Incident beam wavefront detection method based on wavefront reconstruction neural operator

Abstract

The invention belongs to the technical field of optical detection, and particularly relates to an incident beam wavefront detection method based on a wavefront reconstruction neural operator. According to the invention, an optical heterogeneous receiving and self-supervised training wavefront SWRNO technology is adopted; the optical heterogeneous receiver detects light field intensity distribution at different depth positions so as to weaken precision loss caused by uncertain problems; the SWRNO is composed of a neural network embedded by a light field propagation physical model; self-supervision training is carried out on the SWRNO through a pre-training data set collected by a simulation platform, a model obtained through training can establish direct mapping from received light field intensity to a wavefront phase, and the model serves as a neural operator to reconstruct wavefront through light field intensity detected by charge-coupled device image sensors, namely CCD cameras, at different depths; the method has the advantages of higher resolution, lower cost and higher wavefront reconstruction precision; and wavefront fluctuation characteristics with finer granularity can be detected, and the method has great significance for a self-adaptive optical system serving FSO.

Description

Technical Field

[0001] The invention belongs to the technical field of optical detection, and in particular relates to a method for detecting the wavefront of an incident light beam. Background Art

[0002] During the free space transmission, the light field will be disturbed by atmospheric turbulence, causing the spatial light field to distort. The distorted spatial light field will have dispersed light intensity, and the light spot will flicker and drift, resulting in a significant reduction in the number of photons reaching the receiver plane, making it impossible to ensure high-speed and efficient long-distance communication. Traditional adaptive optical wavefront correction technology requires a wavefront detector to perform wavefront detection, or requires multiple iterations to achieve global optimization, resulting in high costs and long computing time.

[0003] In recent years, with the development of artificial intelligence technology, deep learning technology has been widely used in adaptive optics. With the help of the high parallel computing characteristics of GPU, adaptive optics enabled by deep learning technology can complete wavefront perception and reconstruction in a shorter time, making the performance of adaptive optics technology in wireless optical communication systems more stable and reliable. Among them, a large number of related works focus on using deep learning for wavefront perception and turbulence phase inversion, so as to obtain the compensation phase for restoring spatial distortion and reconstructing the light field, and then use spatial phase modulation devices such as deformable mirrors or spatial light modulators to reconstruct the light field. In terms of training and deployment of neural networks, some researchers adopt the strategy of supervised training with known turbulence phase labels, which limits the actual deployment of this method and lacks practical potential; some researchers also try to use self-supervised training strategies to directly deploy untrained neural networks. Each time wavefront perception is performed, the neural network is retrained. Such iteration time and computing power cost limit its potential for application in satellite-to-ground wireless optical communications. Summary of the invention

[0004] The present invention aims to provide a low-latency, high-robustness, and high-precision incident light beam wavefront detection method, which is suitable for adaptive optical systems of free-space optical communications (FSO) over long distances and through turbulent channels, such as satellite-to-ground optical communications and underwater wireless optical communications.

[0005] The incident light beam wavefront detection method provided by the present invention is based on optical heterogeneous reception and self-supervised training wavefront reconstruction neural operator (SWRNO) technology. The optical heterogeneous reception system detects the light field intensity distribution at different depths to reduce the accuracy loss caused by the ill-posed problem. SWRNO is composed of a neural network embedded in a light field propagation physical model. The SWRNO is self-supervised trained using a pre-trained data set collected by a simulation platform built by Matlab. The trained model can establish a direct mapping from the received light field intensity to the wavefront phase, and reconstruct the wavefront as a neural operator using the light field intensity detected by the charge coupled device image sensor (CCD camera) at different depths. Due to the extremely strong robustness and generalization of SWRNO, the obtained pre-trained model can be directly deployed in the system to achieve high-precision wavefront detection. The specific steps are:

[0006] (1) Collect simulation data sets for training based on light field diffraction transmission theory;

[0007] In order to illustrate the performance of the present invention under strong turbulence, ocean turbulence is taken as the research object. The turbulence phase screen generation model adopts the ocean turbulence power spectrum model [1]. This model simultaneously considers the influence of temperature and salt concentration in seawater on the refractive index of seawater medium.

