利用彩虹强度角谱分布对圆柱直径的测量

采用ＣＣＤ线阵的散射光强角分布测量系统,测量了水、酒精液柱、光纤的彩虹角分布。根据严格米氏理论,数值研究了大尺寸参数圆柱的彩虹现象,获得与实验相吻合的数值结果。讨论了几何光学和艾里理论局限性,将米氏理论和几何光学结合,对彩虹现象给予了更为合理的解释。利用第一级彩虹角反演折射率,以及将彩虹强度导数角分布进行快速傅里叶变换获得了角谱反演圆柱粒子的直径。并讨论了利用角谱反演粒子折射率和直径的精度。     

圆形截面微通道的双一阶彩虹现象研究

基于几何光学理论及Debye理论,研究圆形截面微通道这一双层圆柱产生的双一阶彩虹现象。由于全反射现象,双一阶彩虹并非始终存在,故通过数值模拟,得出内外径比的临界值来判断双一阶彩虹的存在性。当双一阶彩虹存在时,双一阶彩虹中的彩虹总是可被观察到;彩虹在某些情况下会因光强较弱而被淹没在以二阶彩虹为主的其他散射结构中。研究发现彩虹位于二阶彩虹主峰右侧时,其可被观测到。为此分析彩虹与二阶彩虹两者主峰散射角重叠这一临界情况,进而提出判断彩虹能否被被观测到的方法。最后,构建实验系统,以充满去离子水的高硼硅玻璃毛细管为对象进行实验研究,通过CCD相机拍摄彩虹图像。结果表明,毛细管内径为550 m、外径为600 m时,其内外径比大于上述临界值0.7485,故双一阶彩虹存在。但是由上述判断方法得出彩虹无法被观测到,这一结论与仅能从拍摄图像中获得彩虹结构的现象相符。     

Der Regenbogeneffekt und Interferenzerscheinungen bei molekularen Stößen

Crossed beam measurements of differential elastic scattering cross sections for collisions of alkali atoms with mercury and xenon atoms as well as with different molecules are presented. Special attention is given to the rainbow effect including supernumary rainbows and to interference effects connected with rainbow scattering. The observation of well resolved primary and supernumary rainbows together with interference patterns make the determination of a three parameter potential model possible. Partial wave numerical calculations of differential cross sections are used to evaluate potential parameters and to discuss the limits of the semiclassical rainbow theory. Elastic scattering between reactive collision partners is investigated too and interpreted in terms of a simple optical model.     

Nature’s optics and our understanding of light

Optical phenomena visible to everyone have been central to the development of, and abundantly illustrate, important concepts in science and mathematics. The phenomena considered from this viewpoint are rainbows, sparkling reflections on water, mirages, green flashes, earthlight on the moon, glories, daylight, crystals and the squint moon. And the concepts involved include refraction, caustics (focal singularities of ray optics), wave interference, numerical experiments, mathematical asymptotics, dispersion, complex angular momentum (Regge poles), polarisation singularities, Hamilton’s conical intersections of eigenvalues (‘Dirac points’), geometric phases and visual illusions.     

Relation between Debye series and generalized Lorentz--Mie theory of laser beam scattering by multilayer cylinder

With the recursive relations of Bessel function and applying inductive approach, the consistency between the scattering coefficient formula of Debye series and that of the generalized Lorentz-Mie theory (GLMT) in the scattering of a multilayer cylinder illuminated by a laser beam is proved in detail. As an application example, rainbow phenomenon in the scattering of a two-layer cylinder is discussed by the Debye series components. It can be concluded that the radius and the refractive index of a two-layer cylinder have an effect on the twin-primary rainbow, and the high-order Debye series components which are associated with the high-order rainbows are more complex than those of a homogeneous cylinder.     

