Wavefront distortion prediction method based on self-supervised deep learning under effect of boundary layer

Abstract

A wavefront distortion prediction method based on self-supervised deep learning under the effect of a boundary layer comprises the following steps: constructing a neural network model based on self-supervised deep learning and training, and inputting beacon light into the trained neural network model based on self-supervised deep learning to obtain beacon light wavefront distortion prediction; the training process comprises the following steps: taking a boundary layer result obtained by using a beacon optical signal through ANSYS software as a truth value label # imgabs0 #, and sending the truth value label # imgabs1 # into a diffraction model to obtain an actual receiving signal Srecv; inputting the four-channel data into a self-supervised deep learning neural network to obtain an estimation result # imgabs2 # of a boundary layer, sending an estimation result # imgabs3 # into a diffraction model to obtain an estimation optical signal # imgabs4 # interfered by the boundary layer, and calculating loss by using the estimation optical signal # imgabs5 # and an actual received signal Srecv; the self-supervised training network model is adopted to predict phase distortion information caused by the boundary layer, wavefront distortion caused by the boundary layer effect is effectively reduced, and the coupling efficiency is improved.

Description

Technical Field

[0001] The present application belongs to the field of wavefront distortion technology, and specifically relates to a wavefront distortion prediction method based on self-supervised deep learning under the action of a boundary layer. Background Art

[0002] Boundary layer refers to a layer of gradient air formed on the surface of an aircraft when the aircraft is moving at high speed. The airflow passes through the surface of the aircraft and is affected by the viscosity of the air. The airflow velocity gradually increases from zero to the mainstream velocity. It is also called the boundary layer. According to different properties, the boundary layer is mainly divided into two types: laminar flow and turbulent flow. When the thickness of the boundary layer is small, the velocity gradient in the boundary layer is large, and the effect of viscous stress is also large. At this time, the flow in the boundary layer is laminar. When the Reynolds number reaches a certain value, the laminar flow in the boundary layer turns into turbulent flow after passing through a transition zone. At the calibrated operating altitude and Mach number in the atmosphere, there are turbulent boundary layers adjacent to the aerodynamic surface. When light passes through the boundary layer near the optical window of the aircraft, it will cause various boundary layer effects, and will cause Strehl loss, beam diffusion and beam tilt on the detector. Therefore, the boundary layer is a key issue that cannot be avoided in the study of airborne quantum secure communication.

[0003] With the rapid development of the information age, information security has become a global focus. Quantum Key Distribution (QKD), as a secure communication method based on the principles of quantum mechanics, has the characteristics of unbreakability and security of information transmission, and is regarded as an important means to ensure information security. The airborne QKD system applies this secure communication method to the aviation field to ensure the security and confidentiality of air communications. Considering that airborne platforms play a key role in establishing a comprehensive quantum network across air and space, quantum key distribution has more advantages than fiber-optic quantum key distribution.

[0004] The boundary layer effect will affect the transmission and reception of quantum signals, which may lead to the loss of quantum signals, phase distortion and increased bit error rate, and reduce the performance and security of airborne QKD systems. In order to overcome the impact of boundary layer effects on airborne QKD systems, it is necessary to deeply study and understand the mechanism and characteristics of boundary layer effects, and take corresponding technical means to resist their influence. In the existing studies on airborne QKD under the action of boundary layer, the background is mainly based on aircraft-ground station, while QKD based on satellite-aircraft scenarios is rarely studied. As a link between satellite and ground, QKD based on satellite-aircraft scenarios is an important part of the future construction of an integrated quantum communication system between space and ground. Since the receiving end is transferred from the ground station to the aviation platform, it is more necessary to consider the effects of link loss, wavefront distortion, quantum state decoherence, etc. caused by the complex atmospheric environment and boundary layer. Summary of the invention

[0005] In order to overcome the above-mentioned technical problems and further enhance the security and performance of the airborne QKD system, the present application proposes a wavefront distortion prediction method based on self-supervised deep learning under the action of the boundary layer, and uses a self-supervised trained network model to predict the phase distortion information caused by the boundary layer, which effectively reduces the wavefront distortion caused by the boundary layer effect and improves the coupling efficiency, thereby increasing the generation of the final key amount in the QKD system in the satellite-aircraft scenario.

[0006] In order to achieve the above purpose, the technical solution adopted in this application is as follows:

[0007] A wavefront distortion prediction method based on self-supervised deep learning under the action of boundary layer, comprising:

[0008] Build and train a neural network model based on self-supervised deep learning;

[0009] The beacon light is input into the trained neural network model based on self-supervised deep learning to obtain the prediction result of the beacon light wavefront distortion;

[0010] Among them, the neural network model of self-supervised deep learning includes 15 convolutional layers and 3 deconvolutional layers. In the encoding stage, 3 maximum pooling layers are used for downsampling to gradually reduce the feature dimension to 1 / 8 of the input. In the decoding stage, 3 deconvolutional layers are used for upsampling to gradually restore the features to their original size.