[0008] Considering the diffraction transmission of the incident light beam in the turbulent channel, only the electric field component of the light field is taken as the light field under study and treated as a scalar. The diffraction integral formula is generally used to calculate the light field at a straight-line propagation distance d in space. When discussing the case of non-infinite transmission, the Fresnel diffraction integral [5] is usually used for calculation. The Fresnel diffraction integral can be expressed as:

[0009]

[0010] Among them, E(x, y, d) is the light field distribution of the incident light beam transmitted to point d on the transverse plane perpendicular to the propagation direction, k is the wave number of the light field, which is calculated by k = 2π / λ, and E(u, v, 0) is the light field at the origin.

[0011] To make the expression and calculation more concise, formula (1) can also be expressed as:

[0012]

[0013] in, and Corresponding to the fast Fourier transform and inverse Fourier transform, φ(u,v,0) is the initial phase of the light field, and H is the Fresnel diffraction propagation operator, which is expressed as:

[0014] H=exp(i2π / λd) / iλd·exp[iπ(u 2 +v 2) / λd] (3)

[0015] When collecting simulation data sets, the parameter settings need to be consistent with the optical heterogeneous receiving system, that is, the emission light field E(u,v,0) and the transmission distance d of the actual system where the present invention needs to be deployed should be used for simulation. Replace φ(u,v,0) with the turbulent phase screen. After the light field is transmitted over distances d1 and d2, the light fields E1(x,y,d1) and E2(x,y,d2) are obtained, and then the square law detection is performed on the complex amplitude light field as a simulation of the acquisition process of two CCD cameras in the optical heterogeneous receiving system:

[0016] I1(x,y,d1)=|E1(x,y,d1)| 2 ,I2(x,y,d2)=|E2(x,y,d2)| 2 (4)

[0017] Changing different turbulence intensities And each time a turbulent phase screen is generated, a different two-dimensional random number is taken. After the above simulation calculation, multiple groups of light intensity distributions {I1(x, y, d1), I2(x, y, d2)} are collected and used as the data set for SWRNO training.

[0018] (2) Construct a neural network embedded with the light field transmission model as a wavefront reconstruction neural operator;

[0019] The wavefront reconstruction neural operator (SWRNO) architecture of the present invention consists of two parts, see Figure 1 As shown; the first part is the neural network that ultimately realizes the wavefront reconstruction function, which becomes SWRNO after training; the second part is the forward propagation layer of the neural network built based on the physical model of light field propagation, which enables SWRNO to perform self-supervised training.

[0020] The neural network has multiple models capable of extracting and generating two-dimensional features, and specifically adopts a U-Net with fine-tuned structure. The specific structure and structural parameters of the model are as follows Figure 2 As shown. Let the forward propagation operation of the neural network be operator R θ (R θ Characterize the forward propagation operation of the fine-tuned U-Net, whose input is the two light intensity distributions I detected at different propagation distances received by the optical heterogeneous receiving system RX1 (x,y,d1) and I RX2 (x,y,d2), the output of which is the turbulent phase screen predicted by the model It is expressed as:

[0021]

[0022] In the forward propagation layer of the neural network, Fresnel diffraction (Formula (1) and Formula (2)) and square law detection (Formula (3)) are used as the forward propagation layer that can be embedded in the neural network. The parameters of the light field transmission layer are frozen and are not used as trainable parameters. The specific representation of the light field transmission layer is as follows:

[0023] Will The light field intensity distribution E at the transmitting end TX (x,y,0) is combined as a beam with wavefront distortion:

[0024]

[0025] E0(x, y, 0) enters two optical field transmission layers with different transmission distances to obtain the received optical field of the optical heterogeneous receiving system predicted by SWRNO and They are respectively expressed as:

[0026]

[0027] Then perform square law detection on them respectively to obtain the predicted received light field intensity distribution:

[0028]

[0029] All the outputs of SWRNO are obtained: turbulence phase screen and two reconstructed receiving end light field structures. In the adaptive optical system, the predicted turbulence phase screen can be directly conjugated to obtain the conjugate wavefront of the received light field after wavefront distortion, which is used as the compensation phase for wavefront reconstruction in the adaptive optical system.

