Adaptive optics: wave-front correction by use of adaptive filtering and control

A class of adaptive-optics problems is described in which phase distortions caused by atmospheric turbulence are corrected by adaptive wave-front reconstruction with a deformable mirror, i.e., the control loop that drives the mirror adapts in real time to time-varying atmospheric conditions, as opposed to the linear time-invariant control loops used in conventional adaptive optics. The basic problem is posed as an adaptive disturbance-rejection problem with many channels. The solution given is an adaptive feedforward control loop built around a multichannel adaptive lattice filter. Simulation results are presented for a 1-m telescope with both one-layer and two-layer atmospheric turbulence profiles. These results demonstrate the significant improvement in imaging resolution produced by the adaptive control loop compared with a classical linear time-invariant control loop.     

Minimum variance control structure for adaptive optics systems

The adaptive optics minimum variance control problem is formulated as a linear-quadratic-Gaussian optimization. The formulation incorporates the wavefront sensor frame integration in discrete-time models of the deformable mirror and incident wavefront. It shows that, under nearly ideal conditions, the resulting minimum variance controller approaches the integral controller commonly used in adaptive optics systems. The inputs to the controller dynamics are obtained from a reconstructor with the maximum a posteriori structure that uses the estimation error covariance of the wavefront error. The ideal conditions assumed to obtain the integral controller are as follows; isotropic first-order (but nonstationary) temporal atmospheric aberrations, no computational loop delay, and no deformable mirror dynamics. The effects of variations in these conditions are examined.     

Application of eigenmode in the adaptive optics system based on a micromachined membrane deformable mirror

The construction process and characteristics of a deformable mirror eigenmode are introduced. The eigenmode of a 37-element micromachined membrane deformable mirror (MMDM) from OKO, Ltd. is analyzed. The Gaussian-Seidel low-order aberrations are fitted with eigenmodes as basic functions. An experimental adaptive optics (AO) system is constructed with the MMDM as the wavefront corrector, a deformable mirror eigenmode as the wavefront control algorithm, and a Shack-Hartmann wavefront sensor as the wavefront detector. The experimental results demonstrate that the deformable mirror eigenmode can act as the wavefront control algorithm for the AO system based on the MMDM.     

基于MEMS技术的自适应光学系统的研究

用自适应光学系统来校正由大气湍流等产生的波前畸变,能够得到很好的效果.通过对自适应光学系统的工作原理进行研究,提出了一种基于MEMS技术的微小型自适应光学系统校正波前畸变的方法,将MEMS技术应用于变形反射镜,并构建了具体的实验平台,用来校正一种人为产生的波前畸变,且阐述了具体的实验过程.实验结果表明,基于MEMS技术的自适应光学系统能够很好地闭环校正波前畸变,且其体积小、质量轻、校正性能稳定,为自适应光学技术在星载相机上的应用提供了依据.     

Multiconjugate adaptive optics results from the laboratory for adaptive optics MCAO/MOAO testbed

We report on the development of wavefront reconstruction and control algorithms for multiconjugate adaptive optics (MCAO) and the results of testing them in the laboratory under conditions that simulate an 8 meter class telescope. The University of California Observatories (UCO) Lick Observatory Laboratory for Adaptive Optics multiconjugate testbed allows us to test wide-field-of-view adaptive optics systems as they might be instantiated in the near future on giant telescopes. In particular, we have been investigating the performance of MCAO using five laser beacons for wavefront sensing and a minimum-variance algorithm for control of two conjugate deformable mirrors. We have demonstrated improved Strehl ratio and enlarged field-of-view performance when compared to conventional AO techniques. We have demonstrated improved MCAO performance with the implementation of a routine that minimizes the generalized isoplanatism when turbulent layers do not correspond to deformable mirror conjugate altitudes. Finally, we have demonstrated suitability of the system for closed loop operation when configured to feed back conditional mean estimates of wavefront residuals rather than the directly measured residuals. This technique has recently been referred to as the "pseudo-open-loop" control law in the literature.     

Adaptive Control of a Micromachined Continuous Membrane Deformable Mirror for Aberration Compensation

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The influence of high-frequency phase and correction distance on the phase correction effect

By studying the propagation characteristics of the wavefront phase of laser beams in adaptive optics systems, the influence of the high-frequency phase on the correction effect has been analyzed and the variations of correction effect with the position of optical deformable mirror have been analyzed quantitatively. The results show that the beam quality of the corrected beam in far field obviously degrades with an increase of high-frequency phase in a distorted wavefront, and the correction effect becomes worse and worse. In addition, the correction effect is related to the position of the deformable mirror; with an increase of the distance between the deformable mirror and the output mirror of the laser the correction effect is better. For a deformable mirror with a given unit size, when the distance of correction is more than 20?m the correction effect is perfect.     

