Coherent Scattering by Multiple Particles in Phase Doppler Interferometry

A theoretical model has been developed for studying the response of the phase Doppler interferometer when multiple particles are simultaneously present within the measurement probe volume. The developed model incorporates the geometrical optics theory for describing the coherent interaction between the scattered light signals of multiple particles, eachhaving different size, velocity, trajectory, and arrival time. The resulting Doppler signal is processed by a theoretical signal processor which can simulate the performance characteristic of different signal processing schemes that are widely used in phase Doppler interferometry, namely, zero-crossing counter, covariance, autocorrelation and DFT parocessors. The application of the developed model for studying the coherent scattering by two particles has been specifically addressed in this paper. It has been shown that a DFT processor can be used to simultaneously measure the size and velocity of the two particles in most instances. However, for more than two particles, the signal processing scheme becomes more complex because of a quadratic increase in the beat frequency components.     

Light Scattering Simulation and Measurement of Monodisperse Spheroids using a Phase Doppler Anemometer

Mathematical tools are provided for the computation of the scattered field produced by non-spherical particles moving through the measurement volume of a phase Doppler anemometer. The phase distribution of a spheroid with random orientation is computed by using the rigorous extended boundary condition method and the ray theory. In a phase Doppler experiment the spheroid parameters are obtained by fitting the measured phase distribution with the simulated phase distribution. The numerical simulations are supported by experimental results on monodisperse spheroids.     

Sizing of Irregular Particles Using a Phase Doppler System

Response of a phase Doppler system to irregularly shaped particles is examined and shown to deviate qualitatively as well as quantitatively from the spherical particles. Nevertheless, the measured phase distributions based on an ensemble of particles exhibit a high degree of order and simplicity. The experimental data and the stochastic modeling of the process have shown that the phase Doppler technique can be used successfully for in-situ sizing and velocimetry of irregular particles. In the case of irregular crystalline particles, mean size and standard deviation can be deduced without requiring any assumptions regarding the functional form of the size distribution. As opposed to other optical techniques, phase Doppler can be used, in principle, near the backscattering location, so that a single optical window would be employed for transmission of laser light and collection of the scattered signals. Furthermore, size measurements can be velocity-resolved, i.e. a size distribution can be associated with each bin of the velocity histogram.     

Doppler Effect in a Moving Medium

The great increase in the accuracy of Doppler measurements in space requires a rigorous definition of the observed quantity in a moving medium, such as the solar wind. This is usually done in two different ways: in the phase point of view it is the time derivative of the correction to the optical path; in the ray point of view—suitable when the medium is confined to a small part of the ray—the signal is obtained from the deflection produced in the ray. They can be reconciled by using the time derivative of the optical path in the Lagrangean sense, i.e., differentiating from ray to ray. A rigorous derivation of this result requires an understanding, through relativistic Hamiltonian theory, of the delicate interplay between rays and phase; this is accomplished with the help of a general perturbation theorem which generalizes the concept of the Doppler effect as a Lagrangean derivative. Relativistic corrections O(v) due to retardation are obtained, well within the expected sensitivity of Doppler experiments near solar conjunction.     

Particle Sizing by Planar-Phase Doppler System

Conventional phase Doppler systems are useful for sizing particles in the order of microns, but sensitive to the Gaussian beam defect which can cause sizing errors. The defect can be significant when a large size is measured. In this paper, we present a new phase Doppler system using a planar optical layout which permits large particles to be measured in a forward scattering scheme without the Gaussian beam errors. The optical system design is discussed by numerical simulation based on the Mie theory.     

Some formulations of light scattering in laser flowmeters employing differential Doppler heterodyning

The theory for the Doppler shifted light is developed by diffraction theory combined with galilean transformation. The theory developed is applied to a differential Doppler heterodyning technique in which two beams are brought simultaneously, but at different angles, into the same area, and the cross region made by the two beams becomes a probing volume. When the concentration of scattering particles is so low that only one particle is found in the probing volume, the theory can be classified into two cases of a single particle and many particles depending on the analysing time for the Fourier transform, i.e. whether the time, during which one particle passes through the probing volume, is longer than the observing time or not. When the concentration of particles in the probing volume becomes dense, the light scattered by the different particles interferes and the theory shows great complexity. The cases of two particles and many particles showing a very high density are studied. Comparisons are made for the difference between differential Doppler heterodyning and normal heterodyning techniques.     

Some Far-Field Scattering Characteristics of Radially Inhomogeneous Particles

The finely stratified sphere model was used to calculate scattered electromagnetic fields from radially inhomogeneous spherical particles illuminated by electromagnetic plane waves. The calculation results show that radial gradients of the real part of the refractive indices change the ray paths into curved lines inside large spherical particles, resulting in fluctuations of rainbow positions for droplets during heat transfer processes. The light intensity in the forward scattering region is found to be useful to infer information about the profile of the imaginary part of the refractive index.     

