# Optimal Design of Small-Aperture Optical Terminals for Free-Space Links
## 3 Results and Discussion
### Power Throughput Optimisation  
The total power throughput, \(\eta_{net}\), depends both on the coupling and geometric power losses of the FSO link through \(\eta_{net}=G_{link}\eta_{c}\). For a given link, as \(D_{TX}\) increases, the divergence of the transmitted beam decreases, and so geometric losses decrease. As \(D_{RX}\) increases, the ratio \(D_{RX}/r_{0}\) increases, implying more wavefront perturbations and hence a higher coupling loss. This paper considers the case where \(D_{RX}=D_{TX}=D\), representative of bidirectional FSO terminals. In this case, there will be a common aperture diameter that will maximise \(\eta_{net}\). This is plotted in Figure 3A, showing \(\eta_{c}\), \(G_{link}\), and \(\eta_{net}\) for a range of link lengths and \(C_{n}^{2}\) values. Three chosen values of \(C_{n}^{2}\), representing the low, medium, and high turbulence conditions expected over each link, are chosen based on the \(C_{n}^{2}\) values our research group has observed over the specified link lengths in Perth, Western Australia. The total power throughput in Figure 3 is given by a band, with the lower and upper bounds corresponding to the uncompensated and TT-compensated cases. Each \(\eta_{net}\) band has a peak value corresponding to an ideal choice for the aperture diameter, \(D\). These peaks correspond to the minimum aperture size required for the beam to be minimally truncated at the receiver. The optimal \(\eta_{net}\) ranges between \(-1\) dB to \(-9\) dB for the link lengths and turbulence strengths being analysed. In general, geometric losses are seen to have more impact on the \(\eta_{net}\) than coupling losses. As a result, the ideal \(D\) is strongly dependent on the FSO link length. For lengths on the order of a kilometre, \(D\) of less than 30 mm will incur significant power throughput losses. The ideal \(D\) varies from 30 to 120 mm over this range. With the aperture size set, Equation (6) can be used to set the terminal's effective focal length, resulting in a value between 152 and 574 mm. The optimal aperture size and the resulting \(\eta_{net}\) for each link and turbulence condition are summarised in Table 1.  
Beyond a link length of 10 km, the optimal aperture sizes of \(>\)0.12 m become inappropriate for a'small-aperture' optical terminal. On telescopes this large, implementing only TT compensation has diminishing improvements on the coupling efficiency, since wavefront perturbations are distributed into higher-order Zernike modes [29]. As such, \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**L [m]** & \(C_{n}^{2}\) [m\({}^{-2/3}\)] & \(r_{0}\) [mm] & **D [mm]** & \(f_{\text{eff}}\) [mm] & \(\eta_{net}\) [dB] \\ \hline \multirow{3}{*}{750} & \(1\times 10^{-15}\) & 371–410 & \multirow{3}{*}{32.4} & \multirow{3}{*}{152} & \(-0.899\) \\  & \(5\times 10^{-15}\) & 141–158 & & & \(-0.948\) \\  & \(1\times 10^{-14}\) & 93.5–107 & & & \(-1.02\) \\ \hline \multirow{3}{*}{2400} & \(1\times 10^{-15}\) & 187–280 & \multirow{3}{*}{57.9} & \multirow{3}{*}{272} & \(-0.994\) \\  & \(5\times 10^{-15}\) & 74.8–117 & & & \(-1.43\) \\  & \(1\times 10^{-14}\) & 5.27–8.42 & & & \(-1.85\) \\ \hline \multirow{3}{*}{10,600} & \(1\times 10^{-15}\) & 125–144 & \multirow{3}{*}{122} & \multirow{3}{*}{574} & \(-2.24\) \\  & \(5\times 10^{-15}\) & 5.98 & & & \(-5.90\) \\ \cline{1-1}  & \(1\times 10^{-14}\) & 3.99–4.00 & & & \(-8.69\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Optimal aperture diameter, D, corresponding required focal length, \(f_{\text{eff}}\), and resulting power throughput \(\eta_{net}\) for a given link length and turbulence condition. The range of \(r_{0}\) values from Equation (4) for the transmit beam sizes considered is also included. Figure 2: Generalised optical terminal diagram. \(D\) is the aperture stop, \(f_{\text{eff}}\) is the effective focal length, and \(W_{m}\) is the mode field radius of the fibre. large aperture terminals generally require higher-order compensation systems to improve coupling efficiency.