A method of predictive correction of wavefront distortion

Abstract

The application provides a wavefront distortion prediction correction method, and relates to the technical field of atmospheric turbulence prediction correction. The method comprises the following steps: acquiring a historical wavefront state time sequence collected by a wavefront sensor; inputting the historical sequence into a trained probability prediction model to output probability distribution parameters of a wavefront state at a future time; calculating a prediction uncertainty measure based on the probability distribution parameters; comparing the prediction uncertainty measure with a preset threshold to dynamically adjust a control parameter, and fusing a prediction value with a current measurement value to generate a control signal; and driving a wavefront corrector to realize closed-loop correction. The application explicitly quantifies the prediction uncertainty through a probability prediction framework, fits a complex turbulence distribution by using a negative log-likelihood function, improves noise robustness by combining Monte Carlo sampling, and constructs a confidence-driven adaptive control interface, thereby significantly improving the reliability and precision of wavefront correction in a complex turbulence environment.

Description

Technical Field

[0001] This application relates to the field of atmospheric turbulence prediction and correction technology, and more specifically, to a method for predicting and correcting wavefront distortion. Background Technology

[0002] Adaptive optics (AO) technology effectively suppresses the degradation of beam quality caused by atmospheric turbulence by measuring wavefront distortion caused by atmospheric turbulence in real time and compensating for it using a wavefront corrector to generate a conjugate phase. It has become a key technology in fields such as astronomical observation, laser communication, and high-energy laser transmission. A typical adaptive optics system includes a wavefront sensor, a controller, and a corrector. The wavefront sensor acquires the slope or phase distribution of the distorted wavefront at a fixed sampling frequency. The controller calculates a control signal based on the measurements, driving a deformable mirror to generate a compensating wavefront, thereby achieving dynamic correction of turbulent aberrations.

[0003] However, inherent time delays exist in practical adaptive optics systems. The readout time of the wavefront sensor, the calculation time of the controller, and the digital-to-analog conversion typically introduce a delay of 2–3 sampling periods, resulting in a significant lag between the compensated wavefront generated on the deformable mirror and the actual changing distorted wavefront. When the atmospheric coherence length is short and the Greenwood frequency is high, this lag effect can significantly increase the correction residual, and in severe cases, even lead to instability of the closed-loop system. Therefore, overcoming the effects of time delay and improving the dynamic correction performance of the system has become a research hotspot in the field of adaptive optics.

[0004] To address these issues, researchers have proposed various wavefront prediction and correction methods, attempting to use historical wavefront data to estimate the wavefront state at future moments in order to compensate for system delays.

[0005] Recursive Least Squares (RLS) is one of the earliest methods introduced into open-loop voltage prediction in adaptive optics. This method updates prediction weights by recursively minimizing the sum of squared errors, which can reduce time delay errors to some extent. However, RLS is based on a linear system model and the assumption that the error follows a Gaussian distribution. The wavefront evolution of actual atmospheric turbulence exhibits significant nonlinear characteristics, especially under strong turbulence conditions, leading to inherent model mismatch in linear prediction structures. Furthermore, the performance of RLS is highly dependent on the selection of the forgetting factor. Under low-light conditions or with high sensor noise, its recursive covariance matrix is ​​prone to ill-conditioned behavior, resulting in prediction divergence.

[0006] Predictive Fourier Control (PFC) is based on the Taylor frozen turbulence assumption and uses atmospheric crosswind speed in the Fourier domain to compensate for turbulence motion. While the physical meaning of this method is clear, its performance heavily relies on prior knowledge of the wind speed vector, making online real-time estimation impossible. Subsequent researchers proposed the Predictive Time-domain Correction (PTC) method, attempting to estimate wind speed in real-time from the closed-loop residual slope. However, this method uses the Gauss-Newton method for iterative solutions, resulting in slow convergence and limited real-time performance. Furthermore, the residual slope measurement itself loses a significant amount of crosswind information, affecting prediction accuracy.

[0007] In recent years, with the development of deep learning technology, Long Short-Term Memory (LSTM) networks have been applied to wavefront prediction due to their excellent nonlinear temporal modeling capabilities. LSTM effectively learns the long-term dependencies of turbulence evolution through gating mechanisms, without relying on physical priors such as wind speed. However, existing LSTM-based wavefront prediction and correction methods have the following shortcomings: First, LSTM outputs deterministic point predictions, failing to provide confidence intervals or probability distributions for the prediction results. When turbulence intensity changes abruptly or scintillation occurs, the model still outputs predictions in a "deterministic" form, but cannot inform the control system of the reliability of the current prediction. Second, the training process of LSTM typically aims to minimize the mean squared error (MSE). This loss function implicitly assumes that the prediction error follows a unimodal symmetric distribution. However, actual atmospheric turbulence data under strong turbulence conditions often exhibits time-varying non-Gaussian and multimodal distribution characteristics, causing LSTM to tend to learn "averaged" prediction results, smoothing out peaks and abrupt changes in the turbulent structure. Third, under low signal-to-noise ratio conditions, MSE loss is difficult to effectively distinguish between real turbulent dynamics and sensor noise, easily mislearning noise patterns as turbulent features, leading to overfitting and reducing the generalization ability and stability of the prediction.