[0011] The initial convolution layer of the neural network model based on self-supervised deep learning uses a convolution kernel with a kernel size of 5×5 to extract data information in the receptive field. Other convolution layers and deconvolution layers use convolution kernels with a kernel size of 3×3. The Batch-Normal layer performs batch normalization and uses the ReLu activation function.

[0012] The output of the neural network model based on self-supervised deep learning is the wavefront distortion prediction result of a single channel. The output uses a Sigmoid activation function to compress the output to the (0,1) interval, and multiplies it by π to map the output to the (0,π) interval.

[0013] Training of neural network models based on self-supervised deep learning, including:

[0014] The boundary layer result of the beacon light signal obtained by ANSYS software is used as the true value label The true value label The actual received signal S is sent to the diffraction model recv ;

[0015] The number of channels of the neural network model based on self-supervised deep learning is 4, which are the ideal test signal O and origin The real and imaginary components of the signal, as well as the actual received signal O that should be disturbed by the boundary layer boundary The real and imaginary components of the 4-channel data are input into the neural network based on self-supervised deep learning to obtain the estimation result of the boundary layer. The estimated results Send it into the diffraction model to obtain the estimated light signal disturbed by the boundary layer

[0016] Using the estimated optical signal The actual received signal S recv Calculate the loss, the loss function used is:

[0017]

[0018] In the formula, loss Loss = L2 2 +α·L1 is divided into two parts, and L2 loss is the estimated optical signal and the actual received signal S recv The square of the difference between the two is the L1 loss, which indicates the estimated optical signal and the actual received signal S recv The corresponding losses are the real part and the real part, the imaginary part and the imaginary part, respectively, and α is the weight of the L1 loss.

[0019] When training the neural network model based on self-supervised deep learning, a random atmospheric turbulence phase screen is used to replace the ideal probe signal acting on the boundary layer as the actual receiving signal after the boundary layer interference.

[0020] When training neural network models based on self-supervised deep learning, the training device uses NVIDIA RTX3060 GPU.

[0021] A wavefront distortion prediction system based on self-supervised deep learning under the action of boundary layer, comprising:

[0022] Model construction and training: Build a neural network model based on self-supervised deep learning and train it;

[0023] Wavefront distortion prediction module: input the beacon light into the trained neural network model based on self-supervised deep learning to obtain the beacon light wavefront distortion prediction;

[0024] Among them, the neural network model of self-supervised deep learning includes 15 convolutional layers and 3 deconvolutional layers. In the encoding stage, 3 maximum pooling layers are used for downsampling to gradually reduce the feature dimension to 1 / 8 of the input. In the decoding stage, 3 deconvolutional layers are used for upsampling to gradually restore the features to their original size.

[0025] A wavefront distortion prediction device based on self-supervised deep learning under the action of a boundary layer, comprising:

[0026] Memory: used to store the wavefront distortion prediction method based on self-supervised deep learning under the action of a boundary layer;

[0027] Processor: used to implement a wavefront distortion prediction method based on self-supervised deep learning under the action of the boundary layer when executing the computer program.

[0028] A computer-readable storage medium stores a computer program, which, when executed by a processor, can implement a wavefront distortion prediction method based on self-supervised deep learning under the action of a boundary layer.

[0029] Compared with the prior art, the beneficial effects of this application are:

[0030] A deep learning network model is used to predict and compensate the phase distortion information caused by the boundary layer. In order to solve the problem of difficulty in obtaining the ground truth label (Ground Truth) of the wavefront distortion caused by the boundary layer effect, a self-supervised training network model is proposed. It also solves the problem that supervised learning requires a large amount of labeled data to obtain better performance, but the cost of obtaining a large amount of labeled data is extremely high.

[0031] Furthermore, compared with directly using a complex neural network, the present application can obtain the desired estimation result by decomposing the real and imaginary parts of the signal and processing it in the real domain. At the same time, it can greatly reduce the number of network parameters and the complexity of error gradient back propagation, greatly improving the training efficiency of the network. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 Schematic diagram of satellite-aircraft quantum communication link.

[0033] Figure 2 Schematic diagram of the satellite-aircraft QKD model structure.

[0034] Figure 3 Comparison of the diffraction of beacon light after passing through atmospheric turbulence and boundary layer.

[0035] Figure 4 Schematic diagram of the decomposition of the real and imaginary parts of the beacon light before and after passing through the boundary layer.

[0036] Figure 5 It is the forward prediction process of the convolutional neural network structure.

[0037] Figure 6 It is an ideal test signal.

[0038] Figure 7 To actually receive the signal.

[0039] Figure 8 The self-supervised working process of convolutional neural network.

[0040] Fig. 9 The true value and prediction result of the atmospheric turbulence phase screen.

[0041] Fig.10 is the loss curve of the training loss value versus the number of training steps.

