A closed-loop control method and system for a wavefront-sensing-free adaptive optics system

Abstract

This invention relates to a closed-loop control method and system for a wavefront-sensorless adaptive optics system, belonging to the field of optical communication technology. It addresses the challenge of achieving stable, real-time, and reliable wavefront correction in wavefront-sensorless adaptive optics systems under the combined effects of strong turbulence, closed-loop delay, and deformable mirror actuator constraints. The method involves acquiring and preprocessing a focal plane PSF image; estimating the residual Zernike coefficient estimation vector of the current frame using a residual wavefront estimation neural network; predicting the residual wavefront using an autoregressive prediction model, and aligning it to the actual effective time of the deformable mirror command after non-integer frame delay compensation; and using a constrained model predictive controller to solve for the optimal deformable mirror voltage increment in the first step under voltage amplitude and voltage change rate constraints, outputting the corresponding control command to the deformable mirror actuator to achieve stable closed-loop adaptive optics correction. This invention improves the real-time performance, stability, and engineering feasibility of closed-loop control under high-speed dynamic turbulence.

Description

Technical Field

[0001] This invention relates to the field of optical communication technology, specifically to a closed-loop control method and system for a wavefront-sensorless adaptive optics system. Background Technology

[0002] Adaptive optics was initially designed to address wavefront distortion caused by light propagating through complex media such as atmospheric turbulence, optical system errors, and biological tissue scattering. Simply put, ideally, a light beam should form a relatively concentrated focal spot or a clear image after passing through an optical system. However, in actual propagation, the refractive index of the medium is not perfectly uniform, especially when passing through atmospheric turbulence, where factors such as temperature, pressure, and wind speed cause random fluctuations in the refractive index. After propagating in such media, the phase of the light wave undergoes spatial and temporal perturbations, ultimately manifesting as wavefront distortion at the receiver, broadening of the point spread function (PSF), dispersion of beam energy, image blurring, and a decrease in the Strehl ratio.

[0003] In scenarios such as astronomical observation, long-distance imaging, laser communication, and free-space optical communication, wavefront distortion directly impacts system performance. For example, in astronomical imaging, atmospheric turbulence can cause star images to expand, resulting in an actual angular resolution far below the telescope's diffraction limit. In long-distance imaging, target images may exhibit blurring, jitter, and decreased contrast. In free-space optical communication, turbulence can cause the received light spot to drift, expand, and flicker, reducing receiver coupling efficiency and signal stability. In coherent optical communication or fiber-coupled receiver systems, wavefront distortion can also reduce mixing efficiency and single-mode fiber coupling efficiency, thereby affecting communication bit error rate and link reliability. Therefore, how to rapidly measure and compensate for dynamic wavefront aberrations introduced by the propagation path is a key issue in these optical systems.

[0004] Adaptive optics (AO) was developed to address this problem. A typical adaptive optics system usually consists of three parts: a wavefront sensor, a real-time controller, and a wavefront corrector. The wavefront sensor measures the distortion of the current incident wavefront, the real-time controller calculates correction commands based on the measurement results, and the wavefront corrector typically uses a deformable mirror (DM) or a spatial light modulator to apply reverse phase compensation to the incident wavefront. Through this closed-loop process, the system can correct the originally distorted wavefront as close as possible to a plane wave or an ideal wavefront, thereby improving the focal spot concentration and image quality.

[0005] In traditional adaptive optics, commonly used wavefront sensors include Shack-Hartmann wavefront sensors, pyramid wavefront sensors, and curvature wavefront sensors. Shack-Hartmann wavefront sensors divide the incident wavefront into multiple sub-apertures using a microlens array and estimate the local wavefront slope based on the focal spot offset of each sub-aperture. Pyramid wavefront sensors typically use pyramidal prisms near the focal plane to divide the beam into multiple pupil images and then infer the wavefront error based on the intensity distribution. Curvature wavefront sensors estimate the wavefront curvature by utilizing the difference in intensity distribution before and after focus. These methods have been widely used in astronomical observations and high-resolution imaging and represent relatively mature adaptive optics technologies.

[0006] However, while traditional wavefront sensing adaptive optics can directly obtain wavefront information, it still has some engineering limitations. First, the system requires an additional wavefront sensor and a beam splitter, resulting in a complex overall structure and high debugging and calibration costs. Second, the measurement optical path of the wavefront sensor is often not entirely the same as the scientific optical path used for imaging or communication, which introduces so-called non-common-path aberration (NCPA). That is, there may be a discrepancy between the aberration measured by the wavefront sensor and the aberration actually experienced by the scientific camera or communication receiver; this error needs additional calibration, otherwise it will remain in the system. Third, in low photon count, strong turbulence, extended targets, or irregular scenarios, the measurement sensitivity and stability of traditional wavefront sensors decrease. For example, the Shaker-Hartmann sensor relies on sub-aperture focal spot localization; when light intensity is insufficient, the focal spot is severely distorted, or the sub-aperture signal quality is poor, wavefront slope estimation becomes unreliable.

[0007] From a control perspective, adaptive optics not only needs to be "accurate in measurement" but also "capable of keeping up." Atmospheric turbulence changes over time, and the wavefront state is not static. In his classic study on adaptive optics bandwidth (Greenwood, Bandwidth specification for adaptive optics systems, Journal of the Optical Society of America, 1977), Greenwood pointed out that turbulence correction systems need to meet certain time bandwidth requirements; otherwise, even if the wavefront measurement is accurate at a certain moment, the correction command may lag behind the actual turbulence state by the time it reaches the deformable mirror. For high-speed free-space optical communication or strong turbulence imaging scenarios, millisecond-level delays in the system's sampling, calculation, and execution processes can all translate into significant correction errors. Therefore, the performance of an adaptive optics system depends not only on the accuracy of wavefront estimation but also on closed-loop delay, control algorithms, and actuator constraints.

[0008] This problem is even more pronounced in the field of free-space optical communication. Free-space optical communication utilizes atmospheric channels to transmit optical signals, offering advantages such as high bandwidth, high speed, and resistance to electromagnetic interference. However, atmospheric turbulence can cause beam drift, beam spread, intensity flicker, and phase distortion. For coherent reception or single-mode fiber-coupled reception systems, the receiver is not only concerned with the light intensity but also with the wavefront quality, as a distorted wavefront reduces the matching degree between the beam and the local oscillator or single-mode fiber mode. Existing research (e.g., Liu et al., Adaptive optics for the free-space coherent optical communications, Optics Communications, 2016) has shown that introducing adaptive optics correction can improve mixing efficiency, fiber coupling efficiency, and link performance in free-space coherent optical communication. Therefore, in free-space optical communication systems, adaptive optics is not only a tool for improving imaging quality but can also be considered a key module for improving communication reception efficiency and stability.

[0009] Beyond astronomy and communications, adaptive optics is increasingly being used in high-resolution microscopy (e.g., Booth, Adaptive optical microscopy: the ongoing quest for a perfect image, Light: Science & Applications, 2014), particularly for imaging deep biological tissues. The complex refractive index distribution within biological tissues leads to aberrations and scattering of the light beam during propagation, resulting in decreased resolution and signal-to-noise ratio in microscopic imaging. Compensating for system and sample-induced aberrations using adaptive optics can improve the clarity of deep imaging and achieve near-diffraction-limited imaging capabilities. In other words, the core idea of ​​adaptive optics is not limited to atmospheric turbulence correction; essentially, it involves real-time compensation for wavefront distortions caused by various propagation paths or systematic errors.

[0010] In summary, in optical systems such as astronomical observation, long-distance imaging, free-space optical communication, and biological microscopy, propagation medium and systematic errors introduce dynamic wavefront distortion, leading to PSF broadening, image blurring, spot energy dispersion, and decreased communication reception efficiency. Traditional adaptive optics uses a closed-loop structure of "wavefront sensor + real-time controller + deformable mirror" for correction, which is a classic technical approach to solve this problem. However, traditional solutions rely on dedicated wavefront sensors and independent measurement optical paths, resulting in system complexity, non-common-path aberrations, measurement difficulties under low-photon conditions, and delay sensitivity under high-speed dynamic turbulence. Therefore, there is a practical need to develop wavefront-sensorless adaptive optics and its fast estimation and stable control methods in scenarios requiring simpler hardware, measurement paths closer to actual imaging / communication channels, and high-speed closed-loop correction.

