# _Sci_
## 3 Results
### Technical Challenges of Employing Lasers versus Radio Frequency Communications
#### 3.2.3 Atmospheric Impacts  
For all the above challenges, the efforts expended to achieve a closed laser communications link may be for nothing if atmospheric impacts are not accounted for. Assuming an atmosphere-penetrating wavelength is selected, the transmitted signal must overcome two  
Figure 5: Divergence Examples—Radio and Laser [43]. detractors: scattering (i.e., fades) and absorption. As a laser communications beam's wave front transits the atmosphere, it encounters air with non-uniform density. This differing uniformity changes the air's index of refraction. These changes induce error into the transmitted signal, which registers as an increased bit error rate and is referred to as fade [61]. A laser beam produces self-induced change to the index of refraction when they heat the air through which it propagates. This index change results in the beam spreading or \"blooming\", losing focus and reducing the transmitted power. Remedies to blooming include reducing the transmitted power, selecting an atmosphere-appropriate wavelength, or using means to spread the beam's power (e.g., slewing or increasing the optical aperture of the transmitting telescope) [92]. While clear air causes fade, occluded air causes the beam to scatter. Scattering is generated by molecular and aerosol absorption, as well as large particulates in the air, including precipitation, such as rain, fog, clouds, and snow. The application of Beer's Law is recommended in determining the loss due to this scattering and absorption [59]. Many of the atmosphere-induced link closing difficulties can be addressed through the application of test pulses and adaptive optics [92]. The creation and transmission of a distorted wave front that uses the atmosphere-like glasses to \"correct\" the beam at the receiver is beyond the scope of this manuscript but is a key requirement for address in initial capabilities documents (ICDs) and via key performance parameters (KPPs). With this basic discussion of technical challenges and recent progress addressing the challenges, the final section of this manuscript summarizes advantages and disadvantages and additionally makes specific recommendations for key performance parameters for initial capability documents for near-future satellite acquisition and development. Transmittance through the atmosphere is described by Equation (2), where \(\theta\) is zenith angle and \(\gamma(\lambda,h)\) is the atmospheric attenuation coefficient. The integrand \(h\) is the vertical height of the atmosphere up to a specified \(H\) from nominal \(h_{0}\)[55]. The phase coherence radius is expressed using variable \(\rho\). \[\textit{Atmospheric transmittance}=\textit{ e}^{-sec\rho\int_{0}^{H}\gamma( \lambda,h)dt} \tag{3}\]  
Atmospheric turbulence further complicates things in three ways: (1) wander of a beam with initial size of a beam of \(W_{0}\), as described in Equation (4), (2) beam spreading, and (3) beam scintillation, as described in Equation (5) for phase various coherence radii \(\rho_{0},\ \rho_{1},\ \rho_{2}\), which may be calculated using [93]. \[\textit{Root mean square beam wander}\approx 0.54(H-h_{0})^{2}(\frac{\lambda}{2W_{0}})^{2 }(\frac{2W_{0}}{r_{0}})^{\frac{5}{3}} \tag{4}\]  
\[\textit{Scintilled coherence}=\textit{ e}^{-(\frac{\left\lfloor\rho_{1}-\rho_{2} \right\rfloor}{\rho_{0}})^{\frac{5}{3}}} \tag{5}\]  
Attenuation in Fog  
Fog introduces problems of both scattering and absorption [58]. Equation (4) illustrates the empirical model for Mie scattering [93]. The scattering coefficient is taken from [94] and displayed in Table 2, and whose result may be seen in the novel plot in Figure 6.  
\[\textit{Fog attenuation}=\frac{3.921}{\textit{visible range}\left[km\right]}( \frac{\textit{wavelength}\left[nm\right]}{550})^{-\textit{scattering coefficient}} \tag{6}\]Note in Figure 4 the nominally similar attenuation regardless of laser wavelength.