## 3 Proposed System Concept Architecture
### Turbulence Compensation
#### 3.2.2 Aperture Averaging  
If the receiving aperture is smaller than the correlation width of the irradiance fluctuations, it can be considered a point receiver. However, when the aperture size exceeds this correlation width, it observes multiple fluctuations. As a result, these fluctuations  
Figure 4: Scintillation index reduction for varying ratios of temperature-to-salinity fluctuation \(w\) with adaptive optics. Curves marked with circles represent the uncompensated case, while those marked with squares correspond to the compensated case, where adaptive optics have been applied with the first seven Zernike modes removed.  
are averaged out by the larger aperture. This leads to a reduction in scintillation called aperture averaging. Aperture averaging changes the frequency content of irradiance fluctuations. Studies have shown that aperture averaging shifts the power concentration of scintillation from higher to lower frequencies, averaging out the fastest fluctuations in the irradiance power spectrum. This reduces high-frequency turbulence effects, as small-scale fluctuations that contribute to rapid intensity fluctuations are suppressed. In addition, it has been shown that the spatial frequency content of the irradiance is shifted by aperture averaging, as the fluctuations caused by small-scale turbulence structures are averaged over the aperture. As a result, the scintillation measured by a receiving aperture is mainly influenced by large-scale turbulence effects. Thus, with a larger aperture, the scintillation is due to slower, larger-scale variations, making the system less sensitive to rapid irradiance fluctuations [23; 32; 50]. The scintillation index of a spherical wave after aperture averaging with a lens with a diameter \(D\) is derived in [50] as follows:  
\[\sigma_{lsp}^{2}(D)=\exp\left[\frac{0.196\,\sigma_{R}^{2}}{(1+0.18\,d^{2}+0.1 86\,\sigma_{R}^{12/5})^{7/6}}\,+\frac{0.204\,\sigma_{R}^{2}\,(1+0.23\,\sigma_{R} ^{12/5})^{-5/6}}{1+0.9\,d^{2}+0.207\,d^{2}\,\sigma_{R}^{12/5}}\right]-1, \tag{18}\]  
where \(d=\sqrt{\frac{kD^{2}}{4L}}\). Without a lens (\(D=0\)), Equation (18) is a minor variation of Equation (8), which is the scintillation index of a point receiver. The scintillation indices for varying temperature to salinity fluctuation ratios before and after compensation with aperture averaging are shown in Figure 5a.  
Figure 5b illustrates how aperture averaging significantly reduces the scintillation index at different turbulence strengths. Note that the minimum value of the lens diameter corresponds to the receiver aperture size without any lens. Aperture averaging even with a small lens drastically reduces the scintillation index. For instance, for \(D=5\,\)cm the scintillation indices are \(2.4\times 10^{-2}\), \(4.4\times 10^{-3}\), and \(3.6\times 10^{-4}\) for strong, moderate, and weak turbulence strengths, respectively. In all these three cases, the scintillation index is negligible, whereas without aperture averaging, the scintillation indices are \(2.31\), \(1.36\), and \(0.12\), respectively.  
Figure 5: **(a)** Scintillation index reduction for varying ratios of temperature-to-salinity fluctuation \(w\) with a 5 cm diameter aperture averaging lens. **(b)** Scintillation index vs. the diameter of the aperture averaging lens for varying ratios of temperature to salinity fluctuation \(w\) for 20 m link distance.