Objective Atmospheric turbulence causes a random fluctuation in the refractive index. When a laser propagates in atmospheric turbulence, the light intensity fluctuation phenomenon during beam propagation occurs, seriously influencing laser propagation. Because different atmospheric turbulence intensities have different effects on laser propagation, it is significantly important to estimate the atmospheric turbulence intensity. In general, the refractive index structural constant Cn2 of the atmospheric turbulence is used to measure the turbulence intensity. The value of Cn2 is directly proportional to the impact of turbulence on laser propagation. Traditional estimation methods include instrument measurement and model estimation. The instrument measurement allows building an experimental platform to directly measure Cn2, in contrast, the model estimation allows obtaining Cn2 by measuring other atmospheric parameters and establishing a model. In recent years, deep learning has allowed achieving good results in the field of image processing, which can extract the feature information of an image layer by layer. This study proposes a method to estimate the refractive index structural constant Cn2 of atmospheric turbulence based on deep convolutional neural networks. The neural network model is built to extract the features of the light spot images under the influence of atmospheric turbulence and the turbulence information is obtained to estimate the turbulence intensity.

Methods A spot image under the turbulence influence contains the turbulence information. In deep learning, neural networks can extract the characteristic parameters of an image. Based on the above mentioned information, neural network models are built to estimate the turbulence intensity. According to the phase screen theory, the Gaussian beam spot images under the influences of different turbulences are simulated. The spot images are divided into a dataset and a test set. Three-thousand images are selected as the training set, and a neural network model is used to obtain the estimation models. Three-hundred images are used as a test set to analyze the estimated results. In addition, the influences of different network structures on the estimation results are analyzed, which provides a new way for estimating turbulence intensity.

Results and Discussions In this study, a traditional AlexNet network model and a VGG16 deep convolutional neural network model are established. VGG16 is optimized on the basis of the traditional convolutional neural network, which increases the layer numbers of the network, reduces the size of the convolution kernel, and has more advantages on feature information extraction of images. The light spot images at different moments under the same turbulence intensity are selected as the inputs of the neural network to verify the feasibility of the above mentioned method and obtain the corresponding estimation results. Moreover, the standard deviation is calculated, and the estimation results are analyzed. The results show that the method can well estimate the turbulence intensity, and the standard deviation increases with the turbulence intensity. To better analyze the results of the neural network model and measure the estimation results, four statistics, i.e., mean absolute error (E_MAE), mean relative error (E_MRE), root-mean-square variance (E_RMSE), and correlation coefficient (R_xy), are selected. The spot images under the influences of different turbulence intensities are randomly selected as the inputs of the neural network model to obtain the corresponding output. The estimation results of the two neural network models are shown in Table 5. After 20 iterations, the estimation result of the VGG16 neural network model is relatively ideal, the correlation coefficient reaches 99%, and E_MAE, E_MRE, and E_RMSE are controlled within 5%. After 500 iterations, E_MAE, E_MRE, and E_RMSE are further reduced to 2%. By analyzing Table 5, it can be seen that both models can well estimate the turbulence intensity after 500 iterations, and the estimation effect of VGG16 is better than that of the AlexNet neural network model. When the number of iterations is the same, E_MAE,E_MRE, and E_RMSE estimated by the VGG16 neural network model are less than half of those of the AlexNet neural network model. Compared with the traditional AlexNet neural network model, the VGG16 neural network model optimizes the network structure and improves the estimation effect to a certain extent.

Conclusion In this study, a method based on deep convolutional neural network model is proposed to estimate turbulence intensity. First, the laser spot images under the influence of turbulence can be simulated according to the classical phase screen theory. Then, the laser spot images under the influence of turbulence are taken as the inputs of the deep convolutional neural network model, and the convolutional layer of the deep convolutional neural network model is used to extract feature information of images layer by layer. After the training of a large number of datasets, the network model is obtained, and the turbulence intensity is estimated. Finally, the estimated effect is analyzed. Compared with the traditional AlexNet neural network model, the VGG16 model adopts a small convolution kernel, which can better retain the image properties, and has high advantages on image feature extraction and better estimation effect. Therefore, the neural network model can be further optimized to improve the estimation effect, which provides a new way to estimate turbulence intensity.