## 4 Experimental Verification
### Results and Discussion  
We measured the optical power of the incident beam before the coupling lens and an optical power meter was connected with the SMF so that the CE affected by turbulence could be calculated. The \(r_{0}\) was analyzed using a wavefront reconstruction algorithm based on the data from the wavefront sensor. We counted the CE and normalized it with theoretical PDF, as shown in Figure 9a-e. The green dotted line represented the experimental CE, the blue line was for the theoretical PDF built with the Kolmogorov model and the red line was for the PDF using the non-Kolmogorov model. In order to evaluate the accuracy of the PDF, we calculated the correlation coefficient with the experimental distribution. The results are shown in Table 6.  
Figure 8: Experimental layout. (**a**) overall layout, (**b**) SMF coupling system. \begin{table}
\begin{tabular}{c c} \hline \hline
**Items** & **Value** \\ \hline Wavelength & 1550 \(\pm\) 0.5 nm \\ Divergence angle of the fiber collimator & 1.2 mrad \\ Magnification of beam expander system (2 and 4) & 10\(\times\) \\ Diameter of coupling lens & 12.7 mm \\ Focal length of coupling lens & 53 mm \\ Magnification of the receiving telescope (10 and 15) & 1/3\(\times\) \\ Single-mode fiber & Corning SMF-28e \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Key parameters of the experimental system. As observed in Table 6, \(r_{0}\) ranges from 0.134 m down to 0.016 m, which means that the atmospheric turbulence gets stronger. In Figure 9a, the \(r_{0}\) equals to 0.134 m, whereby the turbulence was weak compared with the diameter of receiving aperture, so that the CE distributed mainly between 0.2 and 0.6. When the \(r_{0}\) came to 0.016, as shown in Figure 9e, the CE distributed only between 0 and 0.2, in which case the intensity of the turbulence was strong. The PDF of the CE based on the Kolmogorov model and the non-Kolmogorov model was calculated. As shown in Figure 9a-c, the correlation coefficients using the non-Kolmogorov model were all greater than 0.95, which comes to 0.9898 in Figure 9d. On the contrary, the correlation coefficients using the Kolmogorov model were less than 0.9 and only equaled to 0.6546 in Figure 9a. As to Figure 9d,e, the correlation coefficients were all greater than 0.9, no matter whether the PDFs were built on the non-Kolmogorov model. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{\(r_{0}\) (m)} & \multicolumn{2}{c}{**Non-Kolmogorov Model**} & \multicolumn{2}{c}{**Kolmogorov Model**} \\ \cline{2-3}  & \(\beta\) & **Correlation Coefficients** & **Correlation Coefficients** \\ \hline
0.134 & 2.79 & 0.9765 & 0.6546 \\
0.105 & 2.89 & 0.9537 & 0.8378 \\
0.035 & 3.78 & 0.9783 & 0.9213 \\
0.023 & 3.95 & 0.9898 & 0.9762 \\
0.016 & 3.61 & 0.9945 & 0.9908 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Correlation coefficients of experimental distribution and theoretical PDFs. Figure 9: Experimental distribution fits theoretical distribution based on non-Kolmogorov model and Kolmogorov model. (**a**) \(r_{0}=0.136\) m; (**b**) \(r_{0}=0.104\) m; (**c**) \(r_{0}=0.034\) m; (**d**) \(r_{0}=0.023\) m; (**e**) \(r_{0}=0.017\) m.  
model or the Kolmogorov model. This means that the PDFs built on the non-Kolmogorov model fit the experimental distribution better than those built on the Kolmogorov models, whether the turbulence was strong or weak. The results listed in Table 6 and shown in Figure 9a-e indicate that the Kolmogorov model is not suitable for all cases, for it has strong boundary conditions. When the Kolmogorov model is used, it is assumed that the eddies of the turbulence are much smaller than its outer scale and much bigger than its inner scale. What is more, the eddies that belong to the turbulence should be statistically homogeneous and isotropic. It is difficult to find such conditions in actual communication links, especially in cities where human activities are complex and massive.