Atmospheric turbulence parameter inversion method based on physical information neural network

Abstract

The invention discloses an atmospheric turbulence parameter inversion method based on a physical information neural network, and relates to the technical field of atmospheric turbulence inversion. According to the method, training data conforming to physical characteristics are generated through the Kolmogorov turbulence model, the error-physical constraint loss function is combined, the PINN model is trained by utilizing grid loss and random uniform perturbation, a high-error region can be focused, overfitting is avoided, high-precision, physically consistent and high-generalization inversion of atmospheric turbulence parameters is realized, and the method is suitable for large-scale popularization and application. The problem that the inversion result of a traditional data-driven model violates the physical law of backlight field propagation is solved, the optimization efficiency of a difficult-to-learn area is improved through grid loss, the adaptability of the inversion model to continuous spatial distribution can be enhanced through perturbation factors, and the defects of low training efficiency and weak generalization ability are further overcome. And the turbulence phase screen and atmospheric turbulence parameters obtained by inversion are highly matched with real turbulence characteristics.

Description

Technical Field

[0001] This invention relates to the field of atmospheric turbulence inversion technology, and in particular to a method for inverting atmospheric turbulence parameters based on a physical information neural network. Background Technology

[0002] When laser beams propagate through the atmosphere, they are affected by refractive index fluctuations caused by atmospheric turbulence, resulting in phenomena such as speckle, distortion, energy spread, and centroid drift. These effects not only reduce the signal-to-noise ratio and transmission efficiency of optical communication systems but also severely impact lidar, free-space optical communication, and precision imaging systems. Therefore, accurately obtaining statistical parameters of atmospheric turbulence is of great significance for atmospheric optics applications.

[0003] Existing methods for inverting atmospheric turbulence parameters mainly rely on experimental measurements and empirical formulas. For example, the laser speckle method estimates turbulence parameters by analyzing speckle contrast and drift, but its accuracy is limited by experimental noise and model simplification. Numerical simulation methods can generate turbulent phase screens, but their correspondence with actual measurement data is insufficient. Traditional deep learning methods can fit the relationship between "distorted speckle and phase screen," but due to the lack of physical constraints, they often suffer from overfitting, resulting in insufficient generalization ability and making them difficult to apply directly to complex real-world atmospheric environments. Therefore, there is an urgent need for a method that can combine experimental measurements with physical models to achieve high-precision inversion of atmospheric turbulence parameters under limited experimental sample conditions. Summary of the Invention

[0004] The purpose of this invention is to provide a method for inverting atmospheric turbulence parameters based on a physical information neural network, so as to improve the above-mentioned technical problems.

[0005] To achieve the above-mentioned objectives, the embodiments of the present invention provide the following technical solutions:

[0006] A method for inverting atmospheric turbulence parameters based on a physical information neural network, comprising:

[0007] The statistical correlation of Zernike coefficients is generated based on the Kolmogorov turbulence model. Combined with angular spectrum propagation theory and the coherence length is adjusted, inversion training data is generated. The inversion training data includes training turbulence phase screens and training distortion spots under different coherence lengths.

[0008] Based on the light field propagation process, a differentiable propagation operator is determined; based on the supervision error and the differentiable propagation operator, an error-physical constraint loss function is constructed; the error-physical constraint loss function includes a supervision loss function and a physical consistency constraint loss function.

[0009] An initial turbulence inversion model is constructed; based on the error-physical constraint loss function and inversion training data, the initial turbulence inversion model is trained through grid loss and random uniform perturbation to obtain the turbulence inversion model; the initial turbulence inversion model adopts the PINN model;

[0010] A laser speckle method was used to conduct a light spot experiment, generating real light spot data. This data was then inverted using a turbulence inversion model to obtain a turbulence phase screen. Atmospheric turbulence parameters were calculated based on the turbulence phase screen. Attached Figure Description

[0011] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0012] Figure 1 This is a flowchart of the method in Embodiment 1 of the present invention;

[0013] Figure 2 This is the experimental optical path diagram of the laser speckle method in Embodiment 1 of the present invention;

[0014] Figure 3 This is a system structure diagram in Embodiment 1 of the present invention;

[0015] Figure 4 This is a schematic diagram of the training distortion spot and the training turbulence phase screen with a coherence length of 0.0017m in Embodiment 2 of the present invention;

[0016] Figure 5 This is a schematic diagram of the training distortion spot and the training turbulence phase screen with a coherence length of 0.017m in Embodiment 2 of the present invention.

