**3. Result and discussion**

When the aspect radio exceeds 10, fiber particle, a common shape sort in aerosol, can be considered infinitely long cylinder. Generally, particles with effective radius less than 10um are inhaled[20]. However, in 1990, the U.S. National Institute for Occupational Safety and Health stated "no evidence for a threshold or 'save' level of asbestos exposure[21]. Flying particles are inclined to keep their long axes consistent with axes of carried gas, which ensures scattering light relatively steady.

## **3.1. Wave theory for infinitely long cylinder**

The scattering geometry of infinitely long cylinder is shown in Fig.5. The *z* axis of the cylindrical coordinates *r z* , , is defined along the central axis of the cylinder. The angle between the incident ray and the negative *z* axis is denoted as . is defined as an oblique incident angle which is the complement angle of . The *x* axis is defined in the plane containing the direction of the incident ray and the *z* axis. This plane defines the angles 0 and . The coordinate *r* is then contained on the *xy* plane such that the cylinder occupies the region *r a* , where *a* is the cross-section radius of the cylinder[22,23]. To illustrate the scattering geometry, a cylinder whose diameter is larger than the incident wavelength so that the geometric optics will be used. The rays externally reflected, refracted, and internally reflected on the surface of the cylinder follow the Snell laws.

The scattering angle , which is defined as the angle between the direction of the incident wave and the scattered wave, is obtained:

$$
\cos \theta = \sin^2 \alpha + \cos^2 \alpha \cos \phi \tag{2}
$$

 is defined as an observation angle to distinguish it from the scattering angle. and are equal only at normal incidence. In all other cases, the values of are always more than that of . So there is no true backscattering for an infinitely long cylinder. Starting from Maxwell equations, after complex algebraic operations, the scattering coefficients *na* and *nb* are deduced as below:

$$\begin{aligned} b\_{n1} &= P\_n \frac{\mathbb{Q}\_n^2 + A\_n(\varepsilon\_1) B\_n(\varepsilon\_2)}{\mathbb{Q}\_n^2 + A\_n(\varepsilon\_1) A\_n(\varepsilon\_2)} \\ a\_{n2} &= P\_n \frac{\mathbb{Q}\_n^2 + B\_n(\varepsilon\_1) A\_n(\varepsilon\_2)}{\mathbb{Q}\_n^2 + A\_n(\varepsilon\_1) A\_n(\varepsilon\_2)} \\ a\_{n1} &= -b\_{n2} = P\_n \mathbb{Q}\_n \frac{A\_n(\varepsilon\_1) - B\_n(\varepsilon\_1)}{\mathbb{Q}\_n^2 + A\_n(\varepsilon\_1) A\_n(\varepsilon\_2)} \end{aligned} \tag{3}$$

Where

400 Atmospheric Aerosols – Regional Characteristics – Chemistry and Physics

*m* .

effective diameter higher than 1

**3. Result and discussion** 

cylindrical coordinates *r z* ,

angles

that of

0 and

follow the Snell laws. The scattering angle

classified according to relevant shape and size.

ensures scattering light relatively steady.

 

wave and the scattered wave, is obtained:

than the incident wavelength

**3.1. Wave theory for infinitely long cylinder** 

oblique incident angle which is the complement angle of

between the incident ray and the negative *z* axis is denoted as

are equal only at normal incidence. In all other cases, the values of

acquired by the CCD video microscope, at the same time, the scattering light of corresponding particle is collected by optical fibers and transmitted to PMT. The speeds of aerosol particles are controlled by pressure difference of inner and outer hollow sphere. By adjusting the pressure difference, the particle speeds can be restrained less than 0.4 *m s*/ for

Since scattering light contains the information about shape of particle, more significant conclusion can be obtained by comparing experimental results and calculation from theory. The shapes of aerosol particles can be deduced through scattering light distribution, and the result will be Verified by corresponding images from CCD. So the data library of scattering and image about aerosol particles is gradually built, moreover, the aerosol particles are

