Combinational-deformable-mirror adaptive optics system for compensation of high-order modes of wavefront

A new kind of adaptive optics(AO)system,in which several low spatial frequency deformable mirrors (DMs)with optical conjugation relationship are combined to correct high-order aberrations,is proposed. The phase compensation principle and the control method of the combinational AO system are introduced. The numerical simulations for the AO system with two 60-element DMs are presented.The results indicate that the combinational DM in the AO system can correct different aberrations effectively as one single DM with more actuators,and there is no change of control method.This technique can be applied to a large telescope AO system to improve the spatial compensation capability for wavefront by using current DM.     

Dual-thread parallel control strategy for ophthalmic adaptive optics

To improve ophthalmic adaptive optics （AO） speed and compensate for ocular wavefront aberration of high temporal frequency, the AO wavefront correction is implemented with a control scheme including two parallel threads： one is dedicated to wavefront detection and the other conducts wavefront reconstruction and compensation. With a custom Shack-Hartmann wavefront sensor that measures the ocular wave aber-ration with 193 subapertures across the pupil, AO achieves a closed-loop updating frequency up to 110 Hz, and demonstrates robust compensation for ocular wave aberration up to 50 Hz in an AO scanning laser ophthalmoscope.     

Analysis and demonstration of PID algorithm based on arranging the transient process for adaptive optics

The fastness and robustness of a control algorithm are highly important in the performance of adaptive optics systems. The proportional-integral-derivative control with arranging the transient process, which is designed using a tracking differentiator, is applied into an adaptive optics system. This control algorithm greatly improves the dynamic properties of the control system. To identify the underlying reasons for these improvements, the influence of the control algorithm is theoretically discussed. The control algorithm is verified by a simple adaptive optics system for tip/tilt correction. The experimental results demonstrate that the control algorithm is fast and robust.     

Comparison between iterative wavefront control algorithm and direct gradient wavefront control algorithm for adaptive optics system

Among all kinds of wavefront control algorithms in adaptive optics systems, the direct gradient wavefront control algorithm is the most widespread and common method. This control algorithm obtains the actuator voltages directly from wavefront slopes through pre-measuring the relational matrix between deformable mirror actuators and Hartmann wavefront sensor with perfect real-time characteristic and stability. However, with increasing the number of sub-apertures in wavefront sensor and deformable mirror actuators of adaptive optics systems, the matrix operation in direct gradient algorithm takes too much time, which becomes a major factor influencing control effect of adaptive optics systems. In this paper we apply an iterative wavefront control algorithm to high-resolution adaptive optics systems, in which the voltages of each actuator are obtained through iteration arithmetic, which gains great advantage in calculation and storage. For AO system with thousands of actuators, the computational complexity estimate is about O(n2) ～ O(n3) in direct gradient wavefront control algorithm, while the computational complexity estimate in iterative wavefront control algorithm is about O(n) ～(O(n)3/2), in which n is the number of actuators of AO system. And the more the numbers of sub-apertures and deformable mirror actuators, the more significant advantage the iterative wavefront control algorithm exhibits.     

Frequency-invariant robust adaptive beamforming based on interference covariance matrix reconstruction

Consider the problems of frequency-invariant beampattern optimization and robustness in broadband beamforming.Firstly,a global optimization algorithm,which is based on phase compensation of the array manifolds,is used to construct the frequency-invariant beampattern.Compared with some methods presented recently,the proposed algorithm is not only available to get the global optimal solution,but also simple for physical realization.Meanwhile,a robust adaptive broadband beamforming algorithm is also derived by reconstructing the covariance matrix.The essence of the proposed algorithm is to estimate the space-frequency spectrum using Capon estimator firstly,then integrate over a region separated from the desired signal direction to reconstruct the interference-plus-noise covariance matrix,and finally caleulate the adaptive beamformer weights with the reconstructed matrix.The design of beamformer is formulated as a convex optimization problem to be solved.Simulation results show that the performance of the proposed algorithm is almost always close to the optimal value across a wide range of signal to noise ratios.     

Correcting dynamic residual aberrations of conformal optical systems using AO technology

This paper analyses the dynamic residual aberrations of a conformal optical system and introduces adaptive optics (AO) correction technology to this system. The image sharpening AO system is chosen as the correction scheme. Communication between MATLAB and Code V is established via ActiveX technique in computer simulation. The SPGD algorithm is operated at seven zoom positions to calculate the optimized surface shape of the deformable mirror. After comparison of performance of the corrected system with the baseline system, AO technology is proved to be a good way of correcting the dynamic residual aberration in conformal optical design.     