[0011] Wavefront-less adaptive optics systems no longer directly use dedicated wavefront sensors. Instead, they utilize focal plane spread function (PSF) images acquired by scientific cameras to deduce wavefront aberrations or Zernike mode coefficients. This simplifies the hardware structure, allows more light energy to enter the imaging or communication detection channels, and reduces the impact of non-common-path aberrations. However, this approach also introduces new technical challenges: PSF images provide focal plane intensity information but lack phase information. Therefore, inverting the wavefront phase from a single PSF image is a nonlinear, ill-conditioned, and potentially non-unique problem. Different wavefront phase distributions can produce similar PSF intensity images, especially in the presence of phase sign ambiguity, noise perturbations, and strong turbulent distortion, making the mapping from a single PSF image to Zernike coefficients even more difficult.

[0012] Existing wavefront-free sensing methods typically employ phase diversity, multiple perturbation measurements, image quality evaluation function optimization, or iterative search to estimate the wavefront. These methods often require multiple frames of images, multiple deformable mirror probes, or lengthy optimization processes. While they can operate under static or slowly changing aberration conditions, they are prone to problems such as insufficient estimation speed, response lag, and difficulty in real-time loop closure in scenarios with rapidly changing atmospheric turbulence. Especially in free-space optical communication, long-distance imaging, and high-speed adaptive optics correction, turbulence may change on a millisecond timescale, and multiple iterative measurements can lead to changes in the actual wavefront state before the estimation results are completed.

[0013] Deep learning methods can rapidly estimate residual Zernike coefficients from a single-frame PSF image using neural networks, thereby reducing the time overhead of traditional iterative wavefront-free methods. However, relying solely on the Zernike coefficients of the current frame output by the neural network is still insufficient to guarantee closed-loop correction performance. This is because, in practical closed-loop adaptive optics systems, there is a non-negligible time delay between the formation of the PSF image and the actual correction effect of the deformable mirror. This delay includes at least the equivalent measurement delay introduced by camera exposure integration, image transmission and neural network inference time, control computation time, and deformable mirror drive response time. In other words, the residual wavefront estimate output by the neural network does not strictly correspond to the moment when the deformable mirror actually applies correction, but rather to the wavefront state at a past moment or near the center of the exposure time.

[0014] Under conditions of strong turbulence or rapid time-varying turbulence, wavefront aberrations continue to evolve within the aforementioned delay time. If the controller directly uses the current neural network estimate to drive the deformable mirror, it is equivalent to using a wavefront estimate from the "past moment" to correct the actual wavefront at the "future execution moment," resulting in a misalignment between the measurement and execution times. This time mismatch causes a lag in the deformable mirror's compensation phase, leading to an increase in the residual root mean square (RMS), a decrease in PSF energy concentration, and a reduction in the Strehl ratio. In severe cases, it may even cause oscillations or performance degradation in the closed-loop control. Therefore, it is necessary to solve the problem of predicting the residual Zernike coefficients estimated by the neural network to the actual moment when the deformable mirror command takes effect under conditions without wavefront sensing, thereby reducing the correction lag caused by the closed-loop delay.

[0015] Furthermore, the closed-loop delay in practical systems is usually not an integer multiple of the sampling period. For example, camera exposure can be equivalent to a measurement delay of half an exposure period, while neural network inference time and deformable mirror response time may be on the order of several milliseconds or microseconds. The total delay obtained by adding these three factors often corresponds to a non-integer number of frames. If the control method simply compensates for the delay in integer frames, such as predicting 2 or 3 frames forward, a sub-frame-level time deviation will remain. In high-speed adaptive optics systems, even such a deviation of less than one frame can lead to considerable residual errors. Therefore, it is also necessary to address the residual wavefront prediction and time alignment problems under non-integer frame closed-loop delays.

[0016] Meanwhile, deformable mirrors, as actuators, are not ideal control elements with infinite bandwidth and infinite stroke. Each actuator in a real deformable mirror has limitations on voltage amplitude range, maximum stroke, inter-frame voltage change rate, drive response speed, and mechanical fatigue. If the controller does not explicitly consider these constraints and directly calculates the deformable mirror voltage based on the estimated Zernike coefficients, it may generate excessively large voltage commands or excessively rapid voltage changes. Under strong turbulence conditions, the required correction amplitude is even greater, and direct control or fixed-gain integral control can easily cause the voltage of some actuators to approach or even exceed the safe range, resulting in drive saturation, correction distortion, and even increasing the long-term operational risk of the deformable mirror. Therefore, it is also necessary to solve the problem of how to ensure the wavefront correction effect while making the deformable mirror control command meet the voltage amplitude and inter-frame change rate constraints.

[0017] In summary, although existing technologies can achieve correction for both wavefront-sensing adaptive optics and wavefront-free adaptive optics to a certain extent, they still have the following shortcomings for the application scenario of "wavefront-free, high-speed closed-loop, strong turbulence, and constrained control of deformable mirrors":

[0018] I. Traditional wavefront sensing adaptive optics systems have complex hardware structures and are easily affected by non-common-path aberrations:

[0019] Traditional adaptive optics systems typically employ Shack-Hartmann wavefront sensors, pyramidal wavefront sensors, or curvature wavefront sensors to directly measure wavefront distortion, followed by a real-time controller calculating deformable mirror control commands. While effective in many scenarios, this approach requires additional wavefront sensors, beam splitters, and independent measurement optical paths, resulting in a relatively complex system structure and high assembly and calibration costs. Furthermore, the measurement optical path of traditional wavefront sensors is often not entirely consistent with the actual imaging or communication detection optical path, introducing non-common-path aberrations and affecting the final correction results.

[0020] II. Traditional wavefront-sensorless adaptive optics systems typically require multiple frames of measurement or iterative optimization, resulting in a slow response speed.

[0021] Common methods employed in existing wavefront-less adaptive optics systems include phase diversity, image quality evaluation function optimization, SPGD-like stochastic parallel gradient descent methods, and mode-by-mode perturbation search methods. These methods share the characteristic of not directly using traditional wavefront sensors, but rather inferring or optimizing wavefront correction amounts based on changes in focal plane image quality. However, these methods typically require multiple image acquisitions, multiple perturbations, or iterative searches to find an optimal deformable mirror correction command. This strategy works under static aberration or slowly changing aberration conditions; however, in rapidly changing atmospheric turbulence, the wavefront state continuously changes during iteration, causing the aberration to be corrected to change before the algorithm converges. Therefore, these methods are prone to insufficient response speed, control lag, and poor real-time performance in high-speed, highly turbulent scenarios.

[0022] Third, existing deep learning wavefront estimation methods mostly focus on static estimation accuracy and do not fully consider closed-loop control delay:

[0023] In recent years, methods have also emerged that use CNNs, Transformers, or other deep neural networks to estimate wavefront aberrations or Zernike coefficients from PSF images. These methods offer a speed advantage over traditional iterative, wavefront-sensorless methods, as they can output wavefront estimation results from a single frame. However, existing deep learning wavefront estimation methods typically focus primarily on the static estimation problem of whether the current PSF image can accurately regress the current wavefront coefficients, without fully considering the time delay in actual closed-loop control. In real-world systems, there is a time lag between camera exposure, image readout, neural network inference, control calculation, and the deformable mirror drive response. That is, the wavefront estimation result output by the neural network corresponds to the wavefront state near the measurement moment or exposure center, while by the time the deformable mirror actually applies compensation, the actual turbulent wavefront has already evolved to a new state. In weak turbulence or slowly changing scenarios, this time mismatch may not be significant; however, in strong turbulence and high-speed closed-loop scenarios, this delay will cause control commands to lag, leading to increased residual wavefront RMS, decreased PSF energy concentration, reduced Strehl ratio, and even exacerbated fluctuations in direct closed-loop control.

[0024] IV. Existing methods are insufficient in handling delays in non-integer frames, easily leaving sub-frame level time errors:

[0025] In real-world systems, the closed-loop delay is not necessarily equal to an integer number of frames, such as 1, 2, or 3 frames. Camera exposure can be equivalent to the measurement delay of half an exposure cycle, neural network inference time may be several milliseconds, and deformable mirror response time may be tens of microseconds or higher. Adding these times together and dividing by the sampling period often yields a non-integer frame delay.

[0026] For example, with a sampling period of 1ms, an exposure centering delay of approximately 0.5ms, a neural network inference time of approximately 2ms, and a deformable mirror response time of approximately 20µs, the total delay corresponds to approximately 2.52 frames. If existing methods compensate only on an integer frame basis, such as simply predicting 2 or 3 frames, a time deviation of approximately 0.52 or 0.48 frames will still remain. For high-speed adaptive optics systems, this sub-frame level deviation can still cause significant residual phase errors.

[0027] V. Traditional direct control or fixed gain control does not explicitly consider the voltage constraint of the deformable mirror, resulting in insufficient control stability and actuator safety.