[0008] Therefore, there is an urgent need for a wavefront distortion prediction and correction method that can overcome the above-mentioned defects in order to improve the dynamic correction performance and robustness of adaptive optics systems in complex turbulent environments. Summary of the Invention

[0009] The purpose of this application is to provide a method for predicting and correcting wavefront distortion, which can solve at least one of the technical problems mentioned above. The specific solution is as follows: According to a specific embodiment of this application, this application provides a method for predicting and correcting wavefront distortion, comprising the following steps: By measuring the incident beam using a wavefront sensor, wavefront state data that changes over time is obtained, and time-series wavefront state data is constructed. Training samples are constructed based on the time-series wavefront state data; A probability prediction model is constructed and trained based on the training samples, so that the probability prediction model establishes a mapping relationship between the historical wavefront state sequence and the probability distribution of the wavefront state at future time. The real-time acquired historical wavefront state sequence is input into the trained probability prediction model, which outputs the probability distribution parameters of the wavefront state at future time. The statistical expectation value of the probability distribution parameter is used as the wavefront prediction value, and the prediction uncertainty measure is calculated based on the probability distribution parameter. The prediction uncertainty metric is compared with a preset threshold, the control parameters are dynamically adjusted based on the comparison result, and the wavefront prediction value is fused with the current measured wavefront state based on the adjusted control parameters to generate a control signal. The control signal drives the wavefront corrector to generate a compensated wavefront, thereby achieving closed-loop correction of wavefront distortion.

[0010] Furthermore, the time-series wavefront state data includes: wavefront slope data or Zernike coefficient sequence.

[0011] Furthermore, the time-series wavefront state data is obtained by either simulating generation through an atmospheric turbulence phase screen or acquiring data under actual atmospheric turbulence conditions using an adaptive optics system.

[0012] Furthermore, the training samples include historical wavefront state sequences and corresponding future wavefront states.

[0013] Furthermore, the time-series wavefront state data is normalized, and the training samples are constructed based on a sliding window method.

[0014] Furthermore, the probabilistic prediction model employs an autoregressive recurrent neural network structure, which includes long short-term memory network units.

[0015] Furthermore, the probability distribution parameters include the mean and variance, or the weights, mean and variance of a Gaussian mixture distribution; the training of the probability prediction model uses a negative log-likelihood function as the loss function.

[0016] Furthermore, before using the statistical expectation value of the probability distribution parameters as the wavefront prediction value, the method further includes: The probability distribution corresponding to the probability distribution parameter is sampled multiple times by Monte Carlo sampling to generate multiple wavefront evolution trajectories; the multiple wavefront evolution trajectories are statistically processed to obtain the statistical expectation value and the prediction uncertainty measure.

[0017] Furthermore, the step of dynamically adjusting the control parameters based on the comparison results includes: When the prediction uncertainty metric is below a preset threshold, the control gain is increased; when the prediction uncertainty metric is above the preset threshold, the control gain is decreased or the system switches to pure feedback control mode.

[0018] Furthermore, the method for fusing the predicted wavefront value with the current measured wavefront state to generate a control signal is as follows: The predicted wavefront value is fused with the current measured wavefront state using either linear combination or Kalman filtering.

[0019] Compared with the prior art, the above-described solutions of this application have at least the following beneficial effects: 1. This application discloses a prediction and correction method for wavefront distortion. By constructing a probabilistic prediction model, it outputs the probability distribution parameters of the wavefront state at future times, thereby enabling explicit calculation of the prediction variance or confidence interval width as a measure of prediction uncertainty. Based on this, the prediction uncertainty measure is compared with a preset threshold, and control parameters are dynamically adjusted: when the uncertainty is below the threshold, the control gain is increased; when it is above the threshold, the gain is decreased or pure feedback control is switched. Compared to existing deterministic prediction methods such as recursive least squares and traditional long short-term memory networks, this application enables the control system to perceive the reliability of the prediction in real time, avoiding the output of erroneous compensation commands to the deformable mirror when the prediction is unreliable. This effectively solves the problem of the control system blindly trusting the prediction results and significantly improves the system's survivability and robustness under harsh conditions such as strong turbulence and flickering effects.

[0020] 2. This application discloses a prediction and correction method for wavefront distortion. It employs a negative log-likelihood function as the training loss function for the probabilistic prediction model, instead of the mean squared error loss used in traditional methods. This allows the model to directly learn the true probability distribution of wavefront data. Especially when using a Gaussian mixture distribution output, it can flexibly fit the non-Gaussian, multimodal, and heteroscedastic distribution characteristics of atmospheric turbulence. Traditional long short-term memory networks (LSM) predictions targeting mean squared error often exhibit a fuzzy effect, reverting to the mean and losing information about turbulent peaks and abrupt changes. In contrast, this application, through the distribution fitting capability of the probability likelihood function, can accurately capture the extreme values ​​and asymmetric distributions of wavefront distortion, significantly improving the prediction accuracy for key events such as abrupt changes in higher-order aberrations and intermittent bursts of turbulence, thus achieving superior correction results under strong turbulent conditions.

