A primary-secondary mirror calibration method based on a neural network algorithm

Abstract

The present application relates to the technical field of intelligent precision calibration of optical instruments, and particularly relates to a primary and secondary mirror calibration method based on a neural network algorithm, comprising the following steps: step 1: synchronously collecting multi-physical field coupling data of the primary and secondary mirrors; step 2: constructing a dual-mode neural network model, wherein the dual-mode neural network model comprises; step 3: performing kinematic feasibility verification and dynamic optimization on the initial predicted value, including avoiding rotation degree of freedom singular points by using a Lie group space parameterization method, and verifying and adjusting the reachable working space of the platform through a Jacobian matrix; and step 4: driving the secondary mirror adjustment platform based on the optimized adjustment parameters, and triggering online incremental learning of the neural network model according to actual wavefront residual errors. Through the innovative application of the neural network algorithm, the present application solves a plurality of technical problems of the traditional optical system calibration method under extreme environments and high-frequency dynamic conditions, and improves the calibration accuracy, real-time performance and efficiency through self-learning and self-adaptive capabilities.

Description

Technical Field

[0001] This invention relates to the field of intelligent precision calibration technology for optical instruments, and in particular to a primary and secondary mirror calibration method based on a neural network algorithm. Background Technology

[0002] In the field of optical imaging systems, the precise calibration of primary and secondary mirrors is a core technology for ensuring image quality. This is especially true in high-end equipment such as space telescopes and high-resolution microscopy, where even micrometer-level deviations in mirror position can lead to a significant decrease in imaging resolution. As applications expand into extreme environments, traditional calibration methods reveal the following key technical shortcomings:

[0003] Current mainstream calibration devices rely on precision mechanical adjustment mechanisms (such as six-degree-of-freedom actuators) to achieve mirror attitude adjustment. However, in the on-orbit operation scenario of space optical systems, the satellite platform continuously endures severe thermal cycling from -150°C to +120°C, causing nonlinear thermal deformation of the mirror material. When traditional mechanical adjustment mechanisms compensate for such deformation, the differences in the thermal expansion coefficients of their own metal components introduce secondary attitude deviations. Furthermore, in live-cell microscopy, high-frequency micro-vibrations (1-200Hz) caused by the physiological activities of the sample can lead to submicron-level dynamic shifts in the secondary mirror, and the response delay of mechanical adjustment mechanisms (typically >10ms) cannot achieve real-time tracking and compensation.

[0004] Zernike polynomial-based wavefront reconstruction methods are widely used for aberration analysis, but they have inherent limitations in separating primary and secondary mirror coupling errors. When the primary mirror experiences asymmetric surface shape errors (such as triceps aberration) due to thermal deformation, traditional methods cannot effectively distinguish this error from higher-order aberration components caused by secondary mirror tilt / eccentricity. Experiments show that under conditions with temperature gradients exceeding 20℃ / m, the error separation degree of existing algorithms is less than 60%, resulting in a secondary mirror compensation calculation deviation exceeding λ / 10 (λ=632.8nm). This problem is particularly prominent in off-axis optical systems, severely limiting the correction accuracy of adaptive optics systems.

[0005] Therefore, developing a calibration method that can integrate multi-source sensor data, separate coupling errors in real time, and has self-learning capabilities has become an urgent need to improve the performance of high-end optical equipment. Summary of the Invention

[0006] To achieve the above objectives, the present invention provides a primary and secondary mirror calibration method based on a neural network algorithm, comprising the following steps:

[0007] Step 1: Synchronously acquire multi-physics coupling data of the primary and secondary mirrors, including obtaining the circumferential temperature gradient distribution of the primary mirror through a temperature sensor array, obtaining the time-domain acceleration signal of the secondary mirror adjustment platform through a vibration sensor, and obtaining the wavefront phase distribution of the optical system through a wavefront sensor.

[0008] Step 2: Construct a bimodal neural network model, which includes:

[0009] The physical feature extraction subnetwork takes the temperature gradient distribution and time-domain acceleration signal as input, extracts non-uniform deformation features through deformable convolutional layers, and performs regularization processing using a physical constraint layer that embeds thermoelasticity equations.

[0010] An optical feature extraction subnetwork is input with the wavefront phase distribution, and the wavefront slope contribution of each sub-aperture region is dynamically weighted through an attention mechanism convolutional layer.

[0011] The gated fusion unit performs cross-modal correlation between the physical features and optical features to generate initial predicted values ​​for the six-degree-of-freedom adjustment of the secondary mirror.

[0012] Step 3: Perform kinematic feasibility verification and dynamic optimization on the initial predicted values, including using the Lie group space parameterization method to avoid singular points in rotational degrees of freedom and verifying the reachability of the platform's workspace through the Jacobian matrix.

