**3.1 Aerosols**

Aerosols are particles suspended in the atmosphere such as fog, haze, dust and smog, and they have diverse nature, shape, and size. Aerosols can vary in distribution, constituents, and concentration. The larger concentration of aerosols is in the boundary layer (a layer up to 2 km above the earth surface). Above the boundary layer, aerosol concentration rapidly decreases [3].

Scattering is the main interaction between aerosols and a propagating beam. Because the sizes of the aerosol particles are comparable to the wavelength of interest in optical communications, Mie scattering theory is used to describe aerosol scattering [17].


Table 3. Radius Ranges for Various Types of Particles.

Such a theory specifies that the scattering coefficient of aerosols is a function of the aerosols, their size distribution, cross section, density, and wavelength of operation. The different types of atmospheric constituents' sizes and concentrations of the different types of atmospheric constituents are listed in Table (3) [6], [18].

## **3.2 Visibility runway visual range (RVR)**

Visibility defined as (Kruse model) means of the length where an optical signal of 550 nm is reduced to 0.02 of its original value. It is characterized by the transparency of the atmosphere, estimated by a human observer. Visibility is a useful measure of the atmosphere containing fog, smog, dust, haze, mist, clouds and other contaminating particles. Thick fog can reduce visibility down to a few meters; and maritime mist and clouds can affect visibility in the same way [19].

Low visibility will decrease the effectiveness and availability of FSO systems, and it can occur during a specific time period within a year or at specific times of the day. Low visibility means the concentration and size of the particles are higher compared to average visibility. Thus, scattering and attenuation may be caused more in low visibility conditions [20]. Attenuation can reach hundreds of dB per km for low visibility values, and is higher at shorter wavelength [21]. Low visibility and the associated high scattering coefficients are the most limiting factors for deploying FSO systems over longer distances [4].

## **3.3 Atmospheric attenuation**

Atmospheric attenuation is defined as the process whereby some or all of the electromagnetic wave energy is lost when traversing the atmosphere. Thus, atmosphere causes signal degradation and attenuation in a FSO system link in several ways, including absorption, scattering, and scintillation. All these effects are time-varying and will depend on the current local conditions and weather. In general, the atmospheric attenuation is given by the following Beer's law Eq. (1) [22]:

$$
\pi = \exp(-\beta L) \tag{1}
$$

Where:

48 Optical Communications Systems

increases with increasing distance. Third, scattering and absorption effect accumulates with longer distances. Therefore, the value for the scintillation fading margin in the overall power budget will increase to maintain a predefined value for the BER. Most commercially available FSO systems are rated for operation between 25–5000 m, with high-powered military and satellite systems capable of up to 2000 km. Most systems rated for greater than 1 km incorporate three or more lasers operating in parallel to mitigate distance related to issues. It is interesting to note that in the vacuum of space, FSO can achieve distances of

Free space optical communication link requires a good understanding of the atmosphere as the laser beam has to propagate through it. The atmosphere not only attenuates the light wave but also distorts and bends it. Attenuation is primarily the result of absorption and scattering by molecules and particles (aerosols) suspended in the atmosphere. Distortion, on the other hand, is caused by atmospheric turbulence due to index of refraction fluctuations. Attenuation affects the mean value of the received signal in an optical link whereas distortion results in variation of the signal around the mean. Often, atmospheric attenuation can be the limiting factor in an optical communication link through the atmosphere [16].

Aerosols are particles suspended in the atmosphere such as fog, haze, dust and smog, and they have diverse nature, shape, and size. Aerosols can vary in distribution, constituents, and concentration. The larger concentration of aerosols is in the boundary layer (a layer up to 2 km above the earth surface). Above the boundary layer, aerosol concentration rapidly

Scattering is the main interaction between aerosols and a propagating beam. Because the sizes of the aerosol particles are comparable to the wavelength of interest in optical

Such a theory specifies that the scattering coefficient of aerosols is a function of the aerosols, their size distribution, cross section, density, and wavelength of operation. The different types of atmospheric constituents' sizes and concentrations of the different types of

communications, Mie scattering theory is used to describe aerosol scattering [17].