[0021] 3. This application discloses a prediction and correction method for wavefront distortion. After obtaining the probability distribution parameters, the probability distribution is sampled multiple times using Monte Carlo sampling to generate multiple possible wavefront evolution trajectories. These trajectories are then statistically processed to obtain the wavefront prediction value and a prediction uncertainty measure. On the one hand, the probability averaging of multiple trajectories effectively suppresses the interference of measurement noise, maintaining stable prediction performance even in low-light conditions or scenarios with high sensor noise. This overcomes the problems of ill-conditioned covariance matrix in recursive least squares methods under low signal-to-noise ratios and the tendency of traditional long short-term memory networks to mislearn noise as signals. On the other hand, the generated multiple possible evolution trajectories provide rich hypothetical paths for subsequent control systems, supporting the implementation of advanced strategies such as multi-frame fusion control and fault-tolerant control, further improving the overall performance of adaptive optics systems in complex environments. Attached Figure Description

[0022] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application. It is obvious that the drawings described below are merely some embodiments of this application, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort. In the drawings: Figure 1 This is a flowchart illustrating a wavefront distortion prediction and correction method according to an embodiment of this application.

[0023] Figure 2 This is a schematic diagram of the structure of an adaptive optics system shown in an embodiment of this application.

[0024] Figure 3 This is a schematic diagram illustrating the control of a probability prediction model in an embodiment of this application.

[0025] Figure 4 This is a schematic diagram of the structure of the probability prediction network model shown in an embodiment of this application. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0027] The terminology used in the embodiments of this application is for the purpose of describing particular embodiments only and is not intended to limit the application. The singular forms “a,” “said,” and “the” used in the embodiments of this application and the appended claims are also intended to include the plural forms, and “multiple” generally includes at least two unless the context clearly indicates otherwise.

[0028] It should be understood that the term "and / or" used in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0029] It should be understood that although the terms first, second, third, etc., may be used in the embodiments of this application, these descriptions should not be limited to these terms. These terms are only used to distinguish the descriptions. For example, first may also be referred to as second without departing from the scope of the embodiments of this application, and similarly, second may also be referred to as first.

[0030] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a product or device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a product or device. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the product or device that includes that element.

[0031] The optional embodiments of this application are described in detail below with reference to the accompanying drawings.

[0032] This application provides a method for predicting and correcting wavefront distortion, the flowchart of which is shown below. Figure 1 As shown.

[0033] S1. The incident beam is measured by a wavefront sensor to obtain wavefront state data that changes over time, and time-series wavefront state data is constructed.

[0034] The technical solutions of the embodiments of this application will now be described in detail with reference to existing adaptive optics systems. Adaptive optics systems, such as… Figure 2 As shown, the adaptive optics system includes: a wavefront corrector, a wavefront sensor, a wavefront controller, a high-voltage amplifier, and a far-field camera.

[0035] In this embodiment, the wavefront sensor is a Shaker-Hartmann wavefront sensor, used to measure the wavefront slope of the incident beam in real time and form a feedback control signal; the wavefront controller is a high-performance computer or embedded processor, responsible for executing prediction and control algorithms; the wavefront corrector is a deformable mirror, driven by a high-voltage amplifier to generate a compensated wavefront; the far-field camera is used to monitor the quality of the far-field spot as a reference for system performance evaluation.

[0036] The incident beam is measured by a wavefront sensor, and wavefront distortion data is acquired at a fixed sampling frequency to obtain wavefront state data that changes over time, thus constructing a time-series wavefront state data. The wavefront distortion data acquired at the sampling frequency can be wavefront slope data or Zernike coefficient sequences. The wavefront controller integrates the real-time measurement results with the future wavefront prediction values ​​output by the probabilistic prediction model, calculates the correction command through the control algorithm, and drives the wavefront corrector to achieve wavefront compensation through a high-voltage amplifier.

[0037] In the technical solution of this application embodiment, the wavefront slope data is the direct output of the Shaker-Hartmann wavefront sensor, which can be used for probabilistic prediction model training and prediction without additional conversion, thus reducing computational overhead; the Zernike coefficient sequence has a clear physical meaning and can decompose wavefront distortion into aberration patterns of different orders, which facilitates selective prediction and correction for specific orders, such as low-order aberrations, thereby improving the targeting and efficiency of prediction.

[0038] S2. Construct training samples based on time series wavefront state data.

[0039] To train a probabilistic prediction model, it is necessary to construct training samples containing historical wavefront state sequences and corresponding future wavefront states. This application provides two methods for obtaining time-series wavefront state data.

