Wavefront-free adaptive optics method based on subspace trust region optimization

Abstract

This application provides a wavefront-free adaptive optics correction method based on subspace trust region optimization, belonging to the field of adaptive optics correction technology. The method includes: acquiring a far-field spot image and calculating the power in the bucket as the objective function; dividing the image into multiple subspace stages according to the increasing Zernike mode order, gradually expanding the subspace dimension from low to high order; constructing a local quadratic interpolation model within the current stage subspace, solving the model under the trust region radius constraint to generate candidate solutions, and updating the trust region radius and iteration point based on the ratio of the actual drop to the predicted drop; embedding the optimal solution of the current stage into the next stage subspace when the stage termination condition is met; and mapping the final Zernike mode coefficient vector to a deformable mirror control voltage after completing all stages, driving the wavefront corrector to complete wavefront correction. This application eliminates the need for bilateral perturbations and explicit gradient calculations, and has the advantages of fast convergence speed, high search efficiency, and high correction accuracy.

Description

Technical Field

[0001] This application relates to the field of adaptive optics correction technology, and more specifically, to a wavefront-free adaptive optics correction method with subspace trust region optimization. Background Technology

[0002] Adaptive optics is a key technology for correcting dynamic wavefront distortion in optical systems and restoring imaging resolution. The core principle of an adaptive optics system is to detect the distorted wavefront in real time, then use a controller to calculate a control signal to drive a phase modulation device to generate a conjugate compensation wavefront, thereby correcting the distorted wavefront aberration.

[0003] Traditional adaptive optics systems employ a wavefront sensor-based approach, using devices such as Shak-Hartmann wavefront sensors or curvature sensors to measure wavefront distortion in real time, and then compensating for it with wavefront correctors such as deformable mirrors. However, this wavefront sensor-based approach has the following drawbacks: First, the measurement system is complex and costly, and suffers from non-common optical path errors, affecting correction accuracy. Second, wavefront sensors require a significant amount of light energy; in scenarios with low light energy, such as strong turbulence or biological tissue fluorescence imaging, wavefront sensors struggle to obtain high signal-to-noise ratio measurements, failing to effectively detect the wavefront and causing the adaptive optics system to fail.

[0004] Wavefront-free adaptive optics systems offer a new technological approach to solving the aforementioned problems. These systems eliminate the need for independent wavefront sensors, directly utilizing indicators such as far-field spot intensity or encirclement radius as optimization functions. An optimization control algorithm iteratively optimizes the control voltage of the deformable mirror until the evaluation function reaches its optimal value. Compared to traditional adaptive optics systems that rely on wavefront sensors, wavefront-free systems, through simplified system design, reduce dependence on high-precision hardware, lower system complexity, and improve system flexibility and environmental adaptability. They offer significant cost-effectiveness and reliability advantages, demonstrating substantial advantages in applications such as free-space optical communication, microscopic imaging, astronomical observation, and laser fusion.

[0005] The core challenge of wavefront-less sensing adaptive optics systems lies in efficiently and rapidly reaching the optimal solution of the optimization function. Currently, iterative optimization algorithms are widely used in wavefront-less sensing adaptive optics systems, with stochastic parallel gradient descent and simulated annealing being representative examples. The stochastic parallel gradient descent algorithm estimates the gradient by applying random perturbations to the control variables and measuring the changes in the evaluation function, then updates the control variables along the gradient direction, gradually approaching the optimal solution.

[0006] However, existing wavefront-sensorless adaptive optics control technology still faces the following technical challenges: First, the algorithm suffers from numerous iterations and slow convergence. In wavefront-less adaptive optics systems, each calculation of the evaluation function requires acquiring a single camera image for evaluation metric calculation. The camera exposure and readout processes are significantly time-consuming, becoming a key bottleneck restricting the system's closed-loop response speed. To achieve gradient estimation, the stochastic parallel gradient descent algorithm requires bilateral perturbations (positive and negative) and the acquisition of two images for each, resulting in numerous evaluation iterations and a large total number of image frames required for convergence, making it difficult to meet the real-time requirements of dynamic aberration correction.

[0007] Second, the optimization dimensionality is high and the search efficiency is low. In wavefront-less adaptive optics systems, the number of deformable mirror drivers can typically reach tens to hundreds. If optimization is performed directly in the original voltage space, the control variables are highly dimensional and the search space is huge, resulting in slow algorithm convergence and a tendency to get trapped in local optima.

[0008] Third, fixed pattern subspaces struggle to balance coarse and fine search requirements. Traditional pattern subspace methods typically employ a fixed pattern order. If the order is too low, it becomes difficult to represent higher-order aberration components, limiting correction accuracy; if the order is too high, the solution space remains complex, leading to a decrease in convergence speed.

