Sensorless Adaptive Optics System Research Articles

Hybrid control method for generating airy beam in wavefront sensorless adaptive optics system

In order to reduce the complexity of Airy beams generation based on adaptive optics with a wavefront sensor, a wavefront sensorless adaptive optics system, which employs a camera to measure the far-field intensity distribution as the feedback for optimizing the control voltages of the deformable mirror, is proposed for generating high-quality Airy beams. A hybrid control method combining hill-climbing algorithm and open-loop control method is developed to correct the aberrations of the system and produce the cubic phases. High-quality tunable Airy beams were generated successfully. The properties of the generated Airy beams, such as non-diffraction, self-acceleration and self-healing, were verified. The experimental results coincide with the theoretical results, showing the proposed method has potential applications such as Airy beam light-sheet microscope and optical manipulation.

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.

Residual network-based aberration correction in a sensor-less adaptive optics system

The performance of free-space optical communication (FSOC) is often affected by atmospheric turbulence. The sensor-less adaptive optics (SLAO) system is an effective method for overcoming the effects of atmospheric turbulence. The performance of the control algorithm in the SLAO system directly determines whether the SLAO system can effectively correct wavefront aberrations. In this study, we introduce a residual network (ResNet) as a control algorithm to replace the traditional control algorithm. By lowering the number of iterations, this strategy enhances the real-time performance of the FSOC system. The final ResNet model can achieve an accuracy of 0.98 for training and 0.92 for testing. The simulation results show that stochastic parallel gradient descent (SPGD) algorithm takes 700 times longer and requires at least 500 iterations to achieve the same performance as ResNet. And we verify the feasibility of the ResNet model by setting up an experiment.

Model Predictive Control of Time-Varying Aberrations for Sensorless Adaptive Optics

We propose a model predictive control (MPC) method to compensate for the time-varying phase aberrations in a sensorless adaptive optics (AO) system. The approximate model for the point spread function (PSF) of the imaging system with phase diversity is mathematically derived, and its validity is verified. The proposed MPC, which considers the operating limits of the deformable mirror (DM), computes the optimal applied voltage of each actuator over a prediction horizon, and the receding horizon scheme is applied as feedback control. Numerical case studies with the time-varying phase aberrations generated by an atmospheric turbulence simulator are presented to demonstrate the correction performance of the MPC strategy. The proposed method caused a 50% improvement in the reduction in residual aberration, making it competitive with a saturation linear quadratic regulator (LQR). The computational feasibility of the proposed method is validated using fast MPC, which approximates the primal barrier method.

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.

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.

Beamshaping for infrared hyperspectral imaging: a sequential optimization for infrared source coupling.

Focal plane array (FPA) detectors have escalated Fourier transform infrared (FTIR) microspectroscopy to a potent hyperspectral imaging method. Yet, despite the instrumental multiplex/multichannel advantages, the fidelity of the hyperspectral images relies on the throughput as the total flux of the source is divided among each FPA pixel. Additionally, maintaining the spectral resolution requires a certain level of collimation of the beam which adversely affect the flux of high étendue source. To this end, we propose an implementation of two deformable mirror (DM) sensorless adaptive optics system for infrared (IR) source coupling. The deflection shape of each DM membrane is optimized individually to deal with the beam intensity and the rays' direction in a separate manner, while preserving the spectral quality across the entire mid-IR range. This paper contemplates the choice of metrics in sequential optimization in conjunction with two variations of stochastic parallel gradient descent optimization algorithm. We discuss this approach with respect to a state-of-the-art FTIR microscope.