[0028] In some existing schemes, after the neural network or estimation algorithm outputs the wavefront coefficients, the deformable mirror voltage command can be directly generated through pseudo-inverse mapping, fixed-gain integrators, or simple proportional control. These methods are structurally simple, but they do not explicitly consider the physical constraints of the deformable mirror actuators. Each actuator in a real deformable mirror has upper and lower voltage limits, maximum stroke, inter-frame voltage change rate limits, and mechanical response limits. If the controller directly generates the voltage command based on the estimation error, problems such as excessively large voltage amplitudes, excessively rapid inter-frame voltage changes, and actuator saturation may occur under conditions of strong turbulence or large estimation errors. This not only reduces the actual correction effect but may also increase the driving burden on the deformable mirror and the risk of long-term mechanical fatigue.

[0029] VI. While using only unpredictable MPC can improve stability, time mismatch issues still exist under strong turbulence:

[0030] Compared to direct control, Model Predictive Control (MPC) can optimize the deformable mirror voltage command within a certain prediction time domain and incorporate actuator constraints, thus improving closed-loop stability. However, if MPC still uses the residual coefficients output by the neural network at the current measurement moment, without predicting these residual coefficients to the actual execution moment of the deformable mirror, a time mismatch still exists in the control objective. In other words, while MPC without delay compensation can limit the voltage command and reduce over-excitation control, its optimization object may still be an outdated wavefront state. Under strong turbulence conditions, the turbulence changes rapidly, increasing the residual phase difference between the measurement and execution moments, thus limiting the correction performance of non-predictive MPC.

[0031] Therefore, how to quickly estimate the residual wavefront Zernike coefficients based solely on focal plane PSF images without using traditional wavefront sensors, and how to predict and compensate for non-integer frame time delays in strongly turbulent closed-loop systems, while simultaneously optimizing control commands under conditions where the amplitude and rate of change of deformable mirror voltage are limited, in order to achieve stable closed-loop correction of wavefront-free adaptive optics systems in dynamic turbulent environments, improve residual wavefront error suppression capabilities, and enhance imaging and communication spot quality, are urgent problems to be solved in wavefront-free adaptive optics systems. Summary of the Invention

[0032] The purpose of this invention is to provide a closed-loop control method and system for a wavefront-sensorless adaptive optics system. This system enables residual wavefront estimation based solely on focal plane PSF images without relying on traditional wavefront sensors. Through online autoregressive prediction and non-integer delay compensation, the estimation results are aligned to the actual effective time of the deformable mirror. Finally, a constrained model predictive controller generates deformable mirror control commands that meet voltage amplitude and voltage change rate limits, thereby achieving stable, real-time, and reliable wavefront correction.

[0033] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0034] A closed-loop control method for a wavefront-sensorless adaptive optics system includes the following steps:

[0035] Step 1: The scientific camera continuously acquires the focal plane spread function image after turbulence and compensation by the current wavefront corrector at a preset sampling frequency;

[0036] Step 2: Preprocess the spread function image of the focal plane point to obtain the preprocessed image;

[0037] Step 3: Input the preprocessed image into the pre-trained residual wavefront estimation neural network to obtain the residual Zernike coefficient estimation vector of the current frame;

[0038] Step 4: Based on the residual Zernike coefficient estimates of the current frame and historical frames, update the parameters of the autoregressive prediction model online, and use the updated autoregressive prediction model to predict the residual Zernike coefficient vector for future time moments.

[0039] Step 5: Calculate the total closed-loop delay of the wavefront-sensorless adaptive optics system. When the number of frames corresponding to the total closed-loop delay is not an integer, perform non-integer frame delay compensation. After compensation, obtain the residual Zernike coefficient prediction vector at the actual effective time of the deformable mirror command.

[0040] Step 6: Establish the mapping relationship between the voltage of the deformable mirror actuator and the wavefront compensation phase, including the deformable mirror influence matrix and the Zernike basis matrix, and construct a constrained model predictive controller based on the deformable mirror influence matrix and the Zernike basis matrix;

[0041] Step 7: Input the residual Zernike coefficient prediction vector into the constrained model predictive controller. The constrained model predictive controller solves the optimization objective function, including at least the current control cycle, under the condition of satisfying the voltage amplitude constraint and voltage change rate constraint of the deformable mirror, and obtains the first step optimal deformable mirror voltage increment of the current control cycle.

[0042] Step 8: Apply the optimal deformable mirror voltage increment from step 1 to the deformable mirror actuator to compensate for the incident wavefront until the scientific camera acquires the next frame image, then continue with step 2.

[0043] Accordingly, the present invention also provides a closed-loop control system for a wavefront-less adaptive optics system, comprising:

[0044] A scientific camera is used to continuously acquire focal plane point spread function images at a preset sampling frequency after turbulence and compensation by the current wavefront corrector.

[0045] The image preprocessing module is used to preprocess the focal plane point spread function image to obtain a preprocessed image;

[0046] The residual wavefront estimation module is used to input the preprocessed image into a pre-trained residual wavefront estimation neural network to obtain the residual Zernike coefficient estimation vector of the current frame.

[0047] The online prediction module is used to update the parameters of the autoregressive prediction model online based on the residual Zernike coefficient estimates of the current frame and historical frames, and to use the updated autoregressive prediction model to predict the residual Zernike coefficient vector for future time moments.

[0048] The delay compensation module is used to calculate the total closed-loop delay of the wavefront-sensorless adaptive optics system. When the number of frames corresponding to the total closed-loop delay is not an integer, non-integer frame delay compensation is performed. After compensation, the residual Zernike coefficient prediction vector at the actual effective time of the deformable mirror command is obtained.

[0049] The controller construction module is used to establish the mapping relationship between the voltage of the deformable mirror actuator and the wavefront compensation phase, including the deformable mirror influence matrix and the Zernike basis matrix, and to construct a constrained model predictive controller based on the deformable mirror influence matrix and the Zernike basis matrix.

[0050] The optimization solution module is used to input the residual Zernike coefficient prediction vector obtained by the delay compensation module into the constrained model predictive controller. The constrained model predictive controller solves the optimization objective function, including at least the current control cycle, under the condition of satisfying the voltage amplitude constraint and voltage change rate constraint of the deformable mirror, to obtain the first step optimal deformable mirror voltage increment of the current control cycle.

[0051] The drive module is used to apply the first step of the optimal deformable mirror voltage increment to the deformable mirror actuator to compensate for the incident wavefront.

[0052] Compared with the prior art, the beneficial effects of the present invention include:

[0053] (1) Existing adaptive optics methods based on wavefront-free sensing usually rely on multi-frame perturbation, phase diversity or iterative optimization, resulting in slow response speed. Or, although deep networks such as CNN and Transformer are used to estimate wavefront coefficients from single-frame PSF images, they mainly solve the static estimation problem of "current image to current wavefront" and do not fully consider the time delay caused by camera exposure, neural network inference and deformable mirror response in the actual closed-loop system. In contrast, this invention, based on the estimation of residual Zernike coefficients in a single-frame residual wavefront estimation neural network, further introduces an online autoregressive prediction model and non-integer frame delay compensation, aligning the residual wavefront prediction from the measurement time to the actual effective time of the deformable mirror command. Therefore, it can reduce the correction lag caused by time mismatch under strong turbulence conditions and improve the residual wavefront RMS suppression capability and Strehl ratio stability.

[0054] (2) In addition, existing direct control or simple pseudo-inverse control methods usually do not explicitly consider the voltage amplitude and inter-frame voltage change rate limits of the deformable mirror actuator. Under strong turbulence or large estimation errors, they are prone to generating excessive control commands, which affect the closed-loop stability and actuator safety. However, this invention inputs the residual Zernike coefficient prediction vector after delay compensation into the constrained model predictive controller. When optimizing the voltage increment of the deformable mirror, it simultaneously considers the residual wavefront error, voltage change smoothness, voltage amplitude constraints and voltage change rate constraints. This not only retains the advantages of the wavefront-free sensor scheme, which has a simple hardware structure and does not require a dedicated wavefront sensor, but also improves the real-time performance, stability and engineering feasibility of closed-loop control under high-speed dynamic turbulence. Attached Figure Description

[0055] Figure 1 This is a flowchart of the closed-loop control method for the wavefront-less adaptive optics system according to an embodiment of the present invention;

[0056] Figure 2 This is a schematic diagram of the structure of a residual wavefront estimation neural network;

[0057] Figure 3 This is a closed-loop delay timing diagram;

[0058] Figure 4 A flowchart for delay compensation of non-integer frames;

[0059] Figure 5 The schematic diagram of a constrained model predictive controller;

[0060] Figure 6 This is a schematic diagram of the closed-loop control system of the wavefront-free adaptive optics system described in an embodiment of the present invention. Detailed Implementation

[0061] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings and preferred embodiments.