[0009] Furthermore, existing optimization algorithms exhibit significant lack of robustness when facing large-scale, strongly nonlinear wavefront distortions. On the one hand, most algorithms lack an effective global search mechanism, and when the objective function exhibits a multi-peak or multi-valley distribution, the correction results are highly sensitive to initial values, making it difficult to stably converge to the global optimum. On the other hand, as the number of deformable mirror elements and aberration complexity increase, the computational burden and engineering implementation difficulty of the algorithms increase significantly, limiting their widespread application in large-aperture systems and strongly turbulent environments.

[0010] Therefore, there is an urgent need for a novel wavefront prediction and correction method that can overcome the above-mentioned defects in order to improve the dynamic correction performance and robustness of wavefront-less adaptive optics systems in complex environments. Summary of the Invention

[0011] The purpose of this application is to provide a wavefront-free adaptive optics correction method based on subspace trust region optimization, which can solve at least one of the aforementioned technical problems. The specific solution is as follows: According to a specific embodiment of this application, this application provides a wavefront-free adaptive optics correction method with subspace trust region optimization, comprising the following steps: Acquire a far-field spot image, calculate the power in the bucket based on the far-field spot image, and generate an objective function value; The control variables of the deformable mirror are mapped to the Zernike mode space through the influence function matrix to generate the Zernike mode coefficient vector, and the Zernike mode coefficient vector is used as the optimization variable. The subspace is divided into multiple stages according to the increasing order of the Zernike pattern. In the initial stage, a low-order Zernike pattern is selected to construct a low-dimensional subspace, and in the subsequent stages, a high-order Zernike pattern is gradually introduced to expand the subspace dimension. Within the current stage subspace, an interpolation point set is selected around the current iteration point, and a local quadratic interpolation model is constructed based on the objective function value corresponding to the interpolation point set. The local quadratic interpolation model includes a gradient approximation term and a Hessian matrix approximation term. Under the current trust region radius constraint, the local quadratic interpolation model is minimized to generate candidate solutions, and the ratio of the actual decrease in the objective function corresponding to the candidate solution to the model's predicted decrease is calculated. When the ratio is greater than the first threshold, the candidate solution is accepted as a new iteration point and the trust region radius is expanded; when the ratio is less than the second threshold, the candidate solution is rejected and the trust region radius is reduced; in each iteration, the iterative update is completed based on the single evaluation result of the objective function corresponding to the candidate solution. When the termination condition is met in the current stage, the optimal Zernike mode coefficient vector of the current stage is embedded into the expanded subspace as the initial solution for the next stage. After all stages are completed, the final Zernike mode coefficient vector is mapped to the deformable mirror control voltage, which drives the wavefront corrector to complete the wavefront correction.

[0012] Furthermore, the local quadratic interpolation model is constructed using the NEWUOA algorithm.

[0013] Furthermore, the number of interpolation points in the local quadratic interpolation model is set to twice the dimension of the subspace at the current stage plus one, and each interpolation point corresponds to a set of Zernike mode coefficient sampling values ​​and the corresponding objective function value.

[0014] Furthermore, the method of embedding the optimal Zernike mode coefficient vector of the current stage into the expanded subspace as the initial solution for the next stage is as follows: The coefficient vector of the low-dimensional Zernike mode corresponding to the optimal solution in the current stage is used as the first few dimensions of the starting point for the next stage of optimization, and the coefficients of the newly added high-order Zernike modes in the next stage are initialized to zero.

[0015] Furthermore, the termination condition of the current stage is at least one of the following conditions: The power improvement rate in the bucket is lower than the preset improvement rate threshold, the number of iterations reaches the preset evaluation budget limit, and the trust region radius shrinks to the preset minimum trust region radius.

[0016] Furthermore, if the first threshold is greater than the second threshold, and the ratio is between the second threshold and the first threshold, a candidate solution is accepted as a new iteration point while the current trust region radius remains unchanged.

[0017] Furthermore, when dividing the subspace into multiple subspace stages according to the increasing order of the Zernike pattern, the order of the Zernike pattern contained in each stage subspace is determined according to a preset increasing sequence, and the dimension of the subspace in the later stage is greater than the dimension of the subspace in the previous stage.

[0018] Furthermore, the method of mapping the deformable mirror control variables to the Zernike mode space through the influence function matrix is ​​as follows: By multiplying the generalized inverse matrix of the deformable mirror influence function matrix with the Zernike mode basis function matrix, a linear mapping relationship is established between the Zernike mode coefficient vector and the control voltage of each actuator of the deformable mirror.

[0019] Furthermore, the Zernike mode space is replaced with the Carlo-Logate mode space or the intrinsic mode space.

[0020] Furthermore, the method for mapping the final Zernike mode coefficient vector to the deformable mirror control voltage is as follows: The control voltage vector of each actuator of the deformable mirror is obtained by multiplying the final Zernike mode coefficient vector with the pseudo-inverse matrix of the deformable mirror influence function matrix.