When the aspect radio exceeds 10, fiber particle, a common shape sort in aerosol, can be considered infinitely long cylinder. Generally, particles with effective radius less than 10um are inhaled[20]. However, in 1990, the U.S. National Institute for Occupational Safety and Health stated "no evidence for a threshold or 'save' level of asbestos exposure[21]. Flying particles are inclined to keep their long axes consistent with axes of carried gas, which

The scattering geometry of infinitely long cylinder is shown in Fig.5. The *z* axis of the

plane containing the direction of the incident ray and the *z* axis. This plane defines the

the cylinder occupies the region *r a* , where *a* is the cross-section radius of the cylinder[22,23]. To illustrate the scattering geometry, a cylinder whose diameter is larger

externally reflected, refracted, and internally reflected on the surface of the cylinder

2 2 cos sin cos cos

 

is defined as an observation angle to distinguish it from the scattering angle.

, is defined along the central axis of the cylinder. The angle

so that the geometric optics will be used. The rays

. The coordinate *r* is then contained on the *xy* plane such that

, which is defined as the angle between the direction of the incident

 

. So there is no true backscattering for an infinitely long cylinder. Starting from

 . 

. The *x* axis is defined in the

(2)

 and 

are always more than

is defined as an

$$\begin{aligned} A\_n(\boldsymbol{\varepsilon}\_{1,2}) &= j \frac{H\_n^{(2)}(la)}{H\_n^{(2)}(la)} - \boldsymbol{\varepsilon}\_{1,2} \frac{\boldsymbol{I}\_n(ja)}{\boldsymbol{I}\_n(ja)} \\ B\_n(\boldsymbol{\varepsilon}\_{1,2}) &= j \frac{\boldsymbol{I}\_n^{(2)}(la)}{\boldsymbol{I}\_n^{(2)}(la)} - \boldsymbol{\varepsilon}\_{1,2} \boldsymbol{I}\_n \frac{\boldsymbol{I}\_n(ja)}{\boldsymbol{I}\_n(ja)} \cdot \begin{cases} \boldsymbol{\varepsilon}\_1 = 1 \\ \boldsymbol{\varepsilon}\_2 = m^2 \end{cases} \\ P\_n &= \boldsymbol{I}\_n \left(la\right) \Big/ H\_n^{(2)}\left(la\right) \\ Q\_n &= \inf\{\boldsymbol{l}^2 - \boldsymbol{j}^2\} \big/ \text{xlj} \\ \boldsymbol{\chi} &= ka = 2\pi a \boldsymbol{j} / \lambda \end{aligned} \tag{4}$$

If 0*<sup>o</sup>* , then 1 2 0 *n n a b* . It should be noted that these coefficients depend on the refractive index, the size parameter and the oblique incident angle.

**Figure 5.** Geometry for light scattered by an infinitely long cylinder

Now we shall consider two simple cases separately. First, the electric vector *E* is parallel to the incident plane. This is sometimes called the TM mode. For the second case, the electric vector *E* is perpendicular to the incident plane and called the TE mode. The intensities of the scattered light in any direction are:

$$\begin{aligned} I\_{TM-11} &= 2i\_{11}I\_0 / \,\pi kR \\ I\_{TM-12} &= 2i\_{12}I\_0 / \,\pi kR \end{aligned}$$

$$\begin{aligned} I\_{TE-22} &= 2i\_{22}I\_0 / \,\pi kR \\ I\_{TE-21} &= 2i\_{21}I\_0 / \,\pi kR \end{aligned} \tag{5}$$

A Method Analyzing Aerosol Particle Shape and Scattering Based on Imaging 403

refractive index, incident wavelength and cylinder diameter, is saved in form of .txt. The data will be more analysed through Origin software and compared with information from structure

The interface of the program for calculation is shown in Fig.7, which contains input parameter area and display windows of calculating results. The display windows contain 11 *i* , <sup>22</sup> *i* and 12 *i* , also their logarithmic format. The input parameters include refractive index, laser wavelength, incident angle and radius of cylinder. In a general way, the whole process for calculation is shorter than 30s. With the increase of incident angle, the calculation time

The effective radius of selected fiber cotton particles for experiment are about 10um, compared to 1mm laser beam, the condition of infinitely long for irradiated cotton is satisfied. The incident laser with 0.65um wavelength is transformed to linear polarized light by Glan-Talyor lens.

