Abstract: The conventional phase retrieval wavefront sensing approaches mainly refer to a series of iterative algorithms，such as G-S algorithms ,Y-G algorithms and error reduction algorithms ,these methods use intensity information to calculate the wavefront phase. However, most of the traditional phase retrieval algorithms are difficult to meet the real-time requirements and depend on the iteration initial value used in iterative transformation or iterative optimization to some extent, their practicality is limited. To overcome these problems, in this paper ,a phase-diversity phase retrieval wavefront sensing method based on wavelet transform image fusion and convolutional neural network is proposed. Specifically, the image fusion method based on wavelet transform is used to fuse the point spread functions at the in-focus and defocus image planes, so as to simplify the network inputs without losing the image information. CNN can directly extract image features and fit the required nonlinear mapping. In this paper, the CNN is utilized to establish the nonlinear mapping between the fusion images and wavefront distortions (represented by Zernike polynomials), that is, the fusion images are taken as the input data and the corresponding Zernike coefficients as the output data. The network structure of the training in this paper is 22 layers, including 1 input layer, 13 convolution layers, 6 pooling layers, 1 flatten layer and 1 full connection layer, that is, the output layer. The size of the convolution kernel is 3×3 and the step size is 1. The pooling method selects the maximum pooling and the size of the pooling kernel is 2×2. The activation function is ReLU, the optimization function is Adam, the loss function is the MSE, and the learning rate is 0.0001. The number of training data is 10000, which is separated into three parts:training set,validation set and test set, accounting for 80%, 15% and 5% respectively. Trained CNN can directly output the Zernike coefficients of order 4-9 to a high precision with these fusion images serving as the input, which is more in line with the real-time requirements. Abundant simulation experiments prove that the wavefront sensing precision is RMS 0.015λ, when the dynamic ranges of Zernike coefficients of order 4-9 are [-0.5λ,0.5λ]. In practical application, according to the system aberration characteristics, the number of network output layer units can be changed and the network structure can be adjusted based on the method presented in this paper so as to train the new network suitable for higher order aberration to realize high-precision wavefront sensing. It is also proved that the proposed method has certain robustness to noise, and when the relative defocus error is within 7.5%, the wavefront sensor accuracy is acceptable.

Keywords: 
• phase retrieval /
• convolutional neural network /
• image fusion /
• sensing accuracy