Method for correcting distorted vortex beam based on convolutional neural network

Abstract

The invention discloses a method for correcting a distorted vortex beam based on a convolutional neural network, and the method specifically comprises the following steps: 1, obtaining a distorted light intensity pattern after ocean turbulence and a corresponding standard light intensity pattern through numerical simulation, and building a data set; 2, designing and building a convolutional neural network; 3, performing data preprocessing on the training data obtained in the step 1, and sending the data into the network designed in the step 2 for model training; and step 4, testing the effect of correcting the distorted vortex beam by the convolutional neural network by using the test set. The method provided by the invention can directly and accurately correct the distorted vortex beam influenced by turbulence.

Description

Technical Field

[0001] The invention belongs to the technical field of wireless optical communications and relates to a method for correcting a distorted vortex light beam based on a convolutional neural network. Background Art

[0002] Free Space Optical (FSO) technology has become a research hotspot in the field of communications. When a vortex beam is transmitted in an inhomogeneous medium such as atmospheric turbulence or optical fiber, its spiral wavefront will be distorted, causing the OAM spectrum of the beam to be broadened, which has a serious impact on its practical application. Therefore, how to correct the distortion of the vortex beam, eliminate the influence of turbulence, and maintain the reliability and stability of the system communication has become an urgent problem to be solved.

[0003] There are many technical solutions for correcting the distortion of vortex beams, including the use of non-wavefront detection methods such as the GS algorithm and the SPGD algorithm to correct the distorted vortex beam. Although these methods can achieve good vortex beam correction effects, they have limitations such as complex systems and insufficient system response time. With the success of deep learning algorithms in the fields of semantic segmentation, medical image processing, and image recognition, researchers have applied deep learning to the field of correcting distorted vortex beams, learning and calculating the corresponding distortion phase information, and then correcting the distorted vortex beam by loading the reverse phase. Summary of the invention

[0004] The purpose of the present invention is to provide a method for correcting a distorted vortex light beam based on a convolutional neural network, which can directly and accurately correct the distorted vortex light beam affected by turbulence.

[0005] The technical solution adopted by the present invention is a method for correcting a distorted vortex beam based on a convolutional neural network, which specifically includes the following steps:

[0006] Step 1, obtain the distorted light intensity pattern after ocean turbulence and the corresponding standard light intensity pattern through numerical simulation, and establish a data set;

[0007] Step 2: Design and build a convolutional neural network;

[0008] Step 3, preprocess the training data obtained in step 1 and send it to the network designed in step 2 for model training;

[0009] Step 4: Use the test set to test the effect of the convolutional neural network in correcting the distorted vortex beam.

[0010] The present invention is also characterized in that:

[0011] Step 1 is implemented according to the following specific steps:

[0012] Step 1.1, based on the power spectrum inversion method, realize the numerical simulation of the random phase screen of ocean turbulence;

[0013] First, generate a complex Gaussian random matrix h(k x ,k y ), and then use the seawater refractive index fluctuation spectrum Φ(k x ,k y ) to filter it, and finally obtain the ocean turbulence random phase screen by inverse Fourier transform This process is expressed in the formula:

[0014]

[0015] Where: x, y represent the directions on the rectangular coordinates, k x , k y represent the wave number in the x and y directions respectively, C is the constant factor controlling the variance of the phase screen, h(k x ,k y ) is a complex Gaussian random matrix, Δz is the distance of the turbulent layer, k = 2π / λ is the wave number of the light beam, λ is the wavelength, Φ(k x ,k y ) is the seawater refractive index fluctuation spectrum proposed by Nikishov et al., i is an imaginary number;

[0016] The refractive index fluctuation spectrum of seawater Φ(k x ,k y ), whose expression is:

[0017]

[0018] In the formula, k x , k y represents the wave number in the x and y directions respectively, ε is the energy dissipation rate per unit volume of seawater, from the depth to the surface of the seawater; χ T is the temperature dissipation rate from the deep sea to the sea surface; w is the ratio of ocean turbulence caused by temperature to ocean turbulence caused by salinity; η is the Kolmogorov microscale (internal scale); the other parameters in formula (2) are: A T =1.863×10 -2 ,A S =1.9×10 -4 ,A TS =9.41×10 -3 ;

[0019] It is known that the light field expression of Laguerre-Gaussian beam is:

[0020]

[0021] Where: r, φ represent the polar diameter and direction angle on polar coordinates, z is the transmission distance, Z R is the Rayleigh length, w(z) is the beam radius of the beam at z; is the Laguerre polynomial, k represents the wave number of the light wave, p is the radial index, and l is the topological charge number;

[0022] According to the Fresnel principle, the electric field of a light beam is U(x,y,z). After the light beam is transmitted a distance Δz in the ocean turbulence, its electric field function U(z+Δz,x,y) is expressed as:

[0023]

[0024] Where: k0 is the wave number, FFT -1 is the inverse Fourier transform, is the Fresnel transmission coefficient, It is the random phase screen of ocean turbulence.