[0013] Step 4: Drive the secondary mirror adjustment platform based on the optimized adjustment parameters, and trigger online incremental learning of the neural network model based on the actual wavefront residual.

[0014] Preferably, the synchronous acquisition of multiphysics coupling data in step 1 specifically includes:

[0015] The layout density of the temperature sensor array is determined based on the thermal diffusion characteristics of the primary mirror material, so that the spacing between adjacent sensors can capture nonlinear changes in the temperature gradient.

[0016] The sampling frequency of the wavefront phase distribution is dynamically adjusted according to the dominant frequency component of the spectrum obtained by the vibration sensor to ensure that the sampling frequency and the dominant frequency component of the vibration form a preset multiple relationship.

[0017] The time-domain acceleration signal is used to extract vibration features through time-frequency analysis, including the spectral energy distribution of the dominant frequency component, harmonic components, and random noise, and a vibration feature vector is constructed.

[0018] Preferably, the physical constraint layer in step 2 is implemented as follows:

[0019] The thermoelasticity equation is discretized into a differential operator form, which is then embedded as a regularization term in the neural network training process. The coefficients of the differential operator are dynamically adjusted according to the physical properties of the primary mirror material.

[0020] Stress balance constraints are introduced during the feature mapping process of deformable convolutional layers, and the feature maps are made to satisfy the elasticity equilibrium equations through iterative optimization algorithms.

[0021] Preferably, the implementation of the attention mechanism convolutional layer in step 2 includes:

[0022] Spatial attention weights are generated based on the statistical characteristics of the wavefront slope of each sub-aperture region, wherein the statistical characteristics include the variance and covariance matrix of the slope of the local region.

[0023] A learnable nonlinear transformation module is introduced in the channel dimension, and the initialization parameters of the module are determined by the characteristic distribution law of historical calibration data.

[0024] Preferably, the specific process of kinematic feasibility verification in step 3 is as follows:

[0025] The pose space boundary conditions are constructed based on the mechanical structure parameters of the secondary mirror adjustment platform, and the boundary conditions are dynamically updated through the singular value decomposition of the Jacobian matrix.

[0026] An optimization algorithm with constraints is used to map the initial predicted values ​​to the reachable workspace. The constraints include the kinematic limit parameters of each axis of the platform.

[0027] Preferably, the dynamic optimization in step 3 further includes:

[0028] Establish a time series database of historical adjustment values, and use a time series prediction model to generate pose change trend curves;

[0029] An anti-saturation control mechanism is introduced into the translation component calculation, and the control parameters are dynamically adjusted according to the distance between the current pose of the platform and the physical limit.

[0030] Preferably, the triggering condition for the online incremental learning in step 4 is:

[0031] Modal decomposition was performed on the wavefront residuals before and after adjustment, and the rate of change of higher-order aberration components was calculated.

[0032] When the residual decay rate of higher-order aberration components is lower than a preset threshold, a model update is triggered. The threshold is dynamically calculated based on the statistical distribution of historical calibration data.

[0033] Preferably, the incremental learning is specifically implemented as follows:

[0034] Feature enhancement is performed on the abnormal samples that trigger updates, and the coverage of the training dataset is expanded through adversarial example generation techniques;

[0035] An elastic weight fixation algorithm is used to calculate the importance index of neural network parameters, and the weight distribution of key features is preserved during the parameter update process.

[0036] Preferably, environmental parameter adaptation is included before step 1:

[0037] The temperature cycling strategy is selected based on the type of working environment of the optical system. The strategy includes segmented setting of temperature change rate and dynamic division of temperature range.

[0038] The mechanical vibration frequency range is dynamically set according to the resonance characteristics of the secondary mirror adjustment platform. The resonant frequency band is identified through frequency sweep testing and sensitive frequency ranges are automatically avoided.

[0039] Preferably, step 3 is followed by mechanical resonance avoidance processing:

[0040] Obtain the dynamic response characteristic curve of the secondary mirror adjustment platform and perform frequency domain pre-compensation on the adjustment command;

[0041] The pre-compensation parameters are obtained by fitting the frequency response characteristics of the platform's input and output signals, and an enhanced weighting coefficient is applied to the resonant frequency band during the fitting process.

[0042] The beneficial effects of this invention are:

[0043] 1. This invention utilizes neural network algorithms combined with multi-source sensor data to acquire and analyze the temperature changes and corresponding thermal deformation of the optical lens in real time, avoiding reliance on traditional mechanical adjustment mechanisms. Through dynamic modeling and accurate prediction of the lens's thermal deformation, intelligent algorithms can be directly applied for real-time compensation during thermal deformation, eliminating secondary pose deviations caused by traditional mechanical components. This method overcomes the pose deviation problem caused by thermal deformation, improving the accuracy of optical systems in extreme environments.