非球形气溶胶粒子散射相函数经验公式

散射相函数是研究电磁波传输特性的重要参数，直接影响电磁波传输方程的简化程度和解的精度。基于电磁散射与辐射传输中的基本理论，对非球形粒子散射相函数的经验公式进行了研究。为了很好的模拟非球形粒子的后向散射峰值，提高辐射传输方程的简化程度和解的精度，提出了一种新的相函数经验公式。分析新的相函数对非球形粒子的适用性，以单个沙尘性气溶胶为例，计算了不同形状粒子的Henyey-Greenstein*相函数和新的相函数随角度的变化，并与T矩阵法的计算结果进行了对比，发现椭球形粒子的长短轴比和有限长圆柱形粒子的径长比大于0.5时，新的相函数在大角度后向散射部分与T矩阵法的吻合程度较高。考虑波长变化，对比了尺寸谱满足对数正态分布的四种气溶胶粒子的Henyey-Greenstein*相函数和新的相函数与T矩阵法的计算结果。研究表明，对于椭球形粒子和有限长圆柱形粒子，在大角度(大于90°)后向散射部分，除了0.694时的椭球形海洋性气溶胶，新的相函数均方根差较小的占100%，证明了新的相函数可以较好的模拟非球形粒子的后向散射特征。新的相函数对准确模拟辐射传输过程具有重要意义。     

High‐Temperature Stable Zirconia Particles Doped with Yttrium,Lanthanum, and Gadolinium

Zirconia microspheres synthesized by a wet‐chemical sol–gel process are promising building blocks for various photonic applications considered for heat management and energy systems, including highly efficient reflective thermal barrier coatings and absorbers/emitters used in thermophotovoltaic systems. As previously shown, pure zirconia microparticles deteriorate at working temperatures of ≥1000 °C. While the addition of yttrium as a dopant has been shown to improve their phase stability, pronounced grain growth at temperatures of ≥1000 °C compromises the photonic structure of the assembled microspheres. Here, a new approach for the fabrication of highly stable ceramic microparticles by doping with lanthanum, gadolinium, and a combination of those with yttrium is introduced. The morphological changes of the particles are monitored by scanning electron microscopy, ex situ X‐ray diffraction (XRD), and in situ high‐energy XRD as a function of dopant concentration up to 1500 °C. While the addition of lanthanum or gadolinium has a strong grain growth attenuating effect, it alone is insufficient to avoid a destructive tetragonal‐to‐monoclinic phase transformation occurring after heating to >850 °C. However, combining lanthanum or gadolinium with yttrium leads to particles with both efficient phase stabilization and attenuated grain growth. Thus, ceramic microspheres are yielded that remain extremely stable after heating to 1200 °C.     

光谱法研究等离子体粒子循环和输运

介绍了三高斯拟合技术,首先用单高斯选点拟合了Hα线形分布的远翼,由谱线的多谱勒展宽得出等离子体离子温度为170 eV,再对剩余量进行双高斯拟合,从多谱勒频移求出反射和解吸粒子入射速度分别为3.0×104 m/s和1×104 m/s,从谱线辐射强度推出再循环粒子由60%反射粒子和40%解吸粒子组成。在简化模型下讨论了粒子的输运行为,算出了氢原子密度、体发射系数和粒子约束时间的分布,均与实验结果相符。分析了粒子入射速度大小对粒子约束时间的影响,结果表明,正常放电下,HT 6M托卡马克粒子约束时间在4~8 ms;反射粒子的速度大小直接决定粒子约束时间的大小和空间分布。     

Optimum Seeding Particles for Successful Laser Doppler Velocimeter Measurements

Seeding particles for laser Doppler velocimeter (LDV) measurement have been developed which are of uniform diameter, spherical shape, low loose weight and high melting temperature. Evaluation test results show that the use of the particles can increase the signal quality substantially and extend the measurable field of the LDV, which can hardly be accessed by conventional measurement methods.     

高功率激光传输过程中散射点对光束质量的影响

为了研究高功率激光传输过程中不透明颗粒引起的光束调制,通过分析这些不透明颗粒的形状和分布特点,建立了位置呈随机分布的高斯状散射点模型,从光束的衍射理论和干涉叠加理论出发,得到该模型下散射点对传输光束质量影响的解析式。数值分析了高斯状散射点的大小、密度、散射面积比及其传输距离对输出光束的近场分布、位相分布和光束透过率的影响,结果显示亚毫米量级散射点的衍射效应引起最大调制可达1．4,光学元件散射面积比小于0．003时才能满足元件透过率大于99．5％的需求。该结果可用于评价高功率激光装置光学元件的加工状况,并对光学元件加工要求和激光装置的洁净度要求有指导意义。     

The Phase-Doppler Method Applied to Very Small Particles

Using a computer model based on Lorenz-Mie and generalized Lorenz-Mie theory, various optical confiugurations of a phase-Doppler system were analysed with regard to their suitability for diameter measurements in the sub-micron range. The major concern in this size range is multi-valuedness of the phase-diameter characteristic, the relatively small signal-to-noise ratio obtained with the very low scattered intensity and the small value of the phase difference to be measured. It is shown numerically and by experiment that for particles in a free stream the multi-valuedness and the shot noise need not prohibit measurements in the sub-micron size range. The major source of phase error results from light scattered form objects or material other than the particle inside the measuring volume. Using an optical set-up with nearly counter-propagating incident beams and a large angle between the detectors, measurements were obtained for particle diameters down to 200 nm, and it is estimated that with some improvements in receiver optics measurement down to 100 nm will be possible.     