[0042] Fig.11 It is the difference between the predicted values ​​when the number of iteration epochs is 800 and 1000.

[0043] Fig.12 Visual comparison of the predicted boundary layer and the true boundary layer for different iteration epochs.

[0044] Fig.13 are the true and predicted values ​​of the wavefront distortion caused by the boundary layer.

[0045] Fig.14 When the aircraft is flying due south after adaptive compensation, the (a) total loss, (b) quantum bit error rate, and (c) security key rate of the feasible link vary with time. DETAILED DESCRIPTION

[0046] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0047] Deep learning technology can effectively improve the performance of wavefront sensors in adaptive optical systems, thereby achieving more accurate wavefront detection. Therefore, deep convolutional neural networks are particularly suitable for fitting and estimating the intensity distribution of light beams before and after transmission under turbulent conditions and the value of the phase screen caused by turbulence. Through this data-driven estimation method, better results can be obtained compared with traditional optimization methods. It is a feasible solution to integrate deep learning technology with AO systems and introduce them into airborne QKD systems to compensate for the influence of boundary layer effects.

[0048] A wavefront distortion prediction method based on self-supervised deep learning under the action of the boundary layer predicts the phase distortion information caused by the boundary layer through a deep learning network model, and then restores the wavefront information of the signal light through a classic spatial light modulator, effectively reducing the wavefront distortion caused by the aero-optical effect in the star-machine scenario, thereby improving the coupling efficiency and increasing the final key amount generated. This application effectively reduces the wavefront distortion caused by the boundary layer effect in the star-machine scenario, improves the coupling efficiency, and thus increases the final key amount generated. These studies provide an important theoretical and practical basis for further optimizing the design and performance of airborne QKD systems, which can effectively improve the anti-interference capability and security of airborne QKD systems and promote their widespread promotion and application in practical applications.

[0049] Example 1

[0050] A wavefront distortion prediction method based on self-supervised deep learning under the action of boundary layer, comprising:

[0051] Build and train a neural network model based on self-supervised deep learning;

[0052] The beacon light is input into the trained neural network model based on self-supervised deep learning to obtain the prediction result of the beacon light wavefront distortion;

[0053] Among them, the neural network model of self-supervised deep learning includes 15 convolutional layers and 3 deconvolutional layers. In the encoding stage, 3 maximum pooling layers are used for downsampling to gradually reduce the feature dimension to 1 / 8 of the input. In the decoding stage, 3 deconvolutional layers are used for upsampling to gradually restore the features to their original size.

[0054] The initial convolution layer of the neural network model based on self-supervised deep learning uses a convolution kernel with a kernel size of 5×5 to extract data information in the receptive field. Other convolution layers and deconvolution layers use convolution kernels with a kernel size of 3×3. The Batch-Normal layer performs batch normalization and uses the ReLu activation function.

[0055] The output of the neural network model based on self-supervised deep learning is the wavefront distortion prediction result of a single channel. The output uses a Sigmoid activation function to compress the output to the (0,1) interval, and multiplies it by π to map the output to the (0,π) interval.

[0056] Training of neural network models based on self-supervised deep learning, including:

[0057] The boundary layer result of the beacon light signal obtained by ANSYS software is used as the true value label The true value label y i T is sent into the diffraction model to obtain the actual received signal Srecv ;

[0058] The number of channels of the neural network model based on self-supervised deep learning is 4, which are the ideal test signal O and origin The real and imaginary components of the signal, as well as the actual received signal O that should be disturbed by the boundary layer boundary The real and imaginary components of the 4-channel data are input into the neural network based on self-supervised deep learning to obtain the estimation result of the boundary layer. The estimated results Send it into the diffraction model to obtain the estimated light signal disturbed by the boundary layer

[0059] Using the estimated optical signal The actual received signal S recv Calculate the loss, the loss function used is:

[0060]

[0061] In the formula, loss Loss = L2 2 +α·L1 is divided into two parts, and L2 loss is the estimated optical signal and the actual received signal S recv The square of the difference between the two is the L1 loss, which indicates the estimated optical signal and the actual received signal S recv The corresponding losses are the real part and the real part, the imaginary part and the imaginary part, respectively, and α is the weight of the L1 loss.

[0062] When training the neural network model based on self-supervised deep learning, a random atmospheric turbulence phase screen is used to replace the ideal probe signal acting on the boundary layer as the actual receiving signal after the boundary layer interference.

[0063] When training neural network models based on self-supervised deep learning, the training device uses NVIDIA RTX3060 GPU.

