A method for generating atmospheric turbulence phase screens based on hierarchical physical constraints

Abstract

This invention discloses a method for generating atmospheric turbulence phase screens based on hierarchical physical constraints, belonging to the interdisciplinary field of optical communication and artificial intelligence. This method combines a diffusion probability model with hierarchical atmospheric physical constraints, establishing independent physical constraint loss functions for the atmospheric boundary layer, troposphere, and stratosphere. Power spectral density constraints and structure function constraints ensure that the generated phase screens conform to the statistical characteristics of turbulence in each layer. A physics-guided attention mechanism enhances the feature learning of each layer's phase screens. A time-dependent constraint weighting strategy is designed to adaptively adjust the physical constraint strength during diffusion denoising. This invention solves the technical problems of existing methods, such as ignoring vertical layer differences, insufficient physical consistency, and the dependence of generation quality on large amounts of labeled data. It is particularly suitable for high-fidelity atmospheric turbulence modeling in satellite laser communication links and can also be widely applied to fields such as free-space optical communication system simulation and adaptive optics system design.

Description

Technical Field

[0001] This invention belongs to the fields of atmospheric optics and deep learning technology, and particularly relates to a method for generating atmospheric turbulence phase screens based on hierarchical physical constraints. Background Technology

[0002] Atmospheric turbulence-induced wavefront distortion is a key factor affecting long-distance laser communication, astronomical observation, and other applications. Particularly in satellite laser communication systems, laser signals must traverse the entire atmosphere from the ground to satellite orbit, experiencing disturbances from different turbulent flows in the boundary layer, troposphere, and stratosphere, leading to severe phase distortion and beam spread, directly impacting communication link performance. Accurately simulating the phase screens of these three different atmospheric turbulence layers is crucial for satellite laser communication system design, link budgeting, and verification of adaptive optics compensation algorithms.

[0003] Existing methods for generating phase screens mainly suffer from the following technical problems:

[0004] First, it neglects the characteristics of high-level stratification. Traditional methods typically use a single power spectrum model to describe the entire atmospheric path, which cannot accurately reflect the turbulent physics of the boundary layer, troposphere, and stratosphere. In reality, the boundary layer follows classical Kolmogorov statistical laws, while the troposphere and stratosphere exhibit non-Kolmogorov characteristics. Key parameters such as the spectral index, energy distribution, and outer scale of the power spectrum differ fundamentally among each layer. A single model cannot simultaneously satisfy the physical characteristics of each layer.

[0005] Second, there is insufficient physical constraint. Existing deep learning methods mainly rely on data-driven approaches and lack explicit modeling of physical constraints such as power spectral density and structure function. This results in generated phase screens that may appear visually similar but deviate from real turbulence in statistical properties, affecting the accuracy of subsequent applications.

[0006] Third, the interlayer relationships are missing. The turbulence intensity of the three atmospheric layers is constrained by the variation of atmospheric refractive index structure parameters with altitude, and there is an inherent physical correlation between the layers. Existing methods generate phase screens for each layer independently, ignoring this interlayer relationship, which may lead to non-physical phase distributions.

[0007] Fourth, it relies on a large amount of labeled data. Traditional supervised learning methods require a large amount of real or high-precision simulated phase screen data as training labels, but obtaining high-quality labeled data is costly, which limits the widespread application of the method.

[0008] Therefore, there is an urgent need for a phase screen generation method that can accurately simulate the characteristics of stratified atmospheric turbulence, integrate physical constraints, and reduce dependence on labeled data. Summary of the Invention

[0009] This invention proposes a method for generating atmospheric turbulence phase screens based on hierarchical physical constraints, aiming to address the technical problems of current atmospheric turbulence phase screen generation methods, such as neglecting height-level hierarchical characteristics, insufficient physical constraints, missing inter-layer relationships, and reliance on large amounts of labeled data. This method achieves high-fidelity phase screen generation that accurately reflects the different statistical characteristics of the boundary layer, troposphere, and stratosphere through deep coupling of a diffusion probability model and atmospheric physical priors. This provides an accurate physical model for satellite-to-ground laser communication link simulation and adaptive optics system design.