Cooperative impulsive formation control for networked uncertain Euler–Lagrange systems with communication delays

This paper investigates the cooperative formation problem via impulsive control for a class of networked Euler–Lagrange systems. To reduce the energy consumption and communication frequency, the impulsive control method and cooperative formation control approach are combined. With the consideration of system uncertainties and communication delays among agents, neural networks-based adaptive technique is used for the controller design. Firstly, under the constraint that each agent interacts with its neighbors only at some sampling moments, an adaptive neural-networks impulsive formation control algorithm is proposed for the networked uncertain Euler–Lagrange systems without communication delays. Using Lyapunov stability theory and Laplacian potential function in the graph theory, we conclude that the formation can be achieved by properly choosing the constant control gains. Further, when considering communication delays,a modified impulsive formation control algorithm is proposed, in which the extended Halanay differential inequality is used to analyze the stability of the impulsive delayed dynamical systems. Finally, numerical examples and performance comparisons with continuous algorithm are provided to illustrate the effectiveness of the proposed methods.     

Bimorph deformable mirror based adaptive optics scanning laser ophthalmoscope for retina imaging in vivo

A bimorph deformable mirror(DM) with a large stroke of more than 30 μm using 35 actuators is presented and characterized for an adaptive optics(AO) confocal scanning laser ophthalmoscope application. Facilitated with a Shack–Hartmann wavefront sensor, the bimorph DM-based AO operates closed-loop AO corrections for human eyes and reduces wavefront aberrations in most eyes to below 0.1 μm rms. Results from living eyes, including one exhibiting ～5D of myopia and ～2D of astigmatism along with notable high-order aberrations, reveal a practical efficient aberration correction and demonstrate a great benefit for retina imaging, including improving resolution, increasing brightness, and enhancing the contrast of images.     

Multiple-object Shack–Hartmann wavefront sensor design for a wide field of view on the retina

In order to detect the aberration from a wide field of view(FOV) on the retina with adaptive optics, we present a multiple-object Shack–Hartmann wavefront sensor(MOSHWFS) design. The simulated results indicate that the wavefront from our MOSHWFS can be reconstructed for multiple objects, and the measurement error can be less than λ∕7 with an MOSHWFS with an FOV of 6.7°, for maximum eye aberration. The experimental result with two objects indicates that the measurement error can be less than λ∕14, with the root mean square of the reference wavefront as 0.798λ and 0.895λ, respectively.     

Experimental verification of combinational-deformable-mirror for phase correction

In adaptive optics (AO) system,the phase compensation capability is limited greatly by the actuator num- ber of the deformable mirror (DM).The actuator number of DM is mainly restricted by the manufacture techniques.The spatial correction capability of AO system can be improved by two or more combinational- DMs (CDMs) with conjugation relationship.The CDM AO system for wavefront correction is built,which consists of two 32-element DMs.The experimental results are in agreement with the numerical simulation results.It is indicated that the CDM AO system provides better correction performance than the single 32-element DM AO system.     

A modified phase diversity diffraction wavefront sensor with a grating

The phase diversity wavefront sensor is one of the tools used to estimate wavefront aberration, and it is often used as a wavefront sensor in adaptive optics systems. However, the performance of the traditional phase diversity wavefront sensor is limited by the accuracy and dynamic ranges of the intensity distribution at the focus and defocus positions of the CCD camera. In this paper, a modified phase diversity wavefront sensor based on a diffraction grating is proposed to improve the ability to measure the wavefront aberration with larger amplitude and higher spatial frequency. The basic principle and the optics construction of the proposed method are also described in detail. The noise propagation property of the proposed method is also analysed by using the numerical simulation method, and comparison between the diffraction grating phase diversity wavefront sensor and the traditional phase diversity wavefront sensor is also made. The simulation results show that the diffraction grating phase diversity wavefront sensor can obviously improve the ability to measure the wavefront aberration, especially the wavefront aberration with larger amplitude and higher spatial frequency.     

Approximation-error-ADP-based optimal tracking control for chaotic systems with convergence proof

In this paper, an optimal tracking control scheme is proposed for a class of discrete-time chaotic systems using the approximation-error-based adaptive dynamic programming （ADP） algorithm. Via the system transformation, the optimal tracking problem is transformed into an optimal regulation problem, and then the novel optimal tracking control method is proposed. It is shown that for the iterative ADP algorithm with finite approximation error, the iterative performance index functions can converge to a finite neighborhood of the greatest lower bound of all performance index functions under some convergence conditions. Two examples are given to demonstrate the validity of the proposed optimal tracking control scheme for chaotic systems.     

A weighting orthogonal method for constant beamwidth beamforming matrices

A weighting orthogonal method for constant beamwidth beamforming matrices is proposed. This method multiplies weighting factors to each orthogonal beamforming matrix corresponding to different frequency bins. The method proposed doesn't cause waveform aberration, and doesn't cause additional loss of array signal-to-noise ratio when the sources have uniform spectrum. The waveform aberration and additional loss of array signal-to-noise ratio can not be avoided simultaneously by ordinary orthogonal method. So we can get good detection and estimation performances at the same time by the weightmg method. Simulation results and water tank experiments are presented to confirm the conclusion above.     