[0044] 2. This invention, through the fusion of neural network algorithms and high-frequency sensor data, can track and rapidly compensate for the dynamic offset of the secondary mirror in real time. The neural network can learn and predict the dynamic behavior of the secondary mirror, accurately model vibration frequency and amplitude, and output compensation commands within microseconds, avoiding the error accumulation caused by response delays in traditional mechanical adjustment mechanisms. This method significantly reduces the dynamic offset of the secondary mirror, improving calibration accuracy and stability in microscopic imaging.

[0045] 3. This invention employs a neural network algorithm to fuse multi-source sensor data, enabling not only real-time identification and separation of thermal distortion errors in the primary mirror and higher-order aberrations in the secondary mirror, but also precise estimation of the contribution of each error source. Supported by multi-source sensor data, the neural network can adaptively adjust the error separation strategy, maintaining high efficiency and accuracy in complex environments. This method overcomes the limitations of traditional Zernike polynomial methods, effectively improving error separation and ensuring that the calculation error of the secondary mirror compensation is significantly lower than λ / 10, thereby enhancing the adaptive correction accuracy of the optical system.

[0046] 4. This invention employs a self-learning capability based on neural networks, enabling it to automatically adjust compensation strategies according to different application scenarios and operating conditions (such as temperature changes, micro-vibrations, etc.). This adaptive capability allows the optical system to maintain high-precision calibration results under various environments, especially in off-axis optical systems, where this invention provides significantly improved calibration accuracy. By fusing multi-source sensor data, the neural network can continuously optimize the adaptive strategy, enabling the system to accurately respond to dynamic changes, thereby greatly improving the overall performance and reliability of the system.

[0047] 5. This invention employs a neural network algorithm to generate real-time compensation commands. Its training process enables the model to efficiently and accurately predict state changes in the secondary and primary mirrors. Due to the efficient computational power of the neural network, the system can output compensation signals in an extremely short time (milliseconds), thus significantly improving real-time performance and calibration efficiency. Especially in dynamic environments requiring frequent adjustments and compensation, the real-time response and efficiency of this method can significantly improve the operating efficiency of the optical system. Attached Figure Description

[0048] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only for this invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0049] Figure 1 This is a flowchart of the steps of the method of the present invention;

[0050] Figure 2 This is a flowchart illustrating the implementation of the physical constraint layer in step 2 of the method of the present invention.

[0051] Figure 3 This is a flowchart illustrating the specific process of kinematic feasibility verification in step 3 of the method of the present invention. Detailed Implementation

[0052] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. It should also be noted that, to make the embodiments more comprehensive, the following embodiments are the best and preferred embodiments, and those skilled in the art can use other alternative methods to implement some well-known technologies; moreover, the accompanying drawings are only for more specific description of the embodiments and are not intended to specifically limit the present invention.

[0053] Please see Figures 1-3This invention provides a primary and secondary mirror calibration method based on a neural network algorithm. In step 1, by simultaneously acquiring coupled data from multiple physical fields, more accurate input data can be provided for the subsequent neural network model. First, a temperature sensor array is used to capture the circumferential temperature gradient distribution of the primary mirror, which directly affects mirror deformation and optical performance. A vibration sensor monitors the time-domain acceleration signal of the secondary mirror adjustment platform in real time, providing vibration characteristics. Wavefront phase distribution data acquired by a wavefront sensor is used for subsequent optical performance analysis, ensuring that no influencing factor is ignored during calibration. The combination of these data provides a comprehensive understanding of the system state, ensuring the accuracy of subsequent adjustments.

[0054] In step 2, firstly, the physical feature extraction subnetwork processes data from temperature gradient distribution and acceleration signals. Through deformable convolutional layers, the network extracts complex non-uniform deformation features and performs regularization through a physical constraint layer embedding thermoelasticity equations, ensuring the rigor of the physical laws. Secondly, the optical feature extraction subnetwork processes wavefront phase distribution data through attention-based convolutional layers, dynamically weighting the contribution of the wavefront slope to capture subtle changes in each sub-aperture region. Finally, a gated fusion unit performs cross-modal correlation between the two modalities, generating six-DOF initial predictions for secondary mirror adjustment. This fusion of multimodal learning helps to simultaneously optimize secondary mirror adjustment from multiple perspectives, improving the accuracy and efficiency of the adjustment.

[0055] In step 3, once the initial predicted values ​​are obtained, the system verifies the kinematic feasibility to ensure the practical feasibility of the adjustment scheme. A Lie group space parameterization method is used to avoid singularities in the rotational degrees of freedom, preventing uncontrollable rotational errors during the secondary mirror adjustment process. The Jacobian matrix is ​​used to verify the reachable workspace of the secondary mirror adjustment platform, ensuring that the adjustment process does not exceed the platform's range of motion. This makes the adjustment process not only more accurate but also avoids erroneous operations that could damage the equipment.

