# Experimental Study on Phase Scintillation of Optical Transmission in Atmospheric Turbulence
## 3 Experimental Measurements
### Analysis of the Effects of Wavelength and Temperature on Wavefront Distortion  
The Fried parameter is an important parameter used to describe the impact of atmospheric turbulence on optical wavefronts, also known as the atmospheric coherence length. It is typically denoted by \(r_{0}\), representing the scale of the relatively uniform region through which a light beam propagates in the atmosphere. Specifically, the larger the Fried parameter, the smaller the wavefront distortion. Conversely, the smaller the Fried parameter, the greater the wavefront distortion. According to Equation (15), the relationship between \(C_{n}^{2}\) and \(r_{0}\) under different wavelength conditions is derived. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Weather**} & **Maximum Value** & **Minimum Value** & **Standard Deviation** & \\  & **(\(\mu\)m\({}^{2}\))** & **(\(\mu\)m\({}^{2}\))** & **(\(\mu\)m\({}^{2}\))** & **Mean Value (\(\mu\)m\({}^{2}\))** \\ \hline Sunny & 22.85 & 17.58 & 0.72 & 19.19 \\ Cloudy & 20.39 & 14.20 & 0.72 & 16.02 \\ Light Rain & 40.79 & 28.39 & 1.44 & 32.04 \\ Heavy Rain & 61.87 & 40.10 & 2.94 & 49.32 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Statistical distribution of MSE of wavefront distortion in measured samples for link 2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Weather**} & **Maximum Value** & **Minimum Value** & **Standard Deviation** & \\  & **(\(\mu\)m\({}^{2}\))** & **(\(\mu\)m\({}^{2}\))** & **(\(\mu\)m\({}^{2}\))** & **Mean Value (\(\mu\)m\({}^{2}\))** \\ \hline Sunny & 155.29 & 24.39 & 10.88 & 54.31 \\ Cloudy & 224.39 & 17.93 & 17.83 & 31.21 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Statistical distribution of MSE of wavefront distortion in measured samples for link 3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Weather**} & **Maximum Value** & **Minimum Value** & **Standard Deviation** & \\  & **(\(\mu\)m\({}^{2}\))** & **(\(\mu\)m\({}^{2}\))** & **(\(\mu\)m\({}^{2}\))** & **Mean Value (\(\mu\)m\({}^{2}\))** \\ \hline Sunny & 27.07 & 17.92 & 2.84 & 21.84 \\ Cloudy & 20.34 & 8.50 & 3.32 & 14.40 \\ Light Rain & 67.33 & 23.45 & 9.84 & 37.69 \\ Heavy Rain & 101.67 & 43.17 & 13.13 & 55.18 \\ Dust Storm & 67.88 & 33.98 & 9.88 & 51.40 \\ Snowy & 52.52 & 43.28 & 2.74 & 49.49 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Statistical distribution of MSE of wavefront distortion in measured samples for link 1. From Figure 17, it is evident that the curve for longer wavelengths is significantly higher than that for shorter wavelengths. Under the same \(C_{n}^{2}\) conditions, the greater the wavelength, the larger the \(r_{0}\) and the smaller the wavefront distortion. The impact of atmospheric turbulence on light wave propagation depends on the wavelength. Shorter wavelength beams are more affected by turbulence, leading to a more significant phase distortion. To study the variation in wavefront distortion under different wavelengths, wavefront measurements were conducted on link 1 at 21:00 on 2 July 2024 under clear sky conditions, with an external temperature of 28 \({}^{\circ}\)C and using lasers with wavelengths of 632.8 nm, 532 nm, and 432 nm. The experimental results show that, under the same turbulence conditions, the overall magnitude of wavefront distortion decreases as the wavelength increases, but the complexity and local variations of the distortion patterns do not exhibit a consistent reduction. Under the 632.8 nm condition, compared to the 532 nm and 432 nm conditions, the peak-to-valley value, root mean square value, and mean square error of the wavefront distortion vary within a small range. This indicates that the temporal stability of wavefront distortion at longer wavelengths is better, suggesting that atmospheric turbulence interferes less with long waves than with short waves.