Atmospheric Turbulence Strength Estimation Using Convolution Neural Network

Laser beam transmission in atmospheric turbulence causes image distortion and affects the quality of information transmission in the field of optical communication. The strength of the atmospheric turbulence, which can be characterized by refractive index structure constant
$C^{2}_{n}$
, significantly influences the properties of a laser beam. The accurate estimation of
$C^{2}_{n}$
is essential for understanding the strength of turbulence. Although multilayer perceptron (MLP) and deep neural network (DNN) has been applied to estimate the atmospheric turbulence strength, the estimation accuracy is sensitive to the strength of the turbulence. In this article, we propose a method based on the convolution neural network (CNN) approach to estimate
$C^{2}_{n}$
ranging from
$10^{-17}$
to
$10^{-13}$

$\text{m}^{-2/3}$
. We experimentally demonstrate that the correlation coefficient (
$\rm R^{2}$
) of the model is 99.39%. The mean relative error (MRE), root mean square error (RMSE), and mean absolute error (MAE) are 0.0047, 0.0916, and 0.0684, respectively. For the turbulence strength with the same order of refractive index structure constant
$C^{2}_{n}$
, the estimation accuracy of the weak turbulence is higher than that of medium and strong turbulence. Moreover, the mix training different levels of turbulence strength improves the estimation accuracy of
$C^{2}_{n}$
compared to that with the same order of
$C^{2}_{n}$
. Based on the high estimation accuracy of the CNN in the scheme, the proposed method will be able to provide a way of estimating the strength of atmospheric turbulence without the need for additional optical devices.