# Atmospheric Turbulence Study with Deep Machine Learning of Intensity Scintillation Patterns
## 8 Concluding Remarks and Forthcoming Research Directions  
In this paper, a deep machine learning computational framework is applied for prediction of the atmospheric turbulence refractive index structure parameter \(C_{n}^{2}\) based on DNN processing of short exposure images of turbulence-induced laser beam intensity scintillations. To support the DNN model development and machine learning experiments, several datasets composed of large numbers of instances (scintillation images and the corresponding \(C_{n}^{2}\) values) were collected during several atmospheric measurement trials over a 7 km propagation path, and computer-generated using wave-optics numerical simulations to imitate the experimental trials. A deep convolutional neural network model (Cn^2 Net) containing about 45,000 trainable parameters was developed and optimized via minimization of the \(C_{n}^{2}\) prediction error for the entire range of turbulence strength variations observed during the measurement trials. Prediction of a single \(C_{n}^{2}\) data point by a fully trained Cn^2 Net model required about 0.14 sec, which provides capabilities for high temporal resolution (about seven or more data points per second) \(C_{n}^{2}\) measurements. The developed Cn^2 Net model was applied for:  
* prediction of the data obtained in the atmospheric measurement trials by processing of experimentally captured scintillation images never used for the Cn^2 Net training;
* prediction of values recorded in the experimental trials by the Cn^2 Net model trained on computer-generated scintillation images;
* turbulence profiling by iterative adjustments of a model-based profile by utilizing the measured data;
* comparison of the most prominent atmospheric turbulence models, and the analysis of their parameters impact (inner and outer scales) on scintillations. In this study we show that an optical system comprised of a remotely located laser beacon and an optical receiver acquiring short-exposure intensity scintillation patterns digitally processed with a specially designed and trained DNN, can be utilized as a sensor (Cn^2 Net scintillometer) for in-situ atmospheric turbulence characterization. Such a DNN-based \(C_{n}^{2}\) sensor could be especially efficient for turbulence characterization over relatively long atmospheric propagation paths that are characterized by strong scintillations (Rytov variance \(\sigma_{R}^{2}>1\)). Note that conventional instruments for \(C_{n}^{2}\) monitoring do not provide accurate measurements in strong (saturated) scintillation regimes. The Cn^2 Net scintillometer is less effective when scintillations are relatively weak (low \(C_{n}^{2}\) and/or short propagation path length). In this case, intensity distributions at an optical receiver pupil are relatively weakly effected by the turbulence-induced wavefront aberrations due to an insufficiently long propagation (diffraction) distance and/or too weak turbulence. For the same reason, the Cn^2 Net scintillometer has low sensitivity to turbulence layers located near the optical receiver and, hence, cannot provide accurate turbulence profiling along the entire propagation path. However, the machine learning based atmospheric sensing concept proposed here can be equally applied to optical systems whose performance is strongly affected by turbulence layers located near the optical receiver (e.g., wavefront sensors, directed energy, power beaming, imaging and free-space laser communication systems). At the same time, the measured output optical characteristics in these systems can be insufficiently sensitive to remotely located turbulence layers and for this reason cannot be efficient for turbulence characterization in strong scintillation conditions. One of the major attractions of the machine learning approach for atmospheric turbulence characterization is that it offers a wide range of capabilities for real-time fusion of data flows coming from various optical and meteorological sensors [38; 39].