Chin-Shifrin inversion algorithm for measuring of particle size distribution by laser diffraction method

YANG Fu-gui; WANG An-ting; MING Hai; XU Sheng-li

doi:10.3788/OPE.20111902.0323

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Chin-Shifrin inversion algorithm for measuring of particle size distribution by laser diffraction method

Article | 更新时间：2020-08-12

- Chin-Shifrin inversion algorithm for measuring of particle size distribution by laser diffraction method
- Optics and Precision Engineering Vol. 19, Issue 2, Pages: 323-331(2011)
- 作者机构：
  
  1. 中国科学技术大学光学与光学工程系,安徽合肥,230026
  2. 中国科学技术大学近代力学系,安徽合肥,230026
- 作者简介：
- 基金信息：
- DOI：10.3788/OPE.20111902.0323
  CLC： TN247
- Received：08 October 2010，
  
  Revised：30 October 2010，
  
  Published Online：22 February 2011，
  
  Published：22 February 2011
- 稿件说明：
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杨福桂, 王安廷, 明海, 徐胜利. 激光衍射粒径测量中的Chin-Shifrin反演算法[J]. 光学精密工程, 2011,19(2): 323-331

YANG Fu-gui, WANG An-ting, MING Hai, XU Sheng-li. Chin-Shifrin inversion algorithm for measuring of particle size distribution by laser diffraction method[J]. Editorial Office of Optics and Precision Engineering, 2011,19(2): 323-331
杨福桂, 王安廷, 明海, 徐胜利. 激光衍射粒径测量中的Chin-Shifrin反演算法[J]. 光学精密工程, 2011,19(2): 323-331 DOI： 10.3788/OPE.20111902.0323.

YANG Fu-gui, WANG An-ting, MING Hai, XU Sheng-li. Chin-Shifrin inversion algorithm for measuring of particle size distribution by laser diffraction method[J]. Editorial Office of Optics and Precision Engineering, 2011,19(2): 323-331 DOI： 10.3788/OPE.20111902.0323.

摘要

建立了以线阵CCD作为探测组件的激光衍射粒径测量系统用于颗粒群直径分布的测量。在数值计算的基础上

分析了传统Chin-Shifrin积分变换粒径分布反演算法存在的两个问题:小粒径反演结果的发散和多假峰现象

并结合理论分析给出了这两种现象的物理图像。提出了修正积分变换公式以解决小粒径反演结果发散的问题并针对Chin-Shifrin变换的具体应用

通过对比散射光强角分布特征

研究了Fraunhofer衍射对Mie散射近似的有效角度范围。计算结果显示

最大近似角度是随着粒径参数上升单调下降的

但积分变换的精度是不断提高的。最后

应用改进的Chin-Shifrin反演算法处理了实验测量数据

结果表明

改进的反演算法的精度较高

适合工业领域的应用。

Abstract

By using a linear CCD as the detector module

a measuring system for particle size distribution was established by laser diffraction. Based on numerical computation

the two problems in Chin-Shifrin integration particle size inversion algorithm:the divergence of inversion in a small particle size and its false peaks

were analyzed and the causes of these phenomena were explained. Then

the modification of the integration formula was proposed to resolve the divergence problem. Aiming at the particular application on Chin-Shifrin integral transform

the effective angle range of Fraunhofer diffraction approximation to Mie scattering was studied by comparing the pattern of Mie scattering and that of Fraunhofer diffraction.The numerical result show that the valid angle for diffraction approximation decreases as the angle becomes large

but the precision of the inversion has increased. Finally

this improved Chin-Shifrin inversion algorithm was used to process experimental data. The experimental result shows that the improved inversion algorithm has high precision and is suitable for applications in industry.

关键词

Keywords

references

CHIN J H,SLIEPCEVICH C M, TRIBUS M. Particle size distributions from angular variation of intensity of forwardscattered light at very small angle [J]. J. Phys. Chem., 1955,59:841-844.[2] SHIFRIN K S. Calculation of a certain class of definite integrals containing the square of a first order Bessel function . Tr. Vses. Zoachn. Lesotekhnich. Inst.2 ,1956.[3] SHIFRIN K S,KOLMAKOV I B. Calculation of particle size spectrum from direct and integral values of the indicatrix in the small angle region . Izv. USSR Acad. Sci. Atmos. Oceanic Phys. 3, 1967:749-753. (English translation)[4] VAN D E, HULST H C. Light Scattering by Small Particles[M].Dover, New York, 1981.[5] 戴兵,贺安之. 用线阵CCD 测量颗粒尺寸分布的研究[J]. 仪表技术和传感器, 2002(8):40-42. DAI BING, HE A Z. Research of using linear array CCD for particle-size distribution measurement[J]. Instrument Technique and Sensor, 2002(8):40-42. (in Chinese)[6] HODKINSON J R. Particle sizing by means of the forward scattering lobe[J]. Appl. Opt., 1966,5,839-844.[7] VARGAS-UBERA, GALE D.The range of validity of the Fraunhofer approximation in the estimation of particle size distributions from fight diffraction . 4th Iberoamerican Meeting on Optics and 7th Latin American Meeting on Optics, Lasers, and Their Applications. G. H. Kaufmann. Bellingham, Spie-Int Soc Optical Engineering,2001,4419:435-438.[8] KNIGHT J C, BALL D. Analytical inversion for laser diffraction spectrometry giving improved resolution and accuracy in size distribution [J]. Applied Optics, 1991,30(33):4795-4799.[9] KOO J H,HIRLEMAN E D. Synthesis of integral transform solutions for the reconstruction of particle-size distributions from forward-scattered light [J]. Applied Optics, 1992,31(12):2130-2140.[10] JONES A R. Error contour charts relevant to particle sizing by forward-scattered lobe methods [J]. Journal of Physics D: Applied Physics, 1977,10(13):L163-L165.[11] LIU J J. Essential parameters in particle sizing by integral transform inversions [J]. Applied Optics, 1997,36(22):5535-5545.[12] COSTON S D,GEORGE N. Particle sizing by inversion of the optical transform pattern[J]. Applied Optics, 1991,30(33):4785-4794.

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