Performance analysis of coherent optical communication based on hybrid algorithm

The performance of coherent free-space optical communication (FSOC) is often affected by atmospheric turbulence. Sensorless adaptive optics are widely used in coherent FSOC to mitigate the effect of atmospheric turbulence. However, the control algorithm for sensorless adaptive optics systems remains weak. To enhance the various performance indicators of coherent FSOC, we propose a hybrid algorithm to improve the coupling efficiency and mixing efficiency (ME) of the system while reducing the bit error rate (BER). This algorithm combines the fast convergence rate of the simulated annealing (SA) algorithm at the initial cooling stage and the beneficial convergence effect of the stochastic parallel gradient descent (SPGD) algorithm, avoiding the algorithm’s need for more iterations and its tendency to enter local optimisation. The simulation results show that the performance of the proposed hybrid algorithm outperforms that of the traditional SPGD algorithm, regardless of the intensity of the atmospheric turbulence. The SA and hybrid algorithms display similar performances in strong atmospheric turbulence, while the hybrid algorithm shows better performance than that of the SA algorithm in weak atmospheric turbulence.

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 Sensorless Aberration Correction With Magnetic Fluid Deformable Mirror for Laser Focus Control in Optical Tweezer System

The performance of wavefront corrector (WFC) plays a decisive role in the overall effectiveness of an adaptive optical (AO) system. When compared with commonly used WFCs, magnetic fluid deformable mirrors (MFDMs) have advantages of large stroke, low cost, and smooth continuous surface. However, the application of MFDMs is limited by the measuring range of the wavefront sensor (WFS) in the traditional AO systems. In addition, WFS needs one more optical path to measure the wavefront, which makes the AO system structure complex. In this article, a wavefront sensorless AO system based on MFDM is proposed to eliminate the limitations imposed by WFS. The stochastic parallel gradient descent (SPGD) algorithm is introduced in the control system to deform the surface of MFDM without the need to measure the wavefront. The MFDM with the proposed SPGD algorithm is applied to an optical tweezer system to eliminate the aberration caused by the optical system error and refractive index mismatch. Experimental results show that the divergent beam can be adaptively focused to successfully capture micro-particles.

Error analysis and threshold selection in model-based wavefront sensorless adaptive optics system

Accurate values of masked detector signal (MDS) is the key to the correction capability of wavefront sensorless (WFSless) model-based adaptive optics (AO) system. However, imaging detectors always carry different kinds of noises in real applications, which make MDS deviate from theoretical results. Calculation errors of MDS suffered from the noise were analyzed through theory and simulation. Additionally, considering the method of threshold is usually used to mitigate the noise, we also discussed the influence of threshold on MDS. Results showed that the simulation is consistent with the theory and there exists an optimal threshold to make the error minimum for different noise. A fitting formula, which can accurately calculate optimal thresholds, was proposed based on the simulated data. Above results can provide a plausible method and theoretical basis to mitigate imaging noise of detectors in real applications.

Wavefront sensorless adaptive optics system for extended objects based on linear phase diversity technique

Wavefront sensorless (WFSless) adaptive optics (AO) systems have been widely studied in recent years. However, most of the existing WFSless AO systems require point sources for wavefront sensing. Aimed to correct the turbulence-degraded imaging of extended objects, this document proposes a fast wavefront correction approach for a WFSless AO system based on linear phase diversity (PD) technique. By linearizing the system optical transfer function (OTF) and expanding the influence functions of the deformable mirror (DM) on Zernike basis, this method can establish a linear relationship model between the drive voltages of the DM and the CCD acquired extended images. Then the control signal of the DM can be directly output to generate a compensated wavefront from CCD images and fast adaptive wavefront correction can be realized. Numerical simulations and an experimental validation are performed under different turbulence strengths, the results show that the proposed method has an impressive improvement of root mean square (RMS) of wavefront and can effectively restore the turbulence-degraded extended images with a relatively fast correction speed.

