Atmospheric turbulence prediction method of CPOV light beam based on deep learning

Abstract

The invention belongs to the technical field of optical communication, and particularly relates to a CPOV light beam atmospheric turbulence prediction method based on deep learning. The method comprises the following steps: constructing an atmospheric turbulence prediction model by using a Legendre polynomial which is orthogonal in a square domain; and inputting an intensity distribution diagram of the CPOV light beam after free transmission in the atmospheric turbulence into the atmospheric turbulence prediction model, and respectively predicting Legendre polynomial coefficients of the low-frequency part of the turbulence screen and the high-frequency part of the sub-region so as to obtain the turbulence screen equivalent to the atmospheric turbulence. According to the method, the prediction precision of the turbulence screen is higher by simultaneously predicting the Legendre polynomial coefficients of the low frequency of the turbulence screen and the high frequency of the sub-region. Meanwhile, for CPOV light beams with different turbulence intensities and different OAM modes, the generalization of the atmospheric turbulence prediction model is higher.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of optical communication, and particularly relates to a CPOV light beam atmospheric turbulence prediction method based on deep learning. BACKGROUND

[0002] Optical signal modulation mainly revolves around the amplitude, phase, wavelength / frequency, polarization, time and other basic dimensions of light waves, and has derived corresponding communication technologies, such as time division multiplexing, wavelength division multiplexing, polarization multiplexing, and space division multiplexing. Although the communication speed and communication distance have made great progress, with the further consumption of spectrum resources, it becomes more and more difficult to improve the communication capacity and modulation ability. In recent years, vortex beams with spiral phase have been widely studied, which carry orbital angular momentum (OAM), and OAM modes of different topological charges l are mutually orthogonal, where l can take any integer value, which constitutes an infinite Hilbert space and can carry an infinite number of bits of information. People apply OAM modes to optical communication, which, combined with existing multiplexing technologies, can achieve higher spectral efficiency and larger information capacity transmission.

[0003] However, the larger the value of l of the vortex light is, the larger the aperture required by the receiving optical system is, which seriously limits the maximum value of l that can be used. In 2013, Ostrovsky et al. proposed a perfect optical vortex (POV) beam, the bright ring radius of which is independent of the topological charge of the vortex light, which just overcomes the limitation of ordinary vortex beams. On this basis, Vaity et al. first proposed a method of obtaining a POV beam by Fourier transform of a Bessel beam in 2015, from which POV beams can be generated in the laboratory. In addition, Zhu et al. demonstrated a 2-channel OAM multiplexing free-space optical communication link based on POV beams in 2018.

[0004] On the basis of the POV beam, a concentric perfect optical vortex (CPOV) beam is proposed, which is composed of several POV beams, each of which has the same center and independent orbital angular momentum. This special feature can greatly improve the communication capacity of the orbital angular momentum. However, when the CPOV beam is transmitted in an atmospheric turbulence channel, problems such as OAM dispersion, light intensity flicker and attenuation may occur, which leads to a decrease in the signal-to-noise ratio of the communication system and an increase in the bit error rate. Therefore, how to compensate for atmospheric turbulence and correct the distortion of vortex beams has become the key to improving the performance of OAM optical communication systems.

[0005] Common atmospheric turbulence compensation techniques include the Gerchberg-Saxton (GS) algorithm and the Stochastic Parallel Gradient Descent (SPGD) algorithm. In 2023, Wei et al. used the GS algorithm to correct the wavefront of POV beam distortion, employing multi-class support vector machine classification. This method features high accuracy and fewer communication system components. However, both the GS and SPGD algorithms require multiple iterations, are time-consuming, and are prone to getting trapped in local minima, failing to find the optimal solution. Therefore, they cannot meet the requirements for rapid compensation.

[0006] In recent years, deep learning technology has been widely applied in fields such as object detection, natural language processing, and life sciences. The combination of deep learning and optical communication has also attracted widespread attention from researchers. Using Convolutional Neural Networks (CNNs) to compensate for atmospheric turbulence has been proven to be faster and more accurate than the GS algorithm, but current research focuses only on ordinary vortex beams. Furthermore, based on the information output by the model, CNN-based vortex beam distortion correction techniques can be divided into two main categories: one is CNN predicting Zernike polynomial coefficients; the other is CNN predicting turbulence screens. Among these, the CNN model predicting Zernike polynomial coefficients is more lightweight, but its prediction performance for the high-frequency components of atmospheric turbulence is poor. Summary of the Invention

[0007] In view of this, the purpose of this application is to provide a deep learning-based method for predicting atmospheric turbulence in CPOV beams. By simultaneously predicting the low-frequency Legendre polynomial coefficients of the turbulence screen and the high-frequency coefficients of the sub-regions, the prediction accuracy of the turbulence screen is improved. Furthermore, the atmospheric turbulence prediction model exhibits stronger generalization ability for CPOV beams with different turbulence intensities and different OAM modes.

[0008] This application provides a deep learning-based method for predicting atmospheric turbulence in CPOV beams, including:

[0009] A model for predicting atmospheric turbulence is constructed using Legendre polynomials orthogonal over a square domain.

[0010] The intensity distribution map of the CPOV beam after free propagation in atmospheric turbulence is input into the atmospheric turbulence prediction model to predict the Legendre polynomial coefficients of the low-frequency part and the high-frequency part of the sub-region of the turbulence screen, so as to obtain the turbulence screen equivalent to atmospheric turbulence.

[0011] Furthermore, the construction of the atmospheric turbulence prediction model using Legendre polynomials orthogonal over a square domain includes:

[0012] Atmospheric turbulence is simulated using a random center point displacement interpolation algorithm to generate random phase screens under different atmospheric turbulence intensities.