[0064] A wavefront distortion prediction system based on self-supervised deep learning under the action of boundary layer, comprising:

[0065] Model construction and training: Build a neural network model based on self-supervised deep learning and train it;

[0066] Wavefront distortion prediction module: input the beacon light into the trained neural network model based on self-supervised deep learning to obtain the beacon light wavefront distortion prediction;

[0067] Among them, the neural network model of self-supervised deep learning includes 15 convolutional layers and 3 deconvolutional layers. In the encoding stage, 3 maximum pooling layers are used for downsampling to gradually reduce the feature dimension to 1 / 8 of the input. In the decoding stage, 3 deconvolutional layers are used for upsampling to gradually restore the features to their original size.

[0068] A wavefront distortion prediction device based on self-supervised deep learning under the action of a boundary layer, comprising:

[0069] Memory: used to store the wavefront distortion prediction method based on self-supervised deep learning under the action of a boundary layer;

[0070] Processor: used to implement a wavefront distortion prediction method based on self-supervised deep learning under the action of the boundary layer when executing the computer program.

[0071] A computer-readable storage medium stores a computer program, which, when executed by a processor, can implement a wavefront distortion prediction method based on self-supervised deep learning under the action of a boundary layer.

[0072] Example 2

[0073] A wavefront distortion prediction method based on self-supervised deep learning under the action of a boundary layer, comprising the following steps:

[0074] Step 1: Construct a star-machine QKD model based on the decoyed BB84 protocol;

[0075] Step 2: Construct a neural network model based on self-supervised deep learning to predict wavefront distortion;

[0076] Step 3: Based on the wavefront distortion information obtained in steps 1 and 2 and the parameters of the star-machine QKD model, the predicted value is input into the spatial light modulator at the receiving end to compensate the signal light. Without considering the efficiency of the spatial light modulator and its system, it is assumed that its compensation conversion efficiency is 100%, and only the reduction in QKD performance caused by the neural network prediction error is analyzed. On this basis, the deflection angle, quantum bit error rate, channel loss and security key rate of the transmitted photons are estimated. Among them, the photon deflection offset is realized based on flow field information and ray tracing method; the quantum bit error rate, channel loss and security key rate are realized by calculating the total optical path difference to estimate the Strehl-Ratio (SR).

[0077] 1. Construct a star-machine QKD model based on the decoyed state BB84 protocol. Please refer to the patent application document with publication number CN 115664647A, which is titled "A simulation method for star-machine quantum key distribution under the action of a boundary layer".

[0078] The schematic diagram of the satellite-machine QKD downlink discussed in this application is as follows Figure 1 As shown, the quantum photon source is on the satellite (Alice), the receiving module is on the plane (Bob), the satellite moves according to its preset orbit, and the plane starts from a certain position and moves at a constant speed v and a constant altitude h. B , fly in a certain direction. With known flight speed v and flight altitude h B and the air density ρ h The boundary layer density field around the aircraft can be calculated by combining the actual geometric shape of the aircraft with ANSYS Fluent and other software. The receiving telescope is planned to be located above the nose of the aircraft and conformal to the aircraft. A rectangular coordinate system is constructed with the geometric center of the receiving telescope as the origin O, the zenith direction of the aircraft as the z-axis, the north direction of the aircraft as the x-axis, and the east direction as the y-axis. The position of the satellite is recorded as S, the distance from the origin O to the satellite point S is recorded as d, the angle between the projection line of OS on the xoy plane and the positive direction of the x-axis is the azimuth angle α (0°≤α<360°), and the angle between the projection line of OS on the xoy plane and OS is the pitch angle β (0°≤β≤90°). Usually, the range of 0°≤β<10° is used for link establishment and calibration.

[0079] The satellite-machine QKD scheme mainly includes three steps: link calibration, QKD process and post-processing. After completing the link calibration, a quantum communication link is established between Alice and Bob. In the QKD process, Alice transmits the modulated photons to Bob, and then performs post-processing to extract the final security key.

[0080] In the satellite-to-aircraft downlink QKD scheme, the distance between the boundary layer and the receiving telescope is very small, and the photon deflection and divergence effects caused by the boundary layer effect can be ignored. Regardless of the existence of the boundary layer, the effective beam waist radius of the receiving telescope is constant. When Gaussian distributed photons propagate through the boundary layer to the airborne receiver, the effective beam waist radius of the telescope at the receiving end of the satellite-to-aircraft downlink is ω DP It can be expressed as

[0081]

[0082] where σ T is the pointing error of the transmitting telescope, ω D The receiving beam waist of the ground station without considering the pointing error is:

[0083]

[0084] Where r0 is the zenith angle correlation field coefficient, β is the elevation angle of the receiving telescope, and D T is the diameter of the transmitting telescope.

[0085] According to the proposed satellite-machine downlink QKD scenario setting, a rectangular coordinate system is established with the geometric center of the receiving telescope as the origin, such as Figure 2 As shown. Set the effective beam waist radius ω at the receiving end DP Evenly divided into enough incident points, the initial value of s in the ray tracing operation can be expressed as

[0086]

[0087] Where m is the number of incident points divided, the initial value of F in the ray tracing operation can be expressed as

[0088]

[0089] Where n represents the boundary layer density field distribution, which can be calculated by the boundary layer refractive index field and the Gladstone-Dale formula. The fourth-order Runge-Kutta method is used to solve the partial differential equation to obtain the following expression:

[0090]

[0091] Where Δl is the step length along the propagation direction in the ray tracing method, and D is the partial differential of the refractive index field in the x, y, and z directions.

