Wavefront Sensorless Adaptive Optics Research Articles

Asymptotic proximal point algorithm for wavefront sensorless adaptive optics

Asymptotic proximal point algorithm for wavefront sensorless adaptive optics

Reinforcement Learning Environment for Wavefront Sensorless Adaptive Optics in Single-Mode Fiber Coupled Optical Satellite Communications Downlinks

Optical satellite communications (OSC) downlinks can support much higher bandwidths than radio-frequency channels. However, atmospheric turbulence degrades the optical beam wavefront, leading to reduced data transfer rates. In this study, we propose using reinforcement learning (RL) as a lower-cost alternative to standard wavefront sensor-based solutions. We estimate that RL has the potential to reduce system latency, while lowering system costs by omitting the wavefront sensor and low-latency wavefront processing electronics. This is achieved by adopting a control policy learned through interactions with a cost-effective and ultra-fast readout of a low-dimensional photodetector array, rather than relying on a wavefront phase profiling camera. However, RL-based wavefront sensorless adaptive optics (AO) for OSC downlinks faces challenges relating to prediction latency, sample efficiency, and adaptability. To gain a deeper insight into these challenges, we have developed and shared the first OSC downlink RL environment and evaluated a diverse set of deep RL algorithms in the environment. Our results indicate that the Proximal Policy Optimization (PPO) algorithm outperforms the Soft Actor–Critic (SAC) and Deep Deterministic Policy Gradient (DDPG) algorithms. Moreover, PPO converges to within 86% of the maximum performance achievable by the predominant Shack–Hartmann wavefront sensor-based AO system. Our findings indicate the potential of RL in replacing wavefront sensor-based AO while reducing the cost of OSC downlinks.

Universal adaptive optics for microscopy through embedded neural network control

The resolution and contrast of microscope imaging is often affected by aberrations introduced by imperfect optical systems and inhomogeneous refractive structures in specimens. Adaptive optics (AO) compensates these aberrations and restores diffraction limited performance. A wide range of AO solutions have been introduced, often tailored to a specific microscope type or application. Until now, a universal AO solution – one that can be readily transferred between microscope modalities – has not been deployed. We propose versatile and fast aberration correction using a physics-based machine learning assisted wavefront-sensorless AO control (MLAO) method. Unlike previous ML methods, we used a specially constructed neural network (NN) architecture, designed using physical understanding of the general microscope image formation, that was embedded in the control loop of different microscope systems. The approach means that not only is the resulting NN orders of magnitude simpler than previous NN methods, but the concept is translatable across microscope modalities. We demonstrated the method on a two-photon, a three-photon and a widefield three-dimensional (3D) structured illumination microscope. Results showed that the method outperformed commonly-used modal-based sensorless AO methods. We also showed that our ML-based method was robust in a range of challenging imaging conditions, such as 3D sample structures, specimen motion, low signal to noise ratio and activity-induced fluorescence fluctuations. Moreover, as the bespoke architecture encapsulated physical understanding of the imaging process, the internal NN configuration was no-longer a “black box”, but provided physical insights on internal workings, which could influence future designs.

A Novel SPGD Algorithm for Wavefront Sensorless Adaptive Optics System

Stochastic parallel gradient descent (SPGD) is the most frequently used optimization algorithm for correcting wavefront distortion in the wavefront sensorless adaptive optics(WFS-Less AO)system. However, the convergence speed of the SPGD algorithm becomes slow rapidly as increasing of distortion, and the probability of falling into local optimum is rising owing to the fixed gain coefficient. It cannot meet the requirement of real-time wavefront distortion correction. Therefore, a novel algorithm is proposed in this paper, called as adaptive gain stochastic parallel gradient descent (AGSPGD) based on the AMSGrad optimizer in the deep learning, to improve the convergence speed of the algorithm and to reduce the probability of falling into local optimum. The AGSPGD algorithm adopts the first-order moment and the second-order moment of the performance index, which are combined to dynamically adjust the gain. The numerical simulations are completed in this paper. The results of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$D/r_0=2.5$</tex-math></inline-formula> conditions demonstrate that the AGSPGD can reduce the number of iterations by 25%, and the probability of the algorithm falling into local optimum is reduced from 16% to 4%. In addition, the AGSPGD still outperforms the SPGD as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$D/r_0$</tex-math></inline-formula> increasing.

