*3.3.2. Scattering*

Scattering is defined as the dispersal of a beam of radiation into a range of directions as a result of physical interactions. When a particle intercepts an electromagnetic wave, part of the wave's energy is removed by the particle and re-radiated into a solid angle centered at it. The scattered light is polarized, and of the same wavelength as the incident wavelength, which means that there is no loss of energy to the particle [10].

There are three main types of scattering: (1) Rayleigh scattering, (2) Mie scattering, and (3) nonselective scattering. Figure 8 illustrates the patterns of Rayleigh, Mie and non-Selective scattering.

**Figure 8.** Patterns of Rayleigh, Mie and Non-selective scattering.

The scattering effect depends on the characteristic size parameter x<sup>0</sup>, such as that x<sup>0</sup> = 2πr / λ, where, r is the size of the aerosol particle encountered during propagation [19]. If x0< < 1, the backward lobe becomes larger and the side lobes disappear as shown in Fig. 8 [20] and the scattering process is termed as Rayleigh scattering. If x<sup>0</sup> ≈ 1, the backward lobe is symmetrical with the forward lobe as shown in Fig. 8 and then it is Mie scattering. For x0> > 1, the particle presents a large forward lobe and small side lobes that start to appear as shown in Fig. 8 [20] and the scattering process is termed as non-selective scattering. The scattering process for different scattering particles present in the atmosphere is summarized in Table (4) [21]. It is possible to calculate the scattering coefficients from the concentration of the particles and the effective cross section such as [16]:

$$
\beta\_{\text{scat}} = \alpha\_{\text{scat}} N\_{\text{scat}} \mathbf{[1/km]} \tag{10}
$$

Where:

**Figure 7.** Atmospheric transmittance window with absortion contribution.

there is no loss of energy to the particle [10].

176 Contemporary Issues in Wireless Communications

**Figure 8.** Patterns of Rayleigh, Mie and Non-selective scattering.

Scattering is defined as the dispersal of a beam of radiation into a range of directions as a result of physical interactions. When a particle intercepts an electromagnetic wave, part of the wave's energy is removed by the particle and re-radiated into a solid angle centered at it. The scattered light is polarized, and of the same wavelength as the incident wavelength, which means that

There are three main types of scattering: (1) Rayleigh scattering, (2) Mie scattering, and (3) nonselective scattering. Figure 8 illustrates the patterns of Rayleigh, Mie and non-Selective

*3.3.2. Scattering*

scattering.

βscat: is either Rayleigh (molecular) βm or Mie (aerosols) βascattering.

αscat: is a cross-section parameters [km2 ].

Nscat: is a particle concentration [1 / km3 ].

The total scattering can be written as:

$$
\boldsymbol{\beta}\_{\text{scat}} = \boldsymbol{\beta}\_{\text{m}} + \boldsymbol{\beta}\_{\text{J}} \mathbf{1} / \,\text{km}\mathbf{j} \tag{11}
$$


**Table 4.** Typical atmospheric scattering parameters, with size parameter.

#### *3.3.2.1. Rayleigh (molecular) scattering*

Rayleigh scattering refers to scattering by molecular and atmospheric gases of sizes much less than the incident light wavelength. The Rayleigh scattering coefficient is given by [16]:

$$
\beta\_{\rm m} = \alpha\_{\rm m} N\_{\rm m} \mathbf{\ulcorner} \mathbf{1} \mathbf{/} \text{km} \mathbf{\ulcorner} \tag{12}
$$

Where:

αm: is the Rayleigh scattering cross-section [km2 ].

N m: is the number density of air molecules [1 / km3 ].

Rayleigh scattering cross section is inversely proportional to fourth power of the wavelength of incident beam (λ-4 ) as the following relationship:

$$\alpha\_m = \frac{8\pi^3 (n^2 \cdot 1)^2}{3N^2 \lambda^4} \text{[km}^2\text{]}\tag{13}$$

Where:

n: is the index of refraction.

λ: is the incident light wavelength [m].

N: is the volumetric density of the molecules [1 / km3 ].

The result is that Rayleigh scattering is negligible in the infrared waveband because Rayleigh scattering is primarily significant in the ultraviolet to visible wave range [10].
