*3.3.2.2. MIE (Aerosol) scattering*

Mie scattering occurs when the particle diameter is equal or larger than one-tenth the incident laser beam wavelength, see Table 4. Mie scattering is the main cause of attenuation at laser wavelength of interest for FSO communication at terrestrial altitude. Transmitted optical beams in free space are attenuated most by the fog and haze droplets mainly due to dominance of Mie scattering effect in the wavelength band of interest in FSO (0.5 μm – 2 μm). This makes fog and haze a keys contributor to optical power/irradiance attenuation. The attenuation levels are too high and obviously are not desirable [22].

The attenuation due to Mie scattering can reach values of hundreds of dB/km [19,23] (with the highest contribution arising from fog). The Mie scattering coefficient expressed as follows [10]:

$$
\beta\_s = \alpha\_s N\_s \mathbf{1} \text{ 1/ km} \mathbf{j} \tag{14}
$$

Where:

αa: is the Mie scattering cross-section [km2 ].

Na: is the number density of air particles [1 / km3 ].

An aerosol's concentration, composition and dimension distribution vary temporally and spatially varying, so it is difficult to predict attenuation by aerosols. Although their concen‐ tration is closely related to the optical visibility, there is no single particle dimension distribu‐ tion for a given visibility [24]. Due to the fact that the visibility is an easily obtainable parameter, either from airport or weather data, the scattering coefficient βa can be expressed according to visibility and wavelength by the following expression [11]:

Free Space Optical Communications — Theory and Practices http://dx.doi.org/10.5772/58884 179

$$
\beta\_x = \left(\frac{3.91}{V}\right) \left(\frac{0.55\,\mu}{\lambda}\right)^{\nu} \tag{15}
$$

Where:

αm

N m

Where:

n

λ

N

Where:

αa

Na

of incident beam (

: is the Rayleigh scattering cross-section [

λ-4

178 Contemporary Issues in Wireless Communications

: is the index of refraction.

*3.3.2.2. MIE (Aerosol) scattering*

: is the incident light wavelength [

: is the number density of air molecules [1 /

: is the volumetric density of the molecules [1 /

are too high and obviously are not desirable [22].

: is the Mie scattering cross-section [

: is the number density of air particles [1 /

either from airport or weather data, the scattering coefficient

visibility and wavelength by the following expression [11]:

km2 ].

> km3 ].

> > km

km3 ].

The result is that Rayleigh scattering is negligible in the infrared waveband because Rayleigh

Mie scattering occurs when the particle diameter is equal or larger than one-tenth the incident laser beam wavelength, see Table 4. Mie scattering is the main cause of attenuation at laser wavelength of interest for FSO communication at terrestrial altitude. Transmitted optical beams in free space are attenuated most by the fog and haze droplets mainly due to dominance

fog and haze a keys contributor to optical power/irradiance attenuation. The attenuation levels

The attenuation due to Mie scattering can reach values of hundreds of dB/km [19,23] (with the highest contribution arising from fog). The Mie scattering coefficient expressed as follows [10]:

> km3 ].

An aerosol's concentration, composition and dimension distribution vary temporally and spatially varying, so it is difficult to predict attenuation by aerosols. Although their concen‐ tration is closely related to the optical visibility, there is no single particle dimension distribu‐ tion for a given visibility [24]. Due to the fact that the visibility is an easily obtainable parameter,

2 (13)

μm – 2 μ

(14)

can be expressed according to

βa m). This makes

Rayleigh scattering cross section is inversely proportional to fourth power of the wavelength

) as the following relationship:

m].

scattering is primarily significant in the ultraviolet to visible wave range [10].

of Mie scattering effect in the wavelength band of interest in FSO (0.5

βa= αaNa 1 / km

> km2 ].

3N 2 λ4

αm<sup>=</sup> <sup>8</sup>π3(n<sup>2</sup> - 1)<sup>2</sup> V : is the visibility (Visual Range) km.

λ: is the incident laser beam wavelength μm.

i: is the size distribution of the scattering particles which typically varies from 0.7 to 1.6 corresponding to visibility conditions from poor to excellent.

Where:

$$i = 1.6 \text{ for } V > 50 \text{ km.}$$

$$i = 1.3 \text{ for } 6 \text{ km} \le V \le 50 \text{ km.}$$

$$i = 0.585 \text{ } V^{1/3} \text{ for } V < 6 \text{ km.}$$

Since we are neglecting the absorption attenuation at wavelength of interest and Rayleigh scattering at terrestrial altitude and according to Eq. 8 and Eq. 11 then:

$$
\beta\_{\text{scat}} = \beta\_s \tag{16}
$$

The atmospheric attenuation τis given as:

$$\tau = \exp\left(\cdot \beta\_s L\right) \tag{17}$$

The atmospheric attenuation in dB, τcan be calculated as follows:

$$
\pi = 4.3429 \,\beta\_s L \,\text{[dB]} \tag{18}
$$

#### *3.3.2.3. Rain*

Rain is formed by water vapor contained in the atmosphere. It consists of water droplets whose form and number are variable in time and space. Their form depends on their size: they are considered as spheres until a radius of 1 mm and beyond that as oblate spheroids: flattened ellipsoids of revolution [11].

#### **Rainfall effects on FSO systems:**

Scattering due to rainfall is called non-selective scattering, this is because the radius of raindrops (100 – 1000 μm) is significantly larger than the wavelength of typical FSO systems. The laser is able to pass through the raindrop particle, with less scattering effect occurring. The haze particles are very small and stay longer in the atmosphere, but the rain particles are very large and stay shorter in the atmosphere. This is the primary reason that attenuation via rain is less than haze [24]. An interesting point to note is that RF wireless technologies that use frequencies above approximately 10 GHz are adversely impacted by rain and little impacted by fog. This is because of the closer match of RF wavelengths to the radius of raindrops, both being larger than the moisture droplets in fog [14]. The rain scattering coefficient can be calculated using Stroke Law [25]:

$$\mathcal{B}\_{\text{train } \text{scat}} = \text{ } \pi \text{a}^2 \, N\_\text{a} \mathcal{Q}\_{\text{scat}} \left( \frac{\text{a}}{\text{\AA}} \right) \tag{19}$$

Where:

*a*: is the radius of raindrop, (cm).

Na : is the rain drop distribution, (cm-3).

Qscat: is the scattering efficiency.

The raindrop distribution Nacan be calculated using equation following:

$$N\_g = \frac{R}{1.33 \text{(}\pi s^3\text{)} \, V\_s} \tag{20}$$

Where:

*R*: is the rainfall rate (cm/s),

*V*a: is the limit speed precipitation.

Limiting speed of raindrop [25] is also given as:

$$\mathcal{V}\_{\mathfrak{s}} = \frac{2\mathcal{A}^2 \rho \mathbf{g}}{9\eta} \tag{21}$$

Where:

ρ: is water density, (ρ =1 g / cm<sup>3</sup> ).

g: is gravitational constant, g = 980 cm / sec 2 .

η: is viscosity of air, η = 1.8 \* 10 -<sup>4</sup> g / cm.sec.

The rain attenuation can be calculated by using Beer's law as:

$$\tau = \exp\left(\cdot \beta\_{\text{rain } \text{scat}} L\right) \tag{22}$$

For more details about several weather conditions and the corresponding visibility at various wavelengths readers can refer to references [26,27].