[0092]

[0093] Substituting the initial values ​​s0 and F0 into equation (6), the coordinate s1 at the next step position and the direction vector F1 of the light at this time can be calculated. In this way, the trajectory of the entire transmission process can be deduced, and then the optical path at each position of the receiving end can be calculated. In order to speed up the operation of the computer, the Adams linear multi-step method can be used to simplify the calculation process. The values ​​of s0, F0, s1, F1 and the refractive index field distribution n' are used as the initial parameters of the Adams linear multi-step method, and the interpolation method based on polynomial fitting is combined to speed up the tracking solution process. Therefore, the optical path OPL of the Gaussian distribution light beam when it passes through the boundary layer to the aircraft receiving end telescope can be obtained by the ray tracing method. Finally, the wavefront difference of the received light is calculated by the optical path length formula.

[0094] When light passes through the boundary layer and illuminates the receiving telescope, the transmission efficiency η0 can be calculated as

[0095]

[0096] Where D R is the diameter of the receiving telescope, and τ is the atmospheric extinction thickness (here it refers to the distance from the flight altitude of the aircraft to the infinite space).

[0097] In the satellite-machine QKD system, due to the boundary layer effect, the total transmission efficiency η of photons can be calculated as

[0098] η=η0η s η d (8)

[0099] Among them, η s is the system receiving efficiency caused by components, η d is the detector efficiency.

[0100] In actual QKD systems, the decoyed state protocol is often used, which can effectively resist the photon number separation attack carried out by eavesdroppers based on the vulnerability of multi-photon terms in the light source. Therefore, weak coherent photon sources can be used to replace single photon sources that cannot be developed with existing technology.

[0101] In the star-machine QKD performance evaluation scheme, we use the signal photon intensity μ and the decoy photon intensity ν to execute the vacuum decoy state BB84 protocol (the protocol can be replaced according to actual conditions in future practical use), and the modulation probability of the signal (decoy) state is P s and P d Considering that the polarization characteristics of the quantum state do not change during the transmission process, the polarization calibration error e d Finally, the photon transmission efficiency η is substituted into the key rate formula to calculate the bit error rate QBER and the security key rate R.

[0102] 2. Construct a neural network model based on self-supervised learning to predict wavefront distortion.

[0103] In order to facilitate the intuitive analysis of the relationship between the degree of spot intensity distortion and the boundary layer effect, the point spread function (PSF) can be used to calculate the situation after the ideal Gaussian light passes through the boundary layer. The complex amplitude distribution function of the light within the receiving port diameter can be expressed as:

[0104]

[0105] in is the amplitude distribution of the wavefront of ideal Gaussian light at the receiving telescope, is the wavefront distortion function caused by the boundary layer at the corresponding position. The point amplitude spread function (ASF) can be expressed as

[0106]

[0107] Where B is a constant, the relationship between ASF and PSF is as follows

[0108] PSF(x′,y′)=ASF(x′,y′)·ASF* (x′,y′) (11)

[0109] The PSF can be used to obtain the light intensity attenuation at different positions, and to predict and evaluate the far-field imaging effect. In the airborne QKD scenario, the PSF can be used to obtain the energy distribution of ideal light after passing through the boundary layer.

[0110] In free-space optical communications under atmospheric turbulence, the working principles of adaptive optical systems are generally divided into three categories: phase inversion based on intensity measurement results, direct measurement of wavefront slope or curvature, and wavefront sensing and compensation based on the interference principle. Among them, the phase inversion method based on intensity measurement results was proposed first, with the lowest hardware requirements and is widely used. However, this method has high requirements on the intensity change of the beacon light at the receiving end. For example, through PSF calculation Figure 3 The Gaussian spot shown in (a) is transmitted through Figure 3 After the random phase screen shown in (b), the following is obtained: Figure 3 In this case, the phase inversion method based on the intensity measurement results will be more effective, but if the phase screen is replaced by Figure 3 (e) The boundary layer causes wavefront distortion. Since the boundary layer is very thin and the spatial scale is small, for the satellite-machine QKD scenario, the intensity change of the light spot after passing through the boundary layer is not obvious, such as Figure 3 As shown in (d) and (f), it is difficult to analyze the wavefront information based on intensity alone.