Adaptive digital backward propagation based on variance of intensity noise

An adaptive digital backward propagation(ADBP) algorithm is proposed and experimentally demonstrated based on the variance of the intensity noise. The proposed algorithm can self-determine the unknown nonlinear coefficient γ and the nonlinear compensation parameter ξ. Compared to the scheme based on the variance of phase noise, the proposed algorithm can avoid the repeated frequency offset compensation and carrier phase recovery. The simulation results show that the system's performance compensated by the proposed method is comparable to conventional ADBP schemes. The performance of the proposed algorithm is simulated in40/112 Gb/s polarization-division multiplexing(PDM)-quadrature phase-shift keying(QPSK) and 224 Gb/s PDM-16-quadrature amplitude modulation(QAM) systems and further experimentally verified in a 40 Gb/s PDM-QPSK coherent optical communication system over a 720 km single-mode fiber.     

An NLMS algorithm with optimized preparatory step-size parameters for SQUID-based MCG data processing

We present a new least-mean-square algorithm of adaptive filtering to improve the signal to noise ratio for magnetocardiography data collected with high-temperature SQUID-based magnetometers. By frequently adjusting the adaptive parameter $\alpha $ to systematic optimum values in the course of the programmed procedure, the convergence is accelerated with a highest speed and the minimum steady-state error is obtained simultaneously. This algorithm may be applied to eliminate other non-steady relevant noises as well.     

Determinate joint remote preparation of an arbitrary W-class quantum state

A novel determinate joint remote preparation scheme of an arbitrary W-class quantum state is proposed to improve the probability of successful preparation. The presented scheme is realized through orthogonal projective measurement of the Hadamard transferred basis, which converts a global measurement to several local measurements. Thus orthogonal projective measurement of the Hadamard transferred basis enables quantum information to be transmitted from different sources simultaneously, which is a breakthrough for quantum network node processing. Finally, analysis shows the feasibility and validity of the proposed method, with a 100% probability of successful preparation.     

Robust Blind Adaptive Channel Equalization in Chaotic Communication Systems

Based on the bounded property and statistics of chaotic signal and the idea of set-membership identification, we propose a set-membership generalized least mean square （SM-GLMS） algorithm with variable step size for blind adaptive channel equalization in chaotic communication systems. The steady state performance of the proposed SM-GLMS algorithm is analysed, and comparison with an extended Kalman filter （EKF）-based adaptive algorithm and variable gain least mean square （VG-LMS） algorithm is performed for blind adaptive channel equalization. Simulations show that the proposed SM-GLMS algorithm can provide more significant steady state performance improvement than the EKF-based adaptive algorithm and VG-LMS algorithm.     

Synchronization of hyperchaotic Chen systems: a class of the adaptive control approach

The synchronization of hyperchaotic Chen systems is considered. An adaptive synchronization approach and a cascade adaptive synchronization approach are presented to synchronize a drive system and a response system. By utilizing an adaptive controller based on the dynamic compensation mechanism, exact knowledge of the systems is not necessarily required, and the synchronous speed is controllable by tuning the controller parameters. Sufficient conditions for the asymptotic stability of the two synchronization schemes are derived. Numerical simulation results demonstrate that the adaptive synchronization scheme with four control inputs and the cascade adaptive synchronization scheme with only one control signal are effective and feasible in chaos synchronization of hyperchaotic systems.     

Adaptive step-size modified fractional least mean square algorithm for chaotic time series prediction

This paper presents an adaptive step-size modified fractional least mean square （AMFLMS） algorithm to deal with a nonlinear time series prediction. Here we incorporate adaptive gain parameters in the weight adaptation equation of the original MFLMS algorithm and also introduce a mechanism to adjust the order of the fractional derivative adaptively through a gradient-based approach. This approach permits an interesting achievement towards the performance of the filter in terms of handling nonlinear problems and it achieves less computational burden by avoiding the manual selection of adjustable parameters. We call this new algorithm the AMFLMS algorithm. The predictive performance for the nonlinear chaotic Mackey Glass and Lorenz time series was observed and evaluated using the classical LMS, Kernel LMS, MFLMS, and the AMFLMS filters. The simulation results for the Mackey glass time series, both without and with noise, confirm an improvement in terms of mean square error for the proposed algorithm. Its performance is also validated through the prediction of complex Lorenz series.     

Simulation of the influence of imperfections on dynamical decoupling of a superconducting qubit

Dynamical decoupling is widely used in many quantum computing systems to combat decoherence. In a practical superconducting quantum system, imperfections can plague decoupling performance. In this work, imperfections in a superconducting qubit and its control system are modeled via modified Hamiltonian and collapse operator. A master equation simulation is carried out on the qubit under 1/f environment noise spectrum. The average dephasing rate of qubit is extracted to characterize the impact of different imperfections on the decoupling from dephasing. We find that the precision of pulse position, on–off ratio, and filtering effect are most critical. Bounded pulses have weaker impact,while variation in pulse width and qubit relaxation are insignificant. Consequently, alternative decoupling protocols, jitter mitigation, cascaded mixers, and pulse shaping can be conducive to the performance of decoupling. This work may assist the analysis and optimization of dynamical decoupling on noisy superconducting quantum systems.