# An Experimental Study on the Reflection Characteristics of Laser Echo Light Waves
## 4 Analysis and Discussion
### Light Intensity Fluctuation Probability Density Distribution Characteristics  
To date, there has been extensive research on the probability distribution characteristics of light intensity flicker. It is generally believed that in areas with weak light intensity flicker, the probability distribution of light intensity flicker follows a log-normal distribution, and its probability density function can be expressed as follows: From weak fluctuations to strong fluctuations, the probability distribution of light intensity flicker follows a Gamma-Gamma distribution [20]. Under strong fluctuation conditions, the probability distribution of light intensity fluctuations follows the K distribution; when the communication link length reaches several thousand meters, in the turbulent saturation zone, the probability distribution of light intensity fluctuations exhibits a negative exponential distribution [21].  
This paper normalizes the light intensity data under several different weather conditions, including sunny days, light rain days, moderate rain days, heavy rain days, and cloudy days, to ensure that we can more accurately analyze and understand the statistical characteristics of light intensity changes. After normalization, we further identified the highest and lowest values in these light intensity data, which helped us understand the overall range of light intensity fluctuations. To study the distribution characteristics of light intensity in more detail, we adopted a systematic method based on the amount of data collected in the experiment and evenly divided the data into 20 intervals of equal length. We statistically analyzed the distribution frequencies of light intensity values at  
Figure 3: Refractive index structure constant of the sample measured in Link 2.  
It can be observed from Tables 5 and 6 and Figures 4 and 5 that the light intensity fluctuation of Link 2 is greater than that of Link 1, and in both links, the light intensity fluctuation decreases in the order of sunny days, light rain days, moderate rain days, heavy rain days, and cloudy days. In Link 1, the light intensity fluctuation on snowy days is second only to that on sunny days. In Link 1, under different weather conditions, the fitting effect of the log-normal distribution of the light intensity probability density distribution diagram is better than that of the Gamma-Gamma distribution, and the goodness of fit of the log-normal distribution is more than 0.98, which shows that under the condition of weak light intensity fluctuation, the light intensity value generally follows the law of log-normal distribution. On sunny and snowy days, the probability distribution of light intensity fluctuations is closer to the log-normal distribution. In Link 2, when the experimental background is sunny, lightly rainy, and moderately rainy, the probability density distribution of the measured samples is more consistent with the Gamma-Gamma distribution, and when the experimental background is heavily rainy and cloudy, the probability density distribution of the measured samples is more consistent with the log-normal distribution. This phenomenon can be attributed to the cumulative effect of turbulence scale in long-distance transmission. As the link distance increases, the phase disturbance of the light wavefront increases, resulting in a significant joint effect of large-scale and small-scale turbulent vortices, which is consistent with the applicability of the Gamma-Gamma model to moderate and strong turbulence. In contrast, in the weak-turbulence environment of short-distance links, the light intensity fluctuation is mainly dominated by a single-scale vortex, and is therefore closer to a log-normal distribution.