An Improved Wavefront Reconstruction Method Based on Deep Learning

Abstract

This invention discloses an improved wavefront reconstruction method based on deep learning. Since a single-frame focal point spread function (PSF) corresponds to two sets of wavefronts that are 180° rotated and conjugate with each other, this uncertainty severely affects the reconstruction accuracy of traditional phase retrieval algorithms. To address the limitations of existing phase retrieval algorithms, this invention improves upon conventional phase retrieval algorithms based on deep learning. The dataset and the loss function of the neural network are improved, enabling the network to reconstruct a set of wavefronts corresponding to a single-frame PSF. The improved network model exhibits significantly improved reconstruction accuracy, millisecond-level computation speed, and good robustness under noise testing. This invention overcomes the shortcomings of traditional phase retrieval algorithms, achieving fast and accurate wavefront reconstruction using a single-frame PSF, and can recover one set of wavefronts corresponding to the PSF, which is of great significance in the field of image post-reconstruction.

Description

Technical Field

[0001] This invention relates to an improved wavefront reconstruction method, and more particularly to an improved wavefront reconstruction method based on deep learning. Background Technology

[0002] Ground-based telescope observations are severely affected by atmospheric turbulence, a limitation that adaptive optics (AO) technology can overcome to some extent. However, due to limitations in wavefront sensor detection accuracy, deformable mirror correction capability, and control loop bandwidth, the correction of wavefront distortion by AO systems is partial and incomplete, leaving some residual wavefront disturbances in the corrected images. To achieve the diffraction limit and a large field of view, and further improve image quality, post-image reconstruction is usually required.

[0003] The speckle mask method is a commonly used image post-processing method. However, due to its complexity, long processing time, and inability to quickly process large amounts of observation data, as well as its susceptibility to noise affecting reconstruction accuracy, these drawbacks pose serious problems in practical applications. Multi-band high-resolution synchronous reconstruction technology can overcome these limitations. This method only requires high-resolution statistical reconstruction on an image of one band, deconvolution to obtain the point spread function (PSF) of that band, and reconstruction of the instantaneous wavefront caused by turbulent atmosphere on that band. After only wavelength difference correction, high-resolution reconstruction of other bands can be achieved through deconvolution. This significantly reduces the computational load of multi-band reconstruction, thereby improving the algorithm's processing speed. However, traditional phase retrieval algorithms require multiple iterations to obtain wavefront information, resulting in excessive computation time and a tendency to get trapped in local optima, which has significant limitations in practical applications.

[0004] Convolutional Neural Networks (CNNs) are a class of feedforward neural networks that incorporate convolutional computations and have deep structures. They are one of the representative algorithms of deep learning and have been widely used in the field of wavefront reconstruction in recent years. For example, Nishizaki et al. from Osaka University in Japan used the Xception network to predict the Zernike mode coefficients of wavefronts corresponding to single intensity images. However, the prediction results using a single focal plane image had a large error, and the network inference time was also relatively long. Guo Hongyang et al. from the Institute of Optics and Electronics, Chinese Academy of Sciences, improved the VGG network and used the De-VGG network to train the focal plane and defocus plane PSFs to directly reconstruct the wavefront phase map. The inference time was 12ms, but the real-time performance of the model still needs to be improved. Wu Yu et al. from the Institute of Optics and Electronics, Chinese Academy of Sciences, used PD-CNN to reconstruct Zernike coefficients of orders 3 to 15 based on the focal plane and defocus plane PSFs, achieving high reconstruction accuracy and reconstruction speed.

[0005] Compared to traditional wavefront reconstruction methods, deep learning-based wavefront reconstruction methods can achieve more accurate and faster reconstruction, offering significant advantages in the field. However, the reconstruction accuracy of methods using a single-frame focal plane PSF is still insufficient for practical applications. Therefore, how to achieve fast and accurate wavefront reconstruction using a single-frame focal plane PSF remains a problem that needs to be solved. Summary of the Invention

[0006] To address the limitations of existing phase retrieval algorithms, this invention improves upon traditional phase retrieval algorithms based on deep learning. By refining the dataset and the loss function of the neural network, the network can accurately learn the mapping relationship from the point spread function (PSF) of a single frame to its corresponding set of wavefronts, significantly improving the network's reconstruction accuracy and achieving millisecond-level computation speed. After wavelength correction of the reconstructed wavefronts, the PSFs for other bands are calculated, which can be used for high-resolution image reconstruction in other bands, holding significant importance in the field of post-image reconstruction.