[0021] Compared with the prior art, the above-described solutions of this application have at least the following beneficial effects: 1. This application discloses a wavefront-free adaptive optics correction method based on subspace trust region optimization. By mapping the deformable mirror control variables from a high-dimensional voltage space to a low-dimensional Zernike mode space, the dimensionality of the optimization variables is significantly reduced. A staged subspace expansion strategy from low to high order is adopted. In the initial stage, only a small number of low-order Zernike modes are used to construct a low-dimensional subspace, which quickly approximates the main components of aberrations. A local quadratic interpolation model is constructed using a trust region derivative-free optimization algorithm, which does not require bilateral perturbations and explicit gradient calculations. Each iteration only requires a single objective function evaluation, which significantly reduces the number of camera image acquisitions and iterations, fundamentally improving the closed-loop convergence speed of the system and meeting the real-time requirements of dynamic aberration correction.

[0022] 2. This application discloses a wavefront-free adaptive optics correction method based on subspace trust region optimization. Through a staged subspace expansion strategy, the main aberration components are rapidly corrected in the initial stage to form a bright core for the light spot. Then, as iterations proceed, higher-order Zernike modes are gradually introduced to expand the subspace dimension, refining the correction of higher-order aberration components. A local quadratic interpolation model containing gradient approximation terms and Hessian matrix approximation terms is constructed using a trust region optimization algorithm, which can accurately capture the curvature information of the target function. The trust region radius is dynamically adjusted by the ratio of the actual descent to the predicted descent, ensuring that the iteration step size remains within a reasonable range. This achieves high-precision wavefront correction while ensuring rapid convergence, reaching diffraction-limited imaging quality.

[0023] 3. This application discloses a wavefront-free adaptive optics correction method based on subspace trust region optimization. By setting a dynamic adjustment mechanism for the trust region radius, it avoids the convergence instability problem caused by a fixed step size. By setting three stage termination conditions, it judges the convergence state from multiple dimensions, avoiding infinite iteration or premature termination. It adopts a hot-start strategy to embed the optimal solution of the previous stage into the next stage as the initial point, avoiding searching from zero. This enables the algorithm to stably converge to the optimal solution under different turbulence intensities and aberration conditions, and has wide applicability and robustness. Attached Figure Description

[0024] 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-free adaptive optics correction method with subspace trust region optimization, as shown in an embodiment of this application.

[0025] Figure 2 This is a flowchart illustrating the subspace trust region derivative-free optimization algorithm 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 wavefront-free adaptive optics correction method with subspace trust region optimization, implemented based on existing adaptive optics systems. A hardware environment for a wavefront-free adaptive optics system is constructed, comprising: a 632.8nm laser source, a turbulence simulator, a wavefront corrector, a focusing lens, a high-speed camera, and a wavefront controller. The wavefront corrector uses a deformable mirror with 40 actuators. The high-speed camera is used to acquire far-field spot images. The wavefront controller uses a high-performance computer and integrates staged expansion optimization software based on the NEWUOA algorithm. The selection of the deformable mirror must ensure that it meets the pupil diameter requirements of the adaptive optics system, that the response time matches the system bandwidth, and that the coating's operating wavelength range includes the actual wavelength. The selection of the high-speed camera must ensure that the camera frame rate is higher than the aberration variation frequency, has minimal readout noise, and high sensitivity. The high-speed camera should have its initial exposure time set to approximately 80% of the frame rate period and adjusted according to the actual spot intensity. The adaptive optics system in this application embodiment is to better explain a wavefront-free adaptive optics correction method with subspace trust region optimization. Any adaptive optics system in the prior art can be selected according to the actual situation, and this application embodiment does not limit it.

[0033] A flowchart of a wavefront-free adaptive optics correction method based on subspace trust region optimization is shown below. Figure 1 As shown, the algorithm workflow diagram is as follows: Figure 2 As shown, it includes the following steps: S1. Obtain the far-field spot image, calculate the power in the bucket based on the far-field spot image, and generate the objective function value.

[0034] The technical solution of this application embodiment selects in-bucket power as a performance evaluation index. Wavefront-free adaptive optics systems can also use the average radius of the weighted average distance from the far-field spot centroid to each pixel, the ring energy (the proportion of energy contained within a specific radius near the spot peak to the total energy), peak intensity, or the root mean square of the wavefront residual as performance evaluation indexes. In-bucket power is chosen because it has advantages such as clear physical meaning and simple calculation.

[0035] S2. Map the deformable mirror control variables to the Zernike mode space through the influence function matrix to generate the Zernike mode coefficient vector, and use the Zernike mode coefficient vector as the optimization variable.

[0036] In the technical solution of this application embodiment, the way to map the deformable mirror control variables to the Zernike mode space through the influence function matrix is ​​as follows: by multiplying the generalized inverse matrix of the deformable mirror influence function matrix with the Zernike mode basis function matrix, a linear mapping relationship is established between the Zernike mode coefficient vector and the control voltage of each actuator of the deformable mirror.

[0037] Using the Zernike mode coefficient vector as an optimization variable, the deformable mirror control problem is mapped from the high-dimensional voltage space to the low-dimensional Zernike mode subspace.