[0010] The above objectives are achieved through the following technical solutions:

[0011] A method for generating atmospheric turbulence phase screens based on hierarchical physical constraints, comprising the following steps:

[0012] S1. The atmosphere is divided into three atmospheric turbulence intensity layers: the boundary layer, the troposphere, and the stratosphere. Power spectrum theoretical models are constructed for each layer using the corresponding spectral indices.

[0013] S2. Based on the power spectrum theoretical model constructed in step S1, the spectral inversion method is used to generate training samples of atmospheric turbulence phase screens at each layer. The physical condition parameters are associated with the training samples to construct an initial dataset. The initial dataset is then normalized and divided into samples to construct a diffusion algorithm training dataset.

[0014] S3. Construct a physics-guided diffusion generation network, input the diffusion algorithm training dataset described in step S2 into the diffusion generation network, embed the condition vector obtained by encoding the physical condition parameters and the time step into the diffusion generation network to perform forward computation, and output the boundary layer prediction phase screen, tropospheric prediction phase screen and stratospheric prediction phase screen.

[0015] S4. For the predicted phase screen output in step S3, calculate the hierarchical physical constraint loss function based on the power spectrum theoretical model constructed in step S1 to verify physical compliance. The hierarchical physical constraint loss function includes the power spectral density loss for constraining the frequency domain energy distribution and the structure function loss for constraining spatial correlation.

[0016] S5. For the three-layer predicted phase screen output in step S3, based on the physical distribution law of atmospheric refractive index structural parameters with altitude, calculate the inter-layer relationship constraint loss function used to constrain the relative proportion of variance of the three-layer predicted phase screen, so as to ensure that the total energy distribution of the generated three-layer predicted phase screen on the vertical path conforms to the real atmospheric physical profile.

[0017] S6. Combining the hierarchical physical constraint loss function of step S4, the inter-layer relationship constraint loss function of step S5, and the basic noise reduction loss function, the total loss function is calculated using a time-dependent weight strategy. The total loss function is then used to back-update the weight parameters of the diffusion generation network described in step S3 to obtain the trained diffusion generation model.

[0018] S7. Using the diffusion generation model trained in step S6, perform reverse denoising sampling to generate a three-layer atmospheric turbulence phase screen that satisfies physical constraints from the initial Gaussian noise.

[0019] Further, in step S1, the boundary layer corresponds to an altitude of 0-2km and has a spectral index α=11 / 3; the troposphere corresponds to an altitude of 2-10km and has a spectral index α=10 / 3; and the stratosphere corresponds to an altitude of 10-20km and has a spectral index α=5.

[0020] Furthermore, the theoretical model of the power spectrum of each layer in step S1 adopts the modified von Kármán form, and the expression is as follows:

[0021]

[0022] in, The spatial power spectral density represents the refractive index fluctuations. For space wavenumber, Altitude The refractive index is the structural constant. The outer-scale cutoff wavenumber, The inner-scale cutoff wavenumber, This is the normalization coefficient related to the spectral index.

[0023] Furthermore, the diffusion generation network in step S3 includes a physically consistent attention module, which calculates the attention after physical guidance. The formula is as follows:

[0024]

[0025] Where Q, K, and V are the query matrix, key matrix, and value matrix, respectively, and M is the frequency domain importance mask calculated based on the theoretical distribution of the power spectrum of the corresponding layer. This represents element-wise multiplication. To query the feature dimensions of the matrix and the key matrix, the superscript T indicates the matrix transpose operation.

[0026] Furthermore, the power spectral density loss of the constrained frequency domain energy distribution described in step S4 The calculation method is as follows:

[0027]

[0028] in, This is the predicted phase screen for this layer. For two-dimensional Fourier transform, For the j-th sampling spatial wavenumber point, This is the theoretical model of the power spectrum corresponding to this layer. This represents the total number of sampling points.