[0040] This application provides a preferred technical solution where the training samples consist of a historical wavefront state sequence and corresponding future wavefront states. This clarifies the input-output correspondence in supervised learning, enabling the probabilistic prediction model to establish an accurate conditional probability mapping by learning the temporal dependency between the historical sequence and future states. This sample structure directly serves the core task of wavefront prediction, avoiding unnecessary feature engineering and improving training efficiency and prediction accuracy.

[0041] Approach 1: Generating Simulation Data Based on Turbulence Simulation Theory. Using the atmospheric turbulence phase screen simulation method, a continuously varying dynamic phase screen is generated based on parameters such as atmospheric coherence length, Greenwood frequency, and lateral wind speed, employing either the power spectrum inversion method or the Zernike polynomial method. Following the Taylor frozen turbulence assumption, the phase screen is shifted at a set wind speed, thus obtaining an approximate actual distorted wavefront spatiotemporal sequence. This distorted wavefront spatiotemporal sequence is discretized according to the sampling frequency, and the slope data or Zernike coefficient sequence corresponding to the wavefront sensor is extracted as training samples.

[0042] Approach Two: Data Acquisition on an Actual Adaptive Optics System. Within the established adaptive optics system, wavefront sensor output data under actual atmospheric turbulence conditions is acquired, including wavefront slope, recovery voltage, or Zernike coefficients, and recorded as a continuously varying time series. This continuously varying time series reflects the true characteristics of atmospheric turbulence and is used for model training and validation. In this embodiment, data acquisition is performed using an adaptive optics system.

[0043] The technical solutions of this application provide two methods for acquiring time-series wavefront state data: simulation generation via an atmospheric turbulence phase screen, or acquisition under actual atmospheric turbulence conditions via an adaptive optics system. The advantages of both methods are: simulation data generation is low-cost, can be obtained in batches, and covers various turbulence intensity parameters, providing ample data sources for model training; while actual acquired data reflects the statistical characteristics of real atmospheric turbulence, making the trained model more closely aligned with real-world application scenarios. The two methods complement each other, ensuring both the feasibility of model training and improving the model's generalization ability in real-world systems.

[0044] In this embodiment of the application, the time series wavefront state data obtained by both methods need to be labeled with timestamps to form time series sample pairs consisting of historical observations and corresponding future target values.

[0045] This application provides a preferred technical solution for preprocessing acquired time-series wavefront state data, specifically including normalization and sliding window sequence construction. During normalization, each input feature, such as the Zernike coefficient, is standardized to have a mean of 0 and a standard deviation of 1, to avoid the influence of dimensional differences on model training. Next, a sliding window method is used to divide the continuous time series into a fixed-length input sequence and a corresponding prediction target sequence, namely, the historical wavefront state sequence and the future wavefront state. For example, using data from the past T sampling points to predict the wavefront state of the next K sampling points. In this application's technical solution, T represents the length of the historical sampling window; a T value that is too short will lose long-term dependencies, while a T value that is too long will affect real-time performance and introduce redundant noise. In this application's embodiment, the T value is set between 10 and 50. K represents the predicted sampling value, which is set to 2-3 sampling periods in this application's embodiment, so that the predicted value just compensates for the system's fixed time delay. A T value that is too short will not effectively reduce the correction residual, while a K value that is too long will cause overcompensation. The values ​​of T and K can be set according to the actual situation of the specific application, and this application does not limit them.

[0046] Finally, the preprocessed samples were divided into training, validation, and test sets in a 7:1.5:1.5 ratio: the training set was used for model parameter optimization, the validation set for hyperparameter tuning and early stopping, and the test set for final performance evaluation. A training set that is too large a proportion will result in too few samples, large variance in the evaluation metrics, and potentially poor generalization. Conversely, a training set that is too small a proportion will result in insufficient training data, making it difficult for the model to learn complex turbulent distribution characteristics and increasing the likelihood of underfitting.

[0047] In this embodiment, the time-series wavefront state data is normalized, and training samples are constructed using a sliding window approach. Normalization eliminates dimensional differences between different features, such as Zernike coefficients of different orders, making the probabilistic prediction model training more stable and converging faster. The advantage of using a sliding window to construct samples is that it can generate a large number of overlapping training samples from a finite time series, effectively expanding the dataset while preserving the local temporal characteristics of wavefront evolution. This allows the probabilistic prediction model to learn short-term correlations, making it particularly suitable for the rapidly time-varying characteristics of atmospheric turbulence.

[0048] S3. Construct a probability prediction model and train the probability prediction model based on training samples, so that the probability prediction model establishes a mapping relationship between the historical wavefront state sequence and the probability distribution of the wavefront state at future time.

[0049] In this embodiment, the constructed probabilistic prediction model adopts an autoregressive recurrent neural network structure, which contains two layers of long short-term memory network units, each with 128 units, followed by a fully connected layer to map the features extracted by the network to the probability distribution parameters of the wavefront state at future time moments. Figure 3 and Figure 4 As shown. Figure 4 middle, , , , Let represent the values ​​of the i-th order Zernike coefficient at times t-2, t-1, t, and t+1, respectively. , , Represent the given probability distribution parameters , , The probability density function under the given conditions; , , These represent optional auxiliary inputs, such as wavefront slope or other external variables; , , These represent the hidden states of a Long Short-Term Memory (LSTM) network unit at times t-1, t, and t+1, respectively.