Particles without quarks

Based on a theory of primitive particles presented in two earlier papers, further applications to macro- and microphenomena are considered—for example, weather phenomena, earthquakes, photoemission, collision of particles, violation of parity, and decay modes. A broad class of leptons withSU(3) symmetry is proposed, together with a quarkless model of particles.     

The Phase Doppler Method: Analysis,performance evaluations,and applications

This review of the recent developments in the phase Doppler method provides information on the advances made to the method and delineates some potential error sources. Methods used to eliminate these potential error sources are also discussed. It is shown through comparison to the Lorenz-Mie theory and the GLMT that the geometrical optics theory offers a reliable and efficient computational tool for the analysis of the light scattering with the phase Doppler method. The geometrical optics theory was then used to optimize the measurement parameters in the system designs and a significant reduction in the measurement uncertainty was realized. Limitations on the particle concentrations in which the instrument will operate reliably are also addressed. A brief discussion of the instrumentation and, in particular, the signal processing is presented. The advantages in using the Fourier transform approach are discussed. As a demonstration of the capabilities of the instrument, several performance tests were reviewed and examples of the application to spray combustion and turbulent dispersion of particles are given.     

Influence of Agglomerates of Conducting Spheres on the Response of a Phase-Doppler Anemometer

The influence of agglomerates of solid conducting spheres on the response of a phase-Doppler anemometer (PDA) is described for a two-sphere system by using a ray theory model. First- and second-order reflection and diffraction are considered for far-field calculations of the PDA phase difference. The numerical simulations are accompanied and supported by experimental results. Two-sphere systems of Sn63Pb37 alloy particles were captured inside an electrodynamic trap and investigated with a standard phase-Doppler system.     

Simultaneous Measurement of Velocity and Equivalent Diameter on Non-Spherical Particles

The performance of a laser-based optical technique to measure simultaneously the velocity and equivalent diameter of nonsphercial particles was evaluated. The size information was provided by the absolute intensity of diffractively scattered light by a particle crossing a single laser beam, which is concentric with a laser Doppler probe volume. The response curve (size-intensity relationship) of the technique was estimated by calculations using the Fraunhofer approximation. Experiments with spherical glass and polyethylene and non-spherical metal and ceramic particles ranging from 20 to 200 μm confirmed the operation of the technique and in all the measurements the maximum error of the average diameter was 10 μm as compared with size information provided by a microscope.     

Doppler spectrum-based polar nephelometer

The particle scattering asymmetry parameter of an ensemble of submicrometer particles, as well as the complete scattering phase function (angular distribution), is determined by measuring the Doppler spectrum of the scattered light. No calibration is required. The monitor incorporates a 532?nm laser with long coherence length, an integrating sphere to collect the scattered light, and a heterodyne (interferometric) detection scheme. Measurements of monodisperse polystyrene latex spheres and polydisperse ammonium sulfate particles indicate that the measured value of the asymmetry parameter is generally within ±0.03 of that calculated using Mie theory.     

Zwitters: Particles between quantum and classical

We describe both quantum particles and classical particles in terms of a classical statistical ensemble, with a probability distribution in phase space. By use of a wave function in phase space both can be treated in the same quantum formalism. Quantum particles are characterized by a specific choice of observables and time evolution of the probability density. Then interference and tunneling are found within classical statistics. Zwitters are (effective) one-particle states for which the time evolution interpolates between quantum and classical particles. Experimental bounds on a small parameter can test quantum mechanics.     

Optical correlation techniques in fluid dynamics

Three flow measurement techniques make use of fast digital correlators. The most widely spread is photon correlation velocimetry using crossed laser beams, and detecting Doppler shifted light scattered by small particles in the flow. Depending on the processing of the photon correlation output, this technique yields mean velocity, turbulence level, and even the detailed probability distribution of one velocity component. An improved data processing scheme is demonstrated on laminar vortex flow in a curved channel. In the second method, rate correlation based upon threshold crossings of a high pass filtered laser Doppler signal can be used to obtain velocity correlation functions. The most powerful set-up developed in our laboratory uses a phase locked loop type tracker and a multibit correlator to analyze time-dependent Taylor vortex flow. With two optical systems and trackers, cross-correlation functions reveal phase relations between different vortices. The last method makes use of refractive index fluctuations (eg in two phase flows) instead of scattering particles. Interferometry with bidirectional counting, and digital correlation and probability analysis, constitutes a new quantitative technique related to classical Schlieren methods. Measurements on a mixing flow of heated and cold air contribute new ideas to the theory of turbulent random phase screens.