Calibration and performance of a pyramid wavefront sensor for the eye

We describe the calibration and performance of a pyramid wavefront sensor designed for use in a retinal imaging camera. The effect of the image modulation and the sensor binning on the measurements are explained in detail and various tests to validate the performance are described. The wavefront sensor was incorporated into an adaptive optics system that used a magnetically actuated deformable mirror, and results on static test optics are shown.     

High-resolution retinal imaging with micro adaptive optics system

Based on the dynamic characteristics of human eye aberration, a microadaptive optics retina imaging system set is established for real-time wavefront measurement and correction. This paper analyzes the working principles of a 127-unit Hartmann-Shack wavefront sensor and a 37-channel micromachine membrane deformable mirror adopted in the system. The proposed system achieves wavefront reconstruction through the adaptive centroid detection method and the mode reconstruction algorithm of Zernike polynomials, so that human eye aberration can be measured accurately. Meanwhile, according to the adaptive optics aberration correction control model, a closed-loop iterative aberration correction algorithm based on Smith control is presented to realize efficient and real-time correction of human eye aberration with different characteristics, and characteristics of the time domain of the system are also optimized. According to the experiment results tested on a USAF 1951 standard resolution target and a living human retina (subject ZHY), the resolution of the system can reach 3.6?LP/mm, and the human eye wavefront aberration of 0.728λ (λ=785?nm) can be corrected to 0.081λ in root mean square (RMS) so as to achieve the diffraction limit (Strehl ratio is 0.866), then high-resolution retina images are obtained.     

Adaptive wavefront control with asynchronous stochastic parallel gradient descent clusters

A scalable adaptive optics (AO) control system architecture composed of asynchronous control clusters based on the stochastic parallel gradient descent (SPGD) optimization technique is discussed. It is shown that subdivision of the control channels into asynchronous SPGD clusters improves the AO system performance by better utilizing individual and/or group characteristics of adaptive system components. Results of numerical simulations are presented for two different adaptive receiver systems based on asynchronous SPGD clusters-one with a single deformable mirror with Zernike response functions and a second with tip-tilt and segmented wavefront correctors. We also discuss adaptive wavefront control based on asynchronous parallel optimization of several local performance metrics-a control architecture referred to as distributed adaptive optics (DAO). Analysis of the DAO system architecture demonstrated the potential for significant increase of the adaptation process convergence rate that occurs due to partial decoupling of the system control clusters optimizing individual performance metrics.     

Plenoptic camera wavefront sensing with extended sources

Abstract

The wavefront sensor is used in adaptive optics to detect the atmospheric distortion, which feeds back to the deformable mirror to compensate for this distortion. Different from the Shack–Hartmann sensor that has been widely used with point sources, the plenoptic camera wavefront sensor has been proposed as an alternative wavefront sensor adequate for extended objects in recent years. In this paper, the plenoptic camera wavefront sensing with extended sources is discussed systematically. Simulations are performed to investigate the wavefront measurement error and the closed-loop performance of the plenoptic sensor. The results show that there are an optimal lenslet size and an optimal number of pixels to make the best performance. The RMS of the resulting corrected wavefront in closed-loop adaptive optics system is less than 108 nm (0.2λ) when D/r₀ ≤ 10 and the magnitude M ≤ 5. Our investigation indicates that the plenoptic sensor is efficient to operate on extended sources in the closed-loop adaptive optics system.     

Dynamic eye model for adaptive optics testing

An artificial dynamic eye model is proposed. The prototype enabled us to introduce temporal variations in defocus and spherical aberration, resembling those typically found in the human eye. The eye model consisted of a meniscus lens together with a modal liquid crystal lens with controllable focus. A diffuser placed at a fixed distance from the lenses acted as the artificial retina. Developed software allowed the user to precisely control the dynamic generation of aberrations. In addition, different refractive errors could simultaneously be emulated by varying the distance between the components of the model. The artificial eye was first used as a dynamic generator of both spherical aberration and defocus, imitating the behavior of a real eye. The artificial eye was implemented in an adaptive optics system designed for the human eye. The system incorporated an electrostatic deformable mirror and a Hartmann-Shack wavefront sensor. Results with and without real time closed-loop aberration correction were obtained. The use of the dynamic artificial eye could be quite useful for testing and evaluating adaptive optics instruments for ophthalmic applications.     

Wave-front generation of Zernike polynomial modes with a micromachined membrane deformable mirror

We investigate the characteristics of a 37-channel micromachined membrane deformable mirror for wave-front generation. We demonstrate wave-front generation of the first 20 Zernike polynomial modes, using an iterative algorithm to adjust driving voltages. The results show that lower-order-mode wave fronts can be generated with good accuracy and large dynamic range, whereas the generation of higher-order modes is limited by the number of the actuator channels and the working range of the deformable mirror. The speed of wave-front generation can be as fast as several hundred hertz. Our results indicate that, in addition to generation of wave fronts with known aberrations, the characteristics of the micromachined membrane deformable mirror device can be useful in adaptive optics systems for compensating the first five orders of aberration.     