[0111] Therefore, the present application considers splicing the channel dimensions of the real and imaginary parts of the complex spatial signal of the beacon light, that is, decomposing the real and imaginary parts of the beacon light before and after passing through the boundary layer, such as Figure 4 As shown in the figure, the real and imaginary parts of the light spot before and after passing through the boundary layer are compared respectively. According to the deep learning (DL) technology that has flourished in recent years, the high-dimensional feature information of the data can be extracted and processed, and the models that were difficult to describe by traditional mathematical methods can be highly fitted, and it has a strong representation ability; Convolutional Neural Network (CNN) has made great achievements in image processing fields such as target detection and image segmentation, and has been widely used in computer vision.

[0112] In recent years, relevant research teams at home and abroad have conducted in-depth demonstrations and experiments on the application of deep learning in adaptive optical systems, proving that deep learning technology can effectively improve the performance of wavefront sensors in adaptive optical systems, thereby achieving more accurate wavefront detection. Therefore, deep convolutional neural networks are very suitable for fitting and estimating the intensity distribution of light beams before and after transmission under turbulence and the numerical value of the turbulent phase screen. This data-driven estimation method can achieve better results than traditional optimization methods. Here we design and use a classic encoder-decoder structure deep convolutional network model. The forward prediction process of the convolutional neural network structure is as follows: Figure 5 As shown in Figure 2, the distortion is clearly obtained, which is beneficial for the training of deep learning networks.

[0113] The overall network model consists of 15 convolutional layers and 3 deconvolutional layers. The encoding stage uses 3 maximum pooling layers to gradually reduce the feature dimension to 1 / 8. The decoding part uses 3 deconvolutional layers to upsample the features to restore the features to their original size. The initial convolutional layer uses a convolution kernel with a kernel size of 5×5, which can extract data information in a larger receptive field. After that, both the convolutional layer and the deconvolution layer use a convolution kernel with a kernel size of 3×3. In order to prevent overfitting, the Batch-Normal layer is used for batch normalization, and the ReLu activation function is used. The output of the network is the boundary layer prediction result of a single channel. The output uses the Sigmoid activation function to compress the output to the (0,1) interval, and multiply by π to map the output to (0,π).

[0114] Since the data of boundary layer density field is not easy to obtain, random atmospheric turbulence phase screen is used to replace the ideal test signal of boundary layer during network training. The resolution of network input two-dimensional data is 256×256, and the number of channels is 4 channels, which are the ideal test signal O not affected by the boundary layer. origin and the actual received signal O corresponding to the boundary layer interference boundary The real and imaginary components of Figure 6 , Figure 7 As shown, it is the channel dimension splicing of the real part and the imaginary part of the complex space signal. boundary The acquisition of the real and imaginary parts requires the use of the local oscillator signal at the receiving end to obtain O boundary The signal is separated into zero beats, which places higher requirements on the accuracy of time synchronization between the sender and the receiver. Compared with directly using complex neural networks, by decomposing the real and imaginary parts of the signal and processing it in the real domain, the expected estimation results can be obtained. At the same time, the network parameters and the complexity of error gradient back propagation can be greatly reduced, greatly improving the network training efficiency.

[0115] The commonly used network is supervised, but due to the intense disturbance of the small-scale turbulent structure inside the boundary layer, it is very difficult to obtain the true value label of the wavefront distortion caused by the boundary layer effect. Therefore, the supervised learning method is not very suitable for the prediction task of the aircraft boundary layer effect. To solve this problem, we propose a self-supervised network model such as Figure 8 As shown, the proposed self-supervision method and loss function are introduced next.

[0116] The data set required for network training is generated through simulation, and its data input is O under vacuum channel conditions origin and Gaussian beam O under turbulent channel conditions boundary Complex intensity distribution diagram, and the real and imaginary parts Re{O origin}、Im{O origin}、Re{O boundary} and Im{O boundary} Separate and splice into 4-channel input data in the channel dimension, and use the boundary layer results obtained by ANSYS software as the true value label The true value label is not used as a supervision label to directly calculate the training loss. It is only used when comparing the simulated generated signal with the estimated result: The actual received signal S is sent to the diffraction model recv And the above 4-channel data, and then input the 4-channel data into the self-supervised learning neural network to obtain the estimated result of the boundary layer The estimated results Send it into the diffraction model to obtain the estimated light signal disturbed by the boundary layer Using the estimated optical signal The actual received signal S recv To calculate the loss, the loss function L used is:

[0117]

[0118] In the formula, the loss Loss is divided into two parts, including the first part predicting the received signal and the actual received signal S recv The L2 loss, and and S recv Corresponding to the L1 loss of the real part and the imaginary part, α is the weight of the L1 loss, and α=10 in the experiment.