[0062] like Figure 1 As shown, this embodiment provides a closed-loop control method for a wavefront-less adaptive optics system, which includes the following steps:

[0063] Step 1 (S1): The scientific camera in the wavefront-free adaptive optics system continuously acquires the focal plane point spread function image at a preset sampling frequency. The focal plane point spread function image is the focal plane intensity distribution formed after compensation by turbulence and the current wavefront corrector, wherein the wavefront corrector is a deformable mirror.

[0064] Step 2 (S2): Preprocess the focal plane point spread function image, including uniform image size, image intensity normalization, background processing, and input tensor format conversion, to obtain the preprocessed image;

[0065] Step 3 (S3): Input the preprocessed image into the pre-trained residual wavefront estimation neural network to obtain the residual Zernike coefficient estimation vector of the current frame;

[0066] Step 4 (S4): Based on the residual Zernike coefficient estimates of the current frame and historical frames, update the parameters of the autoregressive prediction model online, and use the updated autoregressive prediction model to predict the residual Zernike coefficient vector at future time points. This step is used to describe the temporal correlation of each Zernike mode in a short period of time.

[0067] Step 5 (S5): Calculate the total closed-loop delay of the wavefront-sensorless adaptive optics system. When the number of frames corresponding to the total closed-loop delay is not an integer, perform non-integer frame delay compensation. After compensation, obtain the residual Zernike coefficient prediction vector at the actual effective time of the deformable mirror command.

[0068] Step 6 (S6): Establish the mapping relationship between the deformable mirror actuator voltage and the wavefront compensation phase, including the deformable mirror influence matrix and the Zernike basis matrix, and construct a constrained model predictive controller based on the deformable mirror influence matrix and the Zernike basis matrix;

[0069] Step 7 (S7): Input the residual Zernike coefficient prediction vector obtained in Step 5 into the constrained model predictive controller. Under the condition of satisfying the voltage amplitude constraint and voltage change rate constraint of the deformable mirror, the constrained model predictive controller solves the optimization objective function including at least the current control cycle to obtain the first optimal deformable mirror voltage increment of the current control cycle.

[0070] Step 8 (S8): Apply the optimal deformable mirror voltage increment from the first step to the deformable mirror actuator to compensate for the incident wavefront until the scientific camera acquires the next frame image, then continue with step 2.

[0071] Specifically, in this embodiment, the focal plane PSF image is used as the input to the closed-loop control method. Wavefront-less sensing means that the system does not use traditional wavefront sensors, but instead directly acquires the intensity image at the final focal plane of the optical system using a scientific camera; that is, the focal plane PSF image. This focal plane PSF image reflects the residual aberration state in the current optical path.

[0072] Zernike polynomials are a commonly used mathematical representation for describing wavefront distortion. Because Zernike polynomials are orthogonal over circular apertures, and different low-order modes can correspond to aberrations with clear optical meanings such as defocus, astigmatism, and coma, they are frequently used in wavefront modeling, aberration analysis, and control in adaptive optics. Noll's 1976 work systematically discussed the relationship between Zernike polynomials and atmospheric turbulence aberrations (Noll, Zernike polynomials and atmospheric turbulence, Journal of the Optical Society of America, 1976), making the representation of major low-order aberrations using a finite number of Zernike coefficients a common practice in adaptive optics. For practical control systems, representing the complex continuous wavefront phase as a finite-dimensional Zernike coefficient vector helps reduce the dimensionality of estimation and control problems.

[0073] For ease of estimation and control, this invention also represents the residual wavefront phase as finite-dimensional Zernike coefficients. Zernike polynomials are a set of orthogonal functions defined on a circular aperture, commonly used to describe aberrations such as defocusing, astigmatism, and coma in optical systems. Let the... The residual wavefront phase at frame time is It can be approximately represented as a linear combination of multiple Zernike modes, as shown in Equation (1). In a preferred embodiment, the residual wavefront phase adopts 28 Zernike modes, that is, outputs a 28-dimensional residual Zernike coefficient vector, corresponding to the residual aberration modes from Z1 to Z28. Its advantage is that it transforms the complex two-dimensional wavefront phase diagram into finite-dimensional control variables, making subsequent neural network estimation and deformable mirror control easier to implement.

[0074] (1)

[0075] in, For the number of Zernike modes, for example ; For the first The residual Zernike coefficient vector of the frame focal plane PSF image; These are Zernike mode functions, also known as basis functions.

[0076] In step 2, the focal plane PSF image acquired by the scientific camera may be affected by photon noise, readout noise, sampling error, and background light. Therefore, before inputting the residual wavefront estimation neural network, the focal plane PSF image is preprocessed. The preprocessing process may specifically include the following steps:

[0077] Standardize image size, for example, process focal plane PSF images to a uniform 64×64 pixels; for different practical systems, image size can be adaptively adjusted according to camera resolution, network structure, and computing resources;

[0078] The image intensity is normalized so that the input under different light intensity conditions falls within a similar numerical range;

[0079] Perform center cropping or spot center alignment as needed;

[0080] Convert a two-dimensional grayscale image into a neural network input tensor.

[0081] The purpose of preprocessing the focal plane PSF image is to make it suitable for the stable input of the residual wavefront estimation neural network.

[0082] In step 3, the residual wavefront estimation neural network preferably employs a residual convolutional attention network. The input to this network is a preprocessed single-frame focal plane PSF image, and the output is a residual Zernike coefficient estimation vector. The residual convolutional attention network comprises a residual convolutional backbone network, an attention module, and a regression output layer. The residual convolutional backbone network extracts local structural features and multi-scale spatial features from the input single-frame image. The attention module, either a convolutional block attention module or a compressed activation module, is used to weight and enhance key channels and key spatial regions. The regression output layer maps the extracted features to a residual Zernike coefficient estimation vector and outputs it.

[0083] Residual convolutional attention networks can employ ResNet-CBAM / SE attention networks. ResNet is a residual convolutional network used to extract local structure and multi-scale spatial features of the input focal plane PSF image; CBAM is a convolutional block attention module that can simultaneously perform channel attention and spatial attention enhancement; SE is a squeeze-excited channel attention module, which can serve as a simplified alternative to CBAM in scenarios with higher computational requirements.

[0084] ResNet residual convolutional networks are primarily used to extract local structural features and multi-scale spatial features from focal plane PSF images, such as spot edges, local blobs, energy distribution, and texture variations at different scales. Residual connections can alleviate the degradation problem during training of deep networks, allowing the network to maintain stable feature extraction capabilities while increasing its depth.

[0085] The CBAM / SE attention module is used to enhance the response to key channels and key spatial regions. Specifically, channel attention can highlight feature channels associated with residual Zernike modes, and spatial attention can enhance spot regions in the focal plane PSF image that are more sensitive to wavefront estimation, thereby improving the robustness of residual wavefront estimation without employing a Transformer structure.

[0086] The final regression output layer in the network maps the extracted features to a residual Zernike coefficient estimation vector. Preferably, the output of the regression output layer is a 28-dimensional vector, corresponding to 28 Zernike modes. The network output can be denoted as... ,in For the first Frame input focal plane PSF image, The regression mapping consists of a ResNet backbone and CBAM / SE attention modules. During training, simulated or experimentally calibrated focal plane PSF images and corresponding residual Zernike coefficients are used as sample pairs. To improve the estimation capability of low-order aberrations, a weighted mean square error loss function can be used to assign higher weights to low-order Zernike modes. Low-order aberrations typically have a significant impact on the overall shape and spot concentration of the PSF; therefore, improving the estimation accuracy of low-order modes is beneficial to the stability of closed-loop control.

[0087] (2)

[0088] in, This is the training loss function for the residual wavefront estimation neural network; The number of Zernike modes selected; For the first The loss weights corresponding to each Zernike mode are preferably assigned higher weights to lower-order modes. The output of the residual wavefront estimation neural network is the first... The residual coefficient estimates corresponding to each Zernike mode, i.e., the residual Zernike coefficient estimates; For the first Frame number Annotated residual coefficients corresponding to selected Zernike modes. During online runtime, Instead of using it as a known quantity in the control, the residual wavefront is used to estimate the output of the neural network. As the current frame (the first) The residual Zernike coefficient estimates for each frame are obtained and then the estimates for consecutive frames are input into the online autoregressive prediction model.

