的消光特性.对微粒增大时的多极子特性以及内半径变动时共振峰的移动作了计算和分析,证实了共振峰位置随内外半径比增大而增大的规律.还对纯金纳米微粒的多极子特性作了计算,并讨论了总消光效率中散射和吸收各自的贡献.     

Simulation of light scattering by two nano-sized circular cylinders using NS-FDTD method and interference analysis

Optical Review - Scattering problem by one cylinder whose radius is comparable to incident wavelength can be solved by Mie theorem. Due to complicated multiple scattering, scattering...     

基于Mie散射理论的C@H_2O复合粒子散射特性研究

大气中大量存在的复合粒子会对激光传输效率产生很大影响。由于空气中水蒸气含量较高,以C作为凝结核外层包裹以水的核壳结构微粒对光传输具有明显的散射效应。本文应用Mie散射理论对C@H_2O核壳结构微粒的散射特性进行了理论分析和数值计算,首先给出了不同入射波长、核粒子半径以及水膜厚度条件下散射强度分布变化曲线;其次给出了不同入射波长、核粒子半径以及水膜厚度条件下偏振变化情况;最后讨论了光学截面与粒子半径之间的关系。结果表明各参数对前向散射强度影响较大,入射波长越大散射强度越弱,C核半径增大粒子的前向散射增强,水膜厚度增大粒子的前向散射增强,而后向散射无明显影响;入射波长较大时,粒子在多个角度出现线偏振光,入射波长增大、碳核半径变大、水膜厚度增大,偏振度峰值都会增多;随着入射波长的增大,散射截面最大峰值位置向着半径增大的方向移动,并伴随一定的振荡现象,散射和消光截面在碳核半径为0.1μm左右达到最大值。     

Maximal degree of polarization for visible light scattered by an aqueous droplet

The maximal degree of polarization (DOP) for the visible solar light scattered by an aqueous droplet at a given scattering angle is found in this paper. Based on the Lorenz-Mie theory, the numerical expression for the DOP of the light scattered by any spherical particle is deduced. For the given scattering angle and aqueous droplet, the DOP dependent on wavelength is calculated according to familiar solar spectral colors. The maximal DOP of each spectral color is exhibited and some analyses are given. This analysis may contribute to applications of indicating atmospheric conditions and polarized light compass navigation.     

Investigation of light scattering from rough periodic surfaces — numerical solutions

The Beckmann scalar scattering model based on the Kirchhoff approximation was used to investigate the scattering of light from periodic surfaces whose roughness amplitude is comparable to, and greater than, the illumination wavelength. Solutions by numerical integration were obtained for surfaces of different profiles and of different roughnesses. It was found that the scattering patterns from these surfaces were very different at large roughness amplitudes. As the incident angle was varied on a given surface, it was also observed that the intensity of any individual diffraction order oscillated and the degree of oscillation was directly related to roughness. By utilizing this property, a new procedure could be developed for surface roughness assessment.     

基于色散偏振度的乳化油光谱检测系统研究

以色散偏振光谱检测技术为背景,着重研究了乳化油颗粒的偏振光学特性及米散射物理模型,构建了色散偏振度光谱检测系统。在400～700nm波长范围内,分别对四种样品进行了301个波段的光谱反射率采集。结合贝塞尔函数和汉克尔函数,推导出了入射光波长与散射光偏振振幅矢量的关系,提取了一个新的特征参数：色散偏振度(DODP)。在暗室条件下,对乳化油样品ND18和ND75进行测量,利用色散偏振公式计算出了样品在各测量波长处的偏振度值,验证了基于DODP值检测乳化油的可行性。研究发现,虽然米散射的解是由单个球体的衍射推导而来,但是只要它们的直径和组成相同,且彼此之间的距离比波长大,也同样可以用于任意数量的球的衍射。在这种情况下,被不同球体散射的光之间没有相干的相位关系,总散射能量等于被一个球体散射的能量乘以它们的整数。当观测平面与入射波电矢量振动方向之间的夹角φ=0或者φ=π/2时,散射光分量E⁽(s))_θ或者E⁽(s))_φ消失。由于ND18的粒径比ND75的粒径小,所以ND18的前向散射波瓣较大,前向散射与后向散...     

Multiple scattering using the Foldy-Twersky integral equation

The importance of multiple scattering processes for the propagation of ultrasound through dispersions is assessed. Under certain well defined conditions, the Foldy-Twersky integral equation can be used to find a value for the amplitude and complex wavenumber of the multiply scattered plane wave collected by either the receiving or the emitting transducer. Expressions for the amplitude and wavenumber are evaluated in terms of particle number density, wavelength of ultrasound and the forward and backward scattering amplitudes. In the case where the wavelength is much greater than the particle size, explicit expressions for the real and imaginary parts of the wavenumber are provided, in terms of the scattering and absorption cross-sections, as far as terms in the square of the number density of particles.     

Experimental Study of the Influence of Thickness and Wavelength on the Ultraviolet Light Scattering of Polyethylene Films

A study of the influence of thickness and wave-length on the ultraviolet scattering of polyethylene films is reported in this paper. The scatter of samples was measured by considering the difference between absorbances values obtained with the sample placed in two positions at different distance from the detector in a UV/Vis Spectrophotometer.

The present work suggests that a linear relationship exists between absorbance and thickness film for the two sample positions, and also between the difference of these absorbances and wavelength. From the obtained equations it is possible to normalize scattering values for a given wavelength and a given thickness, and in this way experimental errors are minimized. This procedure represents a simple way for characterize optically these materials and, analogously, other transparent or translucent polymeric films.     

亚表面圆柱体对热波的多重散射问题

极端条件下的传热问题是工程热物理研究中的重要课题。基于非傅里叶热传导定律,采用波函数展开法,研究了含圆柱缺陷非透明体中热波散射问题。基于热传导波动模型给出了物体中热波多重散射问题的一般解。温度波由调制光束在材料表面激发,缺陷表面的边界条件为绝热。具体分析了几何参量、各物理参量对温度分布的影响,特别分析了热波波长对温度变化的作用,并给出了温度变化的数值结果。研究结果可望为红外辐射技术、热波成像等问题的分析提供理论基础和参考数据。在检测金属材料缺陷空间分布的激光热波探测系统中应用。     

Method for solving the problems of multiple scattering by several bodies in a homogeneous unbounded medium

A method is developed for solving problems of multiple scattering by an aggregate of bodies in a homogeneous unbounded medium. For this purpose, the problem on the multiple scattering produced by two bodies in the field of a plane wave is first considered under the assumption that the initial unperturbed scattering amplitudes of both scatterers are known. The solution is constructed by considering plane waves multiply rescattered by the scatterers. Integral equations are obtained that allow one to calculate the resulting scattering amplitude of each scatterer and the combined scattering amplitude of the system of two scatterers. It is shown that knowledge of the solution to this problem is sufficient to solve the problem on the scattering field of a system consisting of an arbitrary number of scatterers. Expressions for the scattering amplitude in the case of an arbitrary primary field are presented. The relationship between the integral equations describing the multiple scattering in a homogeneous space and the multiple scattering by a single scatterer located near an interface is demonstrated. Approximate expressions are given for calculating the scattering amplitude in the case of multiple scattering.