[0030] (3) Perform self-supervised training based on the gradient descent method to obtain the wavefront reconstruction neural operator;

[0031] The SWRNO training process proposed in this invention is different from the supervised training with labels, and uses the self-supervised training strategy without labels. The goal of iterative optimization is to make the light field intensity distribution of the model output and The light intensity distribution actually detected by the optical heterogeneous receiver at different depths I RX1 (x,y,d1) and I RX2 (x, y, d2) is almost the same, that is, the training makes the model itself a solver of the equation set composed of two transmission processes. The equation set composed of the optical heterogeneous receiving system is as follows:

[0032] E RX1 (x,y,d1)=[I RX1 (x,y,d1)] 1 / 2 exp[iφ RX1(x,y)] (10)

[0033] E RX2 (x,y,d2)=[I RX2 (x,y,d2)] 1 / 2 exp[iφ RX2 (x,y)] (11)

[0034]

[0035] In formula (10) and formula (11), I RX1 (x,y,d1) and I RX2 (x, y, d2) is the intensity distribution of the received light field detected by CCD. Let d1≤d2, φ RX1 (x,y) and φ RX2 (x, y) are the wavefront phases of the two received light fields. Equations (12) and (13) respectively establish two transmission equations for two light fields at different transmission distances from the transmitting end to the receiving end through turbulence through the Fresnel diffraction theory. TX (x, y, 0) is the intensity distribution of the light field emitted by the transmitter, φ T (x, y) is the turbulent phase. In addition, there is an implicit transmission relationship, which is the transmission equation from the light field at z = d1 to the light field at z = d2 expressed by equation (14).

[0036] In the above equations, substituting equations (10) and (11) into equations (12), (13) and (14), the resulting three equations consist of the equation system containing φ RX1 (x,y),φ RX2 (x,y) and φ T Therefore, by receiving the light intensity distribution at different positions, the number of matrices to be solved can be matched with the number of equations and converted into a well-posed problem.

[0037] Therefore, the loss function can be set as follows:

[0038]

[0039] in, The model is calculated from After transmission distance d2-d1 The light field intensity distribution obtained after square law detection. β is an adjustable parameter, which is generally set to 1. During the training process, according to the batch input, the loss function value is calculated in each iteration cycle, and the reverse gradient propagation is calculated to update the weight parameters of the neural network. The convergence process is as follows: Figure 3 shown. Figure 3At the same time, the residual wavefront difference (RWE) between the output wavefront predicted by the model and the actual wavefront of the validation set after each round of training is used as an evaluation indicator, and the calculation method is as follows:

[0040]

[0041] Among them, N x and N y They are the number of pixels in the horizontal direction and the number of pixels in the vertical direction of the phase screen respectively.

[0042] (4) Deploy SWRNO directly to optical heterogeneous receiving systems for wavefront detection;

[0043] The trained SWRNO can be directly deployed in the system that needs wavefront detection. The optical heterogeneous receiving system is also deployed with the SWRNO, that is, the coaxial CCD camera receiving at different depths to detect the light field intensity distribution. The input of the SWRNO is replaced with the light field intensity distribution actually detected by the CCD camera, and the output of the SWRNO is the reconstructed light field wavefront.

[0044] The technical features and performance advantages of the present invention are:

[0045] 1. The wavefront detection technology based on optical heterogeneous receivers that only detects the intensity distribution of CCD for wavefront reconstruction has higher resolution and lower cost than the traditional Shack-Hartmann wavefront detection technology. It is capable of detecting finer-grained wavefront fluctuation characteristics, which is of great significance to the adaptive optical system serving FSO.

