The Fundamentals of Particle Size Analysis by Transmission Fluctuation Spectrometry. Part 1: A Theory of Temporal Transmission Fluctuations in Dilute Suspensions

The extinction of radiation in suspensions is traditionally described by the Bouger-Lambert-Beer law (BLBL). Based on a quasi-continuum approach, the BLBL does not account for the discrete nature of particles or their spatial extension and arrangement. If an extinction measurement is made with a high spatial and temporal resolution, the transmitted intensity signal shows significant fluctuations. The strength of fluctuation is related to the physical properties of the suspension and the process of spatial and temporal averaging. Exploiting this connection, it is possible to calculate the particle size distribution and the particle concentration from transmission measurements. This part of the series of papers provides a method for the temporal decomposition of the transmission's power spectrum, which permits the information on the particle size and concentration to be extracted from the seemingly irregular fluctuation of the transmission signal.     

The Fundamentals of Particle Size Analysis by Transmission Fluctuation Spectrometry.

A transmission signal measured on a flowing suspension of particles with a high spatial and temporal resolution shows significant fluctuations, which contain the complete information on particle size distribution and particle concentration. In Parts 1 and 2, the basic properties of signal fluctuations were studied for temporal averaging by a gliding time window and for spatial averaging by a circular beam of uniform intensity. However, the experimental implementation of such conditions is difficult. Now, the theory is extended for Gaussian beams of variable diameter and averaging by signal filtering in the frequency domain. This provides the basis for an experimental implementation by transmission of a laser beam and analog signal processing by an array of low pass filters.     

Transmission Fluctuation Spectrometry with Spatial Correlation

Transmission fluctuation spectrometry (TFS) is being developed as a new method of particle size analysis. In the early approaches, the particle suspension was illuminated by one beam with finite beam diameter and the transmission signals underwent a process with variable spatial and/or temporal averaging and a subsequent nonlinear operation. The transmission fluctuations were obtained as a spectrum which included the information on particle size distribution and particle concentration. A new approach presented here employs two narrow parallel beams. While changing the beam separation, the transmission fluctuations of these two beams are expressed in terms of the expectancy of the transmission product (ETP). The analytical expression of the ETP through a monolayer is derived and the ETP of a 3‐dimensional suspension is formulated based on the layer model. The deviation between the transition functions of 3‐dimensional suspensions and monolayers is found to be affected by effects from particle overlapping and monolayer structure.     

Transmission Fluctuation Spectrometry in Concentrated Suspensions Part Two: Particle Overlapping

Transmission fluctuations measured on a flowing suspension of particles with a high spatial and temporal resolution can be used to measure the particle size distribution and particle concentration. The theory of transmission fluctuation spectrometry (TFS) was recently developed, whereby the statistical behavior of the entire suspension is described on the basis of a single monolayer, in combination with a layer model describing the suspension as a series of independent monolayers. As the monolayers are assumed to be statistically independent from each other, the transmission through the 3‐dimensional suspension is modeled as the product of transmissions through the monolayers.     

Particle Size Analysis by Transmission Fluctuation Spectrometry: Experimental Results Obtained with a Gaussian Beam and Analog Signal Processing

Transmission fluctuation spectrometry (TFS) is a method for the analysis of particle size distributions based on the statistical fluctuations of a transmission signal. Complete information on the PSD and particle concentration can be retrieved by a special transformation of the transmission signal, whereby the expectancy of the transmission square (ETS) is determined after the signal has been subjected to a procedure of spatial and temporal averaging. By varying the averaging parameters over a wide range, a spectrum of ETSs is obtained and introduced into a linear equation system, which yields the PSD. In the experimental realization presented here, variable temporal averaging is realized in the frequency domain with a series of low pass filters at different cutoff frequencies while spatial averaging inevitably occurs as the particles pass through a focused Gaussian beam of finite cross section. Experimental results on spherical particles (glass beads) and non‐spherical particles (SiC) are presented. The PSDs are resolved in 30 intervals within a particle size range from 1–1000 μm, employing a modified Chahine inversion algorithm. So far, the measurements are limited to moderate particle concentrations. Some influences affecting the measurements, especially for higher particle concentrations, are discussed in detail.     

Locally Resolving Measurements of PSD,Particle Concentration and Particle Velocity by Means of TFS with Dual Beams

Transmission fluctuation spectrometry with spatial correlation (TFS‐SC) is based on transmitting two beams of radiation through a flowing suspension, whereby the distance of the beam centers is varied. Thus, the spatial correlation of the transmission fluctuations of the two beams is determined as a function of the beam distance. By numerical modeling, the transition functions of the correlation are found as a function of beam distance, beam diameters, particle diameter and beam intersection angle. Experimentally determined spatial correlation spectra can be inverted to obtain the particle concentration and particle size distribution by using the theoretical transition functions for mono‐sized particles. In addition, time correlations can be used to extract information on particle velocity. Some experimental results obtained by TFS‐SC are presented and discussed. This method appears promising for application in the local resolving of measurements of PSD, particle concentration and particle velocity in two‐phase flows, both in the laboratory and in process control.     