[0007] The technical solution adopted in this invention is:

[0008] An improved wavefront reconstruction method based on deep learning is implemented through the following steps: A Single-frame Focal-plane Residual Network (SF-ResNet) is constructed to train the mapping relationship from the single-frame focal plane point spread function (PSF) to the corresponding wavefront; a dataset is constructed, using the single-frame PSF as the network input and the two sets of wavefront data corresponding to the PSF as the network's standard output; an improved loss function is used to process the backpropagation loss, with the smaller loss value during backpropagation enabling the network to learn one of the defined mapping relationships.

[0009] The training dataset for SF-ResNet uses Zernike coefficients conforming to the Kolmogorov distribution to describe the wavefront. Each dataset contains a focal point spread function (PSF) and two corresponding sets of wavefront data. and They have the following relationship They correspond to the same point spread function (PSF), that is:

[0010] PSF(x,y)=PSF'(x,y)

[0011] Before inputting the data into the network, the input focal point spread function (PSF) is normalized to between 0 and 1, and then logarithmic. The data is divided into training, validation, and test sets, allowing the neural network to learn the mapping relationship from a single frame's focal point PSF to a wavefront. After training, the accuracy of the network is tested using the test set.

[0012] The loss function expression is as follows:

[0013] loss1 = RMSE(y pred ,y original1 )

[0014] loss2 = RMSE(y pred ,y original2 )

[0015] Loss = min(loss1, loss2)

[0016] Where: y pred y represents the Zernike coefficients output by SF-ResNet in the same batch. original1 and y original2 These are the two sets of Zernike coefficients corresponding to the focal plane PSF, i.e., the standard output. `loss1` and `loss2` are the root mean square errors of a pair of standard outputs and network outputs. `Loss` is the final backpropagation loss of the network. `RMSE` is the root mean square error, and its expression is:

[0017]

[0018] Where y i Let y be the i-th order Zernike coefficient predicted by the network. i ' represents the i-th order Zernike coefficient of the standard output, and N is the total order of the Zernike coefficients.

[0019] The SF-ResNet takes a single focal point spread function (PSF) as input and outputs Zernike coefficients of various orders. The network uses convolutional layers and max pooling layers to extract feature information, uses residual connections to solve the gradient vanishing problem during training, and includes batch normalization layers and activation layers, with the activation function used in the activation layers being ReLU.

[0020] The method described above uses the Adam algorithm as the network optimizer during SF-ResNet training. Based on the backpropagation loss of each batch of data, the Adam algorithm calculates the gradient of the loss with respect to each weight in the network and updates the weights so that the loss can be reduced and eventually converge to a lower level.

[0021] This invention improves upon traditional phase retrieval algorithms by expanding the dataset and optimizing the loss function of the neural network. It trains the neural network to establish a mapping relationship between the focal point spread function (PSF) of a single frame and its corresponding set of wavefronts, achieving fast and accurate wavefront reconstruction. This invention offers high wavefront reconstruction accuracy and a very fast computation speed, reaching millisecond levels. Furthermore, this method only requires high-resolution reconstruction of the deconvolution-derived PSF of a single-band image to reconstruct a set of wavefronts, which can then be used for high-resolution reconstruction of multi-band images, making it of great significance in the field of image post-processing. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the SF-ResNet structure.

[0023] Figure 2 This is a schematic diagram of the SF-ResNet training and inference process.

[0024] Figure 3 This is a graph showing the prediction results on the test set.

[0025] Figure 4 This is a flowchart illustrating its application in multi-band high-resolution synchronous reconstruction technology. Detailed Implementation

[0026] To describe the technical solution and advantages of the invention more specifically, the invention will be described in more detail below with reference to the accompanying drawings.

[0027] The dataset used in this invention describes wavefronts using Zernike coefficients conforming to the Kolmogorov distribution. The original phase map is obtained from the Zernike polynomial. This original phase map is then rotated 180° and inverted to obtain a processed phase map. The processed phase map is then inversely transformed to obtain its corresponding Zernike coefficients. Finally, the corresponding focal point spread function (PSF) is obtained from the phase map. This invention generates datasets under different atmospheric conditions. Each dataset contains one PSF and two sets of complex conjugate wavefront data. The datasets are divided into training, validation, and test sets.

[0028] Before inputting the dataset into the network, the dataset was preprocessed by normalizing it to 0-1 and then taking the logarithm.

[0029] This invention improves the loss function, and the improved loss function is shown in the following formula.