[0046] 2. The SWRNO algorithm proposed in the present invention is obtained by self-supervised training based on the embedded light field transmission physical model. It does not have a strong dependence on the data set distribution itself. Each of its input and output is given practical meaning by the physical model. At the same time, the heterogeneous receiving method makes the reconstruction task itself a well-posed problem. The two as strong constraints make the model extremely versatile and robust, and can maintain a high wavefront reconstruction accuracy when the environmental parameters change. According to experimental tests, under different turbulence intensities, phase reconstruction with a wavefront residual phase difference lower than 0.03λ can be achieved, and the robustness and accuracy are significantly higher than the model that does not use the training strategy in the present invention.

[0047] 3. The inference time required for the wavefront reconstruction task of SWRNO based on optical heterogeneous receivers is extremely short. It only takes 4ms to perform one round of inference on the NVIDIA GeForce RTX 4080 hardware platform, which is much shorter than the traditional iterative wavefront reconstruction algorithm and adaptive optical wavefront compensation algorithm. The extremely high dynamic response characteristics ensure that the present invention has a more critical performance advantage in the FSO adaptive optical system, and can effectively improve the performance upper limit of the existing adaptive optical technology at the level of wavefront detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 The structure, data flow and training flow chart of SWRNO of the present invention.

[0049] Figure 2 This is the architecture of the SWRNO neural network operator part of the present invention, that is, the U-Net after structural adaptability modification.

[0050] Figure 3 It is a schematic diagram and convergence process of the SWRNO training of the present invention and the reference method.

[0051] Figure 4 Schematic diagram of the experimental device of the present invention.

[0052] Figure 5 This is the wavefront reconstruction visualization result of SWRNO in the simulation data set of the present invention.

[0053] Figure 6 This is the visualization result of wavefront reconstruction of the SWRNO deployed in the experimental system of the present invention.

[0054] Figure 7 The performance comparison of the wavefront reconstruction of the present invention in the simulation data set and the experimental system is shown. DETAILED DESCRIPTION

[0055] The present invention is further described below in conjunction with specific simulation and experimental methods and results.

[0056] (1) SWRNO specific structure

[0057] like Figure 2 As shown in the figure, the first part of SWRNO, that is, the specific structure of the neural network that finally realizes the wavefront reconstruction function. Its main part is a fine-tuned U-Net. The neural network structure contains encoding (downsampling) and decoding (upsampling) paths, and passes the feature map of the encoder to the decoder through a jump connection to retain detail information, which is high-frequency information in the image. The size of the two collected light field intensity distributions is 128×128, and the two light field intensity distribution maps are merged into a dual-channel image as input to enter the encoder part of the neural network.

[0058] The encoder part downsamples the input image step by step and extracts multi-level features. Specifically, it includes a convolution module, which contains: a convolution layer with a kernel size of 3×3 and a stride of 1, a batch normalization, and a ReLU activation function. It also includes a downsampling module, which contains: a convolution layer with a kernel size of 3×3 and a stride of 2, a batch normalization, and a ReLU activation function.

[0059] The decoder part performs upsampling through deconvolution (transposed convolution) and concatenates the feature maps of the corresponding layer of the encoder. It includes an upsampling module, which contains: a deconvolution layer with a convolution kernel size of 3×3 and a stride of 2, a batch normalization, and a ReLU activation function.

[0060] The specific structure used in the present invention is as follows: a dual-channel light field intensity distribution image (128×128×2) is used as input, and enters the first layer downsampling module after passing through two layers of convolution modules, at which time the number of channels is 16; then enters the second layer downsampling module after passing through two layers of convolution modules, at which time the number of channels is 32; then enters the third layer downsampling module after passing through two layers of convolution modules, at which time the number of channels is 64; then enters the fourth layer downsampling module after passing through two layers of convolution modules, at which time the number of channels is 128; then enters the first layer upsampling module after passing through two layers of convolution modules, and is spliced ​​with the input of the fourth layer downsampling module, at which time the number of channels is 64. 128; then after two layers of convolution modules, it enters the second layer of upsampling module and splices with the input of the third layer of downsampling module. At this time, the number of channels is 64; then after two layers of convolution modules, it enters the third layer of upsampling module and splices with the input of the third layer of downsampling module. At this time, the number of channels is 32; then after two layers of convolution modules, it enters the fourth layer of upsampling module and splices with the input of the fourth layer of downsampling module. At this time, the number of channels is 16; then it enters two layers of convolution modules, and finally enters a convolution module with a Sigmoid activation function, and outputs a 128×128 image with a channel number of 1. At this time, the image value range is (0,1), which is linearly enlarged to the value range of (-π,π) as the wavefront phase output by the neural network.