Classical theory of atom–surface scattering: The rainbow effect

The scattering of heavy atoms and molecules from surfaces is oftentimes dominated by classical mechanics. A large body of experiments have gathered data on the angular distributions of the scattered species, their energy loss distribution, sticking probability, dependence on surface temperature and more. For many years these phenomena have been considered theoretically in the framework of the “washboard model” in which the interaction of the incident particle with the surface is described in terms of hard wall potentials. Although this class of models has helped in elucidating some of the features it left open many questions such as: true potentials are clearly not hard wall potentials, it does not provide a realistic framework for phonon scattering, and it cannot explain the incident angle and incident energy dependence of rainbow scattering, nor can it provide a consistent theory for sticking. In recent years we have been developing a classical perturbation theory approach which has provided new insight into the dynamics of atom–surface scattering. The theory includes both surface corrugation as well as interaction with surface phonons in terms of harmonic baths which are linearly coupled to the system coordinates. This model has been successful in elucidating many new features of rainbow scattering in terms of frictions and bath fluctuations or noise. It has also given new insight into the origins of asymmetry in atomic scattering from surfaces. New phenomena deduced from the theory include friction induced rainbows, energy loss rainbows, a theory of super-rainbows, and more. In this review we present the classical theory of atom–surface scattering as well as extensions and implications for semiclassical scattering and the further development of a quantum theory of surface scattering. Special emphasis is given to the inversion of scattering data into information on the particle–surface interactions.     

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.     

相对折射率趋近于1的颗粒Mie散射与反常衍射的分析比较

利用Ｍｉｅ散射与反常衍射理论的数值计算，对球形颗粒Ｍｉｅ散射和反常衍射作了大量详细的计算和分析比较，提出了相对折射率趋近于１的颗粒的反常衍射近似替代Ｍｉｅ散射的判据。     

均匀球形液滴二阶和五阶彩虹的重建及应用

从理论和实验两方面研究了不同温度下球形液滴的彩虹强度分布及在粒度测量中的应用。研究结果表明折射率为 1.33附近液滴在 117°～ 134°散射角范围内的散射强度分布不是单一的二阶彩虹强度分布 ,而是二阶和五阶彩虹的干涉强度分布。基于散射强度频谱特点 ,提出了一种从干涉强度谱中重建二阶和五阶彩虹强度分布的方法 :逆快速傅里叶变换 (IFFT)。利用洛伦兹米理论 (LMT)模拟计算了温度为 2 0℃和 80℃下水粒子二阶彩虹的高频结构与粒子直径的关系 ,获得了经验公式。该关系式可用来测量确定温度下均匀水粒子直径。还利用激光彩虹测试系统测量了水柱二阶彩虹角度范围内的散射强度分布。上述理论研究结果与实验结果进行了比较 ,两者吻合得很好。基于上述研究 ,可以从单一阵列探测器获取的彩虹信号提取不同阶次彩虹分布 ,用于液滴多参量的反演测量。     

On rainbows of inhomogeneous spherical droplets

The paper is devoted to the study of the intensity distributions and the angular spectra of the second and fifth rainbows of homogeneous and inhomogeneous spherical particles predicted by Lorenz-Mie theory. The results show that the distribution around the second rainbow angle for a homogeneous sphere of refractive index between 1.32 and 1.33 is due to the interference of the light after two or five internal reflections. The structure of the scattering diagram and the angular spectrum for homogeneous and radially inhomogeneous spheres are studied. For a homogeneous sphere we show that the second and fifth rainbows can be independently reconstructed by filtering the calculated spectrum. Since each order of rainbow penetrates the particle to different depths, such methods could be used to provide information about the refractive index profile or the temperature gradient of an inhomogeneous sphere. The Airy-like peaks of the second and fifth rainbows are closely connected with the refractive index profile, which is beneficial to the measurement of its refractive index profile or temperature gradient.     

Interatomares Potential aus Streuexperimenten: K-Hg

Measurements of rainbow scattering, including supernumerary rainbows, the extrema in the velocity dependence of the total cross section and the oscillations in the differential cross section are used to evaluate the parameters of an?6 Lennard-Jones potential for the collision partners K-Hg.     

彩虹现象和圆柱折射率及直径的反演

彩虹现象和圆柱折射率及直径的反演吴振森李明柱（西安电子科技大学物理系西安７１００７１）ＴｈｅＲａｉｎｂｏｗａｎｄｔｈｅＲｅｖｅｒｓａｌｏｆＣｉｒｃｕｌａｒＣｙｌｉｎｄｅｒＤｉａｍｅｔｅｒａｎｄＲｅｆｒａｃｔｉｖｅＩｎｄｅｘＷｕＺｈｅｎｓｅｎ，ＬｉＭｉ...     