[0089] like Figure 2 As shown, the input to the ResNet-CBAM / SE attention network is a preprocessed focal plane PSF image of a single frame. Shallow convolutions and ResNet residual blocks are used to extract local spot morphology, intensity changes, and multi-scale spatial features. CBAM or SE attention modules are used to weight and enhance key channels and key spatial regions. Finally, the regression output layer outputs the residual Zernike coefficient estimation vector, which serves as the input for subsequent autoregressive (AR) delay prediction and MPC control optimization.

[0090] like Figure 3 As shown, a scientific camera needs exposure integration to form a single focal plane PSF image. Therefore, this image represents not the instantaneous wavefront at the end of the exposure, but rather the average wavefront closer to the center of the exposure. After the image is output, it still needs to undergo inference and control calculations by a residual wavefront estimation neural network before being activated by the deformable mirror. Since the wavefront continues to change during this process, directly using the output value of the residual wavefront estimation neural network to control the deformable mirror will result in a lag in the controlled object. To solve this timing mismatch problem, this invention introduces autoregressive prediction and non-integer delay compensation.

[0091] In step 4, an autoregressive prediction model is used to make short-term predictions of the residual Zernike coefficients. An autoregressive prediction model is established for each Zernike mode. This model can be a first-order autoregressive model, a higher-order autoregressive model, or another short-term prediction model. Taking a first-order autoregressive model as an example, the residual Zernike coefficients in the next frame of the current mode are approximately proportional to the residual Zernike coefficients in the current frame, i.e.: The Zernike mode in the ... The residual Zernike coefficients of the frame are equal to the modality in the th frame. The frame residual Zernike coefficient multiplied by an autoregressive coefficient Add a perturbation term The formula is as follows:

[0092] (3)

[0093] in, For the first The Zernike mode in the ... The residual Zernike coefficients of the frame; For the first The Zernike mode in the ... The residual Zernike coefficients of the frame.

[0094] In practical systems, the true residual Zernike coefficients are usually not directly available. Therefore, the residual Zernike coefficient estimates obtained from the continuous output of a residual wavefront estimation neural network are used. Update autoregression coefficients online When updating the parameters of the autoregressive prediction model online, the autoregressive coefficients of each Zernike mode can be estimated online using any of the following methods: exponentially weighted least squares, sliding window least squares, or recursive least squares. Preferably, exponentially weighted least squares (EWLS) is used to estimate the autoregressive coefficients of each Zernike mode online. This method assigns higher weights to recent data and gradually reduces the weights to earlier data, thus adapting to the slow changes in the temporal correlation of turbulence. Specifically, two statistics are maintained for each Zernike mode. and Each new neural network estimation result is used with a forgetting factor. Update statistics and As shown in formulas (4) and (5). Then, using... Divide by With a very small stable term The sum, as shown in formula (6), yields the estimated value of the autoregressive coefficients for the current mode. To avoid prediction divergence, we can... Cut it to limit it to - arrive Between, among Less than 1. This allows us to utilize the short-term temporal correlation of the residual wavefront without generating excessively large predicted values ​​due to accidental estimation errors, thus improving prediction stability.

[0095] (4)

[0096] (5)

[0097] (6)

[0098] in, It is a forgetting factor, and ; For the first Frame number First-order autocorrelation recursive statistics of Zernike mode estimation sequences; For adjacent frames (the first) Frame and the Cross-correlation recursive statistics between frames; The output of the residual wavefront estimation neural network is the first... Frame number Estimated residual coefficients for each Zernike mode; The output of the residual wavefront estimation neural network is the first... Frame number Estimated residual coefficients for each Zernike mode; To prevent positively stable terms with excessively small denominators.

[0099] In step 5, the present invention specifically considers the time delay in a wavefront-less adaptive optics system. This time delay is not an abstract parameter, but is caused by actual system steps, including camera exposure delay, image readout and transmission delay, neural network inference delay, control optimization calculation delay, deformable mirror actuation delay, and mechanical response delay.

[0100] In a preferred embodiment, the total closed-loop delay mainly includes the following three components: exposure centering delay, neural network inference delay, and deformable mirror response delay. Assume the sampling period is... Then the total closed-loop delay The corresponding frame number is:

[0101] (7)

[0102] in, This indicates the number of frames corresponding to the total closed-loop delay. This indicates a delayed exposure. Indicates the inference delay of the neural network. This indicates a deformable mirror response delay. Exposure centering delay. You can take half the exposure time because a camera frame is not obtained by instantaneous sampling, but by integration within an exposure time window. If the exposure time... Equal to sampling period Then the exposure is centered and delayed. It can be approximated as / 2= / 2.

[0103] Assuming the sampling frequency is 1kHz, the sampling period is... The exposure centering delay is 1ms. Taking 0.5ms, the inference time of the residual wavefront estimation neural network The response time of the deformable mirror is 2ms. If it is 20µs, then the total closed-loop delay is... The frame rate is 2.52. Since 2.52 is not an integer frame rate, compensating for only 2 or 3 frames would leave sub-frame-level time errors. Therefore, non-integer frame delay compensation and alignment are performed in step 5. The compensation process includes: based on the integer part of the total closed-loop delay corresponding to the number of frames, using an autoregressive prediction model to predict the residual Zernike coefficients for at least two adjacent integer frames in the future; and based on the fractional part of the total closed-loop delay corresponding to the number of frames, calculating the predicted vector of residual Zernike coefficients at the actual effective time of the deformable mirror command through interpolation.

[0104] When the total closed-loop delay When the frame value is not an integer, this invention does not use a simple rounding method, but instead performs prediction and interpolation at adjacent integer steps. The delay compensation for non-integer frames specifically includes the following steps:

[0105] Calculate the number of frames corresponding to the total closed-loop delay. integer part ,Right now ,in, This represents the floor function.

[0106] Calculate the number of frames corresponding to the total closed-loop delay. decimal part ,Right now .

[0107] Predict using autoregressive prediction models The residual Zernike coefficients after the frame, and Residual Zernike coefficients after the frame;

[0108] Use the decimal part right Frames and The two residual Zernike coefficient prediction results of the frame are linearly interpolated to obtain the residual Zernike coefficient prediction vector at the actual time when the deformable mirror command takes effect. Optionally, quadratic interpolation or other low-order polynomial interpolation methods can also be used.

[0109] (8)

[0110] (9)

[0111] (10)

[0112] in, For the first The frame residual Zernike coefficient estimate is predicted by Frame after the Predicted residual coefficients for each Zernike mode; For the first The frame residual Zernike coefficient estimate is predicted by Frame after the Predicted residual coefficients for each Zernike mode; For the first Zernike modality Frame autoregressive prediction coefficients; For the first Zernike modality Frame autoregressive prediction coefficients; The first frame obtained through non-integer frame delay compensation Frame time number Predicted residual coefficients for each Zernike mode.

[0113] For example, when The method calculates the predicted residual Zernike coefficients after 2 and 3 frames respectively, and then interpolates them by a ratio of 0.52 to obtain a residual wavefront state that is closer to 2.52 frames later, which is the actual time when the deformable mirror command takes effect. This method avoids the time deviation caused by predicting only 2 or 3 frames, and is especially suitable for closed-loop control under high-speed sampling conditions such as 1 kHz.

[0114] like Figure 4 As shown, the input to the non-integer frame delay compensation process is the residual Zernike coefficient estimation vector of the current frame obtained by the current residual wavefront estimation neural network; next, the number of frames corresponding to the total closed-loop delay is calculated based on the actual hardware delay. Then the frame rate The model is decomposed into integer and fractional parts. Subsequently, the autoregressive prediction model with updated parameters gives the residual Zernike coefficients at two adjacent integer prediction times. Then, the residual Zernike coefficient prediction values ​​at non-integer delay times are obtained by linear interpolation. The resulting residual Zernike coefficient prediction vector consists of the residual Zernike coefficient prediction values ​​corresponding to each selected Zernike mode, and is used as the input of the constrained model prediction controller.

[0115] In this embodiment, the wavefront corrector used in the wavefront-less adaptive optics system is preferably a deformable mirror. The deformable mirror includes a deformable mirror body and multiple actuators. Each actuator forms a local deformation on the mirror surface after a voltage is applied, and this local deformation produces a phase compensation effect on the wavefront. In a preferred embodiment, the deformable mirror has 144 actuators.

