Extracting atmospheric turbulence phase using deep convolutional neural network
Authors: Xu Qi-Wei , Wang Pei-Pei , Zeng Zhen-Jia , Huang Ze-Bin , Zhou Xin-Xing , Liu Jun-Min , Li Ying , Chen Shu-Qing , Fan Dian-Yuan ,   College of New Materials and New Energies, Shenzhen Technology University, Shenzhen 518118, China,   Engineering Technology Research Center for 2D Material Information Function Devices and Systems of Guangdong Province, International Collaborative Laboratory of 2D Materials for Optoelectronics Science and Technology, Shenzhen University, Shenzhen 518060, China,   Synergetic Innovation Center for Quantum Effects and Applications, School of Physics and Electronics, Hunan Normal University, Changsha 410081, China
Published: December 2020

When a light beam transmits in free space, it is easily affected by atmospheric turbulence. The effect on transmitted light is equivalent to adding a random noise phase to it, which leads its transmission quality to deteriorate. The method of improving the quality of transmitted beams is usually to compensate for the phase distortion at the receiver by adding reverse turbulence phase, and the premise of this method is to obtain the turbulence phase carried by the distorted beam. The adaptive optics system is the most common way to extract the phase information. However, it is inefficient to be applied to varying turbulence environments due to the fact that a wave-front sensor and complex optical system are usually contained. Deep convolutional neural network (CNN) that can directly capture feature information from images is widely used in computer vision, language processing, optical information processing, etc. Therefore, in this paper proposed is a turbulence phase information extraction scheme based on the CNN, which can quickly and accurately extract the turbulence phase from the intensity patterns affected by atmosphere turbulence. The CNN model in this paper consists of 17 layers, including convolutional layers, pooling layers and deconvolutional layers. The convolutional layers and pooling layers are used to extract the turbulent phase from the feature image, which is the core structure of the network. The function of the deconvolutional layers is to visualize the extracted turbulence information and output the final predicted turbulence phase. After learning a huge number of samples, the loss function value of CNN converges to about 0.02, and the average loss function value on the test set is lower than 0.03. The trained CNN model has a good generalization capability and can directly extract the turbulent phase according to the input light intensity pattern. Using an I5-8500 CPU, the average time to predict the turbulent phase is as low as s under the condition of <inline-formula><tex-math id="M5">\begin{document}$C_{{n}}^2 = 1 \times {10^{ - 14}}\;{{\rm{m}}^{ - 2/3}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20190982_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20190982_M5.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M6">\begin{document}$ 5 \times {10^{ - 14}}\;{{\rm{m}}^{ - 2/3}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20190982_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20190982_M6.png"/></alternatives></inline-formula>, and <inline-formula><tex-math id="M7">\begin{document}$1 \times {10^{ - 13}}\;{{\rm{m}}^{ - 2/3}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20190982_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20190982_M7.png"/></alternatives></inline-formula>. In addition, the turbulence phase extraction capability of CNN can be further enhanced by improving computing power or optimizing model structure. These results indicate that the CNN-based turbulence phase extraction method can effectively extract the turbulence phase, which has important application value in turbulence compensation, atmospheric turbulence characteristics research and image reconstruction.