[0017] Figure 6 This is a schematic diagram of the training distortion spot and the training turbulence phase screen with a coherence length of 0.17m in Embodiment 2 of the present invention;

[0018] Figure 7 This is a distorted spot pattern of atmospheric turbulence measured by the laser speckle method in Embodiment 2 of the present invention;

[0019] Figure 8 This is a schematic diagram of the turbulent phase screen output by the turbulent inversion model in Embodiment 2 of the present invention. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0021] Example 1:

[0022] Please see Figure 1 This embodiment provides a method for inverting atmospheric turbulence parameters based on a physical information neural network, including:

[0023] S1. Statistical correlation of Zernike coefficients is generated based on the Kolmogorov turbulence model, combined with angular spectrum propagation theory and adjusted coherence length to generate inversion training data; the inversion training data includes training distortion spots and training turbulence phase screens under different coherence lengths;

[0024] S1 includes:

[0025] S11. Based on the angular and radial frequencies, calculate the order-related structure factor and calculate the radial polynomial using hypergeometric functions;

[0026] S12. Construct and simulate the Kolmogorov turbulence model, and generate energy relationships based on coherence length;

[0027] S13. Based on energy relationships and order-related structural factors, set statistical correlations for Zernike coefficients and use them as Zernike coefficient covariance constraints; the Zernike coefficient covariance constraints include energy constraints and individual Zernike coefficient variances.

[0028] When describing the wavefront phase of a vortex light using Zernike polynomials, it is necessary to determine the coefficients of each Zernike polynomial. However, these coefficient variables are not independent of each other. According to the energy relationship, the coefficients of any two Zernike polynomials are... and The covariance between them needs to satisfy the energy constraint:

[0029] S14. Based on the Zernike coefficient covariance constraint and radial polynomial, generate N Zernike coefficients; N takes the value of 600.

[0030] S15. Randomly adjust the coherence length, calculate the Zernike coefficients under different coherence lengths, integrate the multiple Zernike coefficients under all coherence lengths, and generate a set of Zernike coefficients.

[0031] S16. Based on the Zernike coefficient set and Zernike polynomial, calculate the discrete turbulent phase screen to obtain the trained turbulent phase screen;

[0032] S17. Based on the angular spectrum propagation theory, the transmission process of the light field after passing through the training turbulent phase screen is simulated to generate a training distorted light spot.

[0033] Specifically, order-related structural factors The formula is:

[0034] ;

[0035] radial polynomial The formula is:

[0036] ;

[0037] The Kronecker logic symbol has only two values: 0 and 1.

[0038] ;

[0039] The formula for the Zernike polynomial is:

[0040] ;

[0041] The formula for energy constraint is:

[0042]

[0043] Utilizing the statistical symmetry of isotropic turbulence, the covariance matrix can be simplified into a diagonal form that depends only on the radial order *n* and angular frequency *m* of the Zernike polynomial. For the *j*-th Zernike polynomial, the variance of the corresponding individual Zernike coefficients is... The formula is:

[0044] ;

[0045] ;

[0046] The specific process for generating a phase screen using the Zernike polynomial method can be divided into coefficient generation and phase superposition. To obtain Zernike polynomial coefficients that conform to the physical properties of atmospheric turbulence, it is necessary to combine the above formulas to generate coefficients for each model with a mean of zero and a variance of... Independent Gaussian random numbers After (coefficients), the initial discrete phase screen is obtained through linear superposition. The corresponding formula is:

[0047] ;

[0048] For light waves propagating along the z-axis, the cumulative phase disturbance caused by turbulence can be condensed into an equivalent thin phase screen. And as a discrete phase screen, its formula is:

[0049] ;

[0050] The mathematical framework for the complete process of optical field propagation is based on the theory of angular spectrum propagation. When the phase screen is placed at the beginning of propagation, the evolution of the optical field can be divided into two stages: phase modulation and free-space propagation. Let the initial optical field be... The optical field U'(x,y,0) modulated by the phase screen is:

[0051] U'(x,y,0)= ;