1.573-1.581, we choose the middle number 1.577 for calculation. When the electric vector *E*

perpendicular to the incident plane, the corresponding refractive index is 1.524-1.534, we also choose the middle number 1.529 for calculation. In experiment, the angle between cotton and

The "left, right, up and down" in figure 4 refer to figure 1.It can be concluded that the tendency of experiment data keeps uniform with calculation of the infinitely long cylinder for scattering intensity and polarization. A pair of experimental signal lack in polarization

is parallel to the incident plane, the refractive index of fibre cotton is

according to shape given by CCD via microscope.

**Figure 7.** Interface of programming wave theory

**3.2. Analysis of experiment and calculation** 

will be extended slightly.

When electric vector *E*

axes of carried gas is about 5o.

The intensity coefficients for above two cases are defined as:

$$\mathbf{TM} \begin{cases} i\_{11} = \left| b\_{01} + 2 \sum\_{n=1}^{\alpha} b\_{n1} \cos n\phi \right|^2 \\\\ i\_{12} = \left| 2 \sum\_{n=1}^{\alpha} a\_{n1} \sin n\phi \right|^2 \end{cases} \quad \mathbf{TE} \begin{cases} i\_{22} = \left| a\_{02} + 2 \sum\_{n=1}^{\alpha} a\_{n2} \cos n\phi \right|^2 \\\\ i\_{21} = \left| 2 \sum\_{n=1}^{\alpha} b\_{n2} \sin n\phi \right|^2 \end{cases} \tag{6}$$

where *<sup>n</sup>*<sup>1</sup> *a* , *<sup>n</sup>*<sup>2</sup> *b* , <sup>02</sup> *a* and 01 *b* are scattering coefficients. 11 *i* and 22 *i* are the scattered intensities that lies in the same plane as the incident intensities, while 12 *i* and 21 *i* are the cross-polarized scattered intensities that have directions perpendicular to the incident intensities, what's more, 12 21 *i i* .

The polarization of scattering light is defined as[24]:

TM: 11 12 11 11 12 *i i <sup>p</sup> i i* TE: 22 21 22 22 21 *i i <sup>p</sup> i i* (7)

**Figure 6.** Schematic of programming wave theory

LabVIEW is a graphical programming language which has its roots in data acquisition and automation control. Its graphical representation, similar to a process flow diagram was created to provide an intuitive programming environment for users[25]. The language has matured over the last twenty years to become a general purpose programming environment. With LabVIEW, we have self-programmed wave theory as a part of the whole measuring system. The programming structure is demonstrated partly in Fig.6. The program consists of 3 relevant parts, which are similar at format. The calculation data, which is function of incident angle, refractive index, incident wavelength and cylinder diameter, is saved in form of .txt. The data will be more analysed through Origin software and compared with information from structure according to shape given by CCD via microscope.

**Figure 7.** Interface of programming wave theory

402 Atmospheric Aerosols – Regional Characteristics – Chemistry and Physics

The intensity coefficients for above two cases are defined as:

 

11 01 1 1 2 cos *<sup>n</sup> n ib b n*

> 

where *<sup>n</sup>*<sup>1</sup> *a* , *<sup>n</sup>*<sup>2</sup> *b* , <sup>02</sup> *a* and 01 *b* are scattering coefficients. 11

TM: 11 12 11

*i i* .

The polarization of scattering light is defined as[24]:

**Figure 6.** Schematic of programming wave theory

12 1 1 2 sin *<sup>n</sup> n i an*

intensities, what's more, 12 21

11 11 0 12 12 0

22 22 0 21 21 0

2

2

intensities that lies in the same plane as the incident intensities, while 12

11 12 *i i <sup>p</sup> i i* 

*I i I kR I i I kR*

*I i I kR I i I kR*

> 2 / 2 /

<sup>2</sup>

cross-polarized scattered intensities that have directions perpendicular to the incident

