# Experimental Study on Phase Scintillation of Optical Transmission in Atmospheric Turbulence
## 3 Experimental Measurements
### Wavefront Phase Evaluation Metrics  
Since wavefront isophase surfaces can most intuitively reflect the performance of adaptive optical system corrections on plane waves, this paper uses peak-to-valley (\(PV\)) and root mean square (\(RMS\)) values of the wavefront as evaluation metrics for the wavefront phase collected by the Shack-Hartmann wavefront sensor. The peak-to-valley (\(PV\)) value of the wavefront represents the numerical difference between the highest and lowest points of the measured beam's wavefront phase. That is, the difference between the maximum value (highest point) and the minimum value (lowest point) of the wavefront phase elements. Its definition is as follows. \[PV=\phi(r)_{\text{max}}-\phi(r)_{\text{min}} \tag{16}\]  
Here, \(\phi(r)_{\text{max}}\) and \(\phi(r)_{\text{min}}\) represent the maximum and minimum values of the elements in the wavefront phase \(\phi(r)\), respectively. The root mean square (\(RMS\)) value of the wavefront represents the collection of deviations of each point on the wavefront isophase surface relative to the average value, describing the fluctuation degree of the phase values at each point within the optical receiving aperture. Its definition is as follows. \[\text{RMS}=\sqrt{\frac{1}{N}\sum_{i=1}^{N}[\phi(r)-\left<\phi(r)\right>]^{2}} \tag{17}\]  
Here, \(\left<\phi(r)\right>\) is the average value of \(\phi(r)\). \(N\) is the number of valid elements in the wavefront phase. The \(PV\) value of the wavefront only indicates the maximum defect level of the wavefront, without considering the proportion of this defect in the whole wavefront. Therefore, evaluating wavefront quality based solely on the \(PV\) value is not rigorous enough. In contrast, the _RMS_ value of the wavefront emphasizes the overall information of the wavefront, reflecting the deviation of all points from their ideal positions. Thus, combining both metrics provides a more accurate representation of the wavefront condition. Figures 8 and 9 present the _PV_ and _RMS_ values of the wavefront for three links, measured with 1000 sampling points. Based on Figures 8 and 9 and Tables 4 and 5, it is observed that different weather conditions affect the wavefront to varying degrees. In link 1, the mean values of the peak-to-valley (_PV_) and root mean square (_RMS_) wavefront values are lower under sunny and cloudy conditions. Among 4000 sampling points under sunny and cloudy conditions, the _PV_ values fluctuate between 45 \(\upmu\)m and 65 \(\upmu\)m, accounting for 97.5%, while the _RMS_ values fluctuate between 14 \(\upmu\)m and 17.5 \(\upmu\)m, accounting for 89.74%, indicating minimal distortion. In light rain, both the _PV_ and _RMS_ values increase, with the _PV_ values fluctuating between 60 \(\upmu\)m and 80 \(\upmu\)m and accounting for 97.9%, and the _RMS_ values fluctuating between 15 \(\upmu\)m and 18 \(\upmu\)m, accounting for 98% and indicating increased distortion due to light rain. The _PV_ and _RMS_ values under dust storm and snowy conditions are moderate. In a dust storm, the _PV_ values fluctuate between 60 \(\upmu\)m and 85 \(\upmu\)m, accounting for 99.5% while the _RMS_ values fluctuate between 18 \(\upmu\)m and 20 \(\upmu\)m, accounting for 97.9%. In snowy conditions, the _PV_ values fluctuate between 60 \(\upmu\)m and 85 \(\upmu\)m, accounting for 99.5%, and the _RMS_ values fluctuate between 16 \(\upmu\)m and 20 \(\upmu\)m, accounting for 99.3%. In heavy rain, the _PV_ and _RMS_ values increase significantly. The _PV_ values fluctuate between 80 \(\upmu\)m and 160 \(\upmu\)m, accounting for 87.7%, and the _RMS_ values fluctuate between 19 \(\upmu\)m and 40 \(\upmu\)m, accounting for 96.4%. These are the highest mean values, indicating severe wavefront distortion and the most significant wavefront aberrations. The level of distortion decreases in the order of heavy rain, dust storm, snowy conditions, light rain, sunny, and cloudy conditions.