[0038] S3. Divide the space into multiple subspace stages according to the increasing order of the Zernike pattern. In the initial stage, select a low-order Zernike pattern to construct a low-dimensional subspace, and in the subsequent stages, gradually introduce a high-order Zernike pattern to expand the subspace dimension.

[0039] The Zernike pattern is divided into multiple subspace stages according to its increasing order. The total number of patterns is then determined based on the order from lowest to highest. =25 is divided into K subsets, meaning the number of subspace stages is K. Each subset corresponds to one optimization stage. In this embodiment, K=2 is set. In the initial stage, a low-order Zernike pattern is selected to construct a low-dimensional subspace, and in subsequent stages, a high-order Zernike pattern is gradually introduced to expand the subspace dimension.

[0040] The technical solution of this application adopts a search order from low to high order based on the characterization law of wavefront aberration energy by Zernike polynomials and the search characteristics of the optimization algorithm. Low-order Zernike modes account for the vast majority of the total wavefront distortion energy, while the energy proportion of high-order modes decreases sharply with the order. Choosing a search order from low to high order is essentially a coarse-to-fine search strategy. After correcting low-order aberrations first to form a bright core for the light spot, the halo changes caused by high-order aberrations can be further reflected. At this point, expanding the subspace dimension can improve the precision. The advantage of this technical solution is that the convergence speed is faster than using full-dimensional search, and the power in the far-field bucket can be improved in a very short time.

[0041] In the technical solution of this application embodiment, the number of subspace stages K represents the number of progressive levels into which the entire optimization process is divided, based on a balance between algorithm switching overhead and system convergence speed. When K=1, the search is performed directly in the high-dimensional space, incurring high-dimensional modeling overhead at each step and resulting in extremely slow convergence. When K>2, additional stage switching judgment calculations are introduced, and complex judgment conditions may be required to determine whether a switch is needed, introducing more computational overhead and algorithm complexity. This application embodiment selects K=2 to achieve a balance between algorithm switching overhead and system convergence speed. In practical applications, the value can be chosen according to the actual situation, and this application embodiment does not limit this.

[0042] In this embodiment, the order of Zernike patterns in each stage subspace is determined according to a preset increasing sequence, with the dimension of the subspace in each subsequent stage being greater than that in the previous stage. The number of patterns in each stage is 10 and 15 respectively; that is, the first stage uses the first 10 Zernike patterns to construct a low-dimensional subspace, and the second stage introduces Zernike patterns from the 11th to the 25th order to expand the subspace dimension to 25 dimensions. This is the initial stage subspace dimension. =10, Dimension of the second-stage subspace =25. In this embodiment, the total number of modes is also the total number of modes to be calibrated. =25, set the initial Zernike mode coefficient vector to zero.

[0043] Total number of patterns The core design parameter of the subspace trust region optimization-based wavefront-free adaptive optics correction method determines the dimension of the optimization problem, the range of correctable aberrations, and the final correction accuracy of the system. According to Noll's atmospheric turbulence theory, the wavefront distortion variance caused by Kolmogorov turbulence decreases exponentially with the Zernike mode order, meaning that the first 3 to 20th order Zernike modes account for most of the total aberration energy. In this embodiment, the following parameters are set... =25. After correcting the first 25 Zernike modes, the remaining higher-order aberrations account for a very small percentage of the total energy, and their impact on the system performance evaluation index can be ignored.

[0044] when When the value is small, it can greatly improve the convergence speed and is less prone to oscillation, but the correction accuracy is low, and it is difficult to increase the power in the bucket after it reaches a certain level, which may not meet the accuracy requirements. When Larger values ​​can improve correction accuracy, but also significantly increase the correction search time, and may lead to extremely slow convergence or even non-convergence due to an excessively large search space. In this embodiment, the selected... =25, achieving a balance between convergence speed and correction accuracy. In practical applications, this value can be chosen based on actual circumstances; the embodiments in this application do not impose limitations on this.

[0045] Initial stage subspace dimension The search dimension represents the search dimension in the fast search phase, and the dimension of the subspace in the final phase. Refine the search dimensions to represent the characteristics.

[0046] When the initial stage subspace dimension If the value is too small, only the first few orders of aberrations can be corrected. If there are large coma or other aberrations in the system, the light spot will still be asymmetrical, causing the power in the bucket to remain at a low level, making it impossible to trigger the judgment condition for entering a fine search. When the value is too large, it degenerates into an approximate high-dimensional search, the advantage of fast convergence in low-dimensional subspaces weakens, the initial correction accuracy improves but the convergence speed decreases, and the meaning of piecewise search is lost. If the value is too small, although the convergence speed is faster, the initial subspace cannot cover the main aberrations, resulting in poor coarse search performance and potential getting trapped in local optima. In this embodiment, the dimension of the subspace in the initial stage... The value of 10 is based on Noor's atmospheric turbulence theory. The first 10 Zernike models, from the 3rd to the 11th order, cover the main components of atmospheric turbulence wavefront aberrations, including primary aberrations such as tilt, defocus, astigmatism, coma, and spherical aberration. Optimization in a 10-dimensional subspace can ensure fast convergence and good numerical stability.