Air molecules 10-4 1019 Aerosol 10-2 to 1 10 to 103 Fog 1 to 10 10 to 100 Cloud 1 to 10 100 to 300 Raindrops 102 to 104 10-5 to 10-2 Snow 103 to 5×103 N/A Hail 5×103 to 5×104 N/A

Table 3. Radius Ranges for Various Types of Particles.

atmospheric constituents are listed in Table (3) [6], [18].

Type Radius (µm) Concentration ( in cm-3)

thousands of kilometers [4].

**3. Formulations** 

**3.1 Aerosols** 

decreases [3].

�: is the atmospheric attenuation.

�: is the total attenuation coefficient given as:

$$
\beta = \beta\_{abs} + \beta\_{scat} \tag{2}
$$

�: is the distance between (T�) and (R�) in kilometer.

����: is the molecular and aerosol absorption.

�����: is the molecular and aerosol scattering.

#### **3.4 Absorption**

Absorption is caused by the beam's photons colliding with various finely dispersed liquid and solid particles in the air such as water vapor, dust, ice, and organic molecules. The aerosols that have the most absorption potential at infrared wavelengths include water, O�, O�, and CO�. Absorption has the effect of reducing link margin, distance and the availability of the link [4].

The absorption coefficient depends on the type of gas molecules, and on their concentration. Molecular absorption is a selective phenomenon which results in the spectral transmission

$$\mathcal{J}\_{abs} = \left. a\_{abs} N\_{abs} \left[ \frac{1}{km} \right] \right| \tag{3}$$

$$
\beta\_{scat} = a\_{scat} N\_{scat} \, [1/km] \tag{4}
$$

$$
\beta\_{scat} = \beta\_m + \beta\_a [1/km] \tag{5}
$$

$$\mathcal{B}\_m = \, a\_m N\_m \lbrack 1/km \rbrack \tag{6}$$

$$a\_m = \frac{8\pi^3 (n^2 - 1)^2}{3N^2 \lambda^4} [km^2] \tag{7}$$

$$
\beta\_a = |a\_a N\_a| 1/km\text{]} \tag{8}
$$

$$
\beta\_a = \left(\frac{3.91}{\nu}\right) \left(\frac{0.55\mu}{\lambda}\right)^l \tag{9}
$$


$$
\mathcal{B}\_{scat} = \mathcal{B}\_a \tag{10}
$$

$$\pi = \exp(-\beta\_a L) \tag{11}$$

$$
\pi = 4.3429 \beta\_a L \quad \text{[dB]} \tag{12}
$$

$$\beta\_{rainscat} = \pi a^2 N\_a Q\_{scat} \left(\frac{a}{\lambda}\right) \tag{13}$$

$$N\_a = \frac{\,^R}{1.33(\pi a^3)V\_a} \tag{14}$$

$$V\_a = \frac{2a^2 \rho g}{9\eta} \tag{15}$$


$$
\pi = \exp(-\beta\_{rainscat}L) \tag{16}
$$

$$n - 1 \approx 79 \times \frac{p}{r} \tag{17}$$

$$\begin{aligned} \mathcal{L}\_n^2(h) &= 0.00594 \text{(}\upsilon/2\text{7)}^2 \text{(}10^{-5} h\text{)}^{10} \exp(-h/1000) + \\ &2.7 \times 10^{-16} \exp(-\frac{h}{1500}) + A\_o \exp(-\frac{h}{100}) \end{aligned} \tag{18}$$

$$
\sigma\_l^2 = \frac{\langle (l - \langle l \rangle)^2 \rangle}{\langle l \rangle^2} = \frac{\langle l^2 \rangle}{\langle l \rangle^2} - \mathbf{1} \tag{19}
$$

$$
\sigma\_l^2 = 1.23 C\_n^2 k^{7/6} L^{11/6} \tag{20}
$$

Effect of Clear Atmospheric Turbulence on

��: is the transmitted power [mw]. ��*:* is the received power [mw]. �: is the beam divergence [mrad].

�: is the total scattering coefficient [1/km].