[0056] Finally, in step 4, based on the aforementioned optimized adjustment parameters, the secondary mirror adjustment platform is driven to ensure precise mirror adjustment. During the adjustment process, the system monitors the changes in wavefront residuals in real time and triggers online incremental learning of the neural network model based on the actual wavefront residuals. Through online learning, the network can continuously adjust its parameters according to new adjustment data, improving the accuracy of calibration. This real-time learning mechanism can cope with different operating environments and system states, enhancing the overall system's adaptability and robustness.

[0057] In one possible implementation, in step 1, the layout density of the temperature sensor array is determined based on the thermal diffusivity of the primary mirror material. Thermal diffusivity determines the rate of heat conduction and the distribution of the temperature gradient within the material. To capture the nonlinear changes in the primary mirror surface temperature, the spacing between the sensors needs to be optimized according to these characteristics. Specifically, when the primary mirror material has high thermal diffusivity, the distance between the sensors can be appropriately increased; conversely, for materials with poor thermal diffusivity, the sensor spacing needs to be smaller to ensure accurate capture of temperature gradient changes. This layout optimization enables better monitoring of the primary mirror's thermal deformation, thereby providing more accurate data support for subsequent secondary mirror adjustments.

[0058] The sampling frequency of the wavefront phase distribution is closely related to the time-domain acceleration signal acquired by the vibration sensor. In step 1, the sampling frequency of the wavefront phase distribution is dynamically adjusted according to the dominant frequency component of the spectrum acquired by the vibration sensor. This dynamic adjustment ensures that the wavefront sampling frequency is a preset multiple of the dominant frequency of the vibration signal. That is, by ensuring that the wavefront phase sampling frequency is an integer multiple of the dominant frequency of the vibration, the sampling of wavefront data is more accurate, avoiding errors caused by sampling frequency mismatch. This dynamic adjustment can effectively synchronize wavefront data and vibration data, avoid sampling deviations in the time domain, and improve data consistency during the optical system calibration process.

[0059] To extract vibration features, the time-domain acceleration signal was further processed using time-frequency analysis. This process first utilizes time-frequency analysis to extract the dominant frequency component, harmonic components, and spectral energy distribution of random noise from the vibration signal. These spectral energy distributions effectively distinguish different vibration modes within the system and provide a more refined vibration feature vector for secondary mirror adjustment. The dominant frequency component reflects the system's main vibration modes, the harmonic components reveal the system's nonlinear vibration characteristics, and the random noise spectral energy distribution helps distinguish unwanted noise, avoiding interference with calibration accuracy. These extracted vibration features, by constructing a vibration feature vector, become an important data source for subsequent neural network input, further improving the accuracy and robustness of the secondary mirror adjustment process.

[0060] In one possible implementation, in step 2, the thermoelasticity equations are first discretized into differential operator form. The thermoelasticity equations describe the deformation behavior of materials under heat or stress, combining the relationship between temperature change and stress response. By discretizing the equations into differential operator form, the thermoelastic effect can be modeled within the discretized network layers. This differential operator is embedded as a regularization term in the neural network training process. The introduction of the regularization term allows the neural network to consider not only data-driven errors during optimization but also, through physical constraints, reduce computational errors, ensuring that the network model conforms to the physical laws of thermoelasticity theory.

[0061] Furthermore, the coefficients of the differential operator are dynamically adjusted based on the physical properties of the primary mirror material. Parameters such as the coefficient of thermal expansion and elastic modulus of different materials determine their response under various environmental conditions. Therefore, during network training, the coefficients of the differential operator are dynamically adjusted for different material properties to accurately reflect the thermoelastic behavior of the material and ensure the physical rationality of the calibration results.

[0062] In the deformable convolutional layers of neural networks, a stress balance constraint is introduced. This constraint ensures that during feature mapping, the update of the feature map must not only meet the data-driven error minimization requirement but also satisfy the stress balance equations from elasticity. The stress balance equations describe the stress distribution and equilibrium state among points within an object under external forces. By introducing this physical constraint, the feature map conforms to the fundamental principles of mechanical equilibrium during network optimization.

[0063] To meet this constraint, an iterative optimization algorithm was employed. In each iteration, the network adjusts its feature map using feedback stress balance constraints to ensure it satisfies the equilibrium equations of elasticity. Through this iterative optimization process, the neural network can effectively learn a calibration model that conforms to physical laws, rather than simply a data-based mapping. The optimization algorithm ensures that each network update enhances the fit between the feature map and the physical model, ultimately improving the accuracy and reliability of the primary and secondary mirror calibration.

[0064] In one possible implementation, wavefront slope data for each sub-aperture region is acquired during actual observation or simulation of the primary and secondary mirrors. The slope reflects the local trend of wavefront variation and is an important physical characterization of mirror distortion. Specifically, slope statistics are calculated by statistically processing the wavefront slopes of each sub-aperture region to calculate its local variance and covariance matrix. The variance reflects the severity of wavefront variation in that region; the covariance matrix reveals the correlation of wavefront variations between regions.