[0116] To calculate the voltage in the controller, the deformable mirror influence matrix is ​​first established in step 6. The influence function of each actuator can be represented by a Gaussian function to describe the degree of influence of the actuator on the phase at different positions within the aperture. After discretizing multiple sampling points within the circular aperture, the influence matrix of the deformable mirror can be obtained. Deformable mirror influence matrix The influence matrix of a deformable mirror can be obtained by modeling using a Gaussian influence function or through experimental calibration. Each column corresponds to the effect of an actuator on all sampling points. If the first column... The location of each aperture sampling point is , No. The center position of each actuator is Then the Gaussian influence function can be written as:

[0117] (11)

[0118] in, Represents the influence matrix of deformable mirrors The Line number Column element, i.e., the first The deformable mirror actuator for the first The influence of phase compensation at each aperture sampling point; Indicates the first The position vector of each aperture sampling point; Indicates the first The position vector of the center of each deformable mirror actuator; Indicates the first The influence amplitude coefficient of each actuator; Indicates the first The effective influence width of each actuator; Indicates the first The sampling point of the aperture and the first The square of the Euclidean distance between the centers of the actuators.

[0119] At the same time, a Zernike basis matrix was also established. Zernike basis matrix Each column corresponds to the value of a Zernike mode at a sampling point within the aperture. If a total of [number] samples are selected within the aperture... Each sampling point, the residual wavefront is used Each Zernike modal representation, then ,in, The number of deformable mirror actuators, The number of aperture sampling points, It is in the real number field. Thus, the residual Zernike coefficient vector can be obtained through the Zernike basis matrix. This is converted to the residual phase distribution at the aperture sampling points, i.e.:

[0120] (12)

[0121] in, This is the residual phase vector at the aperture sampling point at the actual moment the deformable mirror command takes effect. This is the residual Zernike coefficient prediction vector obtained after non-integer frame delay compensation.

[0122] The residual Zernike coefficient estimation vector and the residual Zernike coefficient prediction vector obtained by the residual wavefront estimation neural network and the autoregressive prediction model, respectively, can be obtained through the Zernike basis matrix. This is converted into a residual phase. The control objective is to minimize the amount of residual phase caused by the compensation phase generated by the deformable mirror. Therefore, in the unconstrained case, a reference voltage command matrix can be obtained using the regularized least squares method. , so that the voltage vector of the deformable mirror Equal to the reference voltage command matrix Multiply by the residual Zernike coefficients to predict the vector. Considering the voltage constraint of the actual deformable mirror, this invention does not directly use the unconstrained voltage as the final command, but instead uses the deformable mirror influence matrix. and Zernike basis matrix The constrained model predictive controller is constructed by incorporating the MPC optimization model and integrating the prediction residual wavefront error, voltage increment penalty, voltage amplitude constraint, and voltage change rate constraint into the constrained model predictive controller.

[0123] Deformable mirror phase compensation can be expressed as:

[0124] (13)

[0125] in, For the first The compensated phase vector generated by the deformable mirror at the aperture sampling point at each frame; The influence matrix of the deformable mirror; For the first The voltage vector of the deformable mirror at frame time.

[0126] The reference voltage command can be obtained through the following regularized least squares problem:

[0127] (14)

[0128] in, The reference deformable mirror voltage vector obtained by regularized least squares when voltage amplitude constraints and voltage change rate constraints are not considered. It is a Zernike basis matrix; Let be the voltage vector of the deformable mirror to be solved; This indicates the phase compensation of the deformable mirror at the aperture sampling point; is the regularization coefficient.

[0129] When using explicit regularization, formula (14) can be written as:

[0130] (15)

[0131] in, Reference voltage command matrix; It is the identity matrix; Represents the influence matrix of deformable mirrors Transpose of; This represents finding the inverse of a matrix.

[0132] Furthermore:

[0133] (16)

[0134] The constrained model predictive controller is the core component of the closed-loop control in this invention, and its inputs include: the voltage vector of the deformable mirror in the previous frame. The residual Zernike coefficient prediction vector obtained after delay alignment in step 5 Deformable mirror influence matrix Zernike basis matrix The upper and lower limits of voltage amplitude and voltage increment are defined. The constrained model predictive controller (MPC) solves for the optimization objective while satisfying the voltage amplitude and rate of change constraints of the deformable mirror, obtaining the first optimal deformable mirror voltage increment. During the optimization process, the upper and lower limits of voltage amplitude and voltage increment are simultaneously constrained for each actuator to ensure safe operation of the deformable mirror and reduce over-excitation control. In a preferred embodiment, the MPC employs a two-step predictive time domain, where the optimization variables of the objective function include the first-step deformable mirror voltage increment of the current control cycle. and the second step deformable mirror voltage increment in the next prediction cycle Based on the voltage applied to the deformable mirror in the previous frame and two voltage increments used as optimization variables, the voltage state of the deformable mirror in the next two steps can be predicted:

[0135] (17)

[0136] in, For the previous frame (the first frame) The voltage vector applied to the deformable mirror (frame); This represents the first step of the deformable mirror voltage increment in the current control cycle. In order to be in The deformable mirror voltage vector for the current control cycle predicted at any given time; For the second step of the deformable mirror voltage increment in the next prediction cycle; In order to be in The deformable mirror voltage vector for the next prediction period. In this embodiment, one control period corresponds to one sampling frame interval, that is, the time interval between two consecutive image acquisitions by the scientific camera. The current control period refers to the control time period corresponding to the current frame, which is consistent with the sampling period, and the next prediction period refers to the control time period corresponding to the next frame.

[0137] Combining the delayed-aligned residual Zernike coefficient predictions, the predicted residual wavefronts for the next two steps are calculated. The predicted residual wavefront errors for the next two steps can be written as:

[0138] (18)

[0139] (19)

[0140] in, In order to be in The residual wavefront error vector of the current control cycle predicted at each moment; In order to be in The residual wavefront error vector for the next prediction period at the predicted time.

[0141] The objective function of the constrained model predictive controller consists of two parts. The first part is the residual wavefront error term, which aims to minimize the L2 norm of the predicted residual wavefront. The second part is the voltage increment penalty term, which aims to avoid excessive voltage changes. This is achieved by setting a weight matrix. and This allows for adjustment of the trade-off between correction effectiveness and control smoothness. The corresponding optimization objective function can be written as:

[0142] (20)

[0143] in, The objective function for the constrained model predicts the controller. In order to be in The residual wavefront error vector of the current control cycle predicted at each moment; In order to be in The residual wavefront error vector for the next prediction period at the predicted time; This represents the first step of the deformable mirror voltage increment in the current control cycle. For the second step of the deformable mirror voltage increment in the next prediction cycle; and These are the weight matrices for the residual wavefront error term and the voltage increment penalty term, respectively; Represents the transpose of a vector or matrix.

[0144] The constraints of the constrained model predictive controller include two types. The first type is voltage amplitude constraint, that is, the voltage of each actuator must be between the preset minimum voltage and the maximum voltage, as shown in formula (21); the second type is voltage change rate constraint, that is, the voltage change of each deformable mirror actuator between adjacent frames cannot exceed the allowable range, that is, the voltage change of each deformable mirror actuator between adjacent frames is between the preset minimum voltage change and the maximum voltage change, as shown in formula (22).

[0145] (twenty one)

[0146] (twenty two)

[0147] in, and These are the lower and upper limits of the voltage vector of the deformable mirror, respectively; and These are the lower and upper limits of the voltage increment of the deformable mirror, respectively.

[0148] This invention employs a rolling optimization approach. After solving the objective function, it only calculates the first step of the deformable mirror voltage increment in the current control cycle. As the first step, the optimal deformable mirror voltage increment is applied to the deformable mirror actuator, i.e., the update:

[0149] (twenty three)

[0150] in, For the current frame (the first frame) (Frame) Deformable mirror voltage vector; For the previous frame (the first frame) (Frame) Deformable mirror voltage vector; where, The first step in optimizing the objective is to obtain the optimal deformable mirror voltage increment.

[0151] The second-step deformable mirror voltage increment obtained after solving the objective function for the next prediction cycle is only used for prediction optimization in the current frame and is not directly applied to the deformable mirror actuator. Its purpose is to improve the smoothness of the control process, avoid excessive voltage increments in the previous step, and work in conjunction with the voltage rate of change constraint to suppress drastic fluctuations in the actuator voltage and reduce excessive actuator changes. After applying the optimal deformable mirror voltage increment from the first step to the deformable mirror actuator, the deformable mirror compensates for the incident wavefront until the scientific camera acquires the next frame image. Then, it returns to step 2 and continues execution, re-preprocessing, re-estimating the residual wavefront, re-predicting the delay alignment state, and re-solving the MPC optimization problem. This allows for continuous use of the latest measurement information to correct control commands and improve closed-loop robustness. It should be noted that the prediction step size of the constrained model predictive controller can be two steps, or it can be extended to more steps depending on the processor's computing power and the system's dynamic characteristics.