基于二阶滤波器的消光起伏谱颗粒测量结果

消光起伏频谱法是一种新的测量两相流系统中颗粒粒径分布和浓度的方法,装置简单,操作方便,适合实时、在线测量。采用二阶低通滤波器对起伏的透射率信号分析,得到消光起伏频谱实验数据,并利用改进的Chahine循环方法计算得到颗粒的粒径分布和浓度信息。重点讨论高浓度情况,包括对特征函数频率响应的修正和对其阶高修正两个方面,得到修正参量并运用到反演算法中从而得到正确的测量结果。测量结果表明,通过高浓度修正,消光起伏频谱法可以在很大的颗粒浓度动态范围得到合理的测量结果,其可测颗粒最大体积分数视颗粒的大小而定。     

Femtosecond magneto-optical Kerr microscopy

We have developed a magneto-optical Kerr microscope that allows us to measure the ultrafast magnetization dynamics of ferromagnetic nanostructures. The magneto-optical signal can be recorded in a confocal reflection geometry with an accurate selection of the polarization. The magnetization dynamics is obtained from pump-probe measurements using frequency nondegenerate collinear pump and probe beams with a temporal resolution of 180 fs. Both probe and pump beams are focused to their diffraction limit, leading to an overall spatial resolution of 600 nm. The efficiency of the apparatus is tested by investigating the magnetization dynamics of individual CoPt(3) disks with a submicrometer diameter and a thickness of 15 nm.     

Experimental Study on Particle Size Distribution and Concentration Using Transmission Fluctuation Spectrometry with the Autocorrelation Technique

Based on the statistical characteristics of the transmission fluctuations in the particle suspension, transmission fluctuation spectrometry with autocorrelation (TFS‐AC) is described theoretically, with the assumptions of geometric ray propagation and completely absorbent particles in the suspension. The experiments presented here are realized in a focused Gaussian beam with the TFS‐AC technique. The acquisition of transmission fluctuation signals is achieved by using a high‐resolution digital oscilloscope. The transition function of TFS‐AC is obtained by varying the autocorrelation time. With a modified iterative Chahine inversion algorithm, solving a linear equation retrieves information on the particle size distribution and particle concentration. Some experimental results on spherical and non‐spherical particles are presented and discussed. The experiments cover a particle size range from 1μm to 1000 μm and a particle concentration of up to 12 %.     

透过率起伏光谱分析法测粒技术

提出的透过率起伏光谱分析法是一种新的颗粒测量方法。采用一细小光束照射匀速流动的颗粒系统,通过采集透射光起伏信号,经统计处理得到透过率的平均值与起伏谱。通过求解逆问题,从透过率的起伏谱中得到颗粒粒径分布信息,再结合透过率的平均值得到颗粒的体积分数信息。给出了关于单层颗粒透过率的平均值与起伏谱的理论表达式,并推广到三维单分散和多分散的颗粒系统。对粒径在32~425μm内的稀薄颗粒系进行了部分实验测试和模拟计算,结果表明该方法可同时对颗粒粒径分布和体积分数进行有效测量。     

一种测量大面积激光束光强分布的复合阵列

针对大面积高能激光束时空分布参数测量的需要,研究了量热和光电法综合测量激光束时空分布的方法。采用现场实时定标技术有效地解决了两类数据融合问题,研制了量热光电复合阵列测量系统。该复合阵列主要由256路量热探测单元、120路光电探测单元、多通道数据采集模块和数据分析处理模块等部分组成,具有量热型探头测量绝对激光能量准确、光电探测器测量时间分辨率高等优点,实现了大面积高能激光束光强分布时间和空间的绝对测量。     

Investigations on the Capability of the Statistical Extinction Method for the Determination of Mean Particle Sizes in Concentrated Particle Systems

Due to the fast growing number of processes involving particulate systems, simple and robust measurement techniques which enable an inline monitoring of the particle size and their concentration are urgently required, since this ensures control but also process optimization. In this work, an inline measurement technique based on the statistical extinction method is developed that provides a process monitoring for a wide range of particulate processes, such as dispersion processes and spray processes. The method allows the determination of the mean size and concentration for particle systems with the size larger than 1 µm. For this purpose, a light beam illuminates the particle system, whereby the fluctuating light intensity due to the particle movement through the light beam is detected. The statistical fluctuation of the signal can be related to a mean particle size and a particle concentration. Since concentrated particle systems cause effects that additionally influence the signal, such as multiple scattering, approaches are needed to reduce or eliminate these effects. In this work, an approach using a spatial frequency filter is applied. The experimental investigations reveal that the effects can be significantly reduced with the spatial frequency filter.     