[0029] The structure function loss of constraint space correlation mentioned in step S4 The calculation method is as follows:

[0030]

[0031] in, Let q be the spatial separation distance. This represents the total number of points in the total sampling interval. To predict the structure function of the phase screen, This is the theoretical structure function corresponding to this layer.

[0032] Furthermore, the inter-layer relationship constraint loss function described in step S5 The calculation method is as follows:

[0033]

[0034] in, , , These are the statistical variances of the boundary layer, troposphere, and stratosphere phase screens in the predicted output, respectively. , , This represents the theoretical expected variance of the boundary layer, troposphere, and stratosphere, calculated based on the input physical parameters and the height profile model.

[0035] Furthermore, the total loss function described in step S6 The calculation method is as follows:

[0036]

[0037] in, The basic denoising loss function is used to measure the difference between predicted noise and actual noise, and is calculated as follows:

[0038]

[0039] in, Represents the mathematical expectation operator; The phase screen is injected with real Gaussian random noise; The noise component predicted by the network; For the current time step The state of the noisy phase screen under the following conditions; Signals guided by physical conditions; This indicates the mean square error calculation. This is the weighted average of the losses from the three-layer hierarchical physical constraints. Loss due to inter-layer relationship constraints. For time-dependent weighting functions, For diffusion time step, The total number of diffusion steps, and These are the weighting coefficients.

[0040] Furthermore, the reverse denoising sampling process described in step S7 employs the following iterative formula:

[0041]

[0042] in, Let t be the phase screen state at the t-th time step. This represents the phase screen state at time step t-1. For physical condition vectors, To predict noise for the network, and For noise scheduling parameters, Standard Gaussian noise, This represents the random noise coefficient during the sampling process.

[0043] The advantages of this invention compared to the prior art are:

[0044] (1) The present invention provides a complete process from training data generation to model output. It systematically generates three-layer phase screen training data that conforms to physical laws through spectral inversion method, which solves the problem of lack of data generation process in traditional methods and reduces data acquisition cost.

[0045] (2) This invention accurately reflects the different spectral characteristics of the boundary layer, troposphere and stratosphere through hierarchical modeling and independent physical constraints. The generated phase screen is highly consistent with the theory in terms of statistical indicators such as power spectrum, structure function and variance. The physical fidelity is significantly better than the existing methods. It is particularly suitable for full-path turbulence modeling of satellite laser communication.

[0046] (3) The present invention ensures that the phase intensity ratio of each layer conforms to the variation law of refractive index structure parameters with height by constraining the interlayer relationship, avoids non-physical phase distribution, and improves the credibility of the overall link simulation.

[0047] (4) Through the physical parameter embedding mechanism, the present invention allows users to flexibly specify physical parameters such as the height of each layer, turbulence intensity, and propagation distance, and generate phase screens that meet specific application requirements, which can simulate satellite laser communication links under different zenith angles, different orbital altitudes, and different atmospheric conditions. Attached Figure Description

[0048] Figure 1 A flowchart illustrating the design of an atmospheric turbulence phase screen generation method based on hierarchical physical constraints according to the present invention.

[0049] Figure 2 This is a schematic diagram of the physically guided diffusion generation network architecture of the present invention.

[0050] Figure 3 This is a schematic diagram of the U-Net network architecture in the diffusion generation network of the present invention;

[0051] Figure 4 This is a schematic diagram illustrating the atmospheric turbulence phase screen effect generated by the present invention. Figure 4 (a), (b), and (c) in the figure respectively show the atmospheric turbulence phase screens in the boundary layer, troposphere, and stratosphere;

[0052] Figure 5 A comparison chart showing the verification results of the phase structure function of the phase screen generated in this invention. Figure 5 (a), (b), and (c) in the figure show the verification results of the phase structure functions of the boundary layer, troposphere, and stratosphere, respectively. Detailed Implementation

[0053] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0054] This invention provides a method for generating atmospheric turbulence phase screens based on layered physical constraints. Its core logic lies in the deep integration of the generation capability of the diffusion probability model with the layered power spectrum, structure function, and vertical profile characteristics in atmospheric optics. The design flow of this method for generating atmospheric turbulence phase screens based on layered physical constraints is shown in Figure 1. The specific execution flow of this embodiment strictly corresponds to the steps in the claims and is divided into the following seven stages:

[0055] S1 atmospheric environment stratification physical modeling ensures that the physical model can cover the non-uniform characteristics of the atmosphere throughout the entire path:

[0056] S1.1 First, based on the physical characteristics of the entire path of satellite-to-ground laser communication, the atmosphere is divided into three turbulent layers with independent statistical characteristics:

[0057] S1.2 Boundary Layer: The altitude ranges from 0 to 2 km. Turbulence in this layer is greatly affected by the surface. The spectral index is set to α = 11 / 3, and a power spectrum model that conforms to the classical Kolmogorov statistical law is adopted.

[0058] S1.3 Troposphere: Altitude range of 2~10km, spectral index set at α= 10 / 3, using a non-Kolmogorov spectral model.

[0059] S1.4 Stratosphere: Altitude range of 10–20 km, spectral index set at α = 5, using a non-Kolmogorov spectral model. This layering provides differentiated physical benchmarks for subsequent processes.

[0060] High-fidelity generation and refined preprocessing of S2 hierarchical training data:

[0061] S2.1 Based on the power spectrum theoretical models constructed in step S1, perform data preparation. Each power spectrum theoretical model adopts the modified von Kármán form, expressed as follows:

[0062]

[0063] in, The spatial power spectral density represents the refractive index fluctuations. For space wavenumber, Altitude The refractive index is the structural constant. The outer-scale cutoff wavenumber, The inner-scale cutoff wavenumber, This is the normalization coefficient.

[0064] S2.2 uses spectral inversion to generate training samples for the atmospheric turbulence phase screen at each layer. The refractive index structure constant is then used. Physical condition parameters such as external scale L0, Fried parameter r0, layer height h, and spectral index α are associated and mapped with the corresponding training samples to construct the initial dataset.

[0065] S2.3 Normalizes the initial dataset, sets the number of samples generated for each phase screen to 1000, and finally obtains 3000 phase screen samples with consistency and reliability. These samples are then divided into training, validation and test sets in an 8:1:1 ratio to form the diffusion algorithm training dataset, ensuring that the diffusion algorithm can learn the physical distribution across scales.

[0066] Architecture construction of S3 physical guided diffusion generation network;

[0067] S3.1 In this embodiment, a diffusion generation network integrating a physical guidance mechanism is constructed. The architecture of this physically guided diffusion generation network is shown in Figure 2. This network adopts an improved U-Net structure, and the specific U-Net structure and conditional injection details are shown in Figure 3.

[0068] S3.2 The encoder path of U-Net contains multiple residual blocks and downsampling layers to extract multi-scale features, while the decoder path of U-Net reconstructs the phase screen through upsampling layers and residual blocks, and directly transmits the encoder features to the corresponding decoder layer through skip connections to preserve high-frequency detail information.

[0069] S3.3 The refractive index structure constants of the boundary layer, troposphere, and stratosphere from step S2 are... external scale Fried parameters Floor height Spectral Index The physical condition vector and the diffusion time step embedding information are encoded by a multilayer perceptron and then injected into the residual block of the network.

[0070] S3.4 Introduces a physically consistent attention module into the network. The module calculates the attention after physical guidance using the following formula:

[0071]

[0072] Where Q, K, and V are the query matrix, key matrix, and value matrix, respectively, and M is the frequency domain importance mask calculated based on the theoretical distribution of the power spectrum of the corresponding layer. This represents element-wise multiplication. To query the feature dimensions of the matrix and the key matrix, the superscript T indicates the matrix transpose operation.

[0073] The diffusion generation network described in S3.5 performs forward computation and outputs the predicted phase screens of atmospheric turbulence at each layer. .

[0074] S4-based hierarchical physical loss calculation based on dual constraints in the frequency and spatial domains:

[0075] S4.1 For the predicted phase screen output in step S3, perform physical compliance verification based on the power spectrum theoretical model constructed in step S1.