[0025] Step 1.2, substitute formula (1) and formula (3) in step 1.1 into formula (4), generate the distorted light intensity map after ocean turbulence and the corresponding standard light intensity pattern, and construct the data set.

[0026] In step 1.1, χ T The temperature dissipation rate ranges from [10 -7 K 2 / s,10 -6 K 2 / s].

[0027] In step 1.2: the data set is divided into training set and test set in a ratio of 10:1.

[0028] Step 2.1, design and build a convolutional neural network structure, the network structure is as follows: input image - the first residual module layer - the first maximum pooling layer - the second residual module layer - the second maximum pooling layer - the third residual module layer - the third maximum pooling layer - the first deconvolution layer - the first convolution layer - the second deconvolution layer - the second convolution layer - the third deconvolution layer - the third convolution layer - the fourth convolution layer - the first saturated nonlinear sigmoid activation function layer. The data after each convolution is normalized (Batch Normalization, BN);

[0029] Step 2.2, design and build the parameters of each layer of the convolutional neural network structure. The parameters are as follows:

[0030] The convolution kernel size of all convolutional and deconvolution layers is 3×3, and the convolution kernel size of the maximum pooling layer is 2×2; the number of channels in each layer of all residual modules is 32; the number of channels in the first maximum pooling layer is 32; the number of channels in the second maximum pooling layer is 32; the number of channels in the third maximum pooling layer is 64; the number of channels in the first deconvolution layer is 64; the number of channels in the second deconvolution layer is 64; the number of channels in the third deconvolution layer is 32; the number of channels in the fourth convolution layer is 3.

[0031] In step 2.1, the structure of each residual module is: the output feature map of the previous layer - the first convolution layer - the first batch normalization layer - the first ReLU activation function layer - the second convolution layer - the second batch normalization layer - the feature map corresponding addition operation; the added feature map is the input feature map and the feature map after passing through the previous operations in sequence - the second ReLU activation function layer.

[0032] Step 3 is implemented according to the following specific steps:

[0033] Step 3.1, before starting training, load the training set created in step 1, set the size of the input distorted intensity map and standard intensity map to 128×128, and convert the data format to tensor type;

[0034] Step 3.2, initialize the weights of the network established in step 2, input the data processed in step 3.1 into the network model for training, set the batch size batch_size = 4, the learning rate learning rate = 0.0001, and use the absolute error loss function L1Loss to calculate the error between the network output value and the target value. Optimize the network model parameters through continuous iteration to minimize the loss function. Save the trained weight model after 20 iterations.

[0035] Step 4 is implemented according to the following specific steps:

[0036] Step 4.1, load the test set divided in step 1, set the size of the input distorted intensity map and standard intensity map to 128×128, and convert the data format to tensor type;

[0037] Step 4.2, load the weight model saved in step 3.2, input the data in step 4.1 into the network model, use the trained model to correct the distorted vortex beam, and use the absolute error loss value and image similarity as evaluation indicators, and calculate the time required to correct all samples in the test set.

[0038] The beneficial effects of the present invention are:

[0039] (1) The method of correcting distorted vortex light beams based on convolutional neural networks in the present invention mainly utilizes the theoretical knowledge of convolutional neural networks to train the network model, corrects the distorted light intensity pattern after transmission, and restores it to the standard light intensity pattern. The results show that the convolutional neural network model can be used to effectively correct the distorted vortex light beam pattern. Compared with the traditional method, this method is not limited by experimental conditions, is simple to operate, easy to implement, and can directly realize the correction of distorted vortex light beams. It can solve the problem that the existing optical method is not accurate enough in correcting distorted vortex light beams, and has important reference value for suppressing the influence of turbulence and improving communication performance.