[0050] Long Short-Term Memory (LSTM) network units, through gating mechanisms, can effectively capture long-term dependencies in time series, overcoming the gradient vanishing problem of traditional recurrent neural networks. For processes like atmospheric turbulent wavefronts with complex temporal evolution, LSM network units can learn the nonlinear dynamic characteristics of turbulence from the past to the future, significantly improving the accuracy of multi-step predictions. Furthermore, the autoregressive recurrent neural network structure is naturally adapted to time series prediction tasks, offering high computational efficiency and facilitating online deployment.

[0051] The probabilistic prediction model used in this application is the DeepAR probabilistic prediction model, but this application is not limited to this. Other temporal neural networks with probabilistic output capabilities can also be used, such as the Transformer model combined with a probabilistic output head, or a temporal convolutional network with a probabilistic output layer. The DeepAR probabilistic prediction model is suitable for strong local temporal dependencies and multi-step advance prediction, with high training efficiency and low inference latency. It can solve the problem that traditional LSTM, which only outputs point predictions, cannot provide confidence, and is robust to heteroscedastic noise. The self-attention mechanism of the Transformer model can capture global long-term dependencies, and its parallel training speed is relatively fast, making it suitable for modeling long sequence dependencies, such as turbulent wind speed drift scenarios. The convolution operation computation graph of the temporal convolutional network is fixed, and its inference is relatively fast, making it suitable for strictly online inference and edge deployment that is sensitive to computing resources. A more suitable prediction model can be selected according to the actual situation of the specific application, and this application does not limit this.

[0052] In this embodiment, the input to the probabilistic prediction model is a historical wavefront state sequence, and the output is the probability distribution parameters of the wavefront state at future times. Based on the control requirements of the adaptive optics system, the output parameters can be designed as the first few Zernike coefficients. This application uses Zernike coefficients from the 3rd to the 15th orders, excluding translation terms. Alternatively, the wavefront sensor sub-aperture slope vector can be directly output. The advantage of using the Zernike scheme lies in dimensionality reduction and decorrelation, compressing the high-dimensional sub-aperture slope vector into a coefficient sequence of tens of dimensions, greatly reducing the output layer size of the probabilistic prediction model, resulting in fast training convergence and less overfitting. Each Zernike order is independent, and the time series of coefficients of each order can be modeled approximately independently. Low-order aberrations concentrate most of the turbulence energy and are the main factors affecting the far-field Strell ratio (SR). Correcting aberrations from the 3rd to the 15th orders can yield significant correction benefits, avoiding the computational burden of high-dimensional slope prediction. The advantage of using the sub-aperture slope vector scheme of wavefront sensors is that, by using the sub-aperture slope vector as the output, the wavefront reconstruction step is eliminated. The predicted slope is directly fused with the current measured slope to drive the voltage, eliminating the delay and accuracy loss caused by a single numerical conversion, while preserving high-frequency spatial information of higher-order aberrations. However, for systems with a high number of sub-apertures, the parameter training workload increases dramatically, significantly raising the training difficulty and inference latency. Furthermore, this scheme is more sensitive to sensor noise. A more suitable scheme can be selected based on the specific application requirements; this application does not impose any limitations on this.

[0053] The design of the output layer depends on the assumed probability distribution type. If the wavefront state is assumed to follow a Gaussian distribution, the output layer outputs the mean and variance of that Gaussian distribution. If the wavefront state is assumed to follow a Gaussian mixture distribution, the output layer outputs the weights, mean, and variance of each Gaussian component. In this application, the embodiments preferably use a Gaussian mixture likelihood function as the probability distribution assumption for the output layer to more flexibly fit the multimodal, non-Gaussian distribution characteristics present in atmospheric turbulence wavefront data, thereby improving the predictive model's adaptability to complex turbulent states.

[0054] During training, the negative log-likelihood function is used as the loss function, and the optimization objective is to maximize the log probability of the training data under the distribution of the probability prediction model.

[0055] In this embodiment, the Gaussian distribution assumption with mean and variance is suitable for scenarios with weak turbulence and low noise, and is computationally simple. The Gaussian mixture distribution, on the other hand, can fit the multimodal and non-Gaussian distribution characteristics of atmospheric turbulence, avoiding the averaging prediction distortion caused by traditional mean square error loss. The negative log-likelihood loss function directly maximizes the log probability of the training data under the model distribution, enabling the model to learn the true probability distribution rather than just fitting the mean. This allows it to accurately capture extreme values ​​and asymmetric distributions of wavefront distortion, significantly improving the prediction accuracy for key events such as abrupt changes in higher-order aberrations and intermittent bursts of turbulence.

