## 2 Materials and Methods
### Link Budget  
The link budget was made for an OWC system equipped with a pulsed QC laser (numbered as #356) developed at the Institute of Electron Technology (Warsaw, Poland). The laser is characterized by a wavelength of \(\sim\)4.5 \(\upmu\)m and high optical power (peak power above 3 W) (Figure 4). It can work at a maximum duty cycle of 8%. The laser beam was formed using an off-axis parabolic mirror with a 3-inch diameter and a 2-inch focal length, obtaining a divergence of less than 1 mrad. This setup allows collecting \(\sim\)75% of the laser power. The laser pulses were focused on the MCT photodetector  
Figure 4: Characteristics of pulsed QC laser (#356). using a 4-inch parabolic mirror. The photodetector was mounted with the designed front-end electronics in a detection module manufactured by the VIGO System company [38]. The applied photodiode is composed of MCT heterostructures as a monolithic chip with integrated optical, detection, and electronic functions providing a concentration of radiation, enhanced absorption, efficient and fast photon collection, suppression of thermal generation, and low parasitic impedances. The photodiode heterostructure is integrated with an immersion lens as an effective optical concentrator. Regarding the hemispherical immersion lens, the optical area is increased \(n^{2}\)-times more than the physical one, where \(n\) is the refractive index of the lens material. This solution allows for the decreasing of an absorber volume and, thus, a reduction in the thermal generation and recombination of carriers (lower noise power). To provide the required operating temperature of the photodiode, below 200 K, the detector is placed on four-stage Peltier coolers. The cooler is controlled with a special driver to stabilize the detector operating temperature at variable ambient ones up to \(\sim\)300 K. The current signal from the photodiode is received by a broadband two-stage amplifier (up to 1 GHz) with a gain of 10 kV/A (Figure 5). The electronic circuitry provides optimized conditions for the photodiode operation, i.e., the constant voltage bias and current mode readout [40]. The first stage is a transimpedance amplifier of a low input resistance based on an operational amplifier OPA 847, characterized by a low input noise voltage of 0.85 nV/Hz\({}^{1/2}\) and a moderate input noise current of 2.5 pA/Hz\({}^{1/2}\). The second stage is a \(\sim\)20 dB voltage amplifier with 50 \(\Omega\) output resistance. The parameters of the applied photodiode are listed in Table 4.  
The analyses of the data link range were performed using an analytical model based on dependencies described in _The Infrared Handbook_ (by [PERSON], [PERSON]) and _Field Guide to Atmospheric Optics_ ([PERSON]) [41; 42]. Regarding this model, the input data of the parameters of the OWC system components and atmosphere attenuation were imported from Figure 2 and Table 4. No influence of pointing errors was assumed. The registered radiation power was determined, taking into consideration, e.g., laser pulse power, beam geometric losses, the reflectivity of mirrors, and transmission of the atmosphere (the extinction coefficient and the refractive index structure constant). The noise level is defined by the noise of the optical receiver and the signal fluctuations due to turbulence. Considering Figure 6, some obtained characteristics of the SNR for different scattering effects (extinction coefficient) and scintillation (no-scintillation: C\({}_{n}\)\({}^{2}\) = 10\({}^{-17}\) m\({}^{-2/3}\) and strong: C\({}_{n}\)\({}^{2}\) = 10\({}^{-14}\) m\({}^{-2/3}\)) were presented. Regarding the analyzed wavelengths, there \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** & **Spectral Characteristics** \\ \hline Active area & 1 \(\times\) 1 mm\({}^{2}\) & \\ Detector resistance & 60 k\(\Omega\) & \\ Current noise density & 2.4 pA/\(\surd\)Hz & \\ Responsivity & 2.25 A/W & \\ Detectivity D\({}^{*}\) & 9 \(\times\) 10\({}^{10}\) cm\(\surd\)Hz/W & \\ \hline \hline \end{tabular}
\end{table}