[0040] (2) The convolutional neural network is introduced into the vortex optical communication system. By using the convolutional neural network and taking the standard light intensity map as the output, the distorted vortex light beam can be directly corrected. Compared with the existing technology, this method simplifies the process of loading the reverse phase and has a high correction accuracy. The present invention is based on a method for correcting a distorted vortex light beam using a convolutional neural network. In order to better correct the distorted vortex light beam, the excellent image processing capability of CNN is utilized, and the distorted LG light beam affected by turbulence is used as the input of CNN, and the standard LG light beam is used as the output. After supervised training and learning of a large number of sample sets, a CNN model that can automatically correct the distorted vortex light beam can be finally obtained. While achieving a good distorted vortex light beam correction effect, this model effectively reduces the complexity of the system and compresses the system response time. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a standard LG light intensity chart;

[0042] Figure 2 is the temperature dissipation rate χ T =1×10 -6 K 2 / s ocean turbulence, the intensity diagram of the distorted vortex beam;

[0043] Figure 3 It is a convolutional neural network structure diagram in the method of the present invention;

[0044] Figure 4 is a graph of the loss rate during the training process of Example 1;

[0045] Figure 5 The distorted light intensity map generated by simulation in Example 1;

[0046] Figure 6 is the standard light intensity diagram generated by simulation in Example 1;

[0047] Figure 7 It is the light intensity map after the distorted LG light intensity map is corrected by using the trained network model in Example 1. DETAILED DESCRIPTION

[0048] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0049] The present invention provides a method for correcting a distorted vortex beam based on a convolutional neural network, which specifically comprises the following steps:

[0050] Step 1, obtain the distorted light intensity pattern after ocean turbulence and the corresponding standard light intensity pattern through numerical simulation, and establish a data set;

[0051] Step 1 is implemented according to the following specific steps:

[0052] Step 1.1, based on the power spectrum inversion method, realize the numerical simulation of the random phase screen of ocean turbulence;

[0053] The basic principle of the ocean turbulence random phase screen based on the power spectrum inversion method is: first, generate a complex Gaussian random matrix h(k x ,k y ), and then use the seawater refractive index fluctuation spectrum Φ(k x ,k y ) to filter it, and finally obtain the ocean turbulence random phase screen by inverse Fourier transform This process is expressed in the formula:

[0054]

[0055] Where: x, y represent the directions on the rectangular coordinates, k x , k y represent the wave number in the x and y directions respectively, C is the constant factor controlling the variance of the phase screen, h(k x ,k y ) is a complex Gaussian random matrix, Δz is the distance of the turbulent layer, k = 2π / λ is the wave number of the light beam, λ is the wavelength, Φ(k x ,k y ) is the seawater refractive index fluctuation spectrum proposed by Nikishov et al., i is an imaginary number;

[0056] The refractive index fluctuation spectrum of seawater Φ(k x ,k y ), whose expression is:

[0057]

[0058] In the formula, k x , k y represents the wave number in the x and y directions respectively, ε is the energy dissipation rate per unit volume of seawater, from the deep sea to the surface of the seawater; χ Tis the temperature dissipation rate from the deep sea to the sea surface; w is the ratio of ocean turbulence caused by temperature to ocean turbulence caused by salinity; η is the Kolmogorov microscale (internal scale); the other parameters in formula (2) are: A T =1.863×10 -2 ,A S =1.9×10 -4 ,A TS =9.41×10 -3 ;

[0059] It is known that the light field expression of Laguerre-Gaussian beam is:

[0060]

[0061] Where: r, φ represent the polar diameter and direction angle on polar coordinates, z is the transmission distance, Z R is the Rayleigh length, w(z) is the beam radius of the beam at z; is the Laguerre polynomial, k represents the wave number of the light wave, p is the radial index, and l is the topological charge number;

[0062] According to the Fresnel principle, the electric field of a light beam is U(x,y,z). After the light beam is transmitted a distance Δz in the ocean turbulence, its electric field function U(z+Δz,x,y) is expressed as:

[0063]

[0064] Where: k0 is the wave number, FFT -1 is the inverse Fourier transform, is the Fresnel transmission coefficient, It is the random phase screen of ocean turbulence.

[0065] Step 1.2, substitute formula (1) and formula (3) in step 1.1 into formula (4) to generate the distorted light intensity pattern after ocean turbulence and the corresponding standard light intensity pattern, as follows: Figure 1 and Figure 2 As shown in the figure, a total of 2750 pairs of samples are used to construct the data set; they are divided into training set and test set in a ratio of 10:1, 2500 pairs of samples are used as CNN training sets, and 250 pairs of samples are used as test sets to test the correction effect of the CNN model.

[0066] Since there are too many factors that affect the power spectrum of ocean refractive index in seawater, this section only considers the effect of temperature dissipation rate during the transmission of the light beam in seawater, where χ T The temperature dissipation rate ranges from [10 -7 K 2 / s,10 -6 K 2 / s]. The temperature dissipation rates are χ T =1×10 -6 K 2 / s,χ T =5×10 -7 K 2 / s,χ T =1×10 -7 K 2 / s, the data set is generated repeatedly.