Adaptive Optical Closed-Loop Control on the Basis of Hyperparametric Optimization of Convolutional Neural Networks

In adaptive optics systems, the precision wavefront sensor determines the closed-loop correction effect. The accuracy of the wavefront sensor is severely reduced when light energy is weak, while the real-time performance of wavefront sensorless adaptive optics systems based on iterative algorithms is poor. The wavefront correction algorithm based on deep learning can directly obtain the aberration or correction voltage from the input image light intensity data with better real-time performance. Nevertheless, manually designing deep-learning models requires a multitude of repeated experiments to adjust many hyperparameters and increase the accuracy of the system. A wavefront sensorless system based on convolutional neural networks with automatic hyperparameter optimization was proposed to address the aforementioned issues, and networks known for their superior performance, such as ResNet and DenseNet, were constructed as constructed groups. The accuracy of the model was improved by over 26%, and there were fewer parameters in the proposed method, which was more accurate and efficient according to numerical simulations and experimental validation.

Adaptive Optical Closed-Loop Control Based on the Single-Dimensional Perturbation Descent Algorithm.

Modal-free optimization algorithms do not require specific mathematical models, and they, along with their other benefits, have great application potential in adaptive optics. In this study, two different algorithms, the single-dimensional perturbation descent algorithm (SDPD) and the second-order stochastic parallel gradient descent algorithm (2SPGD), are proposed for wavefront sensorless adaptive optics, and a theoretical analysis of the algorithms' convergence rates is presented. The results demonstrate that the single-dimensional perturbation descent algorithm outperforms the stochastic parallel gradient descent (SPGD) and 2SPGD algorithms in terms of convergence speed. Then, a 32-unit deformable mirror is constructed as the wavefront corrector, and the SPGD, single-dimensional perturbation descent, and 2SPSA algorithms are used in an adaptive optics numerical simulation model of the wavefront controller. Similarly, a 39-unit deformable mirror is constructed as the wavefront controller, and the SPGD and single-dimensional perturbation descent algorithms are used in an adaptive optics experimental verification device of the wavefront controller. The outcomes demonstrate that the convergence speed of the algorithm developed in this paper is more than twice as fast as that of the SPGD and 2SPGD algorithms, and the convergence accuracy of the algorithm is 4% better than that of the SPGD algorithm.

Compensation for aberrant wavefront in UOWC based on adaptive optics technique employing genetic algorithm

Underwater optical wireless communication (UOWC) has attracted extensive attention due to its merits in transmission latency, bandwidth, and security. However, its performance is usually significantly limited by the scattering, absorption, and turbulence effects. Thus, many schemes have been proposed to enhance its performance via various optimizations at the transmitter, but most of them neglected the wavefront optimization at the receiver. Although traditional adaptive optics based on wavefront detection (AOWD) technology employing wavefront phase sensor (e.g. Shack-Hartmann sensors) and compensator (e.g. deformable mirror) was proposed to alleviate wavefront distortion, it introduced extra challenges in miniaturizing receivers for UOWC. Additionally, traditional AOWD technologies usually employed costly and large computing systems,which reduced their feasibility in reality. In this paper, a novel compensation technology is proposed to optimize the distorted wavefront at the receiver based on the wavefront sensorless adaptive optics (WSAO) technique using improved genetic algorithm (GA). Instead of using the wavefront phase-detector, the proposed technology measures the light intensity via a small photo-detector (PD) and outputs voltage signals though the employed GA to manipulate the deformable mirror (DM) for wavefront compensation. The simulation results indicate that the proposed technology effectively improves the intensity distribution and the Strehl Ratio (SR) of the transmission light in UOWC.

CoolMomentum-SPGD Algorithm for Wavefront Sensor-Less Adaptive Optics Systems

Instead of acquiring the previous aberrations of an optical wavefront with a sensor, wavefront sensor-less (WFSless) adaptive optics (AO) systems compensate for wavefront distortion by optimizing the performance metric directly. The stochastic parallel gradient descent (SPGD) algorithm is pervasively adopted to achieve performance metric optimization. In this work, we incorporate CoolMomentum, a method for stochastic optimization by Langevin dynamics with simulated annealing, into SPGD. Numerical simulations reveal that, compared with the state-of-the-art SPGD variant, the proposed CoolMomentum-SPGD algorithm achieves better convergence speed under various atmospheric turbulence conditions while requiring only two tunable parameters.

Direct model-based wavefront sensorless method with a fixed number of measurements

In wavefront sensorless (WFSL) adaptive optics, the intensity image in the observation plane, instead of the wavefront sensor, is utilised to estimate the input aberration. The number of intensity measurements is critical for applications with ever-changing phase aberration, such as astronomical imaging. This paper details two direct WFSL methods that need a fixed number of intensity measurements to estimate the input aberration. The proposed methods adopt a zonal approach rather than a modal one to estimate the phase aberration. Simulation results demonstrate that after applying the proposed methods, the aberration correction percentage can rise by approximately 70% for large aberrations.