[0061] (2) Simulation settings and experimental results

[0062] In order to verify the wavefront reconstruction performance of the SWRNO based on optical heterogeneous receiver proposed in this invention, an ocean turbulence phase generation model and a beam transmission model were constructed by Matlab as a simulation platform for performance evaluation. and 12,000 sets of data were collected at different turbulence intensities. Each set of data contained two light field intensity distributions received at different transmission distances. The turbulence phase screen and the received light field wavefront were recorded at the same time as the basis for the model output wavefront verification performance. The training data set under turbulence intensity is 7000 groups as training set and 5000 groups as validation set. The convergence process of training is as follows Figure 3 As shown in b. Figure 3 a is the convergence process of the model in the supervised training process without using the self-supervised training method of SWRNO of the present invention. The schematic diagram of the reference method is as follows Figure 3 c. Compared with the reference method, the training loss and validation loss of the SWRNO proposed in the present invention are almost completely consistent during the training process, and there is no overfitting phenomenon or possibility. At the same time, after each round of training, the test set is predicted, and the obtained output is RWE with the turbulence phase. It can be seen that the jitter and oscillation amplitude of SWRNO are smaller and converge to a lower value, which shows that SWRNO has a higher wavefront reconstruction accuracy.

[0063] Figure 5 This is the visualization of the simulation test output results of the two methods. Figure 5 a is The intensity distribution of the light field collected by simulation under turbulence intensity and the intensity distribution reconstructed by SWRNO are almost the same. Figure 5 b shows the comparison and difference between the wavefront and turbulence phase reconstructed by the two methods. The subsequent test is to test the robustness of the model and also to test the performance under the conditions of turbulence intensity fluctuation in the natural environment. The model trained under turbulence is then used for wavefront reconstruction of other turbulence intensities. Figure 5 c is The intensity distribution of the light field collected by simulation under turbulence intensity and the intensity distribution reconstructed by SWRNO, Figure 5 d shows the comparison and difference between the reconstructed wavefront and turbulence phase of the two methods. It can be seen that the performance of SWRNO is almost not degraded, while the performance of the reference method is seriously degraded.

[0064] (3) Experimental platform and experimental results

[0065] After basic simulation, the present invention is verified in a free space turbulent system built in a laboratory. Figure 4This is a schematic diagram of the experimental setup. After the laser is emitted from the laser, it passes through a half-wave plate and a linear polarizer, and is filtered and expanded by a 4-f system. Then it is incident at a small angle on the spatial light modulator SLM1, on which the turbulence phase is modulated. After that, it enters the optical heterogeneous receiving system after 1.4m of free space transmission. Among them, the light beam is first split by a 10:90 beam splitter, and the part carrying less energy enters the optical airspace detection part. After passing through a 50:50 beam splitter, it is received by two CCDs at transmission distances of 1.6m and 1.9m respectively. The detection result is used as the input of SWRNO, and its output predicted turbulence phase is inverted and directly modulated on the spatial light modulator SLM2 to reconstruct the wavefront of the other part of the light beam carrying more energy. Then the phase-compensated light beam is converged on the PD by a lens for communication.

[0066] Figure 6 Visualization of the output results of the two wavefront reconstruction methods in the experimental test. Figure 6 a is The light field intensity distribution collected experimentally under turbulence intensity and the intensity distribution reconstructed by SWRNO are almost the same. Figure 6 b shows the comparison and difference between the wavefront and turbulence phase reconstructed by the two methods. The subsequent test is to test the robustness of the model and also to test the performance under the conditions of turbulence intensity fluctuation in the natural environment. The model trained under turbulence is then used for wavefront reconstruction of other turbulence intensities. Figure 6 c is The intensity distribution of the light field collected experimentally under turbulence intensity and the intensity distribution reconstructed by SWRNO, Figure 6 d shows the comparison and difference between the reconstructed wavefront and turbulence phase of the two methods. It can be seen that the performance of SWRNO is almost not degraded, while the performance of the reference method is seriously degraded.