[0067] Step 2: Design and build a convolutional neural network;

[0068] Step 2 is implemented according to the following specific steps:

[0069] Step 2.1, design and build a convolutional neural network structure. The convolutional neural network theoretical structure established by the present invention is as follows: Figure 3 As shown, the residual module structure is as follows Figure 3 As shown in (a) in the figure. The network structure is as follows: input image - the first residual module layer - the first maximum pooling layer - the second residual module layer - the second maximum pooling layer - the third residual module layer - the third maximum pooling layer - the first deconvolution layer - the first convolution layer - the second deconvolution layer - the second convolution layer - the third deconvolution layer - the third convolution layer - the fourth convolution layer - the first saturated nonlinear sigmoid activation function layer. The data after each convolution is normalized (Batch Normalization, BN).

[0070] Among them, the structure of each residual module is: the output feature map of the previous layer - the first convolution layer - the first batch normalization layer - the first ReLU activation function layer - the second convolution layer - the second batch normalization layer - the corresponding addition operation of the feature map; the added feature map is the input feature map and the feature map after passing through the previous operations in sequence - the second ReLU activation function layer.

[0071] Step 2.2, design and build the parameters of each layer of the convolutional neural network structure. The parameters are as follows:

[0072] The convolution kernel size of all convolutional and deconvolution layers is 3×3, and the convolution kernel size of the maximum pooling layer is 2×2; the number of channels in each layer of all residual modules is 32; the number of channels in the first maximum pooling layer is 32; the number of channels in the second maximum pooling layer is 32; the number of channels in the third maximum pooling layer is 64; the number of channels in the first deconvolution layer is 64; the number of channels in the second deconvolution layer is 64; the number of channels in the third deconvolution layer is 32; the number of channels in the fourth convolution layer is 3.

[0073] The parameters of each layer of the network structure are shown in Table 1.

[0074] Table 1 Convolutional neural network structure parameters

[0075]

[0076] Step 3, preprocess the training data obtained in step 1 and send it to the network designed in step 2 for model training;

[0077] Step 3 is implemented according to the following specific steps:

[0078] Step 3.1, before starting training, load the training set created in step 1, set the size of the input distorted intensity map and standard intensity map to 128×128, and convert the data format to tensor type;

[0079] Step 3.2, initialize the weights of the network established in step 2, input the data processed in step 3.1 into the network model for training, set the batch size batch_size = 4, the learning rate learning rate = 0.0001, use the absolute error loss function L1Loss to calculate the error between the output value of the network and the target value, optimize the network model parameters through continuous iteration, so that the loss function reaches the minimum value, and save the trained weight model after 20 iterations;

[0080] Step 4, using the test set to test the effect of the convolutional neural network in correcting the distorted vortex beam;

[0081] Step 4 is implemented according to the following specific steps:

[0082] Step 4.1, load the test set divided in step 1, set the size of the input distorted intensity map and standard intensity map to 128×128, and convert the data format to tensor type;

[0083] Step 4.2, load the weight model saved in step 3.2, input the data in step 4.1 into the network model, use the trained model to correct the distorted vortex beam, and use the absolute error loss value and image similarity as evaluation indicators, and calculate the time required to correct all samples in the test set.

[0084] Example 1

[0085] Step 1 Unless otherwise specified, set the MATLAB simulation parameters as follows: wavelength λ = 532nm, beam waist radius w0 = 0.03, transmission distance z = 200, phase screen size D = 0.25, kinetic energy dissipation rate ε = 1e -6 m 2 / s 3 , temperature dissipation rate χ T =1×10 -6 K 2 / s, temperature-salinity ratio w = -2, topological charge l = 1, 3, 5, 7, 9, radial index p = 0, construct a data set, generate 550 pairs of each type of topological charge value, a total of 2750 pairs of samples, and randomly divide them into training set and test set at a ratio of 10:1.

[0086] Step 2: Input the training set into the constructed convolutional neural network for training. Set the batch size to 4. The input data will be propagated forward through the network to obtain the output data. The absolute error loss function L1Loss is used to calculate the error between the output value of the network and the target value. The weight is updated through back propagation. After 20 iterations, the trained model is saved. The training loss rate is as follows: Figure 4 As shown, from Figure 4 It can be seen that the overall trend of the loss function value is monotonically decreasing. After a certain number of iterations, it gradually stabilizes and the loss value converges to about 0.0027, indicating that after a certain number of iterations of training, the CNN model can obtain good correction results.

[0087] Step 3 loads the test set divided in step 1, inputs it into the network model trained in step 2, uses the trained model to correct the distorted vortex beam, and outputs the intensity map after the network model correction. Figure 5 As shown in the figure, the standard light intensity diagram generated by simulation is as follows Figure 6 As shown, using the trained network model, the distorted intensity map is input and the corrected intensity map is as follows Figure 7 shown. Figure 6 , Figure 7 The similarity SSIM = 0.9904, which shows that the convolutional neural network is more effective in correcting the distorted vortex beam.