[0013] The CPOV beam was transmitted through each random phase screen to obtain the distorted CPOV beam under different atmospheric turbulence intensities and the corresponding intensity distribution map.

[0014] For the intensity distribution map of each distorted CPOV beam, features are extracted using the ATSPNet model. For the random phase screen that causes the distortion, a Legendre polynomial orthogonal in a square domain is used for fitting. The feature extraction results are correlated with the polynomial fitting coefficients to obtain an atmospheric turbulence prediction model.

[0015] Furthermore, by predicting the Legendre polynomial coefficients of the low-frequency component and the high-frequency component of the sub-region of the turbulence screen respectively, an equivalent turbulence screen to atmospheric turbulence is obtained, including:

[0016] The atmospheric turbulence prediction model uses features extracted at multiple levels to predict the last 90 low-frequency coefficients of the Legendre polynomial. These low-frequency coefficients are then combined with features extracted at the first level to generate the last 20 high-frequency coefficients of the Legendre polynomial. Finally, the last 20 high-frequency coefficients of the Legendre polynomial are used to predict the first high-frequency coefficient of the Legendre polynomial through a fully connected layer, thus obtaining a turbulence screen equivalent to atmospheric turbulence. The first low-frequency coefficient of the Legendre polynomial is a constant.

[0017] Furthermore, for the random phase screen that causes this distortion, fitting is performed using Legendre polynomials orthogonal over a square domain, including:

[0018] The low-frequency component of the random phase screen is obtained by fitting 91 Legendre polynomial coefficients, and the high-frequency component of the random phase screen is obtained by subtracting it from the random phase screen; wherein, the first Legendre polynomial coefficient is a constant.

[0019] The high-frequency portion of the random phase screen is divided into 16×16 sub-regions.

[0020] For each subregion, 21 Legendre polynomial coefficients were used for fitting.

[0021] Furthermore, the random center point displacement interpolation algorithm generates the random phase screen in the following manner:

[0022] Kolmogorov turbulence phenomena can be represented using phase structure function equations:

[0023]

[0024] In the formula, r L Let r be the distance between the two points, and r0 be the atmospheric coherence length; where r0 is specifically represented as:

[0025]

[0026] In the formula, λ is the wavelength of the light beam. denoted as the atmospheric refractive index structure constant, and Δz as the distance traveled in atmospheric turbulence;

[0027] The following formula is used to simulate the phase values ​​A1, A2, A3, and A4 of four initial vertices that have a certain correlation and satisfy the statistical characteristics of the phase structure function:

[0028]

[0029] In the formula, R a R b R c These represent values ​​with a mean of 0 and variances of 0 and 0, respectively. a Gaussian random quantity; where, It has the following relationship:

[0030]

[0031] In the formula, M0 is the side length of the random phase screen;

[0032] Calculate the center point value O of the random phase screen and the midpoint values ​​B1, B2, B3, B4 of each edge from the four initial vertex phase values:

[0033]

[0034] In the formula, Δ0, Δ1, Δ2, Δ3, and Δ4 represent a mean of 0 and variances of 0, 0, 0, 0, and 0, respectively. a Gaussian random quantity; where, It has the following relationship:

[0035]

[0036] By recursively performing N random interpolations, a grid with side length M0 and 2n cells is obtained. N ×2 N Random phase screen.

[0037] Furthermore, before transmitting the CPOV beam through each random phase screen, the method further includes:

[0038] The CPOV beam is generated in the following manner:

[0039] Using a 632.8nm He-Ne laser as the light source, the He-Ne laser light is converted into linearly polarized light by a polarizer after attenuation. After being reflected by the first beam-splitting prism, the linearly polarized light is converted into a coaxial double Bessel-Gaussian beam by a loaded phase grating. Then, the first lens is used to achieve far-field diffraction conditions at the microscope objective, thereby realizing the conversion of the coaxial double Bessel-Gaussian beam into a CPOV beam.

[0040] Furthermore, the distorted CPOV beam and its corresponding intensity distribution map are obtained in the following manner:

[0041] After being collimated by the second lens, the CPOV beam propagates in free space. The transmitted CPOV beam, after passing through the second beam-splitting prism and then through a loaded random phase screen, is reflected by the second beam-splitting prism and converged by the third lens, thus obtaining a distorted CPOV beam. After being reflected by the third beam-splitting prism, a portion of the distorted CPOV beam is acquired by the first CMOS, thus obtaining the intensity distribution map of the distorted CPOV beam.

[0042] Furthermore, after obtaining a turbulence screen equivalent to atmospheric turbulence, the method further includes:

[0043] After inverting the phase of the turbulence screen, the CPOV beam, which has been freely propagating in atmospheric turbulence, is transmitted through the inverted turbulence screen to compensate for atmospheric turbulence.

[0044] Furthermore, after constructing the atmospheric turbulence prediction model, the method also includes:

[0045] The distorted CPOV beam is compensated for in the following way:

[0046] The distorted CPOV beam is input into the atmospheric turbulence prediction model to obtain a predicted turbulence screen equivalent to the random phase screen. The predicted turbulence screen is then inverted and superimposed on the random phase screen. After passing through an anti-spiral phase grating, the energy distribution is acquired by a second CMOS sensor to analyze the OAM mode and corresponding purity of the CPOV beam.