Where:

**3.8 Conclusion** 

Quality of Free Space Optical Communications in Western Asia 57

Looking at this equation, the variables that can be controlled are the aperture size, the beam divergence and the link range. The scattering coefficient is uncontrollable in an outdoor environment. In real atmospheric situations, for availabilities at 99.9% or better, the system designer can choose to use huge transmitter laser powers, design large receiver apertures, design small transmitter apertures and employ small beam divergence. Another variable that can be controlled is link range, which must be of a short distance to ensure that the

FSO communication systems are affected by atmospheric attenuation that limits their performance and reliability. The atmospheric attenuation by fog, haze, rainfall, and scintillation has a harmful effect on FSO system. The majority of the scattering occurred to the laser beam is due to the Mie scattering. This scattering is due to the fog and haze aerosols existed at the atmosphere. This scattering is calculated through visibility. FSO attenuation at thick fog can reach values of hundreds dB. Thick fog reduces the visibility range to less than 50 m, and it can affect on the performance of FSO link for distances as small. The rain scattering (non-selective scattering) is wavelength independent and it does not introduce a significant attenuation in wireless IR links, it affect mainly on microwave

There are three effects on turbulence: scintillation, laser beam spreading and laser beam wander. Scintillation is due to variation in the refractive index structure of air, so if the light travelling through scintillation, it will experience intensity fluctuations. The Geometric loss depends on FSO components design such as beam divergence, aperture diameter of both transmitter and receiver. The total attenuation depends on atmospheric attenuation and Geometric loss. In order to reduce total attenuation, FSO system must be designed so that

FSO system used the laser beam to transfer data through atmosphere. The bad atmospheric conditions have harmful effects on the transmission performance of FSO. These effects could result in a transmission with insufficient quality and failure in communication. So, the implementation of the FSO requires the study of the local weather conditions patterns. Studying of the local weather conditions patterns help us to determine the atmospheric attenuation effects on FSO communication that occurs to laser beam at this area. In this part of this work, we shall discuss the effects of atmospheric attenuation, scattering coefficient during rainy and hazy days and atmospheric turbulence during clear days on the FSO

atmospheric attenuation is not the dominant term in the total attenuation [14].

and radio systems that transmit energy at longer wavelengths.

the effect of geometric loss and atmospheric attenuation is small.

system performance. Finally, we will calculate the atmospheric turbulence.

**4. Simulation results and analysis** 

$$I(l,r) = \frac{2P\_o}{\pi \omega\_{eff}^2(l)} \exp\left(\frac{-2r^2}{\omega\_{eff}^2(l)}\right) \tag{21}$$

Where:

��: is total beam power in W.

�: is the radial distance from the beam center.

The beam will experience a degradation in quality with a consequence that the average beam waist in time will be ����(�) � �(�). To quantify the amount of beam spreading, describes the effective beam waist average as:

$$
\omega\_{eff}(l)^2 = \omega(l)^2(1+T) \tag{2}
$$

Where:

�(�): is the beam waist that after propagation distance � is given by:

$$
\omega(l)^2 = \left[\omega\_o^2 + \left(\frac{2L}{k\omega\_o}\right)^2\right] \qquad \text{( $m^2$ )}\tag{23}
$$

In which �� is the initial beam waist at � = �� �: is the additional spreading of the beam caused by the turbulence. As seen in other turbulence figure of merits, � depends on the strength of turbulence and beam path. Particularly, *T* for horizontal path, one gets [37]:

$$T = 1.33 \sigma\_l^2 \Lambda^{5/6} \tag{24}$$

While the parameter Λ is given by:

$$A = \frac{2L}{k\omega^2(l)}\tag{25}$$

The effective waist, ����(�), describes the variation of the beam irradiance averaged over long term.

As seen in other turbulence figure of merits, ����(�)� depends on the turbulence strength and beam path [37]. Evidently, due to the fact that ����(�) � �(�) beamwill experience a loss that at beam center will be equal:

$$L\_{BE} = 20\log\_{10}\{\omega(\text{l})/\omega\_{eff}(\text{l})\} \text{(dB)} \tag{26}$$

#### **3.7 Total attenuation**

Atmospheric attenuation of FSO system is typically dominated by haze, fog and is also dependent on rain. The total attenuation is a combination of atmospheric attenuation in the atmosphere and geometric loss.