[0030] The loss function expression is as follows:

[0031] loss1 = RMSE(ypred ,y original1 )

[0032] loss2 = RMSE(y pred ,y original2 )

[0033] Loss = min(loss1, loss2)

[0034] Where: y pred y represents the Zernike coefficients output by SF-ResNet in the same batch. original1 and y original2 These are the two sets of Zernike coefficients corresponding to the focal point spread function PSF, i.e., the standard output. loss1 and loss2 are the root mean square errors of a pair of standard outputs and network outputs. Loss is the final backpropagation loss of the network.

[0035] The backpropagation loss is processed by taking a smaller loss and allowing the network to learn and update towards a given solution. This enables the network to learn a specific mapping relationship between the single-frame focal point spread function (PSF) and one of its two corresponding wavefronts, thus allowing the network to accurately predict one of the wavefronts corresponding to the single-frame PSF.

[0036] The SF-ResNet architecture is shown in the diagram below. Figure 1 As shown, the network input is the focal point spread function (PSF) of a single frame, and the network output is a set of corresponding wavefront Zernike coefficients. A schematic diagram of the SF-ResNet training and inference process is shown below. Figure 2 As shown.

[0037] The network is trained using the training set data, and Adam is used as the optimizer to update the network weights. After training, the trained network model is tested on the test set to test the network's prediction accuracy. Figure 3 The results show the prediction results of this invention on the test set. As can be seen from the results, the Zernike coefficients predicted by SF-ResNet have a very high degree of fit with the actual Zernike coefficients, the wavefront residuals are very small, and the prediction accuracy is very high.

[0038] Figure 4 This is a flowchart illustrating the application of the present invention in multi-band high-resolution synchronous reconstruction technology.

[0039] This invention improves upon traditional phase retrieval algorithms by expanding the dataset and optimizing the loss function of the neural network. The improved method achieves prediction accuracy sufficient for practical applications, with millisecond-level computation speed. The method only requires the focal point spread function (PSF) obtained by deconvolution of the focal plane image to predict a set of wavefronts. These wavefronts can be used to achieve synchronous high-resolution reconstruction of multi-band images. The imaging optical path is simple and has low design cost, making it of great significance in the field of image post-processing.

[0040] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any transformations or substitutions that can be conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of the present invention.

Claims

1. An improved wavefront reconstruction method based on deep learning, characterized in that, This is achieved through the following steps: Construct a single-frame focal plane residual network to train the mapping relationship from the single-frame focal plane point spread function (PSF) to the corresponding wavefront; Construct a dataset, using the single-frame PSF as the network input and the two sets of wavefront data corresponding to the single-frame PSF as the network's standard output; Process the backpropagation loss using a loss function, and use the smaller loss during backpropagation to enable the network to learn one of the defined mapping relationships. In the dataset, Zernike coefficients conforming to the Kolmogorov distribution are used to describe the wavefront. Each dataset contains a single-frame focal point spread function (PSF) and its corresponding two sets of wavefront data. The two sets of wavefront data are as follows: and They have the following relationship They correspond to the same single-frame focal point spread function (PSF), namely: Before inputting the data into the network, the input single-frame focal point spread function (PSF) is normalized between 0 and 1, and then logarithmic processing is performed to divide the data into training set, validation set and test set. This allows the neural network to learn the mapping relationship from the single-frame focal point spread function (PSF) to one of the wavefronts. After training, the accuracy of the network after training is tested using the test set. The expression for the loss function is as follows: in: These are the Zernike coefficients output by the single-frame focal plane residual network in the same batch. and These are the two sets of Zernike coefficients corresponding to the focal point spread function (PSF) of a single frame, i.e., the standard output. and It is the root mean square error of a pair of standard outputs and network outputs. It is the final backpropagation loss of the network. The root mean square error is expressed as follows: in For the network prediction of the first Zernike coefficients of order, The first standard output Zernike, This represents the total order of the Zernike coefficients.

2. The improved wavefront reconstruction method based on deep learning according to claim 1, characterized in that: The single-frame focal plane residual network takes a single focal plane point spread function (PSF) as input and outputs Zernike coefficients of various orders. The network uses convolutional layers and max pooling layers to extract feature information, uses residual connections to solve the gradient vanishing problem during training, and includes batch normalization layers and activation layers, with the activation function used in the activation layers being ReLU.

3. The improved wavefront reconstruction method based on deep learning according to claim 1, characterized in that: The single-frame focal plane residual network uses the Adam algorithm as the network optimizer during training. Based on the backpropagation loss of each batch of data, the Adam algorithm calculates the gradient of the loss with respect to each weight in the network and updates the weights so that the loss can be reduced and eventually converge to a lower level.

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