[0047] The dimension of the second-stage subspace, which is also the dimension of the final-stage subspace. The value of 25 is chosen because the first 25 Zernike modes accumulate most of the energy of the turbulent wavefront aberrations. After correction to the 25th order, the remaining higher-order aberrations have a negligible impact on the power in the far-field bucket, and the 25-dimensional subspace achieves a balance between convergence speed and correction accuracy. When the value is too small, the correction accuracy is insufficient, and the objective function is difficult to improve to the target value; when... When the value is too large, the search space becomes too large. Although higher-order aberrations can be corrected, the increased subspace dimension leads to a higher number of optimization iterations, and the condition number of the model point set may deteriorate, affecting numerical stability and convergence efficiency. In practical applications, the value can be selected according to the actual situation, and this application does not limit it in this regard.

[0048] In the technical solution of the embodiments of this application, , The values ​​of K and K are determined according to the following principles: First, based on the number of actuators and fitting ability of the deformable mirror, the maximum correctable mode order is determined. Then, based on the atmospheric turbulence intensity and correction accuracy requirements, the minimum model order that needs to be corrected is determined. The typical value range is =8-15; finally, according to / The ratio determines the number of stages K, where K = 2-4. This application's embodiment employs a two-stage strategy K = 2, directly using... =10 and =25 is used as the dimension of the subspace at each stage.

[0049] S4. Within the current stage subspace, select a set of interpolation points around the current iteration point, and construct a local quadratic interpolation model based on the objective function value corresponding to the set of interpolation points. The local quadratic interpolation model includes gradient approximation terms and Hessian matrix approximation terms.

[0050] For each stage index k, where k = 1, 2, ..., K, construct the mode response matrix corresponding to stage index k. Mode response matrix Its function is to establish the mapping relationship between the Zernike mode coefficient space and the deformable mirror actuator voltage space in the k-th stage. Mode construction essentially involves constructing corresponding response matrices based on the different mode numbers in the two stages; that is, when the stage index k=1, a mode response matrix corresponding to the 10-dimensional subspace is constructed. When the stage index k=2, construct the mode response matrix corresponding to the 25-dimensional subspace. .

[0051] The number of function evaluations, the initial trust region radius, and the minimum trust region radius are set. In this embodiment, the number of function evaluations in the first stage... Number of function evaluations in the second stage The initial trust region radius is set to =0.1, minimum trust region radius is set to =0.0001.

[0052] In the technical solution of this application embodiment, the number of function evaluations in the first stage... The value is determined based on the dimension of the first-stage subspace. =10 matching, a 10-dimensional subspace requires at least 22 interpolation points, and 70 function evaluations are approximately three times the number of interpolation points. This ensures the algorithm converges within 30 to 50 iterations and balances the computational cost of the coarse search phase. The second stage function evaluation count... The value is determined based on the dimension of the second-stage subspace. =25 matching, a 25-dimensional subspace requires at least 52 interpolation points, and 500 function evaluations are about 10 times the number of interpolation points, which ensures that the algorithm has enough iterations to complete the fine search in the high-dimensional space. It takes 200 to 400 iterations to improve the power in the bucket at the end of the coarse search to the diffraction limit.

[0053] The initial trust region radius of 0.1 is chosen to match the typical range of Zernike mode coefficients, ensuring the approximate accuracy of the local quadratic model within the trust region radius. The minimum trust region radius of 0.0001 is chosen to match the calibration accuracy requirements. When the trust region radius shrinks to this value, further adjustments have limited impact on the power in the bucket and can avoid infinite iteration.

[0054] The parameter settings in this embodiment are matched to the turbulence intensity of the selected turbulence simulator, and are empirical values ​​obtained through numerous repeated experiments. If the turbulence intensity changes, the values ​​in this embodiment can be used as initial values, and then adjusted according to the actual situation to achieve the best correction effect. Under weak turbulence conditions, the number of function evaluations can be appropriately reduced, while under strong turbulence conditions, the number of function evaluations can be appropriately increased.

[0055] This application provides a preferred technical solution where the local quadratic interpolation model is constructed using the NEWUOA algorithm. The NEWUOA algorithm is a novel unconstrained optimization algorithm implemented using the PDFO framework. The technical solution in this application uses the NEWUOA algorithm, which is a derivative-free optimization algorithm. It is well-encapsulated within the PDFO framework and can be directly called, eliminating the need to implement the trust region optimization logic from scratch, thus reducing algorithm implementation complexity while ensuring optimization performance.

[0056] The number of interpolation points in the local quadratic interpolation model is set to twice the dimension of the subspace at the current stage plus one, that is, the number of interpolation points is taken as... .in, This represents the dimension of the subspace at the current stage. An incomplete quadratic interpolation model is constructed to reduce modeling costs while preserving the curvature information of the objective function. Each interpolation point corresponds to a set of Zernike mode coefficient samples and the corresponding objective function value. The construction of the interpolation model includes: collecting an interpolation point set, where the number of interpolation points is no less than [number missing]. The number of interpolation points can strike a balance between the preservation of curvature information of the objective function and the computational cost of modeling. By constructing an incomplete quadratic interpolation model, the large number of interpolation points required for a complete quadratic model can be avoided, thus significantly reducing modeling overhead.