[0088] Example 2

[0089] Step 1 Unless otherwise specified, set the MATLAB simulation parameters as follows: wavelength λ = 532nm, beam waist radius w0 = 0.03, transmission distance z = 200, phase screen size D = 0.25, kinetic energy dissipation rate ε = 1e -6 m 2 / s 3 , temperature dissipation rate χ T =1×10 -6 K 2 / s, temperature-salinity ratio w = -2, topological charge l = 1, 3, 5, 7, 9, radial index p = 0, construct a data set, generate 550 pairs of each type of topological charge value, a total of 2750 pairs of samples, and randomly divide them into training set and test set at a ratio of 10:1.

[0090] Step 2: Input the training set into the constructed convolutional neural network for training. Set the batch size to 4. The input data will be propagated forward through the network to obtain the output data. The absolute error loss function L1Loss is used to calculate the error between the output value of the network and the target value. The weight is updated through back propagation. After 20 iterations, the trained model is saved.

[0091] Step 3 loads the test set divided in step 1, inputs it into the network model trained in step 2, uses the trained model to correct the distorted vortex beam, and outputs the turbulent phase map predicted by the network model. The absolute error loss function L1Loss is used to calculate the absolute error loss between 250 pairs of standard intensity maps and corrected intensity maps in the test set. The average error loss loss is 0.0054, and the error loss rate is extremely small. At the same time, the time required to correct a single distorted intensity map is only about 9 milliseconds, indicating that the convolutional neural network has a good correction effect.

[0092] Example 3

[0093] Step 1 Unless otherwise specified, set the MATLAB simulation parameters as follows: wavelength λ = 532nm, beam waist radius w0 = 0.03, transmission distance z = 200, phase screen size D = 0.25, kinetic energy dissipation rate ε = 1e -6 m 2 / s 3 , temperature dissipation rate χ T =1×10 -7 K 2 / s, temperature-salinity ratio w = -2, topological charge l = 1, 3, 5, 7, 9, radial index p = 0, construct a data set, generate 550 pairs of each type of topological charge value, a total of 2750 pairs of samples, and randomly divide them into training set and test set at a ratio of 10:1.

[0094] Step 2: Input the training set into the constructed convolutional neural network for training. Set the batch size to 4. The input data will be propagated forward through the network to obtain the output data. The absolute error loss function L1Loss is used to calculate the error between the output value of the network and the target value. The weight is updated through back propagation. After 20 iterations, the trained model is saved.

[0095] Step 3 loads the test set divided in step 1, inputs it into the network model trained in step 2, uses the trained model to correct the distorted vortex beam, and outputs the intensity map corrected by the network model. The average error loss between all corrected intensity maps and standard intensity maps in the test set is calculated using the absolute error loss function L1Loss. The average error loss loss is 0.0011, and the error loss rate is extremely small. Compared with Example 2, the temperature dissipation rate χ T =1×10-6 K 2 / s, the loss rate result is loss=0.0054. It can be seen that the correction effect is better as the ocean turbulence intensity decreases.

[0096] Example 4

[0097] The method for correcting a distorted vortex beam based on a convolutional neural network specifically includes the following steps:

[0098] Step 1, obtain the distorted light intensity pattern after ocean turbulence and the corresponding standard light intensity pattern through numerical simulation, and establish a data set;

[0099] Step 1 is implemented according to the following specific steps:

[0100] Step 1.1, based on the power spectrum inversion method, realize the numerical simulation of the random phase screen of ocean turbulence;

[0101] First, generate a complex Gaussian random matrix h(k x ,k y ), and then use the seawater refractive index fluctuation spectrum Φ(k x ,k y ) to filter it, and finally obtain the ocean turbulence random phase screen by inverse Fourier transform

[0102] This process is expressed in the formula:

[0103]

[0104] Where: x, y represent the directions on the rectangular coordinates, k x , k y represent the wave number in the x and y directions respectively, C is the constant factor controlling the variance of the phase screen, h(k x ,k y ) is a complex Gaussian random matrix, Δz is the distance of the turbulent layer, k = 2π / λ is the wave number of the light beam, λ is the wavelength, Φ(k x ,k y ) is the refractive index fluctuation spectrum of seawater, i is an imaginary number;

[0105] The refractive index fluctuation spectrum of seawater Φ(k x ,k y ), whose expression is:

[0106]

[0107] In the formula, k x , k y represents the wave number in the x and y directions respectively, ε is the energy dissipation rate per unit volume of seawater, from the deep sea to the surface of the seawater; χ Tis the temperature dissipation rate from the deep sea to the sea surface; w is the ratio of ocean turbulence caused by temperature to ocean turbulence caused by salinity; η is the Kolmogorov microscale; the other parameters in formula (2) are: A T =1.863×10 -2 ,A S =1.9×10 -4 ,A TS =9.41×10 -3 ;