[0065] Using the aforementioned statistical properties, a set of spatial attention weights is generated. These weights weight the input feature map in the spatial dimension of the neural network to highlight regions with significant and complex mirror distortion, while suppressing regions with gentle changes or minimal impact.

[0066] The calculated spatial attention weights are used as masks and embedded into the convolution operation to form a spatial attention mechanism convolutional layer, thereby automatically focusing on the most critical physical distortion regions during feature extraction.

[0067] Introduce a learnable nonlinear transformation module (such as a multilayer perceptron, SE structure, etc.) in the channel dimension. This module can adjust the activation weights according to the response intensity of different channels.

[0068] The initial parameters of the module are not set randomly, but are set according to the characteristic distribution patterns of historical calibration data. Specifically, the initial weights and biases are determined by analyzing the mean, variance, and importance assessment of the characteristics of each channel in a large number of historical primary and secondary mirror calibration samples, in order to accelerate network convergence and enhance physical interpretability.

[0069] During training and inference, the nonlinear transformation module adjusts the characteristic response of each channel, enhances the response of channels with critical calibration significance, suppresses noise or redundant features, and further improves the model's ability to identify structural errors.

[0070] In one possible implementation, firstly, the design and mechanical structure of the platform are adjusted according to the secondary mirror, and its main kinematic parameters, such as the degrees of freedom of each axis, the connection relationships between axes, and the driving mechanism, are collected and organized. These parameters help to establish kinematic models of the platform under different states.

[0071] Using the platform's structural parameters, the pose space boundary conditions of the platform are established. The pose space refers to all possible pose combinations of the platform, including position and orientation. By defining the range of motion for each degree of freedom, a bounding box is constructed to represent the platform's reachable workspace.

[0072] In the kinematic model, the platform's pose adjustment is closely related to the kinematic constraints of its various axes. To further improve model accuracy, the Jacobian matrix is ​​used to describe the linear relationship between the platform's degrees of freedom. By performing singular value decomposition (SVD) on the Jacobian matrix, we can dynamically update the effective range of motion for each axis and determine whether the platform can achieve the target pose adjustment within a given range.

[0073] During training, the neural network predicts initial secondary mirror pose adjustment values, which represent the target position and orientation. Next, these initial values ​​need to be mapped to the actual reachable workspace.

[0074] During the optimization process, kinematic constraints are introduced, including the kinematic limit parameters of each axis of the platform, such as the maximum rotation angle, minimum angle, and maximum linear displacement. These constraints ensure that the optimization results do not exceed the physical motion range of the platform, thereby avoiding unrealizable adjustments.

[0075] Optimization algorithms with constraints (such as gradient descent and constrained SQP) are used to solve for the optimal adjustment scheme of the initial predictions. The optimization objective is to effectively map the predictions into the platform's reachable workspace while satisfying all kinematic limits and boundary conditions, thereby ensuring that the platform can perform calibration tasks.

[0076] In one possible implementation, during multiple primary and secondary mirror calibrations, the adjustment data (including translation and rotation components) of the mirror pose are recorded for each calibration, forming a continuous historical adjustment sequence. This data is stored in chronological order to construct a time-series database.

[0077] A time series model suitable for nonlinear system prediction (such as LSTM, GRU, or Transformer-based time series prediction networks) is selected and trained on historical adjustment data. The goal of the model is to predict the pose change trend curve within a future time window based on past adjustment sequences.

[0078] The trained model is used to predict the pose change trend in the current calibration process in real time, generating a trend curve. The system can adjust the control strategy in advance according to the trend changes, avoiding over-adjustment or repeated oscillations, and improving the stability and foresight of pose adjustment.

[0079] The system acquires the actual pose of the platform in each axis direction in real time and calculates the distance between this state and the physical motion limit (such as the margin between the distance and the maximum translation limit). This information is used as dynamic input for the anti-saturation control mechanism.

[0080] Design an anti-saturation control mechanism based on nonlinear functions, such as hyperbolic tangent functions or exponential decay functions, and adjust the control parameters according to the distance from the limit, so that the output amplitude of the control signal automatically decreases when it approaches the limit, thereby avoiding the control command from causing the limit to exceed the limit.

[0081] The controller adjusts the control gain or the upper limit of the speed command in real time based on the physical limit distance. When the platform is in the intermediate controllable range, faster adjustment is allowed; when approaching the limit range, the system automatically reduces the adjustment rate to prevent control output saturation and ensure equipment safety.

[0082] In one possible implementation, wavefront data before and after mirror adjustment is acquired using a wavefront sensor or other measuring device during each calibration process. This data reflects the mirror's shape and the errors in the optical system.