LabVIEW is a graphical programming language which has its roots in data acquisition and automation control. Its graphical representation, similar to a process flow diagram was created to provide an intuitive programming environment for users[25]. The language has matured over the last twenty years to become a general purpose programming environment. With LabVIEW, we have self-programmed wave theory as a part of the whole measuring system. The programming structure is demonstrated partly in Fig.6. The program consists of 3 relevant parts, which are similar at format. The calculation data, which is function of incident angle,

*TM TM*

*TE TE*     2 / 2 /

21 2 1 2 sin *<sup>n</sup> n i bn*

**TM TE** (6)

 TE: 22 21 22

 

22 02 2 1 2 cos *<sup>n</sup> n ia a n*

 

(5)

*i* and 22

22 21 *i i <sup>p</sup> i i* 

2

*i* are the scattered

*i* are the

*i* and 21

(7)

The interface of the program for calculation is shown in Fig.7, which contains input parameter area and display windows of calculating results. The display windows contain 11 *i* , <sup>22</sup> *i* and 12 *i* , also their logarithmic format. The input parameters include refractive index, laser wavelength, incident angle and radius of cylinder. In a general way, the whole process for calculation is shorter than 30s. With the increase of incident angle, the calculation time will be extended slightly.

## **3.2. Analysis of experiment and calculation**

The effective radius of selected fiber cotton particles for experiment are about 10um, compared to 1mm laser beam, the condition of infinitely long for irradiated cotton is satisfied. The incident laser with 0.65um wavelength is transformed to linear polarized light by Glan-Talyor lens. When electric vector *E* is parallel to the incident plane, the refractive index of fibre cotton is 1.573-1.581, we choose the middle number 1.577 for calculation. When the electric vector *E* perpendicular to the incident plane, the corresponding refractive index is 1.524-1.534, we also choose the middle number 1.529 for calculation. In experiment, the angle between cotton and axes of carried gas is about 5o.

The "left, right, up and down" in figure 4 refer to figure 1.It can be concluded that the tendency of experiment data keeps uniform with calculation of the infinitely long cylinder for scattering intensity and polarization. A pair of experimental signal lack in polarization P11 and P22, since up aperture and aerosol particle inlet with a same positions, similarly to bottom aperture and aerosol particle outlet, too. i11 and P11are more close to calculation than i22 and P22, which might be caused by different outline of fibre cotton particles. Clearly, the difference between cotton fibre in image A and infinitely long cylinder is smaller than that between image B and infinitely long cylinder. The experiment is cursory in describing trendy of scattering intensity and polarization restricted by the number of optical fibre for collecting scattering light; on the one hand, the angle increments between apertures for optical fibre are limited in manufacturing process; on the other hand, the cone angle of receiving plane for every optical fibre is 3o, unlike the elements of calculation, the integral photometric characteristics are much less dependent on particle shape.

A Method Analyzing Aerosol Particle Shape and Scattering Based on Imaging 405

An experimental apparatus has been built to measure the images and light scattering characteristics of aerosol particles simultaneously. The core portion of the analyzer is a homocentric hollow black chamber. Images, corresponding scattering intensity and polarization of fiber cottons are received. Wave theory for infinitely long cylinder has been compiled with LabVIEW. By comparison of experimental data and calculation, the affecting

factors to results are pointed out, which provides a good foundation to further study.

*Key Laboratory of Atmospheric Composition and Optical Radiation, Anhui Institute of Optics and* 

The authors are very thankful to the reviewers for valuable comments. This work was supported by Youth Talent fund from Hefei Institutes of Physics Science under Contract No. Y03AG31141. The theoretical calculations in this paper have been kindly assisted by Lei Hao

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**4. Conclusion** 

**Author details** 

**Acknowledgement** 

**5. References** 

7186(1994).

Corresponding Author

 \*

Shiyong Shao\*, Yinbo Huang and Ruizhong Rao

*Fine Mechanics, Chinese Academy of Sciences, China* 

Environmental optics 3(1), 1-10(2008).

and Yongbang Yao helped with the construction of the apparatus.

**Figure 8.** Photo of fiber micro-particle by CCD and respective scattering and polarization