[0108] It is known that the light field expression of Laguerre-Gaussian beam is:

[0109]

[0110] Where: r, φ represent the polar diameter and direction angle on polar coordinates, z is the transmission distance, Z R is the Rayleigh length, w(z) is the beam radius of the beam at z; is the Laguerre polynomial, k represents the wave number of the light wave, p is the radial index, and l is the topological charge number;

[0111] According to the Fresnel principle, the electric field of a light beam is U(x,y,z). After the light beam is transmitted a distance Δz in the ocean turbulence, its electric field function U(z+Δz,x,y) is expressed as:

[0112]

[0113] Where: k0 is the wave number, FFT -1 is the inverse Fourier transform, is the Fresnel transmission coefficient, It is the random phase screen of ocean turbulence.

[0114] Step 1.2, substitute formula (1) and formula (3) in step 1.1 into formula (4), generate the distorted light intensity map after ocean turbulence and the corresponding standard light intensity pattern, and construct the data set.

[0115] Step 2: Design and build a convolutional neural network;

[0116] Step 3, preprocess the training data obtained in step 1 and send it to the network designed in step 2 for model training;

[0117] Step 4: Use the test set to test the effect of the convolutional neural network in correcting the distorted vortex beam.

[0118] Example 5

[0119] The method for correcting a distorted vortex beam based on a convolutional neural network specifically includes the following steps:

[0120] Step 1, obtain the distorted light intensity pattern after ocean turbulence and the corresponding standard light intensity pattern through numerical simulation, and establish a data set;

[0121] Step 1 is implemented according to the following specific steps:

[0122] Step 1.1, based on the power spectrum inversion method, realize the numerical simulation of the random phase screen of ocean turbulence;

[0123] First, generate a complex Gaussian random matrix h(k x ,k y ), and then use the seawater refractive index fluctuation spectrum Φ(k x ,k y ) to filter it, and finally obtain the ocean turbulence random phase screen by inverse Fourier transform This process is expressed in the formula:

[0124]

[0125] Where: x, y represent the directions on the rectangular coordinates, k x , k y represent the wave number in the x and y directions respectively, C is the constant factor controlling the variance of the phase screen, h(k x ,k y ) is a complex Gaussian random matrix, Δz is the distance of the turbulent layer, k = 2π / λ is the wave number of the light beam, λ is the wavelength, Φ(k x ,k y ) is the refractive index fluctuation spectrum of seawater, i is an imaginary number;

[0126] The refractive index fluctuation spectrum of seawater Φ(k x ,k y ), whose expression is:

[0127]

[0128] In the formula, k x , k y represents the wave number in the x and y directions respectively, ε is the energy dissipation rate per unit volume of seawater, from the depth to the surface of the seawater; χ T is the temperature dissipation rate from the deep sea to the sea surface; w is the ratio of ocean turbulence caused by temperature to ocean turbulence caused by salinity; η is the Kolmogorov microscale; the other parameters in formula (2) are: A T =1.863×10 -2 ,A S =1.9×10 -4 ,A TS =9.41×10 -3 ;

[0129] It is known that the light field expression of Laguerre-Gaussian beam is:

[0130]

[0131] Where: r, φ represent the polar diameter and direction angle on polar coordinates, z is the transmission distance, Z R is the Rayleigh length, w(z) is the beam radius of the beam at z; is the Laguerre polynomial, k represents the wave number of the light wave, p is the radial index, and l is the topological charge number;

[0132] According to the Fresnel principle, the electric field of a light beam is U(x,y,z). After the light beam is transmitted a distance Δz in the ocean turbulence, its electric field function U(z+Δz,x,y) is expressed as:

[0133]

[0134] Where: k0 is the wave number, FFT -1 is the inverse Fourier transform, is the Fresnel transmission coefficient, It is the random phase screen of ocean turbulence;

[0135] In step 1.1, χ T The temperature dissipation rate ranges from [10 -7 K 2 / s,10 -6 K 2 / s].

[0136] Step 1.2, substitute formula (1) and formula (3) in step 1.1 into formula (4), generate the distorted light intensity map after ocean turbulence and the corresponding standard light intensity pattern, and construct the data set.

[0137] Step 2: Design and build a convolutional neural network;

[0138] Step 3, preprocess the training data obtained in step 1 and send it to the network designed in step 2 for model training;

[0139] Step 4: Use the test set to test the effect of the convolutional neural network in correcting the distorted vortex beam.