Modified Gerchberg-Saxton algorithm-based probe-free wavefront distortion compensation of an OAM beam

In the free space optical communication system, atmospheric turbulence (AT) will distort the helical phase of the orbital angular momentum (OAM) beam, resulting in inter-mode crosstalk and system performance degradation. Based on modified Gerchberg-Saxton (GS) algorithm, this paper proposes a wavefront sensorless adaptive optics system to compensate the wavefront distortion of an OAM beam. For the modified GS algorithm, at each iteration, the spatial phase is re-modulated to descend along a new phase gradient direction to improve algorithm convergence. At the same time, in the spatial domain, negative feedback is generated by nonlinear operation to optimize the beam amplitude, so as to speed up the convergence speed of the algorithm. Simulation results show that our modified GS algorithm can better compensate the wavefront distortion of an OAM beam caused by atmospheric turbulence than the traditional GS and hybrid input–output algorithms, which provides a new idea to solve the problem of atmospheric turbulence in free space optical communication system.

The Lattice Geometry of Walsh-Function-Based Adaptive Optics

We show that there is an intrinsic link between the use of Walsh aberration modes in adaptive optics (AO) and the mathematics of lattices. The discrete and binary nature of these modes means that there are infinite combinations of Walsh mode coefficients that can optimally correct the same aberration. Finding such a correction is hence a poorly conditioned optimisation problem that can be difficult to solve. This can be mitigated by confining the AO correction space defined in Walsh mode coefficients to the fundamental Voronoi cell of a lattice. By restricting the correction space in this way, one can ensure there is only one set of Walsh coefficients that corresponds to the optimum correction aberration. This property is used to enable the design of efficient estimation algorithms to solve the inverse problem of finding correction aberrations from a sequence of measurements in a wavefront sensorless AO system. The benefit of this approach is illustrated using a neural-network-based estimator.

Prediction of wavefront distortion for wavefront sensorless adaptive optics based on deep learning.

Aimed at the slow detection speed and low measurement accuracy of wavefront aberration in current wavefront sensorless adaptive optic technology, different convolution neural networks (CNNs) are established to detect the turbulence wavefront, including an ordinary convolutional neural network, a ResNet network, and an EfficientNet-B0 network. By using the nonlinear fitting ability of deep neural networks, the mapping relationship between Zernike coefficients and focal degraded image can be established. The simulation results show that the optimal network model after training can quickly and efficiently predict the Zernike coefficients directly from a single focal degraded image. The root-mean-square errors of the wavefront detection accuracy of the three networks are 0.075λ, 0.058λ, and 0.013λ, and the time consumed for predicting the wavefront from the single degraded image are 2.3, 4.6, and 3.4 ms, respectively. Among the three networks presented, the EfficientNet-B0 CNN has obvious advantages in wavefront detection accuracy and speed under different turbulence intensities than the ordinary CNN and ResNet networks. Compared with the traditional method, the deep learning method has the advantages of high precision and fast speed, without iteration and the local minimum problem, when solving wavefront aberration.

Self-calibrated general model-based wavefront sensorless adaptive optics for both point-like and extended objects.

The deformable mirror (DM) in conventional model-based wavefront sensorless adaptive optics (WFSless AO) must be calibrated in advance by an additional WFS in order to precisely generate predetermined bias modes with known amplitudes. Although the WFS is unnecessary during correction, it will increase system complexity and may be unavailable in real applications. In this paper, the model-based WFSless AO algorithms, either for point-like or extended objects, are generalized to a unified form and the calibration problem comes down to the measurement of a Gram matrix. We proposed a novel self-calibration procedure to obtain the Gram matrix without using a WFS. The calibrated Gram matrix can be used directly for simultaneous correction if using the influence functions of DM as the bias modes, requiring N+1 images to correct N modes. Alternatively, orthogonal or gradient-orthogonal mirror modes obtained from the eigenvectors of the Gram matrix can be used as the modal basis to implement independent sequential correction that requires 2N images to correct N modes. Simulations and experiments have been done to verify the feasibility of proposed self-calibration and correction methods for both point-like and extended objects in a WFSless AO system.

Efficient wavefront sensorless adaptive optics based on large dynamic crosstalk-free holographic modal wavefront sensing.

The correction of wavefront sensorless adaptive optics (WFSless AO) can be significantly accelerated by using a holographic modal wavefront sensor (HMWFS). The HMWFS is realized by a computer-generated hologram (CGH) into which all aberration modes to be detected are encoded and only a single-shot image is required for simultaneous measurement of multiple modes. The conventional HMWFS suffers from a quite limited dynamic range and severe inter-modal crosstalk which deteriorates the sensing accuracy. We proposed a novel HMWFS with a large dynamic range and no crosstalk and validated its performance by simulation and experiment. In the improved HMWFS scheme, the aberration is represented by Lukosz modes whose gradients are orthogonal and the modal coefficients can be estimated independently. Instead of using a binary CGH in conventional HMWFS, a kinoform CGH with high diffraction efficiency is adopted in the improved HMWFS. The kinoform CGH is produced by a phase-only liquid-crystal spatial light modulator (LCSLM) which also serves as a wavefront corrector in our WFSless AO system.

