# Prediction of Power Fluctuations of Gaussian Beams After Transmission Through Turbulent Atmosphere
## 2 Data Acquisition and Processing
As shown in Figure 3, the helium-neon laser was placed on the fifth floor of the Science and Technology Building of Minnan Normal University, and the data acquisition instrument was installed on the fifth floor of the Dali Building. A miniature meteorological station was set up in the transmission path of the laser for the simultaneous acquisition of meteorological data, including atmospheric temperature, atmospheric pressure, atmospheric humidity, wind speed, and ambient illuminance, at fixed intervals. The experiment was conducted at night to minimize the impact of ambient light on the measurements. Before being used for the training of the neural network model and the prediction of laser power fluctuation, all the collected data were first pre-processed. A sliding window algorithm was used to segment the laser power data and meteorological data into groups, each of which contained the laser power and the meteorological parameters collected in one acquisition step. Taking each group of the above data as the input and the laser power collected at the next acquisition step as the output, an input-output data pair was formed, through which a data set was finally established. The data being input into the neural network model were actually a two-dimensional array, each row of which contained the results of one data acquisition step (one time step) and whose columns indicated the parameters being acquired (number of features). The inputs of batch size, time step length, and output dimension were also required for the LSTM model, which are specified in this study as 32, 32 and 8, respectively. These values signify that the model takes 32 data groups coming from 32 consecutive time steps into a batch as a single input, and then predicts the laser power of the 8 time steps following those 32 time steps. The data segmentation and prediction method are illustrated in Figure 4. In addition, the numerical ranges of different features in a data set may vary significantly, which may lead the neural network model to exhibit bias towards features with larger numerical ranges during training, thereby degrading the model's performance. Normalization of the data in the data set is a typical solution to this problem. In this study, a min-max normalization method was utilized, which computes the minimum and maximum values for each feature and then maps the value of each data point to the interval [0,1], ensuring that the model treats all features equally during training. The min-max normalization method is expressed as follows:  
\[\hat{x}=\frac{x-x_{\text{min}}}{x_{\text{max}}-x_{\text{min}}} \tag{1}\]  
After completing the data preprocessing, the data set used for training was inputted into the TSLSTMFCPN. After the training was completed, the TSLSTMFCPN was utilized to predict the laser power fluctuation. Figure 3: The data acquisition setup in the outdoor experiments. (**a**) A schematic diagram of the experimental optical path. (**b**) An actual photograph of the experimental optical path. The length of the optical link is 200 m, and the beam waist radius of the emitted Gaussian beam is 5 mm.