[0047] This application provides a deep learning-based method for predicting atmospheric turbulence in CPOV beams. By simultaneously predicting the low-frequency Legendre polynomial coefficients of the turbulence screen and the high-frequency coefficients of the sub-regions, the prediction accuracy of the turbulence screen is improved. Furthermore, the atmospheric turbulence prediction model exhibits stronger generalization ability for CPOV beams with different turbulence intensities and different OAM modes. Attached Figure Description

[0048] Figure 1 The radial distribution diagram and two-dimensional planar distribution diagram of the intensity of the double-ring CPOV beam provided in the embodiments of this application are shown;

[0049] Figure 2 The diagram shows the intensity distribution of the phase screen and the corresponding CPOV beam under different turbulence intensities provided in the embodiments of this application.

[0050] Figure 3 The following diagrams illustrate the effect of fitting the low-frequency and high-frequency components of the phase screen using Legendre polynomials, as provided in the embodiments of this application.

[0051] Figure 4 A schematic diagram of the structure of the atmospheric turbulence prediction model provided in the embodiments of this application is shown;

[0052] Figure 5 An experimental optical path diagram provided in an embodiment of this application is shown;

[0053] Figure 6 A flowchart of the atmospheric turbulence prediction method for CPOV beams based on deep learning provided in an embodiment of this application is shown;

[0054] Figure 7 The diagram shows the atmospheric turbulence prediction model and the loss function curve of ResNet50 provided in the embodiments of this application;

[0055] Figure 8 This illustrates the atmospheric turbulence prediction model provided in this application and the turbulence screen predicted by ResNet50;

[0056] Figure 9 The following diagram shows the CPOV beam intensity distribution before and after compensation, as provided in the embodiments of this application.

[0057] Figure 10 The figure shows the curves of CPOV model purity before and after atmospheric turbulence compensation as a function of turbulence intensity, provided in the embodiments of this application.

[0058] Figure 11 The diagram shows the OAM pattern recognition accuracy of uncompensated and compensated CPOV beams provided in the embodiments of this application;

[0059] Figure 12 This application provides a communication encoding scheme and a diagram showing the correspondence between 4-bit binary numbers and OAM modes.

[0060] Figure 13 The images shown are decoded images under three atmospheric turbulence intensities, with and without compensation, and with two compensation methods, as provided in the embodiments of this application. Detailed Implementation

[0061] To make the objectives, technical solutions, and advantages of this technical solution clearer, the following detailed description, in conjunction with specific embodiments, further illustrates this technical solution. It should be understood that these descriptions are merely exemplary and not intended to limit the scope of this technical solution.

[0062] Example 1: Theoretical basis of atmospheric turbulence compensation method for CPOV beams:

[0063] (1) Concentric Perfect Vortex Beam:

[0064] An ideal perfect vortex (POV) beam is a vortex beam whose spot radius is independent of the angular momentum mode, whose ring width approaches zero, and whose power density on the ring approaches infinity. An ideal POV beam can be represented as follows:

[0065]

[0066] In the formula, l represents the orbital angular momentum mode, and r represents the polar radius. Let r be the polar angle, δ() represent the Dirac function, and r p Let be the ring radius of the POV beam, and i be an imaginary number.

[0067] However, an ideal POV beam is impossible in reality; therefore, the Bessel expansion is usually used to represent the POV beam:

[0068]

[0069] In the formula, circ() represents the circular domain function, a is the upper limit of the radial coordinate r, N is a constant, and J l () denotes the l-th order Bessel function of the first kind, α l,n For J l The nth zero of ().

[0070] When N in formula (2) is infinite, formula (2) is equivalent to formula (1).

[0071] Based on this, the CPOV beam consists of several POV beams with different ring sizes. For example, please refer to... Figure 1 The diagram shows the radial and two-dimensional planar intensity distributions of the double-ring CPOV beam. In the diagram, N is taken as 30, and the orbital angular momentum mode of the outer ring POV beam is shown. o 1. Outer ring radius r o The orbital angular momentum mode of the inner ring POV beam is 0.1725m. i The inner ring radius is 1, r i It is 0.0850m.

[0072] (2) The effect of atmospheric turbulence on CPOV beams:

[0073] To simulate the propagation of a light beam in free space, atmospheric turbulence in free space is equated to a random phase screen. Therefore, the free propagation of the light beam in atmospheric turbulence is equivalent to the propagation of the light beam through the random phase screen. Methods for generating random phase screens include polynomial expansion, power spectrum inversion, and fractal methods. Among these, the phase screen generated by the fractal method exhibits better performance in both the low-frequency and high-frequency ranges, more closely resembling real atmospheric turbulence phenomena. Therefore, this application employs the fractal method to simulate and generate the phase screen.

[0074] Fractal methods are primarily based on phase structure functions, employing interpolation to simulate the phase value at each point in atmospheric turbulence. The stochastic center point displacement interpolation algorithm is a typical fractal model algorithm that uses a subdivision process to perform adaptive recursive interpolation between points to simulate atmospheric turbulence phenomena.

[0075] The Kolmogorov turbulence phenomenon can be represented using the phase structure function equation:

[0076]

[0077] In the formula, r L Let r be the distance between the two points, and r0 be the atmospheric coherence length, which can be specifically expressed as:

[0078]

[0079] In the formula, λ is the wavelength of the light beam. Δz is the atmospheric refractive index structure constant, and Δz is the distance traveled in atmospheric turbulence.

[0080] In actual numerical simulations, to generate a square phase screen with dimensions M0, it is first necessary to simulate four initial vertex phase values ​​A1, A2, A3, and A4 with a certain correlation, ensuring they satisfy the statistical properties of the phase structure function, specifically expressed as follows:

[0081]

[0082] In the formula, R a R b R c These represent values ​​with a mean of 0 and variances of 0 and 0, respectively. Gaussian random quantities; specifically, It can be represented as:

[0083]

[0084] In the formula, M0 is the side length of the square phase screen.