[0152] like Figure 5 As shown, the inputs of the constrained model predictive controller (CMM) include the deformable mirror voltage vector from the previous frame, the predicted residual Zernike coefficient vector after delay prediction, the deformable mirror influence matrix, the Zernike basis matrix, and actuator constraints (including upper and lower limits for voltage amplitude and voltage rate of change). The CMM first predicts the residual wavefront for the next two steps, and then solves for the voltage increment that minimizes the residual wavefront and smooths the voltage change. Since the actual deformable mirror has a safe operating range, the CMM simultaneously limits both the voltage amplitude and the voltage rate of change. Finally, only the first step of the deformable mirror voltage increment is applied, and steps 2 to 8 are re-executed in the next frame.

[0153] This embodiment addresses the challenge of achieving stable, real-time, and reliable wavefront correction in wavefront-sensorless adaptive optics systems under the combined effects of strong turbulence, closed-loop delay, and deformable mirror actuator constraints. It provides a delay-sensing constrained closed-loop control method for wavefront-sensorless adaptive optics systems. This method does not rely on traditional dedicated wavefront detectors such as Shack-Hartmann wavefront sensors or pyramid wavefront sensors. Instead, it directly uses focal plane point spread function (PSF) images acquired by a scientific camera. A residual wavefront estimation neural network estimates the residual Zernike coefficients from a single-frame focal plane PSF image. An online autoregressive prediction model then predicts the residual wavefront time, and non-integer frame delay compensation aligns the estimation results to the actual effective time of the deformable mirror. Finally, a constrained model predictive controller solves for the optimal deformable mirror voltage increment under the constraints of deformable mirror voltage amplitude and rate of change, outputting the corresponding control command to the deformable mirror actuator, thus achieving stable closed-loop adaptive optics correction under wavefront-sensorless conditions.

[0154] Compared to simple deep learning estimation schemes, which typically only address the mapping from PSF images to Zernike coefficients, this mapping, while applicable to wavefront estimation, is still susceptible to closed-loop delay and actuator constraints if the estimation results are directly used for deformable mirror control. This invention adds two key technical steps after neural network estimation. The first is AR delay prediction and non-integer frame interpolation, aligning the residual Zernike coefficients from the measurement time to the deformable mirror execution time. The second is constrained MPC, ensuring that the deformable mirror control commands meet voltage amplitude and rate of change constraints. In other words, this invention is not simply a neural network recognition method, but a complete closed-loop control solution encompassing image measurement, wavefront estimation, time prediction, constraint optimization, and deformable mirror execution.

[0155] Compared to conventional MPC control schemes, which can consider actuator constraints, the problem of time lag still exists if the residual wavefront estimated in the current frame is directly used as the control objective. Especially under strong turbulence, the wavefront state between the measurement time and the time the deformable mirror takes effect may be significantly different. The MPC input of this invention is not simply the current residual Zernike coefficients, but rather the predicted values ​​of future residual Zernike coefficients after compensation by an AR model and non-integer frame delay. Therefore, MPC optimizes the residual wavefront at the time the deformable mirror takes effect, rather than the outdated measured wavefront. This better reduces correction lag under dynamic turbulence.

[0156] like Figure 6 As shown, another embodiment provides a closed-loop control system for a wavefront-less adaptive optics system, the system comprising:

[0157] A scientific camera, positioned at the focal plane detection location, continuously acquires focal plane point spread function images at a preset sampling frequency after turbulence and compensation by the current wavefront corrector. An optical receiving module receives the incident distorted beam, guiding the turbulence-affected beam to the deformable mirror and the focal plane detection location. Optionally, the optical receiving module may include a telescope, receiving lens group, aperture, beam splitter or focusing element, etc. Optionally, the wavefront corrector is a deformable mirror.

[0158] The image preprocessing module is used to preprocess the focal plane point spread function image to obtain the preprocessed image;

[0159] The residual wavefront estimation module is used to input the preprocessed image into a pre-trained residual wavefront estimation neural network to obtain the residual Zernike coefficient estimation vector of the current frame.

[0160] The online prediction module is used to update the parameters of the autoregressive prediction model online based on the residual Zernike coefficient estimates of the current frame and historical frames, and to use the updated autoregressive prediction model to predict the residual Zernike coefficient vector for future time moments.

[0161] The delay compensation module is used to calculate the total closed-loop delay of the wavefront-sensorless adaptive optics system. When the number of frames corresponding to the total closed-loop delay is not an integer, non-integer frame delay compensation is performed. After compensation, the residual Zernike coefficient prediction vector at the actual effective time of the deformable mirror command is obtained.

[0162] The controller construction module is used to establish the mapping relationship between the voltage of the deformable mirror actuator and the wavefront compensation phase, including the deformable mirror influence matrix and the Zernike basis matrix, and to construct a constrained model predictive controller based on the deformable mirror influence matrix and the Zernike basis matrix.

[0163] The optimization solution module is used to input the residual Zernike coefficient prediction vector obtained by the delay compensation module into the constrained model predictive controller. The constrained model predictive controller solves the optimization objective function, including at least the current control cycle, under the condition of satisfying the voltage amplitude constraint and voltage change rate constraint of the deformable mirror, and obtains the first step of the optimal deformable mirror voltage increment of the current control cycle.

[0164] The drive module applies the first-step optimal deformable mirror voltage increment to the deformable mirror actuators to compensate for the incident wavefront. The drive module receives the first-step optimal deformable mirror voltage increment and converts it into the drive voltage required by each actuator of the deformable mirror.

[0165] Furthermore, the closed-loop control system in this embodiment also includes a storage module, which is used to store trained neural network parameters, deformable mirror influence matrix, Zernike basis matrix, controller parameters, voltage upper and lower limits, voltage change upper and lower limits, sampling period, and non-integer frame delay compensation parameters.

[0166] The working principle of the closed-loop control system in this embodiment is as follows:

[0167] The optical receiving module receives the incident distorted beam, which first passes through a deformable mirror. The deformable mirror applies a compensated phase according to the voltage command given by the constrained model predictive controller. The compensated beam forms a PSF image on the focal plane, which is continuously acquired by the scientific camera. The acquired focal plane PSF image enters the image preprocessing module, where it undergoes image size unification, image intensity normalization, background processing, and input tensor format conversion before being sent to the residual wavefront estimation module. This residual wavefront estimation module outputs the residual Zernike coefficient estimation vector corresponding to the current frame. Since camera exposure, neural network inference, and deformable mirror response all introduce closed-loop delay, the currently estimated residual Zernike coefficients are not directly used to drive the deformable mirror. Instead, the residual Zernike coefficient estimation vector is fed into an online autoregressive prediction model to make short-term predictions of the residual Zernike coefficients. Subsequently, the delay compensation module uses the autoregressive prediction model to interpolate the residual Zernike coefficients predicted based on the integer and fractional parts of the frame number corresponding to the total closed-loop delay, obtaining a residual Zernike coefficient prediction vector that is closer to the actual effective time of the deformable mirror. Finally, the constrained model predictive controller solves for the first step of the optimal deformable mirror voltage increment under voltage amplitude and voltage change rate constraints, and outputs it to each actuator through the deformable mirror drive module to compensate for the incident wavefront until the scientific camera acquires the next frame of the focal plane PSF image. The next frame of the focal plane PSF image reflects the new residual aberration state, and the system continues to operate in a closed loop, forming a closed-loop correction.

[0168] The online closed-loop operation process of the closed-loop control system in this embodiment includes:

[0169] During online operation, the system first initializes the deformable mirror voltage, neural network parameters, autoregressive prediction model statistics, constrained model predictive controller weights, and actuator constraint parameters. After initialization, the scientific camera continuously acquires focal plane PSF images at a fixed sampling frequency. For each acquired focal plane PSF image, the image preprocessing module immediately performs image preprocessing, and the residual wavefront estimation module calls the trained residual wavefront estimation neural network to output the residual Zernike coefficient estimation vector for that frame.

[0170] Subsequently, the online prediction module updates the parameters of the autoregressive prediction model online using the residual Zernike coefficient estimates from the current and historical frames. If the system is in its initial startup phase and historical data is insufficient, preset autoregressive coefficients can also be used initially. The system may not make predictions; after accumulating a certain number of frames, it will switch to online parameter estimation.

[0171] Next, the delay compensation module calculates the number of frames corresponding to the total closed-loop delay based on the pre-calibrated or real-time measured exposure time, inference time, and deformable mirror response time. If the number of frames If it is an integer, then the prediction value corresponding to the step size is used directly; if it is the number of frames... If the value is not an integer, then interpolate the prediction values ​​of two adjacent integer steps to obtain the residual Zernike coefficient prediction vector after delay alignment. This result represents the residual wavefront state at the expected moment when the deformable mirror command takes effect.