[0057] The expression for constructing the local quadratic interpolation model is:

[0058] in, This represents a local quadratic interpolation model; 'a' represents the constant term of the quadratic model, which is numerically equal to the model at the current iteration point. The estimated value at that location; This represents the base point of the i-th iteration in the current stage, which is usually updated from the iteration point accepted in the previous iteration; c represents the gradient estimate; c represents the Zernike mode coefficient vector. Let represent the approximate Hessian matrix for the i-th iteration; both the gradient estimate and the approximate Hessian matrix are obtained through interpolation conditions.

[0059] S5. Under the current trust region radius constraint, minimize the local quadratic interpolation model to generate candidate solutions, and calculate the ratio of the actual decrease in the objective function corresponding to the candidate solution to the model's predicted decrease.

[0060] Perform phased optimization. Initialize the starting point for the k-th phase of optimization. When k=1, let = When k≥2, utilize the optimal solution from the previous stage. To perform a warm start, the expression is:

[0061] The technical solution of this application embeds the optimal solution of the current stage into a higher-dimensional space, and initializes the higher-dimensional extended part to zero, so that the initial point of the hot start is located in the high-power region of the objective function. This method of embedding the optimal solution of the current stage into the extended subspace as the initial solution of the next stage, and initializing the newly added higher-order mode coefficients to zero, achieves a hot start, ensuring that the initial point of the next stage is located in the high-power region of the objective function, avoiding searching from zero and accelerating the convergence of subsequent stages.

[0062] by Starting from the current point, the trust region derivative-free optimization algorithm is used. A local quadratic interpolation model of the objective function is constructed in 3D space.

[0063] The trust region-based derivative-free optimization algorithm in this application embodiment is a derivative-free optimization algorithm that constructs a local surrogate model through function values ​​without calculating the derivative of the objective function, and uses the trust region framework to limit the step size to ensure the model's effectiveness.

[0064] Under the current trust region radius constraint, the local quadratic interpolation model is minimized to generate candidate solutions. The solution process is expressed as follows:

[0065] in, This represents the radius of the trust region in the current iteration.

[0066] In the i-th iteration, candidate points are obtained by minimizing the current local quadratic model within the trust region; the ratio is calculated based on the actual objective function values ​​of the candidate points. It decides whether to accept a candidate point as a new iteration point and updates the trust region radius; at the same time, if the objective function value of the candidate point is better than the current global best record, it updates the global best record.

[0067] Calculate the ratio of the actual decrease in the objective function corresponding to the candidate solution to the model-predicted decrease. To ensure good well-posedness of the interpolation point set, the ratio between the actual decrease and the expected decrease in the objective function is calculated, expressed as:

[0068] in, This represents the ratio in the i-th iteration; This represents the value of the original objective function at the current iteration point; This represents the value of the original objective function at the optimal solution; This represents the model's predicted value at the current iteration point; This represents the model's predicted value at the optimal solution; Let represent the local quadratic interpolation model for the i-th iteration.

[0069] S6. When the ratio is greater than the first threshold, accept the candidate solution as the new iteration point and expand the trust region radius; when the ratio is less than the second threshold, reject the candidate solution and shrink the trust region radius; in each iteration, complete the iterative update based on the single evaluation result of the objective function corresponding to the candidate solution.

[0070] according to Update iteration point and trust region radius: when When the value is greater than the first threshold, the local quadratic model is considered to have a good fit, and the candidate solution is accepted as a new iteration point and the trust region radius is expanded; when When the value is less than the second threshold, the model is considered to have a poor fit or an inappropriate step size; therefore, candidate solutions are rejected and the trust region radius is reduced. When the first threshold is greater than the second threshold, ... When the value falls between the second threshold and the first threshold, a candidate solution is accepted as a new iteration point while maintaining the current trust region radius unchanged. In this embodiment, the first threshold is set to 0.75 and the second threshold is set to 0.1. These thresholds are selected based on conventional empirical values ​​for the trust region algorithm, which can ensure convergence stability while also considering convergence speed.

[0071] In each iteration, the objective function is updated based on the single evaluation result of the candidate solution, without performing positive or negative perturbations to collect the objective function value.

[0072] The technical solution of this application embodiment limits the trust region radius to remain unchanged when the first threshold is greater than the second threshold and the ratio is between the two thresholds, forming a complete trust region radius adjustment strategy, namely, expanding, maintaining, and shrinking. When the model prediction accuracy is acceptable but not perfect, the radius remains unchanged, avoiding instability caused by frequent radius adjustments and enhancing the robustness of the algorithm.

[0073] S7. When the termination condition is met in the current stage, the optimal Zernike mode coefficient vector of the current stage is embedded into the expanded subspace as the initial solution for the next stage.

