Estimating atmospheric Cn2 using deep convolutional neural networks

While many critical technologies such as free-space optical communications, directed energy systems, and astronomical imaging rely on the propagation of optical beams through the atmosphere, atmospheric turbulence limits the performance of such applications by imparting both spatially varying and time-varying distortions to the propagated light. To quantify the extent of these distortions, time-domain scintillometers have traditionally been used to estimate C n 2 , a parameter quantifying the severity of refractive index variations of the atmosphere. While time-domain scintillometry methods are ubiquitous, they are large, complex, and slow, capturing the C n 2 over timespans often greater than 10 s. Recently, spatial-domain scintillometers, which measure the C n 2 from static pupil-plane images of scintillated laser beams using neural networks or analytical algorithms, have been proposed as a faster, simpler, and more compact alternative to the traditional time-domain methods. However, spatial-domain techniques have yet to be shown to be capable of estimating the C n 2 precisely over the full range of possible values. In this paper, we introduce a new neural network scintillometry architecture, to our knowledge, that has been trained on a dataset of over 12,000,000 pupil-plane images of scintillated laser beams captured over a period of almost five months from a 16.2 km laser communications testbed across the Chesapeake Bay. Our neural network models, due to the large dataset they were trained on, are capable of robustly estimating the C n 2 across its full measurement range with high precision and speed. Additionally, we detail the process and results of incorporating measurements of atmospheric conditions, specifically the air–water temperature difference, into the neural network training to augment the C n 2 measurement precision.