[0056] The training set data is input into the probabilistic prediction model, and iterative training is performed using the Adam optimizer. Each batch contains several samples. The model calculates the predicted distribution parameters using forward propagation, calculates the negative log-likelihood loss, and then updates the network weights using backpropagation. An early stopping strategy is implemented: training stops when the validation set loss no longer decreases after 10 consecutive rounds, and the optimal model parameters are saved. After training, the probabilistic prediction model has the ability to output the probability distribution of future wavefront states based on historical wavefront data. Before deployment, the trained weight parameters must be loaded, and the probabilistic prediction model must be placed in evaluation mode.

[0057] During the training process described above, because a probability likelihood function is used instead of the traditional mean squared error loss, the probabilistic prediction model can directly learn the true distribution of turbulent wavefront data, rather than simply fitting the statistical mean. Traditional LSTM predictions targeting mean squared error often exhibit a fuzzy effect of regressing to the mean, losing information about turbulent peaks and abrupt changes. However, the embodiments of this application, through the distribution fitting capability of the probability likelihood function, can accurately capture the extreme values ​​and asymmetric distributions of wavefront distortion, significantly improving the prediction accuracy for key events such as abrupt changes in higher-order aberrations and intermittent bursts of turbulence.

[0058] The trained probabilistic prediction model was validated on a test set to evaluate its prediction accuracy and uncertainty quantification quality. Prediction accuracy was measured using root mean square error (RMSE) and mean absolute error (MAE); probability calibration was evaluated using negative log-likelihood (NLL) and continuous rank probability score (CRPS), and the consistency between the predicted confidence interval and the actual coverage probability was verified by plotting reliability curves. After successful validation, the probabilistic prediction model can be deployed to the wavefront controller of the adaptive optics system.

[0059] S4. Input the real-time acquired historical wavefront state sequence into the trained probability prediction model, and output the probability distribution parameters of the wavefront state at future time.

[0060] S5. Use the statistical expectation value of the probability distribution parameter as the wavefront prediction value, and calculate the prediction uncertainty measure based on the probability distribution parameter.

[0061] In this embodiment of the application, within the closed loop of the adaptive optics system, a wavefront sensor continuously collects current wavefront state data at the system sampling frequency, and a wavefront controller caches historical data from the most recent T moments, forming a real-time acquired historical wavefront state sequence. This historical wavefront state sequence is input into a trained probabilistic prediction model, which outputs probability distribution parameters for the future wavefront state, such as mean and variance.

[0062]

[0063]

[0064] in, It represents the mean of the probability distribution of the wavefront state at time T+K; This represents the weight matrix used to calculate the mean. This represents the hidden state vector output by the probabilistic prediction model at time T; This represents the bias vector used to calculate the mean. The variance of the probability distribution of the wavefront state at time T+K; This represents the weight matrix used to calculate the log-variance. This represents the bias vector used to calculate the logarithmic variance.

[0065] To obtain more robust prediction results, this embodiment performs multiple samplings of the probability distribution through Monte Carlo sampling before using the statistical expectation value of the probability distribution parameters as the wavefront prediction value, generating multiple possible wavefront evolution trajectories.

[0066] Specifically, multiple random samples are taken from the probability distribution output by the probabilistic prediction model, for example, 100 samples, to obtain multiple possible wavefront evolution trajectories. Then, these trajectories are statistically processed: the arithmetic mean of all trajectories is calculated, and this mean is used as the final wavefront prediction value; simultaneously, the variance of each trajectory relative to this mean is calculated, and the variance value is used as a measure of prediction uncertainty. This variance value reflects the reliability of the prediction result; the smaller the variance, the more reliable the prediction, and the larger the variance, the higher the prediction uncertainty. Alternatively, the confidence interval width can be used to characterize prediction uncertainty; that is, based on the distribution of the sampled trajectories, upper and lower bounds at a certain confidence level are determined, and the width of this interval is used as a measure of uncertainty.

[0067] Alternatively, the width of the confidence interval can be used to characterize prediction uncertainty. Given a confidence level, such as 95%, corresponding to a significance level α=0.05, calculate the α / 2 quantile and 1-α / 2 quantile of the sampling trajectory, denoted as the lower bound L and upper bound U, respectively. The width W=UL of this confidence interval is used as a measure of prediction uncertainty. The larger the interval width, the higher the dispersion of the prediction results, i.e., the greater the uncertainty; conversely, the smaller the width, the more concentrated the prediction results, and the higher the reliability.

[0068] The technical solution of this application, through the Monte Carlo sampling mechanism, effectively suppresses measurement noise interference through probability averaging, maintaining stable prediction performance even in low-light conditions or scenarios with high sensor noise. Furthermore, the generated multiple possible evolution trajectories provide a rich data foundation for subsequent advanced control strategies such as multi-frame fusion control. Monte Carlo sampling can generate a large number of possible future trajectories from the probability distribution. By averaging these trajectories to obtain the predicted value, it effectively suppresses measurement noise interference, maintaining stable prediction performance even in low-light conditions or scenarios with high sensor noise. Simultaneously, the multiple trajectories obtained through sampling provide rich probabilistic information for the control system, supporting advanced strategies such as multi-frame fusion control and fault-tolerant control. Moreover, the variance or confidence interval width calculated based on the sampled trajectories, as an uncertainty measure, is more robust than direct analytical calculation, especially suitable for complex Gaussian mixture distributions.