[0052] The phase-modulated light field U'(x,y,0) continues to propagate to the receiving plane. After propagating z meters, the final output field... for:

[0053] ;

[0054]

[0055] in, , Let each represent the i-th Zernike polynomial. and the j-th Zernike polynomial Angular frequency, , Let i and j represent the radial frequencies of the i-th and j-th Zernike polynomials, respectively. This represents a constant value (1 when i and j have the same parity; otherwise, 0). Represents the Gamma function. Indicates the beam diameter. Indicates the coherence length. Indicates atmospheric turbulence, This represents the summation function. These represent the normalized radial and angular directions, respectively. Represents coefficients and The energy values ​​between Indicates the index variable (the ordinal number of each term in the summation expansion). , , These represent the Zernike polynomials with different angular frequencies. , Let these represent the cosine function and the sine function, respectively. Indicates the wavenumber of light. The thickness of the turbulent layer in the light transmission path. Represents the frequency response factor. Indicates the coherence length. It represents the transmission path length (i.e., the distance light travels through the turbulent region of the atmosphere). This represents the atmospheric refractive index structure constant. This indicates the maximum number of terms to expand (which determines the precision of the expansion; the larger Jmax is, the more refined the expansion). Let j represent the j-th basis function. This indicates the integration operation. This indicates the fluctuation in refractive index. Indicates the equivalent action length. This represents the equivalent or effective value of the refractive index perturbation along the light propagation direction (z direction) at point (x, y). The base of the natural logarithm. These represent the spatial frequencies in the x and y directions, respectively. Represents the axial distance of light propagation. Represents the transfer function. Indicates weight, Represents the Fourier function. This represents the inverse Fourier function.

[0056] In addition, since only when -| | The value must be a non-negative even number to ensure the correct invocation of the radial polynomial formula, thus, and All are integers and satisfy ≤ , -| | is an even number.

[0057] S2. Based on the light field propagation process, determine the differentiable propagation operator; based on the supervision error and the differentiable propagation operator, construct the error-physical constraint loss function; the error-physical constraint loss function includes the supervision loss function and the physical consistency constraint loss function;

[0058] S2 includes:

[0059] S21. The optical field propagation process based on the angular spectrum propagation theory is constructed using a differentiable propagation operator through Fourier transform; the formula for the differentiable propagation operator is the same as the formula for the transfer function.

[0060] S22. Calculate the light intensity during the propagation of the light field, and construct a physical consistency constraint loss function based on the differentiable propagation operator;

[0061] Physical consistency constraint loss function The corresponding formula is:

[0062] ;

[0063] S23. Calculate the mean square error between the training turbulent phase screen and the real turbulent phase screen, and construct the supervised loss function; the formula for the supervised loss function is:

[0064] ;

[0065] ;

[0066] in, (·) represents the mean square error function. Indicates the incident light field. Represents a true turbulent phase screen. Indicates light intensity (distribution of intensity of distorted light spot). This represents the training turbulence phase screen. This indicates that it is obtained through a differentiable propagation operator. This represents the parameters of the PINN network. This indicates the PINN network.

[0067] S24. Construct an error-physical constraint loss function based on the supervised loss function and the physical consistency constraint loss function. The corresponding formula is:

[0068] ;

[0069] in, , Both represent loss weights, used to balance supervision error and physical consistency constraints.

[0070] S3. Construct an initial turbulence inversion model; Based on the error-physical constraint loss function and inversion training data, train the initial turbulence inversion model through grid loss and random uniform perturbation to obtain the turbulence inversion model; The initial turbulence inversion model adopts the PINN model;

[0071] By training the PINN network on a large number of simulated samples, it can gradually learn the nonlinear mapping relationship between the distorted light spot and the phase screen. Finally, when a distorted Gaussian light spot obtained from the experiment is input, the network can output the corresponding phase distribution, realizing phase retrieval and wavefront correction based on artificial intelligence.