[0067] Figure 7 This is an experimental test of the robustness of the present invention. First, the performance under different turbulence intensities is tested. We experimentally collect 400 sets of data for different turbulence intensities for prediction. The prediction results are as follows: Figure 7 As shown in Figure 1, by comparing the performance of the reference method, it can be observed that the SWRNO of the present invention has the following characteristics: after pre-training on the simulation data set, the performance difference between the prediction results of the simulation data and the prediction results after direct deployment on the experimental data is not large, that is, SWRNO can adapt to changes in data distribution to a certain extent; and under different turbulence intensities, SWRNO still has a relatively stable wavefront reconstruction performance and a high reconstruction accuracy. The above characteristics prove that the wavefront reconstruction method of the present invention has high accuracy and strong robustness.

[0068] References:

[0069] [1]Preparation.Introduction of a newly developed snowflake system[D].United States of America,2023. DOI:10.27251 / d.cnki.gnjdc.2023.000002.

[0070] [2]X.Long,Y.Gao,Z.Yuan,W.Yan,Z.-C.Ren,X.-L.Wang,J.Ding,H.T.Wang,In-Situ Wavefront Correction via Physics-Informed Neural Network.Laser PhotonicsRev 2024,18,2300833.

[0071] [3]H.Zhan,L.Wang and W.Wang,"Generative Adversarial Network BasedAdaptive Optics Scheme for Vortex Beamin Oceanic Turbulence,"in Journal ofLightwave Technology,vol.40,no.13,pp.4129-4135,1July1,2022.

[0072] [4] Wang, F., Bian, Y., Wang, H. et al.

[0073] [5]Y.Guo,L.Li,J.Wang,C.Gao and S.Fu,"Distortion Compensation forOrbital Angular Momentum Beams:From Probing to Deep Learning,"in Journal ofLightwave Technology,vol.41,no.7,pp.2041-2050,1April1,2023.

[0074] [6]Wang, K., Song, L., Wang, C. et al.Light Sci Appl 13,4(2024).