[0083] The acquired wavefront residual data undergoes mode decomposition (e.g., based on Zernike polynomial expansion) to decompose the wavefront residuals into aberration components of different orders (e.g., low-order aberrations such as spherical aberration and astigmatism, and high-order aberrations such as deformation and elastic modes). The purpose of this process is to clearly separate the contribution of each aberration component, paying particular attention to high-order aberrations, as they have a significant impact on the system's imaging quality.

[0084] By comparing the higher-order aberration component data before and after adjustment, the rate of change (e.g., percentage change or magnitude of change) is calculated. The rate of change of higher-order aberrations reflects the effectiveness of mirror adjustment. If higher-order aberrations are not effectively reduced, the adjustment is insufficient and recalibration is required.

[0085] The system analyzes historical residual changes based on historical calibration data and calculates a dynamic threshold based on statistical distribution. This threshold represents a standardized rate of change; when the rate of decrease of higher-order aberration components falls below this threshold, online incremental learning is triggered.

[0086] Methods for dynamically calculating thresholds may include using standard deviation, mean, or other distribution characteristics to ensure that the threshold is adjusted according to different conditions, such as environmental changes or system status. For example, if historical calibration data shows that the residual decreases slowly under certain conditions, the trigger threshold can be appropriately increased, and vice versa.

[0087] When the residual descent rate of higher-order aberrations falls below a dynamically calculated threshold, the system automatically triggers incremental learning of the neural network model. This means the system will readjust the model parameters to better adapt to the current mirror condition, thereby improving calibration accuracy.

[0088] In one possible implementation, the primary and secondary mirror calibration method based on a neural network algorithm according to claim 8, the specific implementation of incremental learning includes two key technical features: feature enhancement of abnormal samples and adversarial sample generation technology, and the application of the elastic weight solidification algorithm in neural network training. The following is a detailed description of the implementation steps, specific implementation methods, and beneficial effects of these technical features.

[0089] During incremental learning, when a model update is triggered, the system identifies anomalous samples in the current training set. These anomalous samples refer to data samples that exhibit abnormal wavefront residuals or do not conform to normal patterns during the calibration process. These data typically represent potential errors or unpredictable perturbations during mirror adjustment.

[0090] Adversarial example generation techniques (e.g., gradient-based adversarial attack methods such as FGSM or PGD) are used to expand the coverage of training datasets. By applying small perturbations to the current training samples, adversarial examples are generated that can effectively simulate various perturbations and anomalies during mirror adjustment. Adversarial examples not only enhance the diversity of training data but also improve the robustness of neural networks, enabling models to better cope with anomalies that may occur in real-world applications.

[0091] Specific methods for feature enhancement of outlier samples include operations such as rotation, scaling, and noise addition to further improve the adaptability of neural networks. These operations help the network learn more comprehensive features, enhancing its performance when faced with unseen data.

[0092] Elastic Weight Consolidation (EWC) is a technique commonly used in incremental learning. Its core idea is to retain the "consolidation" effect on important parameters when updating neural network parameters. EWC helps avoid excessive forgetting of existing knowledge during the update process by calculating the importance of each neural network parameter.

[0093] EWC first calculates the importance metrics for each network parameter using the initial training dataset. These metrics are based on Fisher information matrices, which reflect the importance of each parameter to the model's performance in the current task. The higher the importance of a parameter, the larger its corresponding Fisher information value, indicating that the parameter is crucial to the network's decision-making.

[0094] In subsequent incremental learning, when new training data is introduced, EWC "solidifies" the weight distribution of important parameters by adding a regularization term to the loss function. Specifically, the regularization term imposes greater constraints on important parameters, reducing their magnitude of variation and preventing the model from losing knowledge of existing tasks when learning new tasks. In this way, the network can retain the weight distribution of key features without forgetting knowledge from previous tasks when learning new tasks.

[0095] In one possible implementation, the temperature cycling strategy is first selected based on the type of operating environment of the optical system. Different optical systems may operate under different environmental conditions, such as space environments, ground-based laboratories, or field testing environments. Depending on the characteristics of the operating environment, the system selects an appropriate temperature cycling strategy. For example, space environments may require consideration of extreme temperature variations, while ground-based environments may have smaller temperature variations.

[0096] The segmented setting of the temperature change rate is dynamically adjusted according to different environmental conditions. In practice, the system sets different temperature change rates based on the temperature variation patterns of the environment. For example, in environments with drastic temperature changes, a slower temperature change rate may be used to reduce the thermal stress on the mirror surface caused by temperature changes, while in environments with relatively stable temperature changes, a faster temperature change rate can be used to improve calibration efficiency.

[0097] The dynamic division of temperature ranges is based on the temperature range and rate of change. This step divides the temperature range into different segments, each of which may have different rates of temperature change and monitoring parameters. The goal of dynamic division is to minimize distortion of the optical system caused by large temperature changes, ensuring that the system can perform stable calibration operations within each temperature range.