[0072] Therefore, the purpose of introducing grid loss is to discretize the training samples into uniformly distributed grid points in space, so that each grid point corresponds one-to-one with the spatial position of the light spot or phase screen, thereby characterizing the model prediction error at a local scale. By calculating the local loss value of each grid point and adjusting the sampling probability accordingly, the model can adaptively focus on high-error regions during training, achieving fine-grained learning of complex speckle structures and edge distortion regions. Simultaneously, by combining a random uniform perturbation mechanism to perturb the coordinates of resampling points, the network's adaptability to continuous spatial distribution can be enhanced, effectively suppressing overfitting and improving generalization performance. By training the PINN network on a large number of simulated samples, the network can gradually learn the nonlinear mapping relationship between the distorted light spot and the phase screen. Finally, when a distorted Gaussian light spot obtained in the experiment is input, the network can output the corresponding phase distribution, realizing phase retrieval and wavefront correction based on artificial intelligence.

[0073] S31. Construct an initial turbulence inversion model based on the PINN model, and use the training turbulence phase screen and the training distortion spot as the input and output of the initial turbulence inversion model, respectively.

[0074] S32. Divide the spatial range of the training turbulent phase screen or the training distorted spot into uniformly distributed discrete grid points to construct a dense grid; within the spatial coordinate range of the training turbulent phase screen or the training distorted spot, set the training turbulent phase screen or the training distorted spot as discrete grid points and uniformly distribute them in the grid within the spatial coordinate range.

[0075] S33. Input each discrete grid point into the initial turbulence inversion model, and calculate the grid loss value and sampling probability of each discrete grid point based on the error-physical constraint loss function;

[0076] The mesh loss value of each discrete mesh point is calculated based on the error-physical constraint loss function.

[0077] Then, according to the formula:

[0078] ;

[0079] Calculate sampling probability .

[0080] S34. Based on the sampling probability, resample each discrete grid point through the category distribution to obtain the resampled point set. ;

[0081] Specifically, firstly, each discrete grid point is divided into different categories according to preset rules (such as turbulence intensity level, spot error magnitude, etc.), and the proportion of each category is determined. Then, the discrete grid points are randomly sampled in a weighted manner according to each sampling probability, so that the sampled resampled point set is consistent with the preset category distribution in terms of category proportion.

[0082] Therefore, the formula for S34 is:

[0083]

[0084] ;

[0085] Represents category distribution, This represents the sampling probability from the first discrete grid point to the next discrete grid point. This represents the set of sampling probabilities for each discrete grid point. Represents the set of sampling probabilities The k-th category index obtained from sampling. This represents the sampling probability corresponding to the set of resampled points.

[0086] S35. Add uniformly distributed perturbation factors to the two-dimensional coordinate directions of each discrete grid point in the resampled point set to obtain the updated resampled point set.

[0087] The S35 includes:

[0088] S351, Based on the half-spacing of dense mesh in two-dimensional coordinate directions , Set a two-dimensional uniform distribution range ;

[0089] S352. Based on the two-dimensional distribution range, randomly generate perturbation factors in the two-dimensional coordinate directions. , The corresponding expression is: .

[0090] S353. Based on the perturbation factor, update the two-dimensional coordinates of each sampling point in the resampling point set, i.e., update the perturbation factor. , The coordinates of each sampling point are added to the two-dimensional coordinates of the sampling points to update their coordinate values, resulting in the updated set of resampled points.

[0091] S36. Based on the error-physical constraint loss function and the updated resampled point set, the network parameters of the initial turbulence inversion model are updated and iterated through the backpropagation algorithm to obtain the turbulence inversion model.

[0092] S4. A laser speckle experiment is conducted to generate real speckle data, which is then inverted using a turbulence inversion model to obtain a turbulence phase screen. Atmospheric turbulence parameters are calculated based on the turbulence phase screen. Atmospheric turbulence parameters include atmospheric refractive index structure constant, internal scale, and coherence length.

[0093] S4 includes:

[0094] S41. Construct the experimental optical path for the laser speckle method, and generate atmospheric turbulence data under different light intensities by adjusting the temperature gradient and airflow velocity of the atmospheric turbulence simulation cavity.

[0095] Specifically, the experimental optical path for the laser speckle method includes a laser, a spatial filter, a lens, a beam splitter, an atmospheric turbulence simulation cavity, and a beam quality analyzer, and is arranged according to... Figure 2 Arrange the positions as shown.

