# Prediction of Power Fluctuations of Gaussian Beams After Transmission Through Turbulent Atmosphere
## 2 Data Acquisition and Processing  
Data represent the foundation of deep learning, and data preprocessing is an indispensable prerequisite step in building efficient machine learning models. In order to train a model with excellent performance, the data used must fully reflect the essential characteristics of the problem to be modeled. Meanwhile, the testing set should have a certain degree of representative consistency with the training set to ensure the model's generalization ability on unseen data. The first step of our research was to obtain adequate and appropriate data to form data sets for training, validating and testing the neural network model proposed. To initially validate the concept, a turbulence pool simulating a turbulent atmosphere was constructed in the laboratory, in which some meteorological parameters can be artificially controlled. A hot plate in the turbulence pool is used to heat the air above it so that a simulated atmospheric turbulence layer is formed above the hot plate, the intensity of which can be effectively controlled by adjusting the temperature of the hot plate. The air in the turbulence pool can be heated up to temperatures well above the atmospheric temperature of natural environments so that a wider range of turbulence intensity can be obtained. Other meteorological data that were collected during the turbulence pool experiment included ambient illuminance, wind speed, and atmospheric pressure, which remained nearly constant during the experimental process. The setup of the turbulence pool experiment is illustrated schematically in Figure 1. A laser beam is expanded and then travels through the simulated atmospheric turbulence in the turbulence pool. An optical power meter and meteorological detection sensors are connected to a computer to measure and record the output laser power and meteorological data in the turbulence pool simultaneously at fixed intervals (time steps). The meteorological data collected include temperature, atmospheric pressure, humidity, wind speed, and illuminance along the laser transmission path. The laser employed is a helium-neon laser, which outputs a Gaussian beam in the fundamental mode. Note that the laser beam is simply expanded without any further modulation of the wave-front phase or polarization, so the beam propagating through the turbulence pool is a Gaussian beam in the fundamental mode. As described above, the atmospheric turbulence in this experiment was simulated in a laboratory setting, and its intensity actually depends merely on the temperature of the hot plate, which directly determines the air temperature along the laser propagation path. In addition, the measured meteorological data showed that the ambient illumination, air pressure, and wind speed in the turbulent pool remained almost constant, but the humidity of the air along the propagation path of the laser beam was significantly different at different hot plate temperatures. The temporal fluctuations of the output laser power at different air temperatures are plotted in Figure 2. Comparing the power fluctuations at different air temperatures, it can be clearly observed that the amplitude of the laser's power fluctuation increases significantly with an increase in the temperature of the air in the laser's transmission path. This reflects that with the elevation of the hot plate temperature, the intensity of the turbulence above the hot plate is remarkably strengthened due to deeper air convection. Figure 1: Diagram of simulated turbulence experimental setup. OBJ: objective; MDS: meteorological detection sensors; PR: photocurrent receiver. Figure 2: Fluctuations in laser power at different temperatures. T: air temperature of the turbulence pool; H: air humidity of the turbulence pool. The ultimate goal of the proposed approach is that it can be used in real-world applications, especially in outdoor applications, so the data acquisition experiment was then moved from the laboratory to outdoors. The outdoor data acquisition setup was similar to that in the laboratory.