[0098] The resonant characteristics of the secondary mirror adjustment platform are crucial for the stability of the calibration process. To avoid unnecessary vibration interference during calibration, the system identifies the platform's resonant frequency band through frequency sweep testing. This process involves gradually changing the frequency and monitoring the platform's response to determine the resonant frequency band. Frequency sweep testing can accurately identify the platform's vibration characteristics at different frequencies, providing data support for subsequent vibration control.

[0099] Once the resonant frequency band of the platform is identified, the system automatically sets the operating frequency range of the mechanical vibration to avoid operation in sensitive frequency ranges. This is achieved by controlling the vibration source to ensure that the mechanical vibration frequency does not overlap with the resonant frequency of the secondary mirror adjustment platform, thereby avoiding the impact of resonance on the mirror calibration accuracy.

[0100] In practical applications, the frequency range of mechanical vibrations may be adjusted according to different operating states and environmental conditions. For example, when the system detects the presence of an external vibration source in the environment, it may automatically adjust its operating frequency to further avoid frequency resonance with the external interference source.

[0101] In one possible implementation, the dynamic response characteristics of the secondary mirror adjustment platform need to be tested first. This is done by exciting the platform with an input signal and acquiring its output response to obtain the frequency domain response characteristics of the secondary mirror adjustment platform. A common method is to apply a series of sinusoidal signals of known frequencies (frequency sweep test) and record the platform's output signals to construct its frequency response curve. This process can accurately describe the platform's vibration response behavior at different frequencies.

[0102] By analyzing the obtained frequency domain response characteristic curves, the response amplitude and phase of the platform at different frequencies can be identified, thereby finding the platform's resonant frequency band. For the secondary mirror adjustment platform, the resonant frequency band is an extremely sensitive region; any vibration within this frequency range will cause the platform to over-respond, thus affecting the calibration accuracy.

[0103] To avoid overresponse in the resonant frequency band, compensation must be made in the frequency domain for the adjustment commands. Frequency domain pre-compensation refers to making adjustments in advance in the adjustment commands based on the platform's dynamic response characteristics to reduce or eliminate overresponse within a specific frequency range. For example, by reducing or adjusting the input signal strength near the resonant frequency band, resonance of the platform can be avoided.

[0104] In practical implementation, digital signal processing techniques can be used to filter and weight the input signal in the frequency domain. By adjusting the frequency components in the command to have a lower amplitude in the resonant frequency band, the platform's response within that frequency range can be reduced.

[0105] The pre-compensation parameters are obtained by fitting the frequency response characteristics of the platform's input and output signals. Frequency response characteristic fitting involves collecting the platform's frequency domain response data and using mathematical modeling methods (such as least squares) to fit the data, resulting in a mathematical model that accurately describes the platform's frequency domain response. This model reflects the platform's response behavior to input signals of different frequencies.

[0106] During the fitting process, to effectively avoid over-response in the resonant frequency band, enhanced weighting coefficients need to be applied to the resonant frequency band. This means that during the fitting process, a higher weight is assigned to the platform's response in the resonant frequency band to ensure that the model can accurately reflect the characteristics of the resonant region. These enhanced weighting coefficients ensure more precise suppression of vibrations in the resonant frequency band during pre-compensation.

[0107] This invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of this invention. To provide the public with a thorough understanding of this invention, specific details are described in detail in the following preferred embodiments; however, those skilled in the art will fully understand the invention even without these details. Furthermore, to avoid unnecessary misunderstanding of the essence of this invention, well-known methods, processes, procedures, components, and circuits are not described in detail.

[0108] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A primary and secondary mirror calibration method based on a neural network algorithm, characterized in that, Includes the following steps: Step 1: Synchronously acquire multi-physics coupling data of the primary and secondary mirrors, including obtaining the circumferential temperature gradient distribution of the primary mirror through a temperature sensor array, obtaining the time-domain acceleration signal of the secondary mirror adjustment platform through a vibration sensor, and obtaining the wavefront phase distribution of the optical system through a wavefront sensor. Step 2: Construct a bimodal neural network model, which includes: The physical feature extraction subnetwork takes the temperature gradient distribution and time-domain acceleration signal as input, extracts non-uniform deformation features through deformable convolutional layers, and performs regularization processing using a physical constraint layer that embeds thermoelasticity equations. An optical feature extraction subnetwork is input with the wavefront phase distribution, and the wavefront slope contribution of each sub-aperture region is dynamically weighted through an attention mechanism convolutional layer. The gated fusion unit performs cross-modal correlation between the physical features and optical features to generate initial predicted values ​​for the six-degree-of-freedom adjustment of the secondary mirror. Step 3: Perform kinematic feasibility verification and dynamic optimization on the initial predicted values, including using the Lie group space parameterization method to avoid singular points in rotational degrees of freedom and verifying the reachability of the platform's workspace through the Jacobian matrix. Step 4: Drive the secondary mirror adjustment platform based on the optimized adjustment parameters, and trigger online incremental learning of the neural network model based on the actual wavefront residual.