[0096] The laser beam emitted by the laser is shaped by a spatial filter, lens, and aperture, and then split by a beam splitter. One beam is monitored by an optical power meter, while the other enters an atmospheric turbulence simulation cavity with adjustable temperature gradient and airflow velocity. Within the cavity, the laser beam undergoes speckle distortion due to turbulence, and is then transmitted through a lens to a beam quality analyzer. A computer collects images of the laser beam under different turbulence conditions, thereby generating atmospheric turbulence data for different light intensities. Furthermore, to protect the laser beam after it passes through the atmospheric turbulence simulation cavity, a black sleeve of length d is used to encase the beam.

[0097] S42. Based on various atmospheric turbulence data, the corresponding distorted spot images are recorded using an optical quality meter to obtain the real spot data and displacement fluctuations;

[0098] In the turbulence conditions corresponding to the generated atmospheric turbulence data (such as turbulence states under different temperature gradients and airflow velocities), the laser beam after being disturbed by the atmospheric turbulence simulation cavity carries turbulence characteristics. Its distorted spot is monitored and recorded in real time by the optical quality instrument, which not only obtains the spatial light intensity distribution image of the spot (i.e., real spot data), but also simultaneously collects the dynamic offset information of the beam center during the propagation process (i.e., displacement fluctuation).

[0099] S43. Input the real spot data into the turbulence inversion model to perform inversion and obtain the turbulence phase screen;

[0100] The turbulence inversion model based on PINN, which was trained in the early stage, was adopted and the distorted light spot image obtained from the experiment was used as the model input. The PINN network has learned the nonlinear mapping relationship between "light spot intensity distribution - phase perturbation" through the supervision error and physical consistency constraints in the early stage. Therefore, it is no longer necessary to explicitly solve the light field propagation equation in the inversion stage. Instead, the corresponding turbulence phase distribution is directly output through the forward propagation of the network.

[0101] Because the sample size of real speckle data generated by the laser speckle method is limited, traditional inversion methods cannot achieve high-precision inversion of atmospheric turbulence parameters under limited sample conditions. However, by using the turbulence inversion model of this invention, the PINN architecture, which integrates physical constraints (differentiable propagation operators) and data-driven approaches, combined with a training strategy of grid loss and random uniform perturbation, can still accurately invert the turbulent phase screen under limited samples. Furthermore, it can calculate parameters such as atmospheric refractive index structure constant and coherence length with high precision, effectively solving the problems of accuracy and generalization when samples are limited.

[0102] S44. Calculate the internal scale based on displacement fluctuation;

[0103] S45. Based on the Kolmogorov turbulence model and turbulent phase screen, calculate the coherence length and atmospheric refractive index structure constant.

[0104] Specifically, when At that time, the internal scale The calculation formula is:

[0105] ;

[0106] when At that time, the internal scale The calculation formula is:

[0107] ;

[0108] in, The laser's angle of arrival is expressed as: ; This indicates the normalized intensity fluctuation (the proportion of light intensity deviating from the average value). Indicates displacement fluctuation; This indicates the length of the black sleeve that encloses the laser beam.

[0109] Coherence length The calculation formula is:

[0110] ;

[0111] Atmospheric refractive index structure constant The calculation formula is:

[0112] ;

[0113] like Figure 3 As shown, an atmospheric turbulence parameter inversion system based on a physical information neural network includes:

[0114] The training data generation module is used to generate statistical correlations of Zernike coefficients based on the Kolmogorov turbulence model, and combine angular spectrum propagation theory and adjust the coherence length to generate inversion training data.

[0115] The loss function construction module is used to determine the differentiable propagation operator based on the light field propagation process; and to construct the error-physical constraint loss function based on the supervision error and the differentiable propagation operator.

[0116] The model training module is used to construct the initial turbulence inversion model. Based on the error-physical constraint loss function and the inversion training data, the initial turbulence inversion model is trained through grid loss and random uniform perturbation to obtain the turbulence inversion model.

[0117] The inversion module is used to conduct light spot experiments using the laser speckle method, generate real light spot data, and perform inversion using a turbulence inversion model to obtain a turbulence phase screen; atmospheric turbulence parameters are calculated based on the turbulence phase screen.

[0118] The loss function construction module includes:

[0119] Operator building unit, used for the optical field propagation process based on angular spectrum propagation theory, constructs differentiable propagation operators through Fourier transform;

[0120] The first loss calculation unit is used to calculate the light intensity during the light field propagation process and construct a physical consistency constraint loss function based on the differentiable propagation operator.

