# Atmospheric Turbulence Study with Deep Machine Learning of Intensity Scintillation Patterns  
[PERSON]  
1 AI Science & Technology LLC, 150 Autumn Ridge Tr., Roswell, GA 30076, USA; [EMAIL_ADDRESS]  
[PERSON]  
2 Intelligent Optics Laboratory, School of Engineering, University of Dayton, 300 College Park, Dayton, OH 45469, USA; [EMAIL_ADDRESS] (G.A.F. ); [EMAIL_ADDRESS] (E.P.) mathematical expressions used for \(C_{n}^{2}\) retrieval, can be substituted by the corresponding time-averaged values computed from the collected measurement data. To \"justify\" this substitution it is assumed that all temporal changes that may occur during optical characteristics sensing are solely caused by wind-induced translation of \"frozen\" refractive index inhomogeneities ([PERSON]'s frozen turbulence hypothesis) [12]. However, even if these basic assumptions are met, collection of a statistically representative dataset comprised of several thousand uncorrelated measurements of optical characteristics used for \(C_{n}^{2}\) retrieval, which are required for accurate statistical estimations based on time-averaging, takes considerable time \(\Delta T\). This time, ranging in conventional \(C_{n}^{2}\) sensors from a few to 10 s minutes defines an unavoidable time delay between subsequent \(C_{n}^{2}\) measurements characterizing temporal resolution in \(C_{n}^{2}\) sensing. In the ideal world of the [PERSON] and [PERSON] turbulence theoretical framework, an increase in averaging time \(\Delta T\) means more data points are available for time averaging resulting in a higher accuracy in \(C_{n}^{2}\) evaluation, since the turbulence is assumed to be alike between sequential measurements. In reality, changes in atmospheric turbulence conditions frequently occur at a few seconds time scale. In these, which are typical for near the ground and slant propagation path sensing scenarios, an increase in averaging time \(\Delta T\) may result in inaccurate representation of actual atmospheric turbulence dynamics, while from the other side, a significant shortening of this time may cause unacceptable errors in \(C_{n}^{2}\) estimation due to an insufficiently small dataset being used for time averaging. For the reasons mentioned above, conventional \(C_{n}^{2}\) sensors based on time-averaging cannot provide sufficiently high temporal resolution for the evaluation of atmospheric turbulence dynamics, which is required for predictive performance assessment of various electro-optical systems including directed energy, free-space laser communication, active imaging and optical surveillance. Another drawback of existing electro-optical \(C_{n}^{2}\) sensors is that they are inherently tied to a very specific (Kolmogorov) theoretical framework and for this reason cannot effectively contest its validity in diverse real world environments, as well as assist in deeper understanding of atmospheric turbulence effects and the development of more advanced theoretical models. The deep machine learning approach that is applied here for atmospheric turbulence sensing offers unexplored opportunities for designing a new class of sensors capable of atmospheric turbulence characterization with high temporal resolution, experimental assessment of turbulence models and sensor calibration. In general terms, the machine learning sensing approach described here does not require the collection of large datasets to perform accurate time-averaging, but rather utilizes real-time extraction and analysis of data features that are characteristic to specific turbulence conditions and \(C_{n}^{2}\) values. This extraction and analysis of data features is performed using a preliminary trained deep neural network (DNN) signal processing system.