The working principle of a laser particle size analyzer

When light passes through an inhomogeneous medium, scattering from its straight-line propagation direction occurs, which is caused by the combined action of absorption, reflection, refraction, transmission, and diffraction. Scattered light forms contain scatterer size, shape, structure and composition, composition and concentration information. Therefore, the light scattering technique can be used to measure the concentration distribution and refractive index of the particle population, and the size distribution of the particle population can also be measured. The structure of the laser particle size analyzer is shown in Figure 1.

Figure 1 Simple device diagram of laser particle size analyzer

The beam emitted by a laser ( typically a He-Ne laser or a semiconductor laser ) . After the spatial filter and the beam expander lens, a parallel monochromatic light beam is obtained, and the light beam is irradiated to the particle sample transmitted by the dispersion system and then scattered. Studies have shown that the angle of scattered light is inversely proportional to the particle diameter, and the scattered light intensity decays logarithmically with increasing angle. These scattered lights are imaged by the Fourier lens on the focal plane of the multi-ring photodetector. The central detector on the multi-ring detector is used to determine the volume concentration of the sample, and the peripheral detector is used to receive the scattered light energy and convert it into an electric signal, and the energy distribution of the scattered light is directly related to the particle size distribution. By receiving and measuring the energy distribution of the scattered light, the particle size distribution characteristics of the particles can be inverted.

The development of the theory of two scattering

The laser particle size analyzer is mainly based on the two optical theories of Fraunhofer diffraction and Mie scattering. The following is a brief explanation of the development history of laser particle size analyzer scattering theory:

The study of scattering theory began in the 1970s of the last century. In 1871, Lord Rayleigh first proposed the famous Rayleigh scattering law and explained the essence of light scattering from an electronic point of view [1] . The application of Rayleigh's law of scattering is that the size of the scatterer is smaller than the wavelength of the light wave. In 1908, G. Mie solved a strict mathematical solution to light scattering through Maxwell's equation of electromagnetic waves , and obtained the scattering law of uniform particles of arbitrary diameter and arbitrary composition. This is the famous Mie theory. [2] . In 1957, H.C. Van de Hulst published a monograph on the phenomenon of light scattering from microscopic particles, summarizing the general laws of particle scattering. It has received extensive attention from people in the scientific and technological community. This monograph is considered to be a classic literature in the field of light scattering theory. [3] . In 1969 , the M. Kerker system discussed the general laws of light and electromagnetic scattering and contributed to the further development of scattering theory [4] . In 1983, C. F. Bo hren, O. R. Huff man Comprehensive results of previous studies, also published on tiny particles of light scattering and absorption of general laws, a more comprehensive explanation of the various light scattering phenomena [5]. At this point, the system of scattering theory was established.

In 1976, J. Swit henbank and others developed the laser particle sizer using the Mie's theory approximative formula of the time (d is the diameter of scattering particles and λ is the wavelength of light waves) [6] . Open up a new field of scattering theory in the measurement test. Because of the wide range of suitable light scattering from the particles affect the electrical and optical characteristics of the characteristic parameter measurement, particle size measurement it has become one of the most important ways within the next thirty years.

Introduction to Triple Scattering Theory

Rayleigh scattering law of

In 1871, Rayleigh first theoretically explained the phenomenon of light scattering, and conducted precise research on the scattering of tiny particles that are much smaller than the wavelength of the light wave. The famous Rayleigh scattering law was obtained, which is the intensity of scattered light and incident light. The wavelength of light is inversely proportional to the fourth power, that is: Isca ≈ 1/λ 4 where Isca is the scattered light intensity corresponding to a viewing direction (theta angle with the incident light) and λ is the wavelength of the incident light. Rayleigh believes that when a beam of light enters the scattering medium, it will cause a forced vibration of each molecule in the scattering medium. These molecules that are forced to vibrate will become new point sources of light and radiate secondary waves outward. The composite wave that these secondary waves are superimposed with the incident wave is the refracted wave that propagates in the scattering medium. For a homogeneous scattering medium, these secondary waves are coherent. As a result of their interference, only the synthetic wave in the direction of the refracted light is strengthened, and the rest of the directions are canceled out by interference. This is the refraction of light. If the scattering medium is inhomogeneous and destroys the positional relationship between the scatterers, each secondary wave is no longer coherent. In this case, the effect of strengthening the synthetic wave refraction due to interference also disappears. There will be light propagation, which is scattering [1] .

2. Mie scattering

Mie Scattering In 1908, G. Mie [7] based on the electromagnetic theory, obtained a strict mathematical solution for the scattering of a planar monochromatic wave by a uniform sphere of arbitrary diameter and arbitrary composition in a uniform scattering medium. According to the Mie scattering theory [8] , the scattering characteristics of incident light by tiny particles in the medium are related to the size of the scattering particles, the relative refractive index, the intensity of the incident light, the wavelength and degree of polarization, and the relative observation direction (scattering angle). . The laser particle size analyzer measures and calculates the different physical quantities of the scattered light, and then obtains the parameters such as the size, distribution, and the concentration of the particles. When a natural or plane polarized light with intensity I 0 is incident on isotropic spherical particles, the scattered light intensity is [9] :

In the formula: θ, λ, a As mentioned before, m = (n-iη) is the refractive index of the particles with respect to the surrounding medium (η is not zero indicates that the particles have absorption), r is the distance from the particle to the observation plane, Φ It is the included angle of the electric vector of the incident light with respect to the scattering surface, and s 1 , s 2 are the amplitude function components of the vertical and parallel to the scattering plane respectively. It is an infinite series composed of the Bessel function and the Legendre function [8] .