Claims

1. A wavefront detection method for an incident light beam based on a wavefront reconstruction neural operator, characterized in that: Optical heterogeneous reception and self-supervised training of wavefront reconstruction neural operator (SWRNO) technology are used; the optical heterogeneous reception system detects the light field intensity distribution at different depths to reduce the accuracy loss caused by the ill-posed problem; SWRNO is composed of a neural network embedded in the physical model of light field propagation; SWRNO is self-supervisedly trained using a pre-training data set collected by a simulation platform built by Matlab, and the trained model can establish a direct mapping from the received light field intensity to the wavefront phase, and as a neural operator, it reconstructs the wavefront through the light field intensity detected by the charge coupled device image sensor, i.e., CCD camera, at different depths; the specific steps are as follows: (1) Collect simulation data sets for training based on light field diffraction transmission theory; Taking ocean turbulence as the research object, the turbulence phase screen generation model adopts the ocean turbulence power spectrum model; this model also considers the influence of seawater temperature and salt concentration on the refractive index of seawater medium; Considering the diffraction transmission of the incident light beam in the turbulent channel, only the electric field component of the light field is taken as the light field under study and treated as a scalar; the Fresnel diffraction integral is used to calculate the light field at the spatial straight-line propagation distance d; the Fresnel diffraction integral is expressed as: Wherein, E(x,y,d) is the light field distribution of the incident light beam transmitted to point d on the transverse plane perpendicular to the propagation direction, k is the wave number of the light field, which is calculated by k=2π / λ, and E(u,v,0) is the light field at the origin; Formula (1) can be expressed as: in, and Corresponding to the fast Fourier transform and inverse Fourier transform, φ(u,v,0) is the initial phase of the light field, and H is the Fresnel diffraction propagation operator, which is expressed as: H=exp(i2π / λd) / iλd·exp[iπ(u 2 +v 2 ) / λd] (3) When collecting simulation data sets, the parameter settings are consistent with those of the optical heterogeneous receiving system, that is, the emission light field E(u, v, 0) and the transmission distance d of the actual system where the present invention is deployed should be used for simulation; φ(u, v, 0) is replaced by the turbulent phase screen; the light field is transmitted through the distance d1 and the distance d2 respectively to obtain the light field E1(x, y, d1) and E2(x, y, d2), and then the square law detection is performed on the complex amplitude light field as a simulation of the acquisition process of two CCD cameras in the optical heterogeneous receiving system: I1(x,y,d1)=|E1(x,y,d1)| 2 ,I2(x,y,d2)=|E2(x,y,d2)| 2 (4) Changing different turbulence intensities And each time a turbulent phase screen is generated, a different two-dimensional random number is taken. After the above simulation calculation, multiple sets of light intensity distributions {I1(x,y,d1),I2(x,y,d2)} are collected and used as the data set for SWRNO training; (2) Construct a neural network embedded in the light field transmission model as a wavefront reconstruction neural operator; The SWRNO architecture consists of two parts. The first part is the neural network that finally realizes the wavefront reconstruction function, which becomes SWRNO after training. The second part is the forward propagation layer of the neural network built based on the light field propagation physical model, which enables SWRNO to perform self-supervised training. The neural network has multiple models with the ability to extract and generate two-dimensional features. Specifically, the U-Net with fine-tuned structure is used. The forward propagation operation of the neural network is denoted as operator R θ , whose input is the two light intensity distributions I detected at different propagation distances received by the optical heterogeneous receiving system RX1 (x,y,d1) and I RX2 (x,y,d2), output is turbulence phase screen It is expressed as: In the forward propagation layer of the neural network, the Fresnel diffraction and square law detection are used as the forward propagation layer that can be embedded in the neural network; the parameters of the light field transmission layer are frozen and are not used as trainable parameters; the specific representation of the light field transmission layer is as follows: Will The light field intensity distribution E at the transmitting end TX (x,y,0) is combined as a beam with wavefront distortion: E0(x, y, 0) enters two optical field transmission layers with different transmission distances respectively, and obtains the received optical field of the optical heterogeneous receiving system predicted by SWRNO and They are respectively expressed as: Then perform square law detection on them respectively to obtain the predicted received light field intensity distribution: Thus, all the outputs of SWRNO are obtained: the turbulence phase screen and two reconstructed receiving end light field structures; (3) Perform self-supervised training based on the gradient descent method to obtain the wavefront reconstruction neural operator; Use unlabeled self-supervised training strategy; the goal of iterative optimization is to make the light field intensity distribution output by the model and The light intensity distribution actually detected by the optical heterogeneous receiver at different depths I RX1 (x,y,d1) and I RX2 (x, y, d2) is almost the same, that is, through training, the model itself is used as a solver of the equations formed by the two transmission processes. The equations formed by the optical heterogeneous receiving system are as follows: E RX1 (x,y,d1)=[I RX1 (x,y,d1)] 1 / 2 exp[iφ RX1 (x,y)] (10) E RX2 (x,y,d2)=[I RX2 (x,y,d2)] 1 / 2 exp[iφ RX2 (x,y)] (11) In formula (10) and formula (11), I RX1 (x,y,d1) and I RX2 (x, y, d2) is the intensity distribution of the received light field detected by CCD. Let d1≤d2, φ RX1 (x,y) and φ RX2 (x, y) are the wavefront phases of the two received light fields respectively; Equations (12) and (13) respectively establish the transmission equations of the two light fields transmitted from the transmitting end through turbulence to the receiving end at different transmission distances, where I TX (x, y, 0) is the intensity distribution of the light field emitted by the transmitter, φ T (x, y) is the turbulence phase; in addition, there is an implicit transmission relationship, that is, the transmission equation from the light field at z = d1 to the light field at z = d2 expressed by equation (14); Substituting equations (10) and (11) into equations (12), (13) and (14), the resulting three equations consist of the equation system containing φ RX1 (x,y),φ RX2 (x,y) and φ T (x, y) three matrices to be calculated; by receiving the light intensity distribution at different positions, the number of matrices to be calculated can be matched with the number of equations and converted into a well-posed problem; therefore, the loss function is set to the following form: in, The model is calculated from After transmission distance d2-d1 The light field intensity distribution is obtained after square law detection, and β is an adjustable parameter. During the training process, according to the batch input, the loss function value is calculated in each iteration cycle, and the reverse gradient propagation is calculated to update the weight parameters of the neural network. After each round of model training, the residual wavefront difference (RWE) between the output wavefront predicted by the validation set and the actual wavefront is used as an evaluation indicator, and the calculation method is as follows: Among them, N x and N y are the number of pixels in the horizontal direction and the number of pixels in the vertical direction of the phase screen respectively; (4) Deploy SWRNO directly to optical heterogeneous receiving systems for wavefront detection; The trained SWRNO is deployed in the system that needs wavefront detection. Along with SWRNO, an optical heterogeneous receiving system is also deployed, that is, a coaxial CCD camera that receives at different depths to detect the light field intensity distribution; the input of SWRNO is replaced with the light field intensity distribution actually detected by the CCD camera, and the output of SWRNO is the reconstructed light field wavefront.