[0140] Example 6

[0141] The method for correcting a distorted vortex beam based on a convolutional neural network specifically includes the following steps:

[0142] Step 1, obtain the distorted light intensity pattern after ocean turbulence and the corresponding standard light intensity pattern through numerical simulation, and establish a data set;

[0143] Step 1 is implemented according to the following specific steps:

[0144] Step 1.1, based on the power spectrum inversion method, realize the numerical simulation of the random phase screen of ocean turbulence;

[0145] First, generate a complex Gaussian random matrix h(k x ,k y ), and then use the seawater refractive index fluctuation spectrum Φ(k x ,k y ) to filter it, and finally obtain the ocean turbulence random phase screen by inverse Fourier transform

[0146] This process is expressed in the formula:

[0147]

[0148] Where: x, y represent the directions on the rectangular coordinates, k x , k y represent the wave number in the x and y directions respectively, C is the constant factor controlling the variance of the phase screen, h(k x ,k y ) is a complex Gaussian random matrix, Δz is the distance of the turbulent layer, k = 2π / λ is the wave number of the light beam, λ is the wavelength, Φ(k x ,k y ) is the refractive index fluctuation spectrum of seawater, i is an imaginary number;

[0149] The refractive index fluctuation spectrum of seawater Φ(k x ,k y ), whose expression is:

[0150]

[0151] In the formula, k x , k y represents the wave number in the x and y directions respectively, ε is the energy dissipation rate per unit volume of seawater, from the depth to the surface of the seawater; χ T is the temperature dissipation rate from the deep sea to the sea surface; w is the ratio of ocean turbulence caused by temperature to ocean turbulence caused by salinity; η is the Kolmogorov microscale; the other parameters in formula (2) are: A T =1.863×10 -2 ,A S =1.9×10 -4 ,A TS =9.41×10 -3 ;

[0152] It is known that the light field expression of Laguerre-Gaussian beam is:

[0153]

[0154] Where: r, φ represent the polar diameter and direction angle on polar coordinates, z is the transmission distance, Z R is the Rayleigh length, w(z) is the beam radius of the beam at z; is the Laguerre polynomial, k represents the wave number of the light wave, p is the radial index, and l is the topological charge number;

[0155] According to the Fresnel principle, the electric field of a light beam is U(x,y,z). After the light beam is transmitted a distance Δz in the ocean turbulence, its electric field function U(z+Δz,x,y) is expressed as:

[0156]

[0157] Where: k0 is the wave number, FFT -1 is the inverse Fourier transform, is the Fresnel transmission coefficient, It is the random phase screen of ocean turbulence;

[0158] In step 1.1, χ T The temperature dissipation rate ranges from [10 -7 K 2 / s,10 -6 K 2 / s].

[0159] Step 1.2, substitute formula (1) and formula (3) in step 1.1 into formula (4), generate the distorted light intensity map after ocean turbulence and the corresponding standard light intensity pattern, and construct the data set.

[0160] In step 1.2: the data set is divided into training set and test set in a ratio of 10:1.

[0161] Step 2: Design and build a convolutional neural network;

[0162] Step 3, preprocess the training data obtained in step 1 and send it to the network designed in step 2 for model training;

[0163] Step 4: Use the test set to test the effect of the convolutional neural network in correcting the distorted vortex beam.

Claims

1. A method for correcting distorted vortex beams based on a convolutional neural network, characterized in that: The specific steps include: Step 1, obtain the distorted light intensity pattern after ocean turbulence and the corresponding standard light intensity pattern through numerical simulation, and establish a data set; Step 2: Design and build a convolutional neural network; Step 3, preprocess the training data obtained in step 1 and send it to the network designed in step 2 for model training; Step 4: Use the test set to test the effect of the convolutional neural network in correcting the distorted vortex beam.