[0076] S4.2 For any layer of the predicted phase screen, its power spectral density loss The calculation method is as follows:

[0077]

[0078] in, For the predicted phase screen of each layer, For two-dimensional Fourier transform, For the j-th sampling spatial wavenumber point, This is the theoretical model of the power spectrum corresponding to this layer. This represents the total number of sampling points.

[0079] S4.3 Calculate the structure function of the predicted phase screen at different spatial scales in the spatial domain. Compared with theoretical value mean square error The calculation formula is as follows:

[0080]

[0081] in, Let q be the spatial separation distance. The number of points in the total sampling interval is a constraint designed to ensure that the statistical correlation of each phase screen generated in the spatial domain conforms to the spectral slope characteristics set in step S1.

[0082] S5 is based on parallel computation of multidimensional loss functions according to physical laws;

[0083] S5.1 Calculates the interlayer energy distribution constraints based on the three-layer predicted phase screen output from step S3. This is based on atmospheric refractive index structure parameters. Physical profile variation with height, and calculation of inter-layer relationship constraint loss function. This loss is defined by comparing the deviation between the actual statistical variance of each predicted phase screen and the theoretical expected variance calculated from the input physical parameters. The formula is as follows:

[0084]

[0085] in, , , These are the statistical variances of the boundary layer, troposphere, and stratosphere phase screens in the predicted output, respectively. , , This represents the theoretical expected variance of the boundary layer, troposphere, and stratosphere, calculated based on the input physical parameters and the height profile model.

[0086] S6 Total Loss Dynamic Weighted Feedback and Network Parameter Optimization;

[0087] S6.1 Iterative optimization of the execution model, total loss function The calculation method is as follows:

[0088]

[0089] in, The basic denoising loss function is used to measure the difference between predicted noise and actual noise, and is calculated as follows:

[0090]

[0091] in, Represents the mathematical expectation operator; The phase screen is injected with real Gaussian random noise; The noise component predicted by the network; For the current time step The state of the noisy phase screen under the following conditions; Signals guided by physical conditions; This indicates the mean square error calculation. This is the weighted average of the losses from the three-layer hierarchical physical constraints. Loss due to inter-layer relationship constraints. For time-dependent weighting functions, For diffusion time step, The total number of diffusion steps, and These are the weighting coefficients. Utilizing... The S3 network parameters are updated through backpropagation until the model converges.

[0092] S6.2 This embodiment calculates the physical loss term. This loss term is not a single value, but a weighted sum of the three types of physical constraints calculated in steps S4 and S5. Specifically, the independent loss values ​​for the boundary layer, troposphere, and stratosphere in terms of power spectral density and structure function are first calculated separately, and then the average value of the three layers is taken to obtain the global loss. and Then, based on the hyperparameters set in the configuration file, these three factors are weighted and summed using the following formula:

[0093]

[0094] S6.3 In this specific embodiment, in order to balance the differences in magnitude of the various physical quantities, a weighting coefficient λ is set. PSD +λ SF =1, thus forming a multidimensional constraint on frequency domain distribution, spatial correlation and overall strength.

[0095] S7 Physical Consistency Backsampling and Atmospheric Phase Screen Generation.

[0096] S7.1 performs inverse denoising sampling using the trained model:

[0097]

[0098] in, Let t be the phase screen state at the t-th time step. This represents the phase screen state at time step t-1. For physical condition vectors, To predict noise for the network, and For noise scheduling parameters, Standard Gaussian noise, This represents the random noise coefficient during the sampling process.

[0099] S7.2 The effect of the three-layer atmospheric turbulence phase screen generated by this invention is as follows: Figure 4 As shown, each phase screen exhibits a high degree of consistency in both visual characteristics and physical statistics.

[0100] To evaluate the quality of the atmospheric turbulence phase screen generated by the diffusion model based on hierarchical physical constraints proposed in this invention, and especially to verify whether the generated results conform to the statistical laws of real atmospheric turbulence, this embodiment uses the phase structure function as the core evaluation index.