[0121] The second loss calculation unit is used to calculate the mean square error between the training turbulent phase screen and the real turbulent phase screen, and to construct the supervised loss function.

[0122] The third loss calculation unit is used to construct the error-physical constraint loss function based on the supervised loss function and the physical consistency constraint loss function.

[0123] The model training module includes:

[0124] The model building unit is used to build an initial turbulence inversion model based on the PINN model, and uses the training turbulence phase screen and the training distortion spot as the input and output of the initial turbulence inversion model, respectively.

[0125] Mesh building units are used to divide the spatial range of the training turbulent phase screen or the training distorted spot into uniformly distributed discrete grid points to build a dense grid;

[0126] The computational unit is used to input each discrete grid point into the initial turbulence inversion model and calculate the grid loss value and sampling probability of each discrete grid point based on the error-physical constraint loss function.

[0127] The resampling unit is used to resample each discrete grid point based on the sampling probability and the class distribution to obtain a set of resampled points.

[0128] The update unit is used to add uniformly distributed perturbation factors to the two-dimensional coordinate directions of each discrete grid point in the resampled point set to obtain the updated resampled point set.

[0129] The training iteration unit is used to update the network parameters of the initial turbulence inversion model based on the error-physical constraint loss function and the updated resampled point set, and then iterates to obtain the turbulence inversion model.

[0130] The update unit includes:

[0131] Range setting sub-cells are used to set the range of a two-dimensional uniform distribution based on the half-spacing of the dense grid in the two-dimensional coordinate direction;

[0132] The perturbation factor calculation subunit is used to randomly generate perturbation factors in the two-dimensional coordinate direction based on the two-dimensional distribution range.

[0133] The update sub-unit is used to update the two-dimensional coordinates of each sampling point in the resampled point set based on the perturbation factor, so as to obtain the updated resampled point set.

[0134] It should be noted that the specific methods by which each module performs operations in the system described in the above embodiments have been described in detail in the embodiments related to the device, and will not be elaborated here.

[0135] Example 2:

[0136] Three different values ​​of coherence length were set ( The values ​​are 0.0017m, 0.017m, and 0.17m respectively. Simulations using Zernike polynomials yielded distorted light spots as shown below. Figures 4 to 6 As shown. Based on Figures 4 to 6 The distorted light spot is used to train the PINN network structure to obtain a turbulence inversion model. The distorted light spot image is then obtained using the laser speckle method, such as... Figure 7 As shown. Finally, the distorted light spot image is input into the turbulence inversion model for inversion, and the obtained turbulence phase screen is as follows. Figure 8 As shown. Figure 8The turbulent phase screen in the model exhibits multi-scale phase fluctuations that perfectly match the physical characteristics of atmospheric turbulence. Different color gradients fall within a reasonable range of phase fluctuations, accurately reproducing the disturbance structure of turbulence from large to small scales. The phase distribution of the turbulent phase screen is continuous and free of obvious non-physical artifacts, further demonstrating that the phase information obtained through the turbulence inversion model is physically consistent and does not introduce spurious features. The detail richness of the turbulent phase screen highly matches the statistical characteristics of real turbulence, improving the accuracy of atmospheric turbulence parameter calculations and fully validating PINN's excellent accuracy performance in turbulence phase inversion tasks.

[0137] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0138] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for inverting atmospheric turbulence parameters based on a physical information neural network, characterized in that, include: The statistical correlation of Zernike coefficients is generated based on the Kolmogorov turbulence model. Combined with angular spectrum propagation theory and the coherence length is adjusted, inversion training data is generated. The inversion training data includes training turbulence phase screens and training distortion spots under different coherence lengths. Based on the light field propagation process, a differentiable propagation operator is determined; based on the supervision error and the differentiable propagation operator, an error-physical constraint loss function is constructed; the error-physical constraint loss function includes a supervision loss function and a physical consistency constraint loss function. An initial turbulence inversion model is constructed; based on the error-physical constraint loss function and inversion training data, the initial turbulence inversion model is trained through grid loss and random uniform perturbation to obtain the turbulence inversion model; the initial turbulence inversion model adopts the PINN model; A laser speckle method was used to conduct a light spot experiment, generating real light spot data. This data was then inverted using a turbulence inversion model to obtain a turbulence phase screen. Atmospheric turbulence parameters were calculated based on the turbulence phase screen.