Atmospheric turbulence compensation with sensorless AO in OAM-FSO combining the deep learning-based demodulator

This study proposed a hybrid framework that is made up of a sensorless adaptive optics (AO) and a convolutional neural network (CNN) to demodulate the multiplexed orbital angular momentum (OAM) signals. The model-based sensorless AO is applied to compensate for the distorted wavefront caused by the atmospheric turbulence in the OAM free-space optical (FSO) communication. The CNN demodulator is trained to achieve the testing accuracy of 99.15% for the testing set without the AO compensation. The newly introduced model-based sensorless AO system helps CNN to identify the information-carrying diffraction patterns of OAM beams at the receiver more accurately. We used the Monte Carlo method to testify the improved performance on the bit error rate (BER) when applied sensorless AO in combination with the CNN demodulator. Amounts of numerical results indicate the superiority of the proposed framework. The purity of OAM modes would be significantly improved, thus BERs under strong turbulence decrease from 10−2 to 10−4, which meet the requirements of the FSO system.

Optimization of random phase diversity for adaptive optics using an LCoS spatial light modulator.

Phase retrieval is an attractive approach for sensor-less adaptive optics (AO) because of its relatively simple implementation. Recently, random phase diversity has shown fast convergence for phase retrieval algorithms. In this study, design optimization using random phase diversity is discussed with respect to a sensor-less AO system using a liquid-crystal-on-silicon (LCoS) spatial light modulator. The extrinsic phase disturbances studied are due to Kolmogorov turbulence. Simulation analysis shows that the size of super-pixel segments of the random phase patterns on the LCoS and the cropped image area of the phasorgrams are determined by Fried's parameter for high-Strehl-ratio and low-iteration-number reconstruction. AO experiments with an LCoS spatial light modulator confirm the simulation results.

Aberration balancing using an image-sharpness metric.

Image-sharpness metrics can be used to optimize optical systems and to control wavefront sensorless adaptive optics systems. We show that for an aberrated system, the numerical value of an image-sharpness metric can be improved by adding specific aberrations. The optimum amplitudes of the additional aberrations depend on the power spectral density of the spatial frequencies of the object.

DNN-based aberration correction in a wavefront sensorless adaptive optics system.

Existing wavefront sensorless (WFS-less) adaptive optics (AO) generally require a search algorithm that takes lots of iterations and measurements to get optimal results. So the latency is a serious problem in the current WFS-less AO system, especially in applications to free-space optics communication. To solve this issue, we propose a deep neural network (DNN)-based aberration correction method. The DNN model can detect the wavefront distortion directly from the intensity images, thereby avoiding time-consuming iterative processes. Since the tip-and-tilt mode of Zernike coefficients are considered, the tip-tilt correction system is not necessarily required in the proposed method. From our simulation results, the proposed method can effectively reduce the computation time and has an impressive improvement of root mean square (RMS) in different turbulence conditions.

Build the Structure of WFSless AO System Through Deep Reinforcement Learning

We report on an aberration correction algorithm for a wavefront sensorless adaptive optics (WFSless AO) system based on deep reinforcement learning. First, it is verified that the reinforcement learning theory can be applied in our system. In addition, the deep deterministic policy gradient algorithm is introduced to build the control structure. After that, deep learning is used to deal with the messy raw images of far-field intensity distribution. We emphatically present how to design a feature extraction with the convolutional neural network in the control structure. To demonstrate the performance of this structure, some comparisons are made with the stochastic parallel gradient descent algorithm and the WFSless AO based on general modes algorithm. The results indicate that the correction speed of our method improves about 9 times and 2.5 times, respectively, for the similar correction effect.

Self-learning control for wavefront sensorless adaptive optics system through deep reinforcement learning

An aberration correction algorithm for wavefront sensorless adaptive optics (WFSless AO) systems based on deep reinforcement learning is presented. An actor–critic structure is designed to evaluate a control policy through the deep deterministic policy gradient (DDPG) algorithm. The algorithm performance is verified with a set-up simulation environment. According to the correction results, the aberration correction process can be expressed as a Markov decision process (MDP). The method exhibits excellent performances in correction capacity and speed. Similar correction effects are obtained with the stochastic parallel-gradient descent (SPGD) algorithm and WFSless AO based on the general-modes (AOG) algorithm. Moreover, the correction speed is improved by approximately 9 and 2.5 times, respectively.