[0069] S6. Compare the prediction uncertainty measure with the preset threshold, dynamically adjust the control parameters according to the comparison result, and fuse the wavefront prediction value with the current measured wavefront state according to the adjusted control parameters to generate a control signal.

[0070] After obtaining the prediction uncertainty metric, it is compared with a preset threshold, and the control parameters are dynamically adjusted based on the comparison result. Specifically: when the prediction uncertainty metric is lower than the preset threshold, the control gain is increased to obtain a fast response; when the prediction uncertainty metric is higher than the preset threshold, the control gain is decreased or the system switches to pure feedback control mode to avoid the risks caused by prediction errors.

[0071] When the uncertainty is too high, it is even possible to switch directly to pure feedback control. Then, based on the adjusted control parameters, the predicted wavefront value is fused with the current measured wavefront state to generate the final control signal.

[0072] The technical solution of this application increases the control gain when the value is below a threshold and decreases the control gain or switches to pure feedback control mode when the value is above the threshold. An adaptive control mechanism driven by prediction confidence is established. When the prediction uncertainty is low, i.e., the model is very confident in the prediction result, a high gain is used to pursue a fast and accurate correction effect; when the prediction uncertainty is high, i.e., the model lacks confidence in the prediction result, the gain is automatically reduced or pure feedback control is switched to avoid the negative impact of erroneous prediction values ​​on the deformable mirror. This effectively solves the problem of blindly trusting prediction results in existing control systems, and significantly improves the survivability and robustness of the system under harsh conditions such as strong turbulence and flickering effects.

[0073] The fusion method can employ either linear combination or Kalman filtering. Linear combination offers advantages such as simple computation, good real-time performance, and the ability to dynamically adjust fusion weights based on uncertainty, facilitating engineering implementation. Kalman filtering, on the other hand, optimally fuses predicted and measured values, estimating the optimal state online using a recursive formula while simultaneously providing the estimation error covariance, exhibiting theoretical optimality and adaptability. Both fusion methods effectively combine the predictive nature of information with the accuracy of measurement information, generating more reliable control signals and thus improving closed-loop correction performance. If linear combination is used, the fusion formula is expressed as:

[0074] in, This indicates the wavefront state after fusion; This represents the wavefront prediction value output by the probabilistic prediction model; This indicates the wavefront state currently measured by the wavefront sensor. This represents the variance of the model output.

[0075] If Kalman filtering is used, the predicted value and the measured value are optimally fused through recursion, and the state estimate and estimation error covariance are updated at the same time.

[0076] The expression for calculating the Kalman gain is:

[0077] in, represents the Kalman gain, the weighting coefficient between the predicted and measured values ​​during fusion, with a value range of [0,1]. R represents the prediction variance; R represents the measurement noise covariance.

[0078] The expression for the fusion formula is:

[0079] in, This represents the updated state estimate; This represents the predicted state value.

[0080] The expression for variance update is:

[0081] in, This represents the updated estimated variance.

[0082] When prediction variance When the value is small, the model prediction is very accurate, and the Kalman gain is high. →1, The fusion result mainly adopts the predicted value; when the measurement noise R is small, the measurement value is very accurate. →0, the fusion results mainly adopt the measured values.

[0083] If Kalman filtering is used, the predicted wavefront value is used as the state prediction, and the current measured wavefront state is used as the observation update. The prediction and measurement are fused by optimal fusion of Kalman gain.

[0084] The technical solution of this application establishes a confidence feedback path from the prediction module to the control module by comparing the prediction uncertainty metric with a threshold and dynamically adjusting the gain. The control system can dynamically adjust the control parameters and even the control architecture according to the current reliability of the prediction, overcoming the limitation of the prediction and control modules being independent in the prior art. When the prediction uncertainty is low, a high-gain, fast-response control strategy can be adopted to pursue the optimal correction effect; when the prediction uncertainty is high, automatic dimensionality reduction, smoothing, or switching to robust feedback control is performed. This collaborative mechanism enables the adaptive optics system to maximize correction performance while ensuring safety.

[0085] S7. Based on the control signal, the wavefront corrector generates a compensation wavefront to achieve closed-loop correction of wavefront distortion.

[0086] The generated control signal is then amplified by a high-voltage amplifier to drive a wavefront corrector to produce a compensated wavefront, thereby achieving closed-loop correction of wavefront distortion. A far-field camera monitors the correction effect in real time, providing system performance feedback.