2. The atmospheric turbulence parameter inversion method based on a physical information neural network according to claim 1, characterized in that, The generated inversion training data includes: Based on the angular and radial frequencies, the order-related structure factor is calculated, and the radial polynomial is calculated through hypergeometric functions. A Kolmogorov turbulence model was constructed and simulated, and energy relationships were generated based on the coherence length. Based on energy relationships and order-related structural factors, statistical correlations of Zernike coefficients are set and used as Zernike coefficient covariance constraints; the Zernike coefficient covariance constraints include energy constraints and individual Zernike coefficient variances. Based on the Zernike coefficient covariance constraint and radial polynomial, N Zernike coefficients are generated. Randomly adjust the coherence length, calculate the Zernike coefficients under different coherence lengths, and generate a set of Zernike coefficients; Based on the Zernike coefficient set and Zernike polynomial, the discrete turbulence phase screen is calculated to obtain the trained turbulence phase screen; Based on the angular spectrum propagation theory, the transmission process of the light field after passing through the training turbulent phase screen is simulated to generate a training distorted light spot.

3. The atmospheric turbulence parameter inversion method based on a physical information neural network according to claim 1, characterized in that, The construction error-physical constraint loss function includes: The optical field propagation process based on the angular spectrum propagation theory is constructed using a differentiable propagation operator through Fourier transform; Calculate the light intensity during the propagation of the light field, and construct a physical consistency constraint loss function based on the differentiable propagation operator; Calculate the mean square error between the trained turbulent phase screen and the real turbulent phase screen, and construct a supervised loss function; An error-physical constraint loss function is constructed based on the supervised loss function and the physical consistency constraint loss function.

4. The atmospheric turbulence parameter inversion method based on a physical information neural network according to claim 1, characterized in that, The initial turbulence inversion model is trained using grid loss and random uniform perturbation, including: An initial turbulence inversion model is constructed based on the PINN model, with the training turbulence phase screen and the training distortion spot used as the input and output of the initial turbulence inversion model, respectively. The spatial range of the training turbulent phase screen or the training distorted spot is divided into uniformly distributed discrete grid points to construct a dense grid; Each discrete grid point is input into the initial turbulence inversion model, and the grid loss value and sampling probability of each discrete grid point are calculated based on the error-physical constraint loss function. Based on the sampling probability, each discrete grid point is resampled according to the category distribution to obtain the resampled point set; A uniformly distributed perturbation factor is added to the two-dimensional coordinate direction of each discrete grid point in the resampled point set to obtain the updated resampled point set. Based on the error-physical constraint loss function and the updated resampled point set, the network parameters of the initial turbulence inversion model are updated and iterated through the backpropagation algorithm to obtain the turbulence inversion model.

5. The atmospheric turbulence parameter inversion method based on a physical information neural network according to claim 4, characterized in that, The updated set of resampled points includes: A two-dimensional uniform distribution range is set based on the half-spacing of the dense grid in the two-dimensional coordinate direction; Based on the two-dimensional distribution range, perturbation factors are randomly generated in the two-dimensional coordinate directions; Based on the perturbation factor, the two-dimensional coordinates of each sampling point in the resampling point set are updated to obtain the updated resampling point set.

6. The atmospheric turbulence parameter inversion method based on a physical information neural network according to claim 1, characterized in that, The calculation of atmospheric turbulence parameters based on the turbulence phase screen includes: An experimental optical path for laser speckle method was constructed, and atmospheric turbulence data under different light intensities were generated by adjusting the temperature gradient and airflow velocity of the atmospheric turbulence simulation cavity. Based on various atmospheric turbulence data, the corresponding distorted spot images are recorded by an optical quality meter to obtain the real spot data and displacement fluctuations; The real spot data is input into the turbulence inversion model for inversion to obtain the turbulence phase screen; Internal scale is calculated based on displacement fluctuations; Based on the Kolmogorov turbulence model and turbulent phase screen, the coherence length and atmospheric refractive index structure constant are calculated.

Images