[0085] Calculate the center point value O of the square region and the midpoint values ​​B1, B2, B3, and B4 of each edge using the phase values ​​of the four initial vertices:

[0086]

[0087] In the formula, Δ0, Δ1, Δ2, Δ3, and Δ4 represent a mean of 0 and variances of 0, 0, 0, 0, and 0, respectively. Gaussian random quantities; specifically, It can be represented as:

[0088]

[0089] By recursively performing N random interpolations, a grid with side length M0 and 2n cells can be obtained. N ×2 N The phase screen.

[0090] As an example, this application uses the fractal method to simulate and generate, according to the simulation parameters shown in Table 1, the following... Figure 2 The diagram shows the intensity distribution of the phase screen and the corresponding CPOV beam under different turbulence intensities. Specifically, (a) and (d) have a turbulence intensity of 1.5, (b) and (e) have a turbulence intensity of 7.5, and (c) and (f) have a turbulence intensity of 15. Figure 2 It is known that atmospheric turbulence causes distortion in the intensity distribution of the CPOV beam, and this distortion intensifies with increasing turbulence intensity.

[0091] Table 1. Simulation Parameters

[0092]

[0093]

[0094] (3) Legendre polynomial:

[0095] Legendre polynomials are a set of orthogonal sequence functions on [-1, 1], which can be represented as:

[0096]

[0097] In the formula, p is the order of the Legendre polynomial, / / means to perform the division of two numbers and return the largest integer not greater than the result, and C is the combination operation.

[0098] A set of two-dimensional Legendre polynomials orthogonal over a square domain can be constructed through specific combinations:

[0099] L n (x,y)=L p (x)·L q (y); (10)

[0100] In the formula, n is the order of the two-dimensional Legendre polynomial, p and q are integers starting from 0, and L... p (x) is a Legendre polynomial with x as the variable, L q (y) is a Legendre polynomial with y as the variable.

[0101] Since a square can be tiled in a two-dimensional plane, a square phase screen can be divided into several sub-phase screens, each fitted with a low-term Legendre polynomial, which can improve the fitting accuracy of the high-frequency part of the phase screen.

[0102] As an example, please refer to... Figure 3 The images shown are the results of fitting the low-frequency and high-frequency components of the phase screen using Legendre polynomials, respectively. Figure 3 (a) is the original phase screen with turbulence intensity d. o / r0 = 15; Figure 3 (b) Considering the phase screen initially fitted using 91 Legendre polynomials, and taking it as the low-frequency component, then... Figure 3 The difference between (a) and 3(b) is the high-frequency component. After dividing the phase of the high-frequency component into 16×16 segments, a 21-term Legendre polynomial fitting is performed on each sub-region to obtain the following results: Figure 3 (c) shows the phase screen for the high-frequency portion. Then, Figure 3 The sum of (b) and 3(c) is the phase screen fitted using the Legendre polynomial, such as Figure 3 As shown in (e).

[0103] To verify the fitting effect of the Legendre polynomial in this application, Figure 3 (d) also presents the phase screen fitted using 91 Zernike polynomials. Figure 3 (d) and (e) are respectively with Figure 4 (a) A comparison shows that using the Legendre polynomial for regional fitting of the high-frequency portion yields a phase screen that is closer to the original phase screen. Therefore, this application uses the Legendre polynomial to fit the phase screen.

[0104] Example 2: Working mechanism of atmospheric turbulence prediction model:

[0105] Please see as follows Figure 4The diagram shows the structure of an atmospheric turbulence prediction model. In the diagram, Stem is the backbone network, Conv2d represents a two-dimensional convolution operation (size represents the kernel size, stride represents the kernel stride), LayrNorm represents a normalization layer, dim represents the size, Downsample represents a downsampling operation, Upsample represents an upsampling operation, GlobalAvg Pooling represents global average pooling, Linear represents a fully connected layer, Flatten represents a smoothing operation, Lowfrequency term represents the low-frequency component, Highfrequency term represents the high-frequency component, and Highfrequencyfirst term represents the first term of the high-frequency component. Furthermore, Figure 4 It also provides structural diagrams of the Block module and Downsmple. Here, Depthwise Conv2d represents a depthwise 2D convolution operation, GELU represents the activation function, and Layer Scale represents the layer size.

[0106] like Figure 5 As shown, the model's input is the intensity distribution map of the distorted CPOV beam (hereinafter referred to as the CPOV intensity map), and the output is the Legendre polynomial coefficients of the low-frequency part and the high-frequency part of the sub-region of the turbulence screen. Since the first term of the Legendre polynomial in the low-frequency part is a constant term and does not cause beam distortion, the Legendre polynomial coefficients of the low-frequency part output by the model do not include the first term.

[0107] Specifically, 1) The backbone network Stem extracts features from the CPOV intensity map through two-dimensional convolution and layer normalization operations, and then runs the Block module twice to obtain the first-level extracted features; 2) One branch performs multi-level feature extraction through several downsampling operations and the Block module, and finally generates the last 90 low-frequency coefficients of the Legendre polynomial through global average pooling, layer normalization, and fully connected operations; 3) Another branch runs the Block module four times in sequence, and then performs two-dimensional convolution operations, and then merges it with the last 90 low-frequency coefficients of the Legendre polynomial that have undergone upsampling operations, and finally obtains the last 20 high-frequency coefficients of the Legendre polynomial through two-dimensional convolution operations; 4) The last 20 high-frequency coefficients of the Legendre polynomial are smoothed and fully connected to obtain the first high-frequency coefficient of the Legendre polynomial.