[0087] This application's embodiments introduce a probabilistic prediction framework, outputting the probability distribution of wavefront states instead of a single deterministic point value. This allows for the explicit calculation of uncertainty measures such as the confidence interval and variance of the prediction results. Compared to existing deterministic prediction methods such as recursive least squares and long short-term memory networks, this application's embodiments enable the adaptive optics control system to perceive the reliability of the current prediction in real time. When the prediction confidence is low, the system can dynamically reduce the control gain, switch to a conservative control mode, or trigger a model update, avoiding the output of erroneous compensation commands to the deformable mirror when the prediction is unreliable. This significantly improves the survivability and robustness of the adaptive optics system under harsh conditions such as strong turbulence and scintillation.

[0088] This application provides a method for predicting and correcting wavefront distortion by introducing a probabilistic prediction model into adaptive optics closed-loop control. The method first acquires time-series wavefront state data using a wavefront sensor, constructs training samples, and trains a probabilistic prediction model. This enables the model to output a probability distribution of the wavefront state at future times, rather than a single deterministic point value. Then, based on the probability distribution parameters, a prediction uncertainty metric is calculated and compared with a preset threshold to dynamically adjust control parameters. Finally, the predicted value is fused with the current measured value to generate a control signal, ultimately driving the wavefront corrector to achieve closed-loop correction.

[0089] The technical solution of this application, a prediction and correction method for wavefront distortion, has the following advantages compared with existing deterministic prediction methods such as recursive least squares or traditional long short-term memory networks: First, it can explicitly quantify prediction uncertainty, enabling the control system to perceive the reliability of the prediction in real time and avoid blindly trusting the prediction results; Second, by comparing the threshold of prediction uncertainty measurement and adjusting dynamic control parameters, it achieves synergistic optimization of prediction and control, significantly improving the robustness and safety of the system in complex turbulent environments; Third, it organically combines probabilistic prediction with closed-loop correction, effectively compensating for the inherent delay of the adaptive optics system and improving dynamic correction performance.

[0090] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0091] The units described in the embodiments of this application can be implemented in software or hardware. The names of the units are not, in some cases, limiting the scope of the unit itself.

Claims

1. A method for predicting and correcting wavefront distortion, characterized in that, Includes the following steps: By measuring the incident beam using a wavefront sensor, wavefront state data that changes over time is obtained, and time-series wavefront state data is constructed. Training samples are constructed based on the time-series wavefront state data; A probability prediction model is constructed and trained based on the training samples, so that the probability prediction model establishes a mapping relationship between the historical wavefront state sequence and the probability distribution of the wavefront state at future time. The real-time acquired historical wavefront state sequence is input into the trained probability prediction model, which outputs the probability distribution parameters of the wavefront state at future time. The statistical expectation value of the probability distribution parameter is used as the wavefront prediction value, and the prediction uncertainty measure is calculated based on the probability distribution parameter. The prediction uncertainty metric is compared with a preset threshold, the control parameters are dynamically adjusted based on the comparison result, and the wavefront prediction value is fused with the current measured wavefront state based on the adjusted control parameters to generate a control signal. The control signal drives the wavefront corrector to generate a compensated wavefront, thereby achieving closed-loop correction of wavefront distortion.

2. The prediction and correction method according to claim 1, characterized in that, The time-series wavefront state data includes: wavefront slope data or Zernike coefficient sequence.

3. The prediction and correction method according to claim 1, characterized in that, The time-series wavefront state data is obtained by either simulating the generation through an atmospheric turbulence phase screen or acquiring it under actual atmospheric turbulence conditions using an adaptive optics system.

4. The prediction and correction method according to claim 1, characterized in that, The training samples include historical wavefront state sequences and corresponding future wavefront states.

5. The prediction and correction method according to claim 1, characterized in that, The time series wavefront state data is normalized, and the training samples are constructed based on a sliding window method.

6. The prediction and correction method according to claim 1, characterized in that, The probabilistic prediction model employs an autoregressive recurrent neural network structure, which includes long short-term memory network units.

7. The prediction and correction method according to claim 5, characterized in that, The probability distribution parameters include the mean and variance, or the weights, mean and variance of a Gaussian mixture distribution; the training of the probability prediction model uses a negative log-likelihood function as the loss function.

8. The prediction and correction method according to claim 7, characterized in that, Before using the statistical expectation value of the probability distribution parameters as the wavefront prediction value, the method further includes: The probability distribution corresponding to the probability distribution parameter is sampled multiple times by Monte Carlo sampling to generate multiple wavefront evolution trajectories; the multiple wavefront evolution trajectories are statistically processed to obtain the statistical expectation value and the prediction uncertainty measure.

9. The prediction and correction method according to claim 1, characterized in that, The dynamic adjustment of control parameters based on the comparison results includes: When the prediction uncertainty metric is below a preset threshold, the control gain is increased; when the prediction uncertainty metric is above the preset threshold, the control gain is decreased or the system switches to pure feedback control mode.

10. The prediction and correction method according to claim 1, characterized in that, The method for fusing the predicted wavefront value with the current measured wavefront state to generate a control signal is as follows: The predicted wavefront value is fused with the current measured wavefront state using either linear combination or Kalman filtering.

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