Fast dynamic correction algorithm for model-based wavefront sensorless adaptive optics in extended objects imaging.

A major concern for wavefront sensorless adaptive optics (WFSless AO) is how to improve the algorithm's efficiency which is critical for dynamic aberration correction. For extended objects and dynamic aberration, a typical model-based WFSless AO algorithm is called "3N" which uses three image measurements to estimate each aberration mode and then corrects it immediately. The three images include an initial aberrated image and two biased images with deliberately introduced predetermined positive or negative modal aberrations. In this paper, an improved algorithm called "2N" that requires only one biased image is proposed. The reduction of one biased image is achieved by the estimation of a parameter that is considered unknown in the 3N algorithm. It is demonstrated that the 2N algorithm can achieve convergence with less image measurements and have better performance in dynamic correction.

Nesterov-accelerated adaptive momentum estimation-based wavefront distortion correction algorithm

In order to improve the wavefront distortion correction performance of the classical stochastic parallel gradient descent (SPGD) algorithm, an optimized algorithm based on Nesterov-accelerated adaptive momentum estimation is proposed. It adopts a modified second-order momentum and a linearly varying gain coefficient to improve iterative stability. It integrates the Nesterov momentum term and the modified Adam optimizer to further improve the convergence speed, correct the direction of gradient descent in a timely fashion, and avoid falling into local extremum. Besides, to demonstrate the algorithm's performance, a wavefront sensorless adaptive optics system model is established using a 6×6 element deformable mirror as wavefront corrector. Simulation results show that, compared with the SPGD algorithm, the proposed algorithm converges faster, and its Strehl ratio after convergence is nearly 6.25 times that of the SPGD algorithm. Also, the effectiveness and superiority of the proposed algorithm are verified by comparing with two existing optimization algorithms.

Wavefront sensor-less adaptive optics using deep reinforcement learning.

Image degradation due to wavefront aberrations can be corrected with adaptive optics (AO). In a typical AO configuration, the aberrations are measured directly using a Shack-Hartmann wavefront sensor and corrected with a deformable mirror in order to attain diffraction limited performance for the main imaging system. Wavefront sensor-less adaptive optics (SAO) uses the image information directly to determine the aberrations and provide guidance for shaping the deformable mirror, often iteratively. In this report, we present a Deep Reinforcement Learning (DRL) approach for SAO correction using a custom-built fluorescence confocal scanning laser microscope. The experimental results demonstrate the improved performance of the DRL approach relative to a Zernike Mode Hill Climbing algorithm for SAO.

Alignment of the active secondary mirror of a space telescope using model-based wavefront sensorless adaptive optics.

The precise alignment of the space telescope with an active secondary mirror (ASM) is essential to high-quality imaging. The traditional alignment methods either require a dedicated wavefront sensor or a lot of iterations to optimize a metric function, which is not suitable for on-orbit instant alignment. A model-based wavefront sensorless adaptive optics method is proposed for the alignment of the ASM of a wide field-of-view space telescope. In our method, the aberration is estimated by introducing a series of modal biases successively into the system using the ASM. Unlike the traditional wavefront sensing methods that intend to measure all aberration modes, only five aberration modes that can be compensated by the ASM are estimated. Two alignment schemes either using single-field or multi-field images are proposed to calculate the control signals of the ASM, depending on if the aberration is mainly caused by the ASM. Simulations are made to evaluate the performance of our method under different scenarios. The influence of image sampling frequency, image size, and image noise on alignment are also investigated.

Optimal, blind-search modal wavefront correction in atmospheric turbulence. Part I: simulations

Modal control is an established tool in adaptive optics. It allows not only for the reduction in the controllable degrees of freedom, but also for filtering out unseen modes and optimizing gain on a mode-by-mode basis. When Zernike polynomials are employed as the modal basis for correcting atmospheric turbulence, their cross-correlations translate to correction errors. We propose optimal modal decomposition for gradient-descent-based wavefront sensorless adaptive optics, which is free of this problem. We adopt statistically independent Karhunen-Loève functions for iterative blind correction and analyze performance of the algorithm in static as well as in dynamic simulated turbulence conditions.

Jointly recognizing OAM mode and compensating wavefront distortion using one convolutional neural network

In this work, a new recognition method of orbital angular momentum (OAM) is proposed. The method combines mode recognition and the wavefront sensor-less (WFS-less) adaptive optics (AO) by utilizing a jointly trained convolutional neural network (CNN) with the shared model backbone. The CNN-based AO method is implicitly applied in the system by providing additional mode information in the offline training process and accordingly the system structure is rather concise with no extra AO components needed. The numerical simulation result shows that the proposed method can improve the recognition accuracy significantly in different conditions of turbulence and can achieve similar performance compared with AO-combined methods.