Total attenuation for FSO system is actually very simple at a high level (leaving out optical efficiencies, detector noises, etc.). The total attenuation is given by the following [38]:

$$\frac{d^{P\_r}}{dt^{P\_t}} = \frac{d\_2^2}{(d\_1 + (\theta L))^2} \times \exp(-\beta L) \tag{27}$$

Where:

56 Optical Communications Systems

The beam will experience a degradation in quality with a consequence that the average beam waist in time will be ����(�) � �(�). To quantify the amount of beam spreading,

> � � � �� ��� � �

� = ������

� = ��

The effective waist, ����(�), describes the variation of the beam irradiance averaged over

As seen in other turbulence figure of merits, ����(�)� depends on the turbulence strength and beam path [37]. Evidently, due to the fact that ����(�) � �(�) beamwill experience a loss

Atmospheric attenuation of FSO system is typically dominated by haze, fog and is also dependent on rain. The total attenuation is a combination of atmospheric attenuation in the

Total attenuation for FSO system is actually very simple at a high level (leaving out optical efficiencies, detector noises, etc.). The total attenuation is given by the following [38]:

> �� ��

<sup>=</sup> �� �

In which �� is the initial beam waist at � = �� �: is the additional spreading of the beam caused by the turbulence. As seen in other turbulence figure of merits, � depends on the strength of turbulence and beam path. Particularly, *T* for horizontal path, one gets [37]:

� (�) ��� � ���� ����

� (�)� (21)

� (��) (23)

��� �⁄ (24)

���(�) (25)

��� = �� �������(�) �⁄ ���(�)�(��) (26)

(���(��))� � ���(���) (27)

����(�)� = �(�)�(���) (22)

�(�� �) <sup>=</sup> ��� �����

�(�): is the beam waist that after propagation distance � is given by:

�(�)� = ���

Where:

Where:

long term.

��: is total beam power in W.

While the parameter Λ is given by:

that at beam center will be equal:

atmosphere and geometric loss.

**3.7 Total attenuation** 

�: is the radial distance from the beam center.

describes the effective beam waist average as:

��: is the transmitted power [mw].

��*:* is the received power [mw].


Looking at this equation, the variables that can be controlled are the aperture size, the beam divergence and the link range. The scattering coefficient is uncontrollable in an outdoor environment. In real atmospheric situations, for availabilities at 99.9% or better, the system designer can choose to use huge transmitter laser powers, design large receiver apertures, design small transmitter apertures and employ small beam divergence. Another variable that can be controlled is link range, which must be of a short distance to ensure that the atmospheric attenuation is not the dominant term in the total attenuation [14].

## **3.8 Conclusion**

FSO communication systems are affected by atmospheric attenuation that limits their performance and reliability. The atmospheric attenuation by fog, haze, rainfall, and scintillation has a harmful effect on FSO system. The majority of the scattering occurred to the laser beam is due to the Mie scattering. This scattering is due to the fog and haze aerosols existed at the atmosphere. This scattering is calculated through visibility. FSO attenuation at thick fog can reach values of hundreds dB. Thick fog reduces the visibility range to less than 50 m, and it can affect on the performance of FSO link for distances as small. The rain scattering (non-selective scattering) is wavelength independent and it does not introduce a significant attenuation in wireless IR links, it affect mainly on microwave and radio systems that transmit energy at longer wavelengths.

There are three effects on turbulence: scintillation, laser beam spreading and laser beam wander. Scintillation is due to variation in the refractive index structure of air, so if the light travelling through scintillation, it will experience intensity fluctuations. The Geometric loss depends on FSO components design such as beam divergence, aperture diameter of both transmitter and receiver. The total attenuation depends on atmospheric attenuation and Geometric loss. In order to reduce total attenuation, FSO system must be designed so that the effect of geometric loss and atmospheric attenuation is small.