2. The primary and secondary mirror calibration method based on a neural network algorithm according to claim 1, characterized in that, The synchronous acquisition of multiphysics coupling data in step 1 specifically includes: The layout density of the temperature sensor array is determined based on the thermal diffusion characteristics of the primary mirror material, so that the spacing between adjacent sensors can capture nonlinear changes in the temperature gradient. The sampling frequency of the wavefront phase distribution is dynamically adjusted according to the dominant frequency component of the spectrum obtained by the vibration sensor to ensure that the sampling frequency and the dominant frequency component of the vibration form a preset multiple relationship. The time-domain acceleration signal is used to extract vibration features through time-frequency analysis, including the spectral energy distribution of the dominant frequency component, harmonic components, and random noise, and a vibration feature vector is constructed.

3. The primary and secondary mirror calibration method based on a neural network algorithm according to claim 1, characterized in that, The physical constraint layer described in step 2 is implemented as follows: The thermoelasticity equation is discretized into a differential operator form, which is then embedded as a regularization term in the neural network training process. The coefficients of the differential operator are dynamically adjusted according to the physical properties of the primary mirror material. Stress balance constraints are introduced during the feature mapping process of deformable convolutional layers, and the feature maps are made to satisfy the elasticity equilibrium equations through iterative optimization algorithms.

4. The primary and secondary mirror calibration method based on a neural network algorithm according to claim 1, characterized in that, The implementation of the attention mechanism convolutional layer in step 2 includes: Spatial attention weights are generated based on the statistical characteristics of the wavefront slope of each sub-aperture region, wherein the statistical characteristics include the variance and covariance matrix of the slope of the local region. A learnable nonlinear transformation module is introduced in the channel dimension, and the initialization parameters of the module are determined by the characteristic distribution law of historical calibration data.

5. The primary and secondary mirror calibration method based on a neural network algorithm according to claim 1, characterized in that, The specific process of verifying the kinematic feasibility in step 3 is as follows: The pose space boundary conditions are constructed based on the mechanical structure parameters of the secondary mirror adjustment platform, and the boundary conditions are dynamically updated through the singular value decomposition of the Jacobian matrix. An optimization algorithm with constraints is used to map the initial predicted values ​​to the reachable workspace. The constraints include the kinematic limit parameters of each axis of the platform.

6. The primary and secondary mirror calibration method based on a neural network algorithm according to claim 1, characterized in that, The dynamic optimization described in step 3 also includes: Establish a time series database of historical adjustment values, and use a time series prediction model to generate pose change trend curves; An anti-saturation control mechanism is introduced into the translation component calculation, and the control parameters are dynamically adjusted according to the distance between the current pose of the platform and the physical limit.

7. The primary and secondary mirror calibration method based on a neural network algorithm according to claim 1, characterized in that, The triggering condition for online incremental learning in step 4 is: Modal decomposition was performed on the wavefront residuals before and after adjustment, and the rate of change of higher-order aberration components was calculated. When the residual decay rate of higher-order aberration components is lower than a preset threshold, a model update is triggered. The threshold is dynamically calculated based on the statistical distribution of historical calibration data.

8. The primary and secondary mirror calibration method based on a neural network algorithm according to claim 7, characterized in that, The specific implementation of the incremental learning includes: Feature enhancement is performed on the abnormal samples that trigger updates, and the coverage of the training dataset is expanded through adversarial example generation techniques; An elastic weight fixation algorithm is used to calculate the importance index of neural network parameters, and the weight distribution of key features is preserved during the parameter update process.

9. The primary and secondary mirror calibration method based on a neural network algorithm according to claim 1, characterized in that, Step 1 also includes environmental parameter adaptation: The temperature cycling strategy is selected based on the type of working environment of the optical system. The strategy includes segmented setting of temperature change rate and dynamic division of temperature range. The mechanical vibration frequency range is dynamically set according to the resonance characteristics of the secondary mirror adjustment platform. The resonant frequency band is identified through frequency sweep testing and sensitive frequency ranges are automatically avoided.

10. The primary and secondary mirror calibration method based on a neural network algorithm according to claim 1, characterized in that, Step 3 is followed by mechanical resonance avoidance processing: Obtain the dynamic response characteristic curve of the secondary mirror adjustment platform and perform frequency domain pre-compensation on the adjustment command; The pre-compensation parameters are obtained by fitting the frequency response characteristics of the platform's input and output signals, and an enhanced weighting coefficient is applied to the resonant frequency band during the fitting process.

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