[0074] This application provides a preferred technical solution where the current stage iteration stops if any of the following conditions are met: the power improvement rate in the bucket at the current stage is below a certain percentage; the number of iterations reaches the upper limit of the evaluation budget; or the trust region radius shrinks to the lower limit. When a stage meets the termination condition, the algorithm stops iterating and records the optimal solution and the corresponding optimal power value in the bucket. Record the optimal solution for the current stage k. And the corresponding optimal power in the bucket. Three termination conditions are set: power improvement rate threshold in the bucket, upper limit of the number of iterations, and lower limit of the trust region radius. The termination of the stage is judged comprehensively from three dimensions: accuracy, computational cost, and convergence, so as to avoid infinite iteration or premature termination and ensure that the optimization of each stage is sufficient and efficient.

[0075] There is no universally applicable fixed formula for the percentage threshold of power improvement rate in the bucket; it needs to be calibrated based on the actual characteristics of the convergence stage. The method used in this embodiment is to observe the trend of the convergence curve through a sliding window. If the power improvement rate in the bucket slows down significantly within a certain window and does not change significantly in a short period of time, it is determined that the algorithm may be trapped in a local extremum or the convergence limit of the coarse search stage. In this case, the stage switching determination can be made based on the actual ratio.

[0076] The value of the trust region radius shrinking to the lower limit is based on the following: In the NEWUOA algorithm, the minimum trust region radius is taken by default as the initial trust region radius multiplied by 0. In this embodiment, the following is selected: This is due to the limitation of voltage quantization accuracy of the deformable mirror actuator. Specifically, the voltage adjustment corresponding to the change of Zernike mode coefficients below 0.0001 root mean square value cannot be actually applied to the deformable mirror, and further optimization has no physical meaning.

[0077] When the termination condition is met in the current stage, the optimal Zernike model coefficient vector of the current stage is embedded into the expanded subspace as the initial solution for the next stage. The method for embedding the optimal solution of the current stage into the expanded subspace as the initial solution for the next stage is as follows: the low-dimensional Zernike model coefficient vector corresponding to the optimal solution of the current stage is used as the first few dimensions of the starting point of the optimization in the next stage, and the coefficients corresponding to the newly added high-order Zernike models in the next stage are initialized to zero.

[0078] The technical solution of this application achieves dimensionality reduction optimization by mapping the voltage space to the Zernike pattern space, significantly reducing the dimensionality of the search space; it adopts a phased subspace expansion strategy from low to high order to achieve progressive optimization from coarse to fine; it uses a trust region derivative-free optimization algorithm to construct a local quadratic interpolation model, which does not require bilateral perturbations and explicit gradient calculations, and only requires a single objective function evaluation per iteration, significantly reducing the number of camera image acquisitions and improving the convergence speed; and it dynamically adjusts the trust region radius by the ratio of the actual descent to the predicted descent to ensure the stability and convergence of the algorithm.

[0079] S8. After completing all stages, the final Zernike mode coefficient vector is mapped to the deformable mirror control voltage to drive the wavefront corrector to complete the wavefront correction.

[0080] When k=K, that is, after the final stage is completed, the complete result is obtained. =Optimal coefficient vector in 25-dimensional Zernike pattern The final Zernike mode coefficient vector is multiplied by the pseudo-inverse of the deformable mirror influence function matrix to obtain the control voltage vector of each actuator of the deformable mirror. Based on this, the control voltage of the deformable mirror is calculated and the wavefront corrector is driven to complete the wavefront correction of the current frame.

[0081] In an alternative embodiment, the Zernike mode space is replaced with the Carlo-Logate mode space or the intrinsic mode space. The advantages of each of the three modes and the criteria for selection are as follows: Zernike models have clear physical meanings and strong versatility, facilitating the analysis of the main components of wavefronts, and are generally chosen as the default basis. Carlo-Loggett models, based on principal component analysis of turbulence statistical models, decompose the turbulent wavefront into a series of statistically independent models. They are linear combinations of Zernike models and can reduce crosstalk between models. However, Carlo-Loggett models depend on specific turbulence models, and their advantages diminish when deviating from the model; furthermore, each model lacks an intuitive physical picture. Eigenmodes decompose the influence function matrix of deformable mirrors using singular value decomposition, representing the most efficient deformation mode of the mirror. However, deformable mirror eigenmodes are highly hardware-dependent; recalculation is required when replacing the mirror, resulting in a large computational burden for deformable mirrors with a large number of actuators. In practical applications, the choice can be made based on specific circumstances; this application does not impose any limitations on this.

