# Experimental Study on Phase Scintillation of Optical Transmission in Atmospheric Turbulence
## 3 Experimental Measurements
### Gaussian Curvature Positive and Negative Peak Values  
The positive and negative peak values represent the local or global maximum positive and negative values of Gaussian curvature at that point or region, indicating significant changes in the wavefront in that area but in opposite directions. Both represent local changes in the wavefront surface. A positive peak value indicates that the wavefront surface at that point or region exhibits a strong convex characteristic, meaning the wavefront is bending outward at that point. The positive peak value indicates an enhancement in the convex characteristic and a positive change in the phase. A negative peak value indicates that the surface at that point or region exhibits a strong concave characteristic, meaning that the wavefront bends inward in one principal direction and outward in the other [16]. The negative peak value indicates an enhancement of the concave characteristic and a negative change in phase. After calculating the Gaussian curvature for each point using Equation (18), the maximum value (positive peak) and minimum value (negative peak) of Gaussian curvature are found by traversing all of the points. Figures 13-15 show the positive and negative curvature peak values over 100 s under different weather conditions for the three links. Based on Figures 13-15 and Tables 6-8, the positive peak values in link 1 decrease in the following order: snowy, dust storm, heavy rain, light rain, sunny, and cloudy. The negative peak values decrease in the order of cloudy, sunny, light rain, dust storm, heavy rain, and snowy. The local distortion is most severe under snowy conditions, with the highest mean and standard deviation for both positive and negative peak values, followed by heavy rain. The local distortion is minimal under cloudy conditions, with the lowest mean and standard deviation and the smallest changes in local distortion. The positive peak values fluctuate significantly under snowy and dusty conditions, indicating notable changes in local distortion. The positive peak values under snowy conditions are generally high, with a mean of 0.530 \(\upmu\)m\({}^{-1}\), indicating greater local wavefront distortion under snowy conditions. In contrast, the positive peak values are lowest and less variable under sunny and cloudy conditions, indicating minimal local distortion. Similarly, the negative peak values under snowy conditions are significantly lower than those in other weather conditions, at -0.850 \(\upmu\)m\({}^{-1}\), further indicating the substantial impact of snow on local wavefront distortion. Overall, the wavefront distortion is greatest under snowy and heavy rain conditions, with significant fluctuations in both the negative and positive peak values. The wavefront distortion is minimal under sunny and cloudy conditions, with smaller fluctuations in both the negative and positive peak values. The wavefront distortion under light rain and dusty conditions is intermediate between sunny and heavy rain conditions. Figure 14: Positive and negative Gaussian curvature peak values of measured samples in link 2. Figure 13: Positive and negative Gaussian curvature peak values of measured samples in link 1. The degree of local wavefront distortion decreases in the order of snowy, heavy rain, dust storm, light rain, sunny, and cloudy. In link 2, the positive peak values decrease in the order of light rain, heavy rain, sunny, and cloudy. The negative peak values decrease in the order of cloudy, sunny, light rain, and heavy rain. Under heavy rain conditions, the fluctuations are strong, with standard deviations of 0.106 \(\upmu\)m\({}^{-1}\) for the positive peak values and 0.21 \(\upmu\)m\({}^{-1}\) for the negative peak values, significantly higher than in other weather conditions and indicating the greatest local distortion. The positive peak values under light rain are higher than those under heavy rain, indicating a greater positive local wavefront distortion in light rain. Overall, the