[0101] The validation process employed Monte Carlo statistical sampling. For each phase screen generated by the model (boundary layer, troposphere, stratosphere), a large number of pixel pairs were randomly selected in the spatial domain. Different spatial separation distances were calculated. Statistical mean of the squared phase difference The calculation formula is as follows:

[0102] ,in, Indicates position Phase value at that point, It represents the ensemble average.

[0103] To visually demonstrate the verification results, this embodiment compares the structure function curve of the model-generated phase screen with the theoretical structure function curve in a logarithmic coordinate system. For example... Figure 5 As shown, the verification results of the phase structure functions of the three height layers generated by the method of this invention are presented. The scatter points in the figure represent the actual structure function values ​​calculated by the phase screen generated by the diffusion model, and the dashed lines represent reference lines calculated based on theoretical formulas. Figure 5 As shown in (a), for boundary layers that follow the Kolmogorov spectral statistics, a preset spectral index is used. The validation results show that the structure function of the generated data exhibits a good linear relationship in logarithmic coordinates, with a fitting slope of approximately 1.67 (i.e., ...). ), and Kolmogorov's theory predicts The scaling laws are highly compatible. For example... Figure 5 As shown in (b), a non-Kolmogorov spectrum (spectral index) is used for the troposphere. The theoretically corresponding slope of the structure function should be 1.33. As can be seen from the figure, the statistical scatter points generating the phase screen closely follow the theoretical dashed line, and the slope accurately reflects... Features, such as Figure 5 As shown in (c), the steep spectral model (spectral index) used for the stratosphere The theoretical structure function exhibits stronger spatial correlation, corresponding to a slope of 3.00. Verification results show that even under such high-order nonlinear physical constraints, the phase screen generated by the model maintains extremely high physical fidelity, with data points falling on the theoretical line with a slope of 3.00.

[0104] In summary, by comparing structure functions at different spatial scales, this invention demonstrates that the proposed method successfully addresses the problem of missing physical meaning in traditional deep learning generation methods. This is thanks to the hierarchical physical constraint loss introduced during training. With a time-dependent weighting strategy, the model not only generates visually realistic phase patterns, but more importantly, it strictly adheres to the specific physical laws of different altitude layers in terms of statistical properties (including Kolmogorov and non-Kolmogorov statistics). The generated phase screen exhibits extremely high physical consistency across the entire frequency band, meeting the stringent requirements of high-fidelity satellite laser communication link simulation and adaptive optics system performance evaluation.

Claims

1. A method for generating atmospheric turbulence phase screens based on hierarchical physical constraints, characterized in that, Includes the following steps: S1. The atmosphere is divided into three atmospheric turbulence intensity layers: the boundary layer, the troposphere, and the stratosphere. Power spectrum theoretical models are constructed for each layer using the corresponding spectral indices. S2. Based on the power spectrum theoretical model constructed in step S1, training samples of atmospheric turbulence phase screens at each layer are generated by the spectral inversion method. Physical condition parameters are associated with the training samples to construct an initial dataset. The initial dataset is then normalized and divided into samples to construct a diffusion algorithm training dataset. S3. Construct a physics-guided diffusion generation network, input the diffusion algorithm training dataset described in step S2 into the diffusion generation network, embed the condition vector obtained by encoding the physical condition parameters and the time step into the diffusion generation network to perform forward computation, and output the boundary layer prediction phase screen, tropospheric prediction phase screen and stratospheric prediction phase screen. S4. For the predicted phase screen output in step S3, calculate the hierarchical physical constraint loss function based on the power spectrum theoretical model constructed in step S1 to verify physical compliance. The hierarchical physical constraint loss function includes the power spectral density loss for constraining the frequency domain energy distribution and the structure function loss for constraining spatial correlation. S5. For the three-layer predicted phase screen output in step S3, based on the physical distribution law of atmospheric refractive index structural parameters varying with altitude, calculate the interlayer relationship constraint loss function used to constrain the relative proportion of the variance of the three-layer predicted phase screen, ensuring that the total energy distribution of the generated three-layer predicted phase screen on the vertical path conforms to the true atmospheric physical profile; the interlayer relationship constraint loss function The calculation method is as follows: ， in, , , These represent the statistical variances of the boundary layer, troposphere, and stratosphere phase screens in the predicted output, respectively. , , This refers to the theoretical expected variances of the boundary layer, troposphere, and stratosphere calculated based on the input physical parameters and the height profile model. S6. Combining the hierarchical physical constraint loss function of step S4, the inter-layer relationship constraint loss function of step S5, and the basic denoising loss function, the total loss function is calculated using a time-dependent weight strategy. The total loss function is then used to back-update the weight parameters of the diffusion generation network described in step S3 to obtain the trained diffusion generation model. S7. Using the diffusion generation model trained in step S6, perform reverse denoising sampling to generate a three-layer atmospheric turbulence phase screen that satisfies physical constraints from the initial Gaussian noise.

