# Atmospheric Turbulence Study with Deep Machine Learning of Intensity Scintillation Patterns
In this study deep machine learning is applied to predict \(C_{n}^{2}\) values via DNN processing of short-exposure laser beam intensity scintillation patterns (images) obtained with both experimental measurement trials conducted over a \(L=7\) km near-horizontal propagation path (Section 2), and the imitation of these trials with wave-optics numerical simulations (Section 3). In the machine learning experiments reported here we utilized datasets comprised of a large number (up to 1.2:10\({}^{5}\)) of data instances consisting of \(C_{n}^{2}\) values and laser beam intensity scintillation images either computed (SIM datasets) or measured during the experimental trials (ATM datasets). A brief description of the developed DNN architecture (referred to as the Cn'2 Net model), major performance characteristics and testing results are outlined in Section 4. The possibility for DNN to be the core element of a new \(C_{n}^{2}\) sensor type was evaluated in the machine learning experiments described in Section 5. In these experiments the ATM datasets were subdivided on two non-overlapping segments (subsets), each containing data representing the full range of \(C_{n}^{2}\) values observed in the experimental trials. One data sub-set was used for the Cn'2 Net training while the second was applied for evaluation of the DNN efficiency in prediction of the true (measured) \(C_{n}^{2}\) values based on scintillation images that had never been utilized (never \"seen\") during the DNN training. The obtained results demonstrate high accuracy in \(C_{n}^{2}\) value predictions withing the entire range of \(C_{n}^{2}\) measurements. This suggests that an optical sensing system with DNN-based signal processing that is side-by-side trained with a \"trusted\" scintillometer could further be independently used as a \(C_{n}^{2}\) sensor (DNN-based scintillometer). It is shown that the Cn'2 Net-scintillometer provides capabilities for significantly higher temporal resolution in \(C_{n}^{2}\) sensing. In other machine learning experiments described in Section 6 we investigated the possibility for the Cn'2 Net to challenge validity of several eminent atmospheric turbulence theoretical models and evaluated them against experimentally measured data. The Cn'2 Net was trained using SIM datasets corresponding to spatially homogeneous turbulence described by the Kolmogorov power spectrum model. The SIM-trained DNN was used to predict the true (measured with a scintillometer) \(C_{n}^{2}\) values via processing of the scintillation images obtained during atmospheric sensing trials (images from the ATM dataset). The results show a significantly larger \(C_{n}^{2}\) prediction error in comparison with what we observed when instances from the same ATM datasets were used for both Cn'2 Net training and \(C_{n}^{2}\) prediction. Prior to making the judgment that during the measurement trials turbulence did not obey the [PERSON] two-thirds power law, or that wave-optics numerical simulations used for SIM dataset generation did not provide a sufficiently accurate representation of the atmospheric measurement trials, we took into account the potential impact of the laser beacon's location on a building rooftop exposed to sunlight leading to a potential turbulence enhancement within a relatively narrow layer near the laser source. To evaluate this hypothesis, the Cn'2 Net model was trained with several SIM datasets corresponding to spatially inhomogeneous (enhanced near the laser beacon) turbulence that still obey [PERSON]'s theoretical model. Fine-tuning of the \(C_{n}^{2}\) profile (degree of turbulence enhancement) in the training SIM datasets allowed significant improvement in DNN prediction of the true (measured) \(C_{n}^{2}\) values within a wide range of turbulence conditions observed during the experimental trials. The Cn'2 Net model was also applied for cross-evaluation of various atmospheric turbulence models.