[0082] The technical solution of this application provides a wavefront-free adaptive optics correction method based on subspace trust region optimization. By using Zernike subspace technology, the optimization problem of a large-scale wavefront-free adaptive optics system is decomposed into smaller sub-problems, significantly reducing computational load and improving system real-time performance. Subspace technology reduces the computational load of each iteration, thereby reducing error accumulation in numerical calculations and improving the numerical stability of the algorithm. Simultaneously, when optimizing in the subspace, the search range of the algorithm is limited to a low-dimensional space, avoiding the instability factors that may arise from global search. The technical solution of this application does not rely on wavefront sensors and is applicable to various complex optical systems, especially in scenarios where wavefront sensors are difficult to use. The trust region optimization algorithm, by constructing a local quadratic model and solving the trust region sub-problems in a low-dimensional subspace, can accurately adjust the control parameters of optical components, effectively improving optimization accuracy.

[0083] 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.

[0084] 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 wavefront-free adaptive optics correction method with subspace trust region optimization, characterized in that, Includes the following steps: Acquire a far-field spot image, calculate the power in the bucket based on the far-field spot image, and generate an objective function value; The control variables of the deformable mirror are mapped to the Zernike mode space through the influence function matrix to generate the Zernike mode coefficient vector, and the Zernike mode coefficient vector is used as the optimization variable. The subspace is divided into multiple stages according to the increasing order of the Zernike pattern. In the initial stage, a low-order Zernike pattern is selected to construct a low-dimensional subspace, and in the subsequent stages, a high-order Zernike pattern is gradually introduced to expand the subspace dimension. Within the current stage subspace, an interpolation point set is selected around the current iteration point, and a local quadratic interpolation model is constructed based on the objective function value corresponding to the interpolation point set. The local quadratic interpolation model includes a gradient approximation term and a Hessian matrix approximation term. Under the current trust region radius constraint, the local quadratic interpolation model is minimized to generate candidate solutions, and the ratio of the actual decrease in the objective function corresponding to the candidate solution to the model's predicted decrease is calculated. When the ratio is greater than the first threshold, the candidate solution is accepted as a new iteration point and the trust region radius is expanded; when the ratio is less than the second threshold, the candidate solution is rejected and the trust region radius is reduced. In each iteration, the iterative update is completed based on the single evaluation result of the objective function corresponding to the candidate solution; When the termination condition is met in the current stage, the optimal Zernike mode coefficient vector of the current stage is embedded into the expanded subspace as the initial solution for the next stage. After all stages are completed, the final Zernike mode coefficient vector is mapped to the deformable mirror control voltage, which drives the wavefront corrector to complete the wavefront correction.

2. The wavefront-free adaptive optics correction method according to claim 1, characterized in that, The local quadratic interpolation model is constructed using the NEWUOA algorithm.

3. The wavefront-free adaptive optics correction method according to claim 2, characterized in that, The number of interpolation points in the local quadratic interpolation model is set to twice the dimension of the subspace in the current stage plus one, and each interpolation point corresponds to a set of Zernike mode coefficient sampling values ​​and the corresponding objective function value.

4. The wavefront-free adaptive optics correction method according to claim 1, characterized in that, The method of embedding the optimal Zernike mode coefficient vector of the current stage into the expanded subspace as the initial solution for the next stage is as follows: The coefficient vector of the low-dimensional Zernike mode corresponding to the optimal solution in the current stage is used as the first few dimensions of the starting point for the next stage of optimization, and the coefficients of the newly added high-order Zernike modes in the next stage are initialized to zero.

5. The wavefront-free adaptive optics correction method according to claim 1, characterized in that, The termination condition for the current stage is at least one of the following conditions: The power improvement rate in the bucket is lower than the preset improvement rate threshold, the number of iterations reaches the preset evaluation budget limit, and the trust region radius shrinks to the preset minimum trust region radius.

6. The wavefront-free adaptive optics correction method according to claim 1, characterized in that, If the first threshold is greater than the second threshold, and the ratio is between the second threshold and the first threshold, a candidate solution is accepted as a new iteration point while the current trust region radius remains unchanged.

7. The wavefront-free adaptive optics correction method according to claim 1, characterized in that, When dividing the space into multiple subspace stages according to the increasing order of the Zernike pattern, the order of the Zernike pattern contained in each stage subspace is determined according to a preset increasing sequence, and the dimension of the subspace in the later stage is greater than the dimension of the subspace in the previous stage.

8. The wavefront-free adaptive optics correction method according to claim 1, characterized in that, The method of mapping the deformable mirror control variables to the Zernike mode space through the influence function matrix is ​​as follows: By multiplying the generalized inverse matrix of the deformable mirror influence function matrix with the Zernike mode basis function matrix, a linear mapping relationship is established between the Zernike mode coefficient vector and the control voltage of each actuator of the deformable mirror.

9. The wavefront-free adaptive optics correction method according to claim 1, characterized in that, Replace the Zernike mode space with the Carlo-Logate mode space or the intrinsic mode space.

10. The wavefront-free adaptive optics correction method according to claim 1, characterized in that, The method for mapping the final Zernike mode coefficient vector to the deformable mirror control voltage is as follows: The control voltage vector of each actuator of the deformable mirror is obtained by multiplying the final Zernike mode coefficient vector with the pseudo-inverse matrix of the deformable mirror influence function matrix.

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