[0108] Example 3: Construction and Evaluation Method of Atmospheric Turbulence Prediction Model:

[0109] Please see as follows Figure 5The experimental optical path diagram is shown below. In the diagram, He-Ne is the laser, ND is the attenuator, P is the polarizer, SLM1 is loaded with a phase grating, SLM2 is loaded with a random phase screen, NPBS1, NPBS2, and NPBS3 are the first, second, and third beam prisms, respectively, L1, L2, and L3 are the first, second, and third lenses, respectively, the Object Lens is the microscope objective, and CMOS1 and CMOS2 are the sensors used for image acquisition.

[0110] To establish an atmospheric turbulence prediction model, the first step is to utilize... Figure 6 The experimental optical path shown acquires the intensity distribution maps of the distorted CPOV beam under different atmospheric turbulence intensities, serving as a dataset. Specifically, this experimental optical path can achieve the following functions:

[0111] (1) Generate CPOV beam: Using a 632.8nm He-Ne laser as the light source, after attenuation by an attenuator (ND), the He-Ne laser is converted into linearly polarized light by a polarizer (P) (the linearly polarized light is in the same direction of vibration as the SLM is sensitive to). After reflection by the first beam splitter prism NPBS1, the linearly polarized light is converted into a coaxial double Bessel-Gaussian beam by loading a phase grating (SLM1). Then, the first lens (L1) is used to achieve far-field diffraction conditions at the microscope objective, thereby realizing the conversion of the coaxial double Bessel-Gaussian beam into a CPOV beam.

[0112] (2) Simulating atmospheric turbulence: After being collimated by the second lens (L2), the CPOV beam propagates in free space. After passing through the second beam splitter prism (NPBS2), the transmitted CPOV beam passes through the loaded random phase screen (SLM2) and is then reflected by the second beam splitter prism (NPBS2) and converged by the third lens (L3), thus obtaining a distorted CPOV beam. After passing through the third beam splitter prism (NPBS3), a portion of the distorted CPOV beam is acquired by the first CMOS, thus obtaining the intensity distribution map of the distorted CPOV beam.

[0113] (3) Compensation for the distorted CPOV beam: The distorted CPOV beam is input into the atmospheric turbulence prediction model to obtain a prediction turbulence screen equivalent to the random phase screen. The prediction turbulence screen is then inverted and superimposed on the random phase screen (SLM2). After passing through the anti-spiral phase grating, the energy distribution is collected by the second CMOS to analyze the OAM mode and corresponding purity of the CPOV beam.

[0114] As an example, the outer ring radius of the CPOV beam is 0.1725m and the inner ring radius is 0.0850m; the atmospheric turbulence intensities include: 1.50, 3.00, 4.50, 6.00, 7.50, 9.00, 10.50, 12.00, 13.50, and 15.00; the resulting OAM modes include: -8, -7, -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7, and 8, and the OAM modes of the inner and outer rings are independent of each other.

[0115] Example 4:

[0116] Please see as follows Figure 6 The flowchart shown is for a deep learning-based method for predicting atmospheric turbulence using CPOV beams. Figure 7 As shown, the method includes:

[0117] S101. Construct an atmospheric turbulence prediction model using Legendre polynomials orthogonal over a square domain.

[0118] In practical implementation, atmospheric turbulence prediction models can be constructed in the following ways:

[0119] Step 1011: Use the random center point displacement interpolation algorithm to simulate atmospheric turbulence to generate random phase screens under different atmospheric turbulence intensities.

[0120] In practical implementation, random phase screens can be generated in the following ways:

[0121] Kolmogorov turbulence phenomena can be represented using phase structure function equations:

[0122]

[0123] In the formula, r L Let r be the distance between the two points, and r0 be the atmospheric coherence length; where r0 is specifically represented as:

[0124]

[0125] In the formula, λ is the wavelength of the light beam. denoted as the atmospheric refractive index structure constant, and Δz as the distance traveled in atmospheric turbulence;

[0126] The following formula is used to simulate the phase values ​​A1, A2, A3, and A4 of four initial vertices that have a certain correlation and satisfy the statistical characteristics of the phase structure function:

[0127]

[0128] In the formula, R a R b R cThese represent values ​​with a mean of 0 and variances of 0 and 0, respectively. a Gaussian random quantity; where, It has the following relationship:

[0129]

[0130] In the formula, M0 is the side length of the random phase screen;

[0131] Calculate the center point value O of the random phase screen and the midpoint values ​​B1, B2, B3, B4 of each edge from the four initial vertex phase values:

[0132]

[0133] In the formula, Δ0, Δ1, Δ2, Δ3, and Δ4 represent a mean of 0 and variances of 0, 0, 0, 0, and 0, respectively. a Gaussian random quantity; where, It has the following relationship:

[0134]

[0135] By recursively performing N random interpolations, a grid with side length M0 and 2n cells is obtained. N ×2 N Random phase screen.

[0136] Step 1012: Transmit the CPOV beam through each random phase screen to obtain the distorted CPOV beam under different atmospheric turbulence intensities and the corresponding intensity distribution map.

[0137] Before transmitting the CPOV beam through each random phase screen, the CPOV beam can also be generated in the following ways:

[0138] Using a 632.8nm He-Ne laser as the light source, the He-Ne laser light is converted into linearly polarized light by a polarizer after attenuation. After passing through the first beam splitter, the reflected linearly polarized light is converted into a coaxial double Bessel-Gaussian beam by a loaded phase grating. Then, the first lens is used to achieve far-field diffraction conditions at the microscope objective, thereby realizing the conversion of the coaxial double Bessel-Gaussian beam into a CPOV beam.