Mie光散射理论的数值计算方法

Mie散射级数的计算速度和精度对颗粒测量结果有着重要的影响。针对不同颗粒直径和相对折射率，一般采用前向递推，后向递推，连分式法等计算Mie散射级数。在这3种方法的基础上提出一种改进算法，即首先通过连分式法计算Mie散射级数的初始值，然后后向递推其余各值。该算法在Matlab中实现时，数据以数组的数据类型存储和调用，程序采用递归算法。通过比较计算结果发现，该算法耗时短且结果不易溢出，具有快速、稳定、不受颗粒直径和折射率范围影响等优点。     

Rainbows with a Si thin crystal

This study is devoted to the transmission of Ne¹⁰⁺ ions through a Si thin crystal. The ion energy is 60 MeV and the crystal thickness is varied from 159 to 478 atomic layers, i.e. within the first rainbow cycle. The analysis is performed by the theory of crystal rainbows. The angular distribution of the transmitted ions is generated by the computer simulation method. Then, the rainbow lines in the scattering angle plane are determined. These lines ensure the full explanation of the angular distribution. Received 11 May 2000     

Mie理论递推公式计算散射相位函数

在激光雷达探测中,关于多次散射雷达回波的研究,散射相位函数是个非常重要的物理量。本文利用Mie理论的递推公式,对单一粒径介质的散射相位函数进行了计算,计算结果与散射理论中前、后向散射峰值大小随粒子半径的增大而增大相一致。同时,对非单一粒径介质的散射相位函数进行了计算,可用于大气、雾和云等气溶胶多次散射的研究。     

Classical surface scattering computations; Rainbows and energy exchange

Computational techniques (a “response-function” method and a molecular dynamics procedure) for classical calculations of atom-surface scattering are described. The methods are illustrated by calculations for a model of neon scattering from the silver (111) surface. Calculations for clamped and initially stationary lattices show complex classical rainbow effects with multiple rainbows due to scattering from different regions of the crystal surface. These effects are not destroyed by inelasticity or energy exchange with cold crystals. Calculations at higher temperatures show, however, that thermal effects do smear out the rainbow effects and lead to rather featureless angular distributions similar to those observed experimentally for this system.     

基于Mie光散射理论的尾流气泡前向散射光特性研究

实验中利用CMOS图像传感器代替传统的光电探测器接受前向散射光,由几何光学和图像处理分析得出不同散射角的散射光与采集图像中的光环相对应.通过计算各个光环的所有像素值的总和就可以得到前向散射光光强的相对值,进而可以得出前向散射光光强变化规律.根据米氏（Mie）光散射理论可以计算出气泡各个方向的散射光光强,通过比较实验结果和Mie理论计算结果可以看出,采用CMOS图像传感器探测和图像处理技术可以准确地得出散射光强度的变化规律.     

On geometric optics and surface waves for light scattering by spheres

A geometric optics approach including surface wave contributions has been developed for homogeneous and concentrically coated spheres. In this approach, a ray-by-ray tracing program was used for efficient computation of the extinction and absorption cross sections. The present geometric-optics surface-wave (GOS) theory for light scattering by spheres considers the surface wave contribution along the edge of a particle as a perturbation term to the geometric-optics core that includes Fresnel reflection–refraction and Fraunhofer diffraction. Accuracies of the GOS approach for spheres have been assessed through comparison with the results determined from the exact Lorenz–Mie (LM) theory in terms of the extinction efficiency, single-scattering albedo, and asymmetry factor in the size–wavelength ratio domain. In this quest, we have selected a range of real and imaginary refractive indices representative of water/ice and aerosol species and demonstrated close agreement between the results computed by GOS and LM. This provides the foundation to conduct physically reliable light absorption and scattering computations based on the GOS approach for aerosol aggregates associated with internal and external mixing states employing spheres as building blocks.     

Differential cross sections for chemically reactive systems

A quantum mechanical theory is developed for the differential and total elastic and reactive scattering cross sections for an electronically adiabatic bimolecular exchange reaction, with the restriction that the three atoms are constrained to move on a straight line, but with the whole system free to rotate in three dimensions. The introduction of a set of natural collision coordinates, together with a vibrationally adiabatic approximation, is used to reduce the scattering problem to the solution of one-dimensional Schrödinger equations. Semi-classical expressions for the elastic and reactive phase shifts are derived. The partial wave summations that occur in the theory are evaluated by semi-classical techniques and elastic and reactive differential cross sections are calculated for three different kinds of potential surface. A feature of the calculations is the appearance of a new kind of rainbow, which is named a ‘cubic’ rainbow since it arises when the deflection function varies cubically with impact parameter. The classical and semi-classical theory of cubic rainbows is developed.