## 2 Materials and Methods
Figure 3: Scattering of light as a function of different visibilities for wavelengths 1.5 and 4.5 \(\upmu\)m.  
length of 1.5 um. For rain and snow, the relationships between particle sizes and radiation wavelengths indicate no spectral benefits [21]. The analysis of the influence of dust shows that signal attenuation is strong because its particle sizes are comparable with the FSO radiation wavelength. This attenuation is even seven times higher than that of fog. With visibility changes from 1 to 0.2 km, attenuation is increased from 50 to 300 dB/km [22]. To summarize the analyses of the radiation attenuation for different weather conditions, some simulations of light propagation at wavelengths of 1.55 and 4.5 um were performed using the PcModWin 6.0 software. The weather conditions were defined by visibility and some kinds of aerosols. The simulation results are listed in Table 4.  
For clear air and high visibility, light attenuation was determined by absorption and the level was comparable for the two wavelengths. In rain and very low visibility (below 500 m), the same beam attenuation was also noted. However, if visibility was increased, the light conditions of propagation at a wavelength of 4.5 um were better. Air turbulence can generate random variations in the refractive index modifying optical path performances [24]. As a result, the beam profile is redistributed, corresponding to beam wander, beam spreading, or scintillation. The signal-to-noise ratio (SNR) can also be randomly changed by scintillations. It is characterized by the scintillation index corresponding to the normalized fluctuation of the signal as follows:  
\[\sigma_{\text{I}}^{2}=\frac{\left\langle\text{I}^{2}\right\rangle-\left\langle \text{I}\right\rangle^{2}}{\left\langle\text{I}\right\rangle^{2}}, \tag{3}\]  
where I is the light intensity on the detector surface, and <I> is its mean value. For the condition of weak turbulence, this signal variance is determined by the refractive index structure parameter (\(\text{C}_{\text{n}}{}^{2}\) index), link range (I), and light wavelength (k = 2\(\pi\)/\(\lambda\)) as follows:  
\[\sigma_{\text{I}}^{2}=1.23\text{C}_{\text{n}}^{2}\text{k}^{\frac{7}{6}}\text {L}^{\frac{11}{6}}. \tag{4}\]  
The \(\text{C}_{\text{n}}{}^{2}\) parameter defines the level of turbulence. Operation in longer wavelengths leads to better transmission during turbulence [25]. However, strong turbulence causes the same attenuation for both FSO wavelengths. Practically, the effect of scintillation can be minimized but not eliminated. The nature and level of scintillations depend on many factors, for example, temperature and pressure distribution, humidity, altitude, and surface type. All parameters and their impact are difficult to predict. However, some mathematical models of the effects have been developed. The influence of scintillation on the FSO data range is calculated according to the analytical dependences described in The Infrared Handbook [26] (by [PERSON] and [PERSON]) and the Field Guide to Atmospheric Optics (by [PERSON]) [27]. In Figure 4, the FSO data link ranges providing SNR = 10 for different levels of turbulence are shown. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & & & & & & & & & & & \\ \cline{2-10}  & \multicolumn{2}{c}{**Only Absorption**} & \multicolumn{2}{c}{**Country, 23 km**} & \multicolumn{2}{c}{**Country, 5 km**} & \multicolumn{2}{c}{**City, 23 km**} & \multicolumn{2}{c}{**Maritime, 23 km**} & \multicolumn{2}{c}{**Desert, 23 km**} & \multicolumn{2}{c}{**Radiant Fog. 0.2 km**} & \multicolumn{2}{c}{**Advection Range, 2 mm/h**} & \multicolumn{2}{c}{**Haze, 12.5 mm/h**} \\ \hline \hline \(\gamma\) (1/km) & 1.5 μm & 0.20 & 0.24 & 0.40 & 0.43 & 0.31 & 0.22 & 8.92 & 20.29 & 0.86 & 2.08 \\  & 4.5 μm & 0.24 & 0.25 & 0.31 & 0.33 & 0.30 & 0.26 & 9.24 & 21.58 & 0.87 & 2.10 \\ \hline \end{tabular}
\end{table} 
Table 4: Extinction coefficient for different weather conditions using the PcModWin 6.0 software [23].