3. Fraunhofer diffraction

The diffraction of light is the deviation of the light wave from the original propagation direction into the geometric shadow area of ​​the obstacle after encountering obstacles in the propagation process, and the uneven distribution of the light intensity is observed on the observation screen behind the obstacle. Fraunhofer diffraction is the diffraction when the light source and the distance from the observation screen to the infinity are all infinity, and the diffraction field can be observed on the back focal plane of the lens. Let the focal length of the lens be f, the diameter of the particle be D, and the wavelength of the incident light in the medium surrounding the particle is λ, then the diffraction intensity of the particle on the focal plane of the lens is [10] :

Where : I 0 is the incident light intensity, a is the particle size parameter (α=πD/λ), S d is the diffraction light amplitude function, i 1 and i 2 are the diffracted light intensity functions (i 1 =i 2 ), J 1 is the first-order Bessel function, and θ is the diffraction angle. For Fraunhofer diffraction, the total extinction coefficient Ke = 2 [3] . In [7], Fraunhofer diffraction was used to directly measure the particle size of large particles. In the 1970s abroad, a laser particle sizer based on Fraunhofer diffraction theory was developed.

4. Comparison of Fraunhofer diffraction and Mie scattering

Theoretical analysis suggests that the Fraunhofer diffraction model itself has higher accuracy when the particle is much larger than the wavelength, which can be seen as an approximation of the Mie scattering [9] . Due to the complexity of Mie's theoretical calculations and the difficulty of computer implementation, early laser particle sizers generally worked on the principle of Fraunhofer diffraction. With the development of science and technology and computers, instrument manufacturers first adopted Mie theory in the submicron range, and later in the full range. Used internally, called the " full Mie theory ." Originally thought that the measurement of large particles can use the Fraunhofer diffraction theory, but in addition to the diffraction effect of the large particles placed in the light field, there is a geometric scattering effect caused by the reflection and refraction of geometric optics, which is much smaller in terms of strength. The former, but the total energy is comparable. The use of diffraction theory to calculate the distribution of light energy clearly ignores the geometrical scattering and therefore has a large error [11] . Mie scattering theory is a rigorous theory that describes the light scattering of particles. Relevant experts [11,12] believe that when non-absorbing particles are analyzed by Fraunhofer diffraction theory, the scattered light energy will be “out of the blue ” and that there are small particle peaks near the lower measurement limit of the instrument (if the instrument can perform multi-peak analysis). ). [12] Comparative results of calculation by the Fraunhofer diffraction and rigorous Mie scattering values indicated, the Fraunhofer diffraction condition is applicable: the instrument measurement limit is greater than 3μm, or absorptive particles are measured and the particle size larger than 1μm. Mie theory should be used when the lower limit of the instrument measurement is less than 1μm, or when the particle size is much larger than 1μm using an instrument with a lower measurement limit of less than 3μm. In addition, the refractive index of the particles also has a great influence on the measurement results. For the absorptive particles, the Fraunhofer diffraction results are basically consistent with the Mie scattering results. For non-absorbing particles, there is a certain bias between the two. Literature [13] considered that when the imaginary part of the relative refractive index of particles is η<0.03 or η>3, Mie theory must be used to calculate the coefficient matrix.

Four conclusions

In this paper, the working principle of laser particle size analyzer departure, briefly discusses the development history scattering theory, and were introduced one by one scattering theory, including the law of Rayleigh scattering, Mie scattering, Fraunhofer diffraction, Fraunhofer diffraction and final article will Mie The scattering theory is qualitatively compared in practical applications. The Mie scattering theory is universal, and the Fraunhofer diffraction theory has many limitations.

references

1 Zhao Kaihua, Zhong Xihua 1 Optics (in Chinese) 1 Beijing: Peking University Press, 1984: 251~254

2 Mie G. Annalen der Physik. 1908;4(25):377

3 Van de Hulst H C. Light Scattering by Small Particles. New York : Wiley, 1957 :(2~5,103)

4 Kerker M. The Scattering of Light and Ot her Electromagnetic Radiation. New York : Academic , 1969 : 1-3

5 Bohren C F , Huff man D R. Absorbtion and Scattering of Light by Small Particles. New York : Wiley 1983 : 2-6

6 Swit henbank J. A laser diagnositic technique for t he measurement of droplet and particle size dist ribution. AIAA Paper ,1976 ;692(76) :69,896

7 Mie G. Beitragezur optikturber medienspeziell kolloedaler   Metallosungen[J]. Annalender Phisik, 1908, 4(25): 377

8 BohrenCF, HuffmanDR. Absorptionand scatteringof   Light bysmall particles[M]. NewYork: WileyPress,1998

9 Wang Naining. Optical Measurement Technology of Particle Size and Its Application[M]. Beijing: Atomic Energy Press, 2000.189

10 Yang Lan, Zhang Zhenxi, Jiang Dazong. Analysis and Comparison of Large Particle Mie Scattering and Fraunhofer Diffraction Problems[J].Laser Technology,1998,22(1):18

11 Zhang Fugen, Rong Yuelong, Cheng Lu. The error of using diffraction theory for measuring large particles by laser scattering method[J]. Powder Science and Technology, 1996,2(1):7

12 Zhang Fugen. The necessity of using modern Mie theory for modern laser particle size analyzers [D]. In Zhang Fugen: Basic theory of particle size measurement and research papers. Zhuhai: Occidental Technology Co., Ltd., 2001.76

13 Xu Feng, Cai Xiaoshu, et al. Discussion of Fraunhofer diffraction theory or Mie theory in light scattering particle size measurement[J]. China Powder Science and Technology, 2003,9(2):1