[0119] The training model data set is the atmospheric turbulence phase screen data generated by random simulation using numerical simulation methods, with 1,000 groups as one epoch for training. Since the self-supervised model is used, the training data are all randomly generated, and there is almost no repetition of training samples. Therefore, there is no need to set a test set and a validation set, and the training results can be fully reflected in the loss of the training set. The turbulence intensity parameter when generating the image is the atmospheric refractive index structure constant. The value range is [10 -14 ,10 -13 ], the communication distance d ranges from 0 to 10000 meters, the distance Δd from the light source to the boundary layer ranges from 0 to 10000 meters, and the beam waist radius ω0 of the Gaussian spot is 15.8×10 -3 m. The true value and prediction results of the data set are as follows Fig. 9 As shown, Fig. 9 (a) is the true value, Fig. 9 (b) is the predicted value. By comparing the true value and the network prediction result, we can see that except for the two-dimensional high-frequency part which is more difficult to predict, the deep neural network is very accurate in estimating the flow field.

[0120] The network training loss curve is as follows Fig.10 As shown, a total of 1000 epochs were trained, and the training loss curve data containing 6000 steps was recorded. The initial learning rate was set to 1e -4 , the learning rate decay strategy of the network is: decay ten times at the 500th and 800th epochs respectively. It can be seen that the network begins to converge stably at the 500th epoch.

[0121] Considering the problem of computational time, the optimal number of iterations is further analyzed. When the number of iterations reaches 800 and 1000 epochs respectively, the predicted wavefront distortion difference is as follows: Fig.11 As shown in the figure, the absolute value of the difference between the two is less than 0.1rad, indicating that the number of iterations has little effect on the learning rate. Therefore, considering the calculation time, the result of the network at the 1000th epoch is finally selected as the predicted value.

[0122] In order to intuitively reflect the changing trend of network prediction ability corresponding to the change of loss, Fig.11 The visualization results of the wavefront distortion caused by the boundary layer predicted by the trained network model at different iteration numbers are shown. Fig.12 It can be seen that when the iterations reach a sufficient number, the predicted phase image information is almost the same as the expected turbulence phase screen information.

[0123] In addition, the training equipment uses NVIDIA RTX 3060 GPU, and the time from input to prediction generation of each image is only about 1ms, which is much shorter than the processing time of traditional iterative optimization algorithms. By using integrated graphics cards and hardware acceleration methods, the processing time can theoretically reach 0.1ms, which can meet the needs of real-time feedback of the system and is closer to the true value, making up for the slow hardware response problem in the actual compensation system implementation, and providing a time basis for the rapid compensation of the signal distortion phase of the airborne QKD system.

[0124] 3. Based on the wavefront distortion information obtained in step 1 and step 2 and the parameters of the star-machine QKD model, the predicted value is input into the spatial light modulator at the receiving end to compensate the signal light. Without considering the efficiency of the spatial light modulator and its system, it is assumed that its compensation conversion efficiency is 100%, and only the reduction in QKD performance caused by the neural network prediction error is analyzed. On this basis, the quantum bit error rate, channel loss and security key rate are estimated. Among them, the quantum bit error rate, channel loss and security key rate are achieved by calculating the total optical path difference to estimate the Strehl-Ratio (SR).

[0125] 4. Embodiment

[0126] This application uses Fluent software to simulate flow field information and uses the ray tracing method based on MATLAB to evaluate the transmission quantum bit error rate, channel loss, security key rate and compensation effect in the star-machine QKD scenario.

[0127] The first step is to obtain the flow field information. Computational fluid dynamics software such as CFX, Fluent, and COMSOL can be used to simulate the density field distribution of the BL. This application uses Fluent to simulate the density field distribution of the aircraft at different altitudes. The refractive index field can be obtained by applying the Gladstone-Dale equation. It is worth noting that in order to simplify the calculation of wavefront distortion, the influence of the atmospheric channel on the transmitted photons is ignored.

[0128] The results of the true value and predicted value of wavefront distortion caused by the boundary layer are as follows: Fig.13 As shown, the color indicates the intensity of the wavefront distortion in rad. Since the size of the receiving telescope is 10 mm in the wavefront analysis, the predicted results within this range are consistent with the true value, while the wavefront conditions outside the telescope aperture can only be roughly estimated. However, since only the wavefront distortion within the receiving port aperture is considered during SR calculation, this phenomenon does not affect the coupling efficiency and other results.

[0129] The predicted value is input into the spatial light modulator at the receiving end to compensate the signal light. Without considering the efficiency of the spatial light modulator and its system, it is assumed that its compensation conversion efficiency is 100%, and only the reduction in QKD performance caused by the neural network prediction error is analyzed. At this time, taking the star-machine scenario as an example, the start and end time is from 12:00 on May 29, 2022 to 12:00 on June 5, 2022. The initial position of the aircraft is (34.265637N, 108.953489E, 10km), and the aircraft is flying due south.

[0130] Through calculation, the performance evaluation results of the star-machine QKD within one week can be obtained, such as Fig.14 In the figure, BL represents the boundary layer. In one week, the total time of all feasible links is 6800 seconds. The effective time of quantum communication in the whole process is also 6800 seconds. The final security key length is about 1.3124×10 7 bit. If there is no boundary layer around the aircraft, the total security key rate will be 1.326×10 7 bit, the total key loss caused by the boundary layer decreased from 49.34% to 1.03%, which shows that the impact originally caused by the boundary layer is basically completely compensated. This is because the main loss in satellite-machine QKD comes from the reduction of coupling efficiency caused by wavefront distortion. By compensating for the wavefront distortion caused by the boundary layer, the boundary layer effect can be effectively suppressed.