2. The incident light beam wavefront detection method based on wavefront reconstruction neural operator according to claim 1 is characterized in that: The fine-tuned U-Net includes encoding (downsampling) and decoding (upsampling) paths, and passes the feature map of the encoder to the decoder through a skip connection to retain detail information; the two collected light field intensity distributions are 128×128 in size, and the two light field intensity distribution maps are merged into a dual-channel image as input to the encoder part of the neural network; The encoder part gradually downsamples the input image and extracts multi-level features; specifically, it includes a convolution module, which contains: a convolution layer with a convolution kernel size of 3×3 and a stride of 1, a batch normalization, and a ReLU activation function; it also includes a downsampling module, which contains: a convolution layer with a convolution kernel size of 3×3 and a stride of 2, a batch normalization, and a ReLU activation function; The decoder part performs upsampling through deconvolution and concatenates the feature map of the corresponding layer of the encoder; it includes an upsampling module, which contains: a deconvolution layer with a convolution kernel size of 3×3 and a stride of 2, a batch normalization and a ReLU activation function.

3. The incident light beam wavefront detection method based on wavefront reconstruction neural operator according to claim 2 is characterized in that: The specific process is as follows: the dual-channel light field intensity distribution image (128×128×2) is used as input, and enters the first layer downsampling module after passing through two layers of convolution modules, at which time the number of channels is 16; then enters the second layer downsampling module after passing through two layers of convolution modules, at which time the number of channels is 32; then enters the third layer downsampling module after passing through two layers of convolution modules, at which time the number of channels is 64; then enters the fourth layer downsampling module after passing through two layers of convolution modules, at which time the number of channels is 128; then enters the first layer upsampling module after passing through two layers of convolution modules, and is spliced ​​with the input of the fourth layer downsampling module, at which time the number of channels is 128; then enters the second layer upsampling module after passing through two layers of convolution modules, and is spliced ​​with the input of the fourth layer downsampling module, at which time the number of channels is 128; The input of the third downsampling module is spliced, and the number of channels is 64 at this time; then after passing through two layers of convolution modules, it enters the third upsampling module and is spliced ​​with the input of the third downsampling module, and the number of channels is 32 at this time; then after passing through two layers of convolution modules, it enters the fourth upsampling module and is spliced ​​with the input of the fourth downsampling module, and the number of channels is 16 at this time; then it enters two layers of convolution modules, and finally enters a convolution module with a Sigmoid activation function, and outputs a 128×128 image with a channel number of 1; at this time, the image value range is (0,1), which is linearly enlarged to the value range of (-π,π) as the wavefront phase output by the neural network.

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