[0139] The distorted CPOV beam and its corresponding intensity distribution map were obtained in the following manner:

[0140] After being collimated by the second lens, the CPOV beam propagates in free space. The transmitted CPOV beam, after passing through the second beam-splitting prism and then through a loaded random phase screen, is reflected by the second beam-splitting prism and converged by the third lens, thus obtaining a distorted CPOV beam. After being reflected by the third beam-splitting prism, a portion of the distorted CPOV beam is acquired by the first CMOS, thereby obtaining the intensity distribution map of the distorted CPOV beam.

[0141] Step 1013: For the intensity distribution map of each distorted CPOV beam, feature extraction is performed using the ATSPNet model. For the random phase screen that causes the distortion, a Legendre polynomial orthogonal in a square domain is used for fitting. The feature extraction results are correlated with the polynomial fitting coefficients to obtain the atmospheric turbulence prediction model.

[0142] In practical implementation, fitting can be achieved using Legendre polynomials orthogonal over a square domain:

[0143] Step 201: Fit the low-frequency part of the random phase screen using 91 Legendre polynomial coefficients, and perform a difference operation with the random phase screen to obtain the high-frequency part of the random phase screen; wherein, the first Legendre polynomial coefficient is a constant.

[0144] Step 202: Divide the high-frequency part of the random phase screen into 16×16 segments to obtain sub-regions.

[0145] Step 203: Fit the model using 21 Legendre polynomial coefficients for each subregion.

[0146] After constructing the atmospheric turbulence prediction model, the distorted CPOV beam can be compensated in the following ways:

[0147] The distorted CPOV beam is input into the atmospheric turbulence prediction model to obtain a predicted turbulence screen equivalent to the random phase screen. The predicted turbulence screen is then inverted and superimposed on the random phase screen. After passing through an anti-spiral phase grating, the energy distribution is acquired by a second CMOS sensor to analyze the OAM mode and corresponding purity of the CPOV beam.

[0148] S102. Input the intensity distribution map of the CPOV beam after it has been freely propagated in atmospheric turbulence into the atmospheric turbulence prediction model, and predict the Legendre polynomial coefficients of the low-frequency part and the high-frequency part of the sub-region of the turbulence screen, respectively, so as to obtain a turbulence screen equivalent to atmospheric turbulence.

[0149] Specifically: The atmospheric turbulence prediction model uses features extracted at multiple levels to predict the last 90 low-frequency coefficients of the Legendre polynomial. These low-frequency coefficients are then combined with features extracted at the first level to generate the last 20 high-frequency coefficients of the Legendre polynomial. The last 20 high-frequency coefficients of the Legendre polynomial are then used to predict the first high-frequency coefficient of the Legendre polynomial through a fully connected layer, thereby obtaining a turbulence screen equivalent to atmospheric turbulence. The first low-frequency coefficient of the Legendre polynomial is a constant.

[0150] After obtaining a turbulence screen equivalent to atmospheric turbulence, the method further includes:

[0151] After inverting the phase of the turbulence screen, the CPOV beam, which has been freely propagating in atmospheric turbulence, is transmitted through the inverted turbulence screen to compensate for atmospheric turbulence.

[0152] Example 5:

[0153] (1) Atmospheric turbulence compensation:

[0154] Please see as follows Figure 8 The loss function curves of the ATSPNet atmospheric turbulence prediction model and the ResNet50 model are shown. Both models used the same dataset, learning rate, optimizer, and number of iterations. Because the corresponding polynomials are different, the networks cannot be compared based on their loss functions alone; therefore, their predictive capabilities regarding turbulence screens will be compared below. The experimental dataset contains 50 samples per class, including 16 modes and 10 atmospheric turbulence intensities, totaling 128,000 samples (61,440 training samples, 15,360 validation samples, and 51,200 test samples).

[0155] Please see as follows Figure 8 The ATSPNet atmospheric turbulence prediction model and the ResNet50 predicted turbulence screen are shown below. For comparison, Figure 8 The first row shows actual turbulence screens under different turbulence intensities. By comparison... Figure 9 As can be seen from the second and third lines, the phase screen predicted by the ATSPNet atmospheric turbulence prediction model in this application contains more high-frequency information than ResNet50, and is therefore closer to the actual turbulence screen.

[0156] Figure 9 (a) to (c) show the CPOV light intensity distribution after turbulence. It can be seen that as the turbulence intensity increases, the light intensity ring structure is destroyed and the distribution is uneven. Figure 9 (d)~(f) show the CPOV light intensity distribution after ResNet50 compensation. Figure 10(g) to (i) show the results after ATSPNet compensation. A comparison reveals that the circular structure of the CPOV is more regular after compensation using the ATSPNet atmospheric turbulence prediction model, indicating that the method proposed in this invention can effectively compensate for the distortion of the CPOV beam caused by atmospheric turbulence.

[0157] To quantitatively evaluate the performance of the atmospheric turbulence compensation technique proposed in this invention, the mode purity of the CPOV before and after compensation was analyzed using an inverted spiral phase hologram. When the vortex beam undergoes an inverted spiral phase, it transforms into a Gaussian beam, with a bright spot at the center. First, the CPOV beam is converted into a Gaussian beam, and the intensity of the bright spot is recorded. Then, the intensity of the CPOV beam after atmospheric turbulence is converted back into a bright spot. The ratio of these two intensities represents the CPOV mode purity after atmospheric turbulence. The compensated CPOV mode purity can also be calculated using the same method.