Ferrite-enhanced MRI monitoring in hyperthermia

In an MRI hyperthermia hybrid system, T₁ changes are investigated for monitoring thermal therapy at 0.2 T. The water bolus, which is needed for power transmission and cooling of the skin, limits MR image quality by signal compression and artifacts. Superparamagnetic ferrofluid in different concentration was investigated with MR relaxometry and MRI methods. We found that using ferrofluid in a low concentration of 70–90 ppm magnetite the water signal can be suppressed without susceptibility artifacts. With our method of signal suppression, a significant improvement of spatial and temporal resolution is possible. The ferrofluid is stable and allows RF heating at 100 MHz. This method of signal extinction may also be useful for other experimental setups where suppression of water is necessary.     

Deconvolution with Maximum Entropy Solution to Determine Local Extinction Coefficient and Local Volume Concentration Values from Laser Diffraction Data

The traditional use of the laser diffraction technique provides line‐of‐sight liquid spray drop‐size distribution. However, deconvolution of the measurements can be performed for axisymmetric spray in order to determine local spray characteristics. In a previous publication, a new deconvolution technique making use of the maximum entropy principle was established and applied to determine the local drop‐size distributions. The entire approach was experimentally validated. In this work, the technique is employed to determine local extinction coefficient values. As in the previous investigation, the measurement procedure consists of scanning a laser beam through the spray cross‐section from the center to the edge of the spray. By use of the transmittance theory, the local extinction coefficients allow the local volume concentrations to be calculated. This theory introduces the mean scattering coefficient. The results show that this coefficient must be determined as a function of the Sauter mean diameter in order to avoid overestimation of the volume concentration. Although no proper validation is presented, the coherence of the overall approach is discussed in detail and solutions for improving the spatial resolution are presented. Finally, the local volume concentrations are combined with the local drop‐size distribution to provide local volume‐weighted, drop‐size distributions. These distributions provide information on the localization of the drops according to their diameter as well as on the spatial liquid distribution. This work illustrates applications and performances of laser diffraction technique that are rarely used.     

光双二进制传输系统的性能研究

光双二进制信号的谱宽是传统二进制信号的一半,采用双二进制传输比二进制传输色散限制的中继距离可增加一倍.本文对采用传统光接收机的光双二进制传输系统用MATLAB进行了通信仿真.结果表明:在完全消光条件下,10 Gb/s双二进制信号在常规单模光纤上传输可达160 km,40 Gb/s双二进制信号在非零色散光纤上为30 km,均比二进制增加了一倍;详细考察了消光比对传输的影响,只有消光比大于25 dB时,双二进制相对于二进制传输的优越性才呈现出来.     

Extinction of Radiation in Sterically Interacting Systems of Monodisperse Spheres. Part 2: Experimental results

The Bouguer-Lambert-Beer law (BLBL), commonly used to describe the extinction of radiation in disperse systems, is known to be valid in the limit of low concentrations only. In Part [1] it was shown that steric particle-particle interactions lead to important effects in the range of high particle concentration and two versions of a more general extinction equation including steric interactions were derived for the regimes of fraunhofer diffraction and ray propagation in this part experimental evidence for the effects of steric interactions on the extinction of radiation in suspensions of monodisperse spherical particles is given. Various experiments on light extinction and on ultrasonic extinction are combined to cover a broad range of particle size parameters, mechanisms of particle-wave interaction and receiver apertures.     

太赫兹波在雾中的多重散射特性

太赫兹(THz)波作为微波和毫米波的延伸,它所提供的通信带宽和容量远大于毫米波。在随机介质中传播时,不但会发生时域和空域的形变,介质中的粒子还会对入射波发生散射,这些都会使得脉冲信号发生衰减。根据Mie理论与随机离散分布粒子的波传播与散射理论,计算了THz波信号入射下雾滴粒子的消光系数。结合雾滴粒子谱分布,得到了雾媒质的平均体系散射特性,采用蒙特卡罗法得到了平流雾对THz信号的多重散射特性,计算了THz波段信号对平流雾的透过率与反射率,分析了THz波段信号的前向、后向散射特性随散射角的分布。结果表明,低能见度大气环境中,雾对THz波产生的吸收和衰减不容忽视。相关研究结果对THz在大气传输、通信等方面的应用具有重要意义。     

An Experiment on Averaging in Extinction Measurements

The discrete nature of particles leads to fluctuations, in both space and time, of the radiation transmitted through a disperse system. The result of a transmission or extinction measurement is commonly expressed, however, as an average value and consecutively converted to a concentration measurement. The experiment discussed here shows that different concentration measures (volume concentration and surface concentration) can be obtained from the same measurement, depending on which level of the signal treatment the averaging procedure is introduced.     

一种大面积高能激光光束参数的在线测量方法

 提出了一种大面积连续波高能激光光束参数的在线测量方法——环形光刀扫描测量法。该方法采用偏心安装的斜面环形光刀高速扫描反射,光电探测器阵列沿反射光圆周均匀布置探测,使得绝大部分被测激光沿原光路传播,只有少量取样光被反射到探测器阵列上。通过对采集得到的探测器响应信号进行空间映射计算和图像复原,得到激光束的光强分布参数。该方法可用于光束直径数百mm的高能激光光束测量,测量空间分辨率约2 mm,时间分辨率为30~50 ms。