## 2 Materials and Methods  
Optical radiation is a physical signal that transmits data in free space. Light is modulated and emitted by a transmitter, propagated through the air channel, and registered by a receiver (Figure 1). The power of the detected signal, \(P_{\mathrm{d}}\), is determined by features of these elements usually described as follows:  
\[P_{\mathrm{d}}=P_{0}\frac{\mathrm{D}_{\mathrm{d}}^{2}}{(\mathrm{D}_{0}+\theta _{\mathrm{div}}\mathrm{L})^{2}}\mathrm{e}^{-\ \gamma(\lambda)\mathrm{L}}, \tag{1}\]  
where \(P_{0}\) is the laser light power, \(\gamma(\lambda)\) is the extinction coefficient, \(L\) is the link distance, \(\theta_{\mathrm{div}}\) is the beam divergence, and \(D_{0}\) and \(D_{\mathrm{d}}\) are the optics diameters of the transmitter and receiver, respectively. To make a connection, there is no need to define parameters of the transmission channel, but the line-of-sight positioning is required for transceiver units. The beam attenuation described by the extinction coefficient is affected by absorption and scattering phenomena resulting from light interaction with air molecules and aerosol particles. Light sources working in the spectral range called \"atmospheric windows\" minimize the influence of radiation absorption. The atmospheric transmission at a distance of 1 km obtained using the HITRAN database is presented in Figure 2.  
In a high transparent spectral range, the operation of an FSO system is limited by scattering (Rayleigh, Mie, and geometrical). To analyze this phenomenon, scattering particle size should be compared to the light wavelength (Table 2). Figure 1: Block scheme of FSO operation. Figure 2: Atmospheric transmission at a distance of 1 km (from the HITRAN database). In practice, visibility is usually read from weather data. Visibility and wavelength can both be used to estimate the scattering coefficient \(\beta(\lambda)\). It was described empirically by [PERSON] [18] as follows:  
\[\beta(\lambda)=\frac{3.91}{\text{Vis}}\left(\frac{\lambda}{\lambda_{0}}\right)^{- \text{q}}, \tag{2}\]  
where \(\lambda_{0}\) = 550 nm is the reference wavelength, and \(q\) is the particle size distribution coefficient [19]. In Figure 3, the calculated scattering coefficient for two wavelengths and different levels of visibility is determined (Figure 3). Commercially available FSO systems use a radiation of 1.5 \(\upmu\)m wavelength; however, longer wavelengths are preferable in the case of light scattering. The mentioned descriptions of scattering are only some approximations of engineering calculations. For example, calculations of fog attenuation are more complex and distinguish the type of impact, i.e., radiation or advection. For advection fog, wavelength dependence of attenuation is linear. The quadratic spectral coefficient is a characteristic of radiation fog and higher light losses are observed. Additionally, the formation of fog is often accompanied by an increase in humidity [20]. The HITRAN database analysis shows that for a wavelength of 4.5 \(\upmu\)m, the air transmission at a distance of 1 km is at least 22% lower as compared with a wave \begin{table}
\begin{tabular}{c c c c c c} \hline
**Type** & **Air Molecules** & **Aerosol** & **Fog** & **Raindrops** & **Snow** \\ \hline Radius (\(\upmu\)m) & \(10^{-4}\) & \(10^{-1}\) to 1 & 1 to 10 & \(10^{2}\) to \(10^{4}\) & \(10^{3}\) to \(5\times 10^{3}\) \\ Concentration (cm\({}^{-3}\)) & \textless{}3 \(\times\)\(10^{19}\) & \(10^{-1}\) to \(10^{4}\) & 10 to 100 & 10 to \(10^{3}\) m\({}^{-3}\) & 0.01-2 g/m\({}^{3}\) \\ Scattering regime & Rayleigh & Rayleigh, Mie & Mie, geometrical & Geometrical & Geometrical \\ \hline \end{tabular} For MWIR radiation, the scattering effects are mainly described using Mie theory and metric based on “visibility (Vis)” [16]. An international visibility code has also been defined [17] with some weather effects (Table 3).  
\end{table} 
Table 2: Typical atmospheric scattering phenomena.