2. The method for generating an atmospheric turbulence phase screen based on hierarchical physical constraints according to claim 1, characterized in that, In step S1, the boundary layer corresponds to an altitude of 0-2km and has a spectral index α=11 / 3; the troposphere corresponds to an altitude of 2-10km and has a spectral index α=10 / 3; and the stratosphere corresponds to an altitude of 10-20km and has a spectral index α=5.

3. The method for generating an atmospheric turbulence phase screen based on hierarchical physical constraints according to claim 1, characterized in that, The theoretical model of the power spectrum of each layer in step S1 adopts the modified von Kármán form, and the expression is as follows: ， in, The spatial power spectral density represents the refractive index fluctuations. For space wavenumber, Altitude The refractive index structure constant is The outer-scale cutoff wavenumber, The cutoff wavenumber at the inner scale. This is the normalization coefficient related to the spectral index.

4. The method for generating an atmospheric turbulence phase screen based on hierarchical physical constraints according to claim 1, characterized in that, The diffusion generation network in step S3 includes a physically consistent attention module, which calculates the attention after physical guidance. The formula is as follows: ， Where Q, K, and V are the query matrix, key matrix, and value matrix, respectively, and M is the frequency domain importance mask calculated based on the theoretical distribution of the power spectrum of the corresponding layer. This represents element-wise multiplication. To query the feature dimensions of the matrix and the key matrix, the superscript T indicates the matrix transpose operation.

5. The method for generating an atmospheric turbulence phase screen based on hierarchical physical constraints according to claim 1, characterized in that, The power spectral density loss of the constrained frequency domain energy distribution mentioned in step S4 The calculation method is as follows: ， in, This is the predicted phase screen for this layer. For two-dimensional Fourier transform, For the j-th sampling spatial wavenumber point, This is the theoretical model of the power spectrum corresponding to this layer. This represents the total number of sampling points; The structure function loss of constraint space correlation mentioned in step S4 The calculation method is as follows: ， in, Let q be the spatial separation distance. This represents the total number of points in the total sampling interval. To predict the structure function of the phase screen, This is the theoretical structure function corresponding to this layer.

6. The method for generating an atmospheric turbulence phase screen based on hierarchical physical constraints according to claim 1, characterized in that, The total loss function described in step S6 The calculation method is as follows: ， in, The basic denoising loss function is used to measure the difference between predicted noise and actual noise, and is calculated as follows: ， in, Represents the mathematical expectation operator; The phase screen is injected with real Gaussian random noise; The noise component predicted by the network; For the current time step The state of the noisy phase screen under the following conditions; Signals guided by physical conditions; This indicates the mean square error calculation. This is the weighted average of the losses from the three-layered physical constraints. Loss due to inter-layer relationship constraints. For time-dependent weighting functions, For diffusion time step, The total number of diffusion steps, and These are the weighting coefficients.

7. The method for generating an atmospheric turbulence phase screen based on hierarchical physical constraints according to claim 1, characterized in that, The reverse denoising sampling process described in step S7 uses the following iterative formula: ， in, Let t be the phase screen state at the t-th time step. This represents the phase screen state at time step t-1. For physical condition vectors, To predict noise for the network, and For noise scheduling parameters, Standard Gaussian noise, This represents the random noise coefficient during the sampling process.

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