[0172] Then, the controller construction module constructs a constrained model predictive controller based on the predicted residual wavefront. The constrained model predictive controller comprehensively considers residual wavefront error, voltage change smoothness, upper and lower limits of voltage amplitude, and upper and lower limits of voltage change rate. The optimization solution module solves the optimization objective under the conditions of satisfying the voltage amplitude and voltage change rate constraints of the deformable mirror. After the solution is completed, the optimal deformable mirror voltage increment from the first step is sent to the drive module, which applies it to the deformable mirror actuator. Upon arrival of the next focal plane PSF image, the above process is repeated to achieve online closed-loop operation.

[0173] Through an online closed-loop operation process, this closed-loop control system realizes a complete closed-loop link from the focal plane PSF image to the deformable mirror safety voltage command. This link not only completes wavefront-free sensing estimation, but also performs time prediction on the estimation results and generates executable control commands under actuator constraints.

[0174] It should be noted that the specific functional implementation methods of the image preprocessing module, residual wavefront estimation module, online prediction module, delay compensation module, controller construction module and optimization solution module in this embodiment are completely consistent with the methods described in steps 2 to 7 of the aforementioned method embodiment, so they will not be repeated here.

[0175] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0176] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A closed-loop control method for a wavefront-less adaptive optics system, characterized in that, Includes the following steps: Step 1: The scientific camera continuously acquires the focal plane spread function image after turbulence and compensation by the current wavefront corrector at a preset sampling frequency; Step 2: Preprocess the spread function image of the focal plane point to obtain the preprocessed image; Step 3: Input the preprocessed image into the pre-trained residual wavefront estimation neural network to obtain the residual Zernike coefficient estimation vector of the current frame; Step 4: Based on the residual Zernike coefficient estimates of the current frame and historical frames, update the parameters of the autoregressive prediction model online, and use the updated autoregressive prediction model to predict the residual Zernike coefficient vector for future time moments. Step 5: Calculate the total closed-loop delay of the wavefront-sensorless adaptive optics system. When the number of frames corresponding to the total closed-loop delay is not an integer, perform non-integer frame delay compensation. After compensation, obtain the residual Zernike coefficient prediction vector at the actual effective time of the deformable mirror command. Step 6: Establish the mapping relationship between the voltage of the deformable mirror actuator and the wavefront compensation phase, including the deformable mirror influence matrix and the Zernike basis matrix, and construct a constrained model predictive controller based on the deformable mirror influence matrix and the Zernike basis matrix; Step 7: Input the residual Zernike coefficient prediction vector into the constrained model predictive controller. The constrained model predictive controller solves the optimization objective function, including at least the current control cycle, under the condition of satisfying the voltage amplitude constraint and voltage change rate constraint of the deformable mirror, and obtains the first step optimal deformable mirror voltage increment of the current control cycle. Step 8: Apply the optimal deformable mirror voltage increment from step 1 to the deformable mirror actuator to compensate for the incident wavefront until the scientific camera acquires the next frame image, then continue with step 2.

2. The closed-loop control method for a wavefront-less adaptive optics system according to claim 1, characterized in that, The residual wavefront estimation neural network is a residual convolutional attention network, comprising a residual convolutional backbone network, an attention module, and a regression output layer. The residual convolutional backbone network is used to extract local structural features and multi-scale spatial features of the input single-frame image. The attention module is a convolutional block attention module or a compressed excitation module, used to weight and enhance key channels and key spatial regions. The regression output layer is used to map the extracted features into a residual Zernike coefficient estimation vector.

3. The closed-loop control method for a wavefront-less adaptive optics system according to claim 1 or 2, characterized in that, The autoregressive prediction model adopts a first-order autoregressive model or a higher-order autoregressive model. During online updates, the autoregressive coefficients of each Zernike mode are estimated online using any one of the following methods: exponentially weighted least squares, sliding window least squares, or recursive least squares.

4. The closed-loop control method for a wavefront-less adaptive optics system according to claim 1 or 2, characterized in that, The non-integer frame delay compensation in step 5 specifically includes: Calculate the number of frames corresponding to the total closed-loop delay. integer part ; Calculate the number of frames corresponding to the total closed-loop delay. decimal part ; Predict using the updated autoregressive prediction model Frame and Residual Zernike coefficients after the frame; Use the decimal part right Frame and The residual Zernike coefficient prediction results of the frame are linearly interpolated to obtain the residual Zernike coefficient prediction vector at the actual time when the deformable mirror command takes effect.

5. The closed-loop control method for a wavefront-less adaptive optics system according to claim 4, characterized in that, The number of frames corresponding to the total closed-loop delay The calculation formula is as follows: (7) in, This indicates a centering delay in exposure. Indicates the inference delay of the neural network; This indicates a delay in the response of the deformable mirror; Indicates the sampling period.

6. The closed-loop control method for a wavefront-less adaptive optics system according to claim 1 or 2, characterized in that, When a two-step prediction time domain is used, the optimization variables of the objective function in step 7 include the first step deformable mirror voltage increment of the current control cycle and the second step deformable mirror voltage increment of the next prediction cycle. The voltage amplitude constraint is that the voltage of each deformable mirror actuator is between a preset minimum voltage and a preset maximum voltage; The voltage change rate constraint is that the voltage change of each deformable mirror actuator between adjacent frames is between the preset minimum voltage change and maximum voltage change.

7. The closed-loop control method for a wavefront-less adaptive optics system according to claim 6, characterized in that, The optimization objective function is: (20) in, In order to be in The residual wavefront error vector of the current control cycle predicted at each moment; In order to be in The residual wavefront error vector for the next prediction period at the predicted time; This represents the first step of the deformable mirror voltage increment in the current control cycle. For the second step of the deformable mirror voltage increment in the next prediction cycle; and These are the weight matrices for the residual wavefront error term and the voltage increment penalty term, respectively; Represents the transpose of a vector or matrix.

8. The closed-loop control method for a wavefront-less adaptive optics system according to claim 1 or 2, characterized in that, The deformable mirror influence matrix is ​​obtained by modeling a Gaussian influence function or by experimental calibration. Each column of the Zernike basis matrix corresponds to the value of a Zernike mode at multiple sampling points within the aperture, and is used to convert the residual Zernike coefficient vector into the residual phase distribution at the aperture sampling points.

9. A closed-loop control system for a wavefront-sensorless adaptive optics system, characterized in that, include: A scientific camera is used to continuously acquire focal plane point spread function images at a preset sampling frequency after turbulence and compensation by the current wavefront corrector. The image preprocessing module is used to preprocess the focal plane point spread function image to obtain a preprocessed image; The residual wavefront estimation module is used to input the preprocessed image into a pre-trained residual wavefront estimation neural network to obtain the residual Zernike coefficient estimation vector of the current frame. The online prediction module is used to update the parameters of the autoregressive prediction model online based on the residual Zernike coefficient estimates of the current frame and historical frames, and to use the updated autoregressive prediction model to predict the residual Zernike coefficient vector for future time moments. The delay compensation module is used to calculate the total closed-loop delay of the wavefront-sensorless adaptive optics system. When the number of frames corresponding to the total closed-loop delay is not an integer, non-integer frame delay compensation is performed. After compensation, the residual Zernike coefficient prediction vector at the actual effective time of the deformable mirror command is obtained. The controller construction module is used to establish the mapping relationship between the voltage of the deformable mirror actuator and the wavefront compensation phase, including the deformable mirror influence matrix and the Zernike basis matrix, and to construct a constrained model predictive controller based on the deformable mirror influence matrix and the Zernike basis matrix. The optimization solution module is used to input the residual Zernike coefficient prediction vector obtained by the delay compensation module into the constrained model predictive controller. The constrained model predictive controller solves the optimization objective function, including at least the current control cycle, under the condition of satisfying the voltage amplitude constraint and voltage change rate constraint of the deformable mirror, and obtains the first step optimal deformable mirror voltage increment of the current control cycle. The drive module is used to apply the first step of the optimal deformable mirror voltage increment to the deformable mirror actuator to compensate for the incident wavefront.

10. The closed-loop control system of the wavefront-free adaptive optics system according to claim 9, characterized in that, It also includes a storage module for storing trained neural network parameters, deformable mirror influence matrix, Zernike basis matrix, controller parameters, voltage upper and lower limits, voltage change upper and lower limits, sampling period, and non-integer frame delay compensation parameters.

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