[0158] Figure 10 Curves showing the variation of CPOV model purity with turbulence intensity before and after atmospheric turbulence compensation are presented. Figure 9 Figures (a) and (b) show the model purity curves before and after compensation for the outer and inner loops of the CPOV, respectively. Each data point represents the average of 5120 test samples. As can be seen from the figures, before compensation, the model purity of the outer loop gradually decreases with increasing turbulence intensity. o The percentage of 70.68% when / r0=1.50 decreased to d o The 8.00% purity at r0 = 15.00 indicates that strong turbulence severely affects the beam mode. After ATSPNet compensation, the mode purity of the outer ring is significantly improved, reaching d... o When / r0=1.50, it increases to 90.71%, while in d o At / r0 = 15.00, the improvement also reached 38.52%. This indicates that ATSPNet performs excellently in atmospheric turbulence compensation, effectively improving beam quality. For comparison, ResNet50 was used for compensation effect analysis, at d o When / r0 = 1.50, the purity of the outer ring mode increases to 90.08%, while in d o When / r0=15.00, the improvement only reaches 21.05%. Although ResNet50 also shows some compensation effect, the improvement is relatively small compared with ATSPNet, especially under strong turbulence conditions. Figure 11 (b) shows that the model purity of the inner loop also exhibits the same trend as the outer loop. It is evident that ATSPNet significantly outperforms ResNet50 in atmospheric turbulence compensation, especially under strong turbulence conditions, effectively improving the model purity of CPOV.

[0159] (2) Pattern recognition of CPOV beams:

[0160] The CPOV beam exhibits an intensity distribution that does not change with the angular momentum mode, but this also presents challenges for identification. This invention employs DVG diffraction to measure the OAM mode of the inner and outer ring beams of the CPOV. When the vortex beam passes through the DVG, if the far-field diffraction (n...) x ,n y If a Gaussian bright spot appears in the diffraction order, then the topological charge of the vortex beam is expressed as:

[0161] l = -l x ·n x -l y ·n y (11)

[0162] Among them l x and l y This refers to the topological charge of the spiral phase superimposed on two mutually perpendicular Damman gratings. The grating used in this application is a 5×5 two-dimensional Damman vortex grating, where l x =-5, l y =-1.

[0163] To utilize CNNs to identify the OAM pattern of CPOV, a recognition dataset was generated using an experimental system. The dataset includes an uncompensated group, a ResNet-compensated group, and an ATSPNet-compensated group, with 320 samples per class in each group, totaling 102,400 samples per group. Of these, 40,960 are training samples, 10,240 are validation samples, and 51,200 are test samples, which were used to train the ResNet18 model separately.

[0164] The atmospheric turbulence prediction model takes as input a grayscale image of the intensity distribution of a CPOV beam diffracted in the far field by a DVG, and outputs the probability distribution of each OAM mode. The cross-entropy loss function is used.

[0165]

[0166] In the formula, x i p(x) represents a possible event. i ) and q(x i ) represent events x respectively i For probabilities in p and q, the smaller the cross-entropy value, the closer the two probability distributions are.

[0167] Figure 12 The OAM pattern recognition accuracy for uncompensated and compensated CPOV beams is presented, with each data point representing the average of 2560 test results. As shown in the figure, atmospheric turbulence compensation improved the recognition accuracy for both methods, but after ResNet50 compensation, the outer ring d... o When / r0 = 15.00, the recognition accuracy is not high, only 73.95%. The inner loop in d...i When / r0 = 7.39, the accuracy is 85.20%. Under the same conditions, after ATSPNet compensation, the outer and inner loop recognition accuracies are 98.01% and 99.73%, respectively. This shows that by using the ATSPNet method proposed in this invention for atmospheric turbulence compensation, the OAM pattern recognition accuracy of CPOV is significantly improved.

[0168] (3) Communication experiment with CPOV beam:

[0169] To evaluate the performance of the proposed atmospheric turbulence compensation scheme in a communication scenario, a 128×128 grayscale image was transmitted using OAM-SK communication. The communication coding scheme adopted is as follows: Figure 12 (a) At the transmitting end, the grayscale values ​​of pixels in the image are converted into two 4-bit binary number sequences. The correspondence between the 4-bit binary numbers and the OAM mode is shown in [reference needed]. Figure 13 (b). The atmospheric turbulence intensity in the experiment includes d o The image is reconstructed using three cases: / r0 = 4, 8, and 12. The results are compared for cases with ResNet50 compensation, ATSPNet compensation, and no compensation. The image is then recovered at the receiver after recognizing the OAM pattern using the previously trained ResNet18.

[0170] Figure 13 Decoded images are presented under three atmospheric turbulence intensities, with and without compensation for two compensation methods. SSIM measures the similarity between two images. SSIM is a perceptual model, meaning it better reflects human visual perception. The formula for calculating SSIM is as follows:

[0171]

[0172] In the formula, μ x It is the average value of x, μ y It is the average value of y, σ x σ is the variance of x. y σ is the variance of y. xy Let c1 be the covariance of x and y. c1 = (k1L) 2 c2 = (k2L) 2 SSIM is a constant used to maintain stability, and L is the dynamic range of grayscale values. The closer SSIM is to 1, the higher the image similarity.

[0173] Table 2, SSIM

[0174]

[0175]

[0176] Table 2 provides the following information: ​The SSIM values ​​of the nine decoded images and the standard image are shown in the table. As can be seen, after ATSPNet compensation, the lowest SSIM value for both the decoded and standard images reaches 0.98 under the three turbulence intensities, which is superior to ResNet50. Therefore, the ATSPNet compensation method proposed in this invention can effectively improve the communication quality of OAM-SK.

[0177] The above content is only a preferred embodiment of the present invention. For those skilled in the art, many changes can be made in the specific implementation and application scope based on the ideas of the present invention. As long as these changes do not depart from the concept of the present invention, they all fall within the protection scope of the present invention.