2. The method for correcting a distorted vortex beam based on a convolutional neural network according to claim 1, characterized in that: Step 1 is implemented according to the following specific steps: Step 1.1, based on the power spectrum inversion method, realize the numerical simulation of the random phase screen of ocean turbulence; First, generate a complex Gaussian random matrix h(k x ,k y ), and then use the seawater refractive index fluctuation spectrum Φ(k x ,k y ) to filter it, and finally obtain the ocean turbulence random phase screen by inverse Fourier transform This process is expressed in the formula: Where: x, y represent the directions on the rectangular coordinates, k x , k y represent the wave number in the x and y directions respectively, C is the constant factor controlling the variance of the phase screen, h(k x ,k y ) is a complex Gaussian random matrix, Δz is the distance of the turbulent layer, k = 2π / λ is the wave number of the light beam, λ is the wavelength, Φ(k x ,k y ) is the refractive index fluctuation spectrum of seawater, i is an imaginary number; The refractive index fluctuation spectrum of seawater Φ(k x ,k y ), whose expression is: In the formula, k x , k y represents the wave number in the x and y directions respectively, ε is the energy dissipation rate per unit volume of seawater, from the depth to the surface of the seawater; χ T is the temperature dissipation rate from the deep sea to the sea surface; w is the ratio of ocean turbulence caused by temperature to ocean turbulence caused by salinity; η is the Kolmogorov microscale; the other parameters in formula (2) are: A T =1.863×10 -2 ,A S =1.9×10 -4 ,A TS =9.41×10 -3 ; It is known that the light field expression of Laguerre-Gaussian beam is: Where: r, φ represent the polar diameter and direction angle on polar coordinates, z is the transmission distance, Z R is the Rayleigh length, w(z) is the beam radius of the beam at z; is the Laguerre polynomial, k represents the wave number of the light wave, p is the radial index, and l is the topological charge number; According to the Fresnel principle, the electric field of a light beam is U(x,y,z). After the light beam is transmitted a distance Δz in the ocean turbulence, its electric field function U(z+Δz,x,y) is expressed as: Where: k0 is the wave number, FFT -1 is the inverse Fourier transform, is the Fresnel transmission coefficient, It is the random phase screen of ocean turbulence; Step 1.2, substitute formula (1) and formula (3) in step 1.1 into formula (4), generate the distorted light intensity map after ocean turbulence and the corresponding standard light intensity pattern, and construct the data set.

3. The method for correcting a distorted vortex beam based on a convolutional neural network according to claim 2, characterized in that: In step 1.1, χ T The temperature dissipation rate ranges from [10 -7 K 2 / s,10 -6 K 2 / s].

4. The method for correcting a distorted vortex beam based on a convolutional neural network according to claim 2, characterized in that: In step 1.2: the data set is divided into training set and test set in a ratio of 10:

1.

5. The method for correcting a distorted vortex beam based on a convolutional neural network according to claim 2, characterized in that: Step 2.1, design and build a convolutional neural network structure, the network structure is as follows: input image - the first residual module layer - the first maximum pooling layer - the second residual module layer - the second maximum pooling layer - the third residual module layer - the third maximum pooling layer - the first deconvolution layer - the first convolution layer - the second deconvolution layer - the second convolution layer - the third deconvolution layer - the third convolution layer - the fourth convolution layer - the first saturated nonlinear Sigmoid activation function layer; normalize the data after each convolution; Step 2.2, design and build the parameters of each layer of the convolutional neural network structure. The parameters are as follows: The convolution kernel size of all convolutional and deconvolution layers is 3×3, and the convolution kernel size of the maximum pooling layer is 2×2; the number of channels in each layer of all residual modules is 32; the number of channels in the first maximum pooling layer is 32; the number of channels in the second maximum pooling layer is 32; the number of channels in the third maximum pooling layer is 64; the number of channels in the first deconvolution layer is 64; the number of channels in the second deconvolution layer is 64; the number of channels in the third deconvolution layer is 32; the number of channels in the fourth convolution layer is 3.

6. The method for correcting a distorted vortex beam based on a convolutional neural network according to claim 5, characterized in that: In step 2.1, the structure of each residual module is: the output feature map of the previous layer - the first convolution layer - the first batch normalization layer - the first ReLU activation function layer - the second convolution layer - the second batch normalization layer - the feature map corresponding addition operation; the added feature map is the input feature map and the feature map after passing through the previous operations in sequence - the second ReLU activation function layer.

7. The method for correcting a distorted vortex beam based on a convolutional neural network according to claim 1, characterized in that: Step 3 is implemented according to the following specific steps: Step 3.1, before starting training, load the training set created in step 1, set the size of the input distorted intensity map and standard intensity map to 128×128, and convert the data format to tensor type; Step 3.2, initialize the weights of the network established in step 2, input the data processed in step 3.1 into the network model for training, set the batch size batch_size = 4, the learning rate learning rate = 0.0001, and use the absolute error loss function L1Loss to calculate the error between the network output value and the target value. Optimize the network model parameters through continuous iteration to minimize the loss function. Save the trained weight model after 20 iterations.

8. The method for correcting a distorted vortex beam based on a convolutional neural network according to claim 1, characterized in that: Step 4 is implemented according to the following specific steps: Step 4.1, load the test set divided in step 1, set the size of the input distorted intensity map and standard intensity map to 128×128, and convert the data format to tensor type; Step 4.2, load the weight model saved in step 3.2, input the data in step 4.1 into the network model, use the trained model to correct the distorted vortex beam, and use the absolute error loss value and image similarity as evaluation indicators, and calculate the time required to correct all samples in the test set.

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