Study of a MEMS-based Shack-Hartmann wavefront sensor with adjustable pupil sampling for astronomical adaptive optics

We introduce a Shack-Hartmann wavefront sensor for adaptive optics that enables dynamic control of the spatial sampling of an incoming wavefront using a segmented mirror microelectrical mechanical systems (MEMS) device. Unlike a conventional lenslet array, subapertures are defined by either segments or groups of segments of a mirror array, with the ability to change spatial pupil sampling arbitrarily by redefining the segment grouping. Control over the spatial sampling of the wavefront allows for the minimization of wavefront reconstruction error for different intensities of guide source and different atmospheric conditions, which in turn maximizes an adaptive optics system's delivered Strehl ratio. Requirements for the MEMS devices needed in this Shack-Hartmann wavefront sensor are also presented.     

Control of the unilluminated deformable mirror actuators in an altitude-conjugated adaptive optics system

Off-axis observations made with adaptive optics are severely limited by anisoplanatism errors. However, conjugating the deformable mirror to an optimal altitude can reduce these errors; it is then necessary to control, through extrapolation, actuators that are not measured by the wave-front sensor (unilluminated actuators). In this study various common extrapolation schemes are investigated, and an optimal method that achieves a significantly better performance is proposed. This extrapolation method involves a simple matrix multiplication and will be implemented in ALTAIR, the Gemini North Telescope adaptive optics system located on Mauna Kea, Hawaii. With this optimal method, the relative H-band Strehl reduction due to extrapolation errors is only 5%, 16%, and 30% when the angular distance between the guide source and the science target is 20, 40 and 60 arc sec, respectively. For a site such as Mauna Kea, these errors are largely outweighed by the increase in the size of the isoplanatic field.     

Concept, modeling, and performance prediction of a low-cost, large deformable mirror

While it is attractive to integrate a deformable mirror (DM) for adaptive optics (AO) into the telescope itself rather than using relay optics within an instrument, the resulting large DM can be expensive, particularly for extremely large telescopes. A low-cost approach for building a large DM is to use voice-coil actuators connected to the back of the DM through suction cups. Use of such inexpensive voice-coil actuators leads to a poorly damped system with many structural modes within the desired bandwidth. Control of the mirror dynamics using electro-mechanical sensors is thus required for integration within an AO system. We introduce a distributed control approach, and we show that the "inner" back sensor control loop does not need to function at low frequencies, leading to significant cost reduction for the sensors. Incorporating realistic models of low-cost actuators and sensors together with an atmospheric seeing model, we demonstrate that the low-cost mirror strategy is feasible within a closed-loop AO system.     

Methods for the characterization of deformable membrane mirrors

We demonstrate two methods for the characterization of deformable membrane mirrors and the training of adaptive optics systems that employ these mirrors. Neither method employs a wave-front sensor. In one case, aberrations produced by a wave-front generator are corrected by the deformable mirror by use of a rapidly converging iterative algorithm based on orthogonal deformation modes of the mirror. In the other case, a simple interferometer is used with fringe analysis and phase-unwrapping algorithms. We discuss how the choice of singular values can be used to control the pseudoinversion of the control matrix.     

Self-characterization of linear and nonlinear adaptive optics systems

We present methods used to determine the linear or nonlinear static response and the linear dynamic response of an adaptive optics (AO) system. This AO system consists of a nonlinear microelectromechanical systems deformable mirror (DM), a linear tip-tilt mirror (TTM), a control computer, and a Shack-Hartmann wavefront sensor. The system is modeled using a single-input-single-output structure to determine the one-dimensional transfer function of the dynamic response of the chain of system hardware. An AO system has been shown to be able to characterize its own response without additional instrumentation. Experimentally determined models are given for a TTM and a DM.     

Fundamental limits on isoplanatic correction with multiconjugate adaptive optics

We investigate the performance of a general multiconjugate adaptive optics (MCAO) system in which signals from multiple reference beacons are used to drive several deformable mirrors in the optical beam train. Taking an analytic approach that yields a detailed view of the effects of low-order aberration modes defined over the metapupil, we show that in the geometrical optics approximation, N deformable mirrors conjugated to different ranges can be driven to correct these modes through order N with unlimited isoplanatic angle, regardless of the distribution of turbulence along the line of sight. We find, however, that the optimal deformable mirror shapes are functions of target range, so the best compensation for starlight is in general not the correction that minimizes the wave-front aberration in a laser guide beacon. This introduces focal anisoplanatism in the wave-front measurements that can be overcome only through the use of beacons at several ranges. We derive expressions for the number of beacons required to sense the aberration to arbitrary order and establish necessary and sufficient conditions on their geometry for both natural and laser guide stars. Finally, we derive an expression for the residual uncompensated error by mode as a function of field angle, target range, and MCAO system geometry.