Claims

1. A method for predicting atmospheric turbulence from CPOV beams based on deep learning, characterized in that, The method includes: A model for predicting atmospheric turbulence is constructed using Legendre polynomials orthogonal over a square domain. The intensity distribution map of the CPOV beam after free propagation in atmospheric turbulence is input into the atmospheric turbulence prediction model to predict the Legendre polynomial coefficients of the low-frequency part and the high-frequency part of the sub-region of the turbulence screen, so as to obtain the turbulence screen equivalent to atmospheric turbulence.

2. The method as described in claim 1, characterized in that, The method of constructing an atmospheric turbulence prediction model using Legendre polynomials orthogonal over a square domain includes: Atmospheric turbulence is simulated using a random center point displacement interpolation algorithm to generate random phase screens under different atmospheric turbulence intensities. The CPOV beam was transmitted through each random phase screen to obtain the distorted CPOV beam under different atmospheric turbulence intensities and the corresponding intensity distribution map. For the intensity distribution map of each distorted CPOV beam, features are extracted using the ATSPNet model. For the random phase screen that causes the distortion, a Legendre polynomial orthogonal in a square domain is used for fitting. The feature extraction results are correlated with the polynomial fitting coefficients to obtain an atmospheric turbulence prediction model.

3. The method as described in claim 1, characterized in that, A turbulence screen equivalent to atmospheric turbulence is obtained by predicting the Legendre polynomial coefficients of the low-frequency component and the high-frequency component of the sub-region of the turbulence screen, respectively, including: The atmospheric turbulence prediction model uses features extracted at multiple levels to predict the last 90 low-frequency coefficients of the Legendre polynomial. These low-frequency coefficients are then combined with features extracted at the first level to generate the last 20 high-frequency coefficients of the Legendre polynomial. Finally, the last 20 high-frequency coefficients of the Legendre polynomial are used to predict the first high-frequency coefficient of the Legendre polynomial through a fully connected layer, thus obtaining a turbulence screen equivalent to atmospheric turbulence. The first low-frequency coefficient of the Legendre polynomial is a constant.

4. The method as described in claim 2, characterized in that, For the random phase screen that causes this distortion, fitting is performed using Legendre polynomials orthogonal over a square domain, including: The low-frequency component of the random phase screen is obtained by fitting 91 Legendre polynomial coefficients, and the high-frequency component of the random phase screen is obtained by subtracting it from the random phase screen; wherein, the first Legendre polynomial coefficient is a constant. The high-frequency portion of the random phase screen is divided into 16×16 sub-regions. For each subregion, 21 Legendre polynomial coefficients were used for fitting.

5. The method as described in claim 2, characterized in that, The random center point displacement interpolation algorithm generates a random phase screen in the following way: Kolmogorov turbulence phenomena can be represented using phase structure function equations: In the formula, r L Let r be the distance between the two points, and r0 be the atmospheric coherence length; where r0 is specifically represented as: In the formula, λ is the wavelength of the light beam. denoted as the atmospheric refractive index structure constant, and Δz as the distance traveled in atmospheric turbulence; The following formula is used to simulate the phase values ​​A1, A2, A3, and A4 of four initial vertices that have a certain correlation and satisfy the statistical characteristics of the phase structure function: In the formula, R a R b R c These represent values ​​with a mean of 0 and variances of 0 and 0, respectively. a Gaussian random quantity; where, It has the following relationship: In the formula, M0 is the side length of the random phase screen; Calculate the center point value O of the random phase screen and the midpoint values ​​B1, B2, B3, B4 of each edge from the four initial vertex phase values: In the formula, Δ0, Δ1, Δ2, Δ3, and Δ4 represent a mean of 0 and variances of 0, 0, 0, 0, and 0, respectively. a Gaussian random quantity; where, It has the following relationship: By recursively performing N random interpolations, a grid with side length M0 and 2n cells is obtained. N ×2 N Random phase screen.

6. The method as described in claim 2, characterized in that, Before transmitting the CPOV beam through each random phase screen, the method further includes: The CPOV beam is generated in the following manner: Using a 632.8nm He-Ne laser as the light source, the He-Ne laser light is converted into linearly polarized light by a polarizer after attenuation. After being reflected by the first beam-splitting prism, the linearly polarized light is converted into a coaxial double Bessel-Gaussian beam by a loaded phase grating. Then, the first lens is used to achieve far-field diffraction conditions at the microscope objective, thereby realizing the conversion of the coaxial double Bessel-Gaussian beam into a CPOV beam.

7. The method as described in claim 2, characterized in that, The distorted CPOV beam and its corresponding intensity distribution map were obtained in the following manner: After being collimated by the second lens, the CPOV beam propagates in free space. The transmitted CPOV beam, after passing through the second beam-splitting prism and then through a loaded random phase screen, is reflected by the second beam-splitting prism and converged by the third lens, thus obtaining a distorted CPOV beam. After passing through the third beam-splitting prism, a portion of the distorted CPOV beam is acquired by the first CMOS, thus obtaining the intensity distribution map of the distorted CPOV beam.

8. The method as described in claim 1, characterized in that, After obtaining a turbulence screen equivalent to atmospheric turbulence, the method further includes: After inverting the phase of the turbulence screen, the CPOV beam, which has been freely propagating in atmospheric turbulence, is transmitted through the inverted turbulence screen to compensate for atmospheric turbulence.

9. The method as described in claim 7, characterized in that, After constructing the atmospheric turbulence prediction model, the method further includes: The distorted CPOV beam is compensated for in the following way: The distorted CPOV beam is input into the atmospheric turbulence prediction model to obtain a predicted turbulence screen equivalent to the random phase screen. The predicted turbulence screen is then inverted and superimposed on the random phase screen. After passing through an anti-spiral phase grating, the energy distribution is acquired by a second CMOS sensor to analyze the OAM mode and corresponding purity of the CPOV beam.

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