[0131] In summary, through the airborne QKD adaptive wavefront distortion compensation method based on deep learning technology, the wavefront distortion caused by the boundary layer can be well predicted. Then, through the classic spatial light modulation system, the wavefront information of the signal light can be restored, the coupling efficiency can be improved, and the generation of the final key amount can be improved.

Claims

1. A wavefront distortion prediction method based on self-supervised deep learning under the action of boundary layer, characterized in that: include: Build and train a neural network model based on self-supervised deep learning; The beacon light is input into the trained neural network model based on self-supervised deep learning to obtain the prediction result of the beacon light wavefront distortion; Among them, the neural network model of self-supervised deep learning includes 15 convolutional layers and 3 deconvolutional layers. In the encoding stage, 3 maximum pooling layers are used for downsampling to gradually reduce the feature dimension to 1 / 8 of the input. In the decoding stage, 3 deconvolutional layers are used for upsampling to gradually restore the features to their original size.

2. According to claim 1, the method for predicting wavefront distortion based on self-supervised deep learning under the action of the boundary layer is characterized in that: The initial convolution layer of the neural network model based on self-supervised deep learning uses a convolution kernel with a kernel size of 5×5 to extract data information in the receptive field. Other convolution layers and deconvolution layers use convolution kernels with a kernel size of 3×3. The Batch-Normal layer performs batch normalization and uses the ReLu activation function.

3. The method for predicting wavefront distortion based on self-supervised deep learning under the action of a boundary layer according to claim 4, characterized in that: The output of the neural network model based on self-supervised deep learning is the wavefront distortion prediction result of a single channel. The output uses a Sigmoid activation function to compress the output to the (0,1) interval, and multiplies it by π to map the output to the (0,π) interval.

4. The method for predicting wavefront distortion based on self-supervised deep learning under the action of a boundary layer according to claim 3, characterized in that: Training of neural network models based on self-supervised deep learning, including: The boundary layer result of the beacon light signal obtained by ANSYS software is used as the true value label The true value label The actual received signal S is sent into the diffraction model recv ; The number of channels of the neural network model based on self-supervised deep learning is 4, which are the ideal test signal O and origin The real and imaginary components of the signal, as well as the actual received signal O that should be disturbed by the boundary layer boundary The real and imaginary components of the 4-channel data are input into the neural network based on self-supervised deep learning to obtain the estimation result of the boundary layer. The estimated results Send it into the diffraction model to obtain the estimated light signal disturbed by the boundary layer Using the estimated optical signal The actual received signal S recv Calculate the loss, the loss function used is: In the formula, loss Loss = L2 2 +α·L1 is divided into two parts, and L2 loss is the estimated optical signal and the actual received signal S recv The square of the difference between the two is the L1 loss, which indicates the estimated optical signal and the actual received signal S recv The corresponding losses are the real part and the real part, the imaginary part and the imaginary part, respectively, and α is the weight of the L1 loss.

5. The method for predicting wavefront distortion based on self-supervised deep learning under the action of a boundary layer according to claim 4, characterized in that: When training the neural network model based on self-supervised deep learning, a random atmospheric turbulence phase screen is used to replace the ideal probe signal acting on the boundary layer as the actual receiving signal after the boundary layer interference.

6. The method for predicting wavefront distortion based on self-supervised deep learning under the action of a boundary layer according to claim 5, characterized in that: When training neural network models based on self-supervised deep learning, the training device uses NVIDIA RTX3060 GPU.

7. A wavefront distortion prediction system based on self-supervised deep learning under the action of boundary layer, characterized in that: include: Model construction and training: Build a neural network model based on self-supervised deep learning and train it; Wavefront distortion prediction module: input the beacon light into the trained neural network model based on self-supervised deep learning to obtain the beacon light wavefront distortion prediction; Among them, the neural network model of self-supervised deep learning includes 15 convolutional layers and 3 deconvolutional layers. In the encoding stage, 3 maximum pooling layers are used for downsampling to gradually reduce the feature dimension to 1 / 8 of the input. In the decoding stage, 3 deconvolutional layers are used for upsampling to gradually restore the features to their original size.

8. A wavefront distortion prediction device based on self-supervised deep learning under the action of boundary layer, characterized in that: include: Memory: used to store the wavefront distortion prediction method based on self-supervised deep learning under the action of a boundary layer; Processor: used to implement a wavefront distortion prediction method based on self-supervised deep learning under the action of the boundary layer when executing the computer program.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it can implement a wavefront distortion prediction method based on self-supervised deep learning under the action of a boundary layer.

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