Generalized aliasing and its implications in modal gain optimization for multi-conjugate adaptive optics

The error of generalized aliasing associated with the limited sampling of the atmospheric turbulence volume due to the finite number of wavefront sensing directions in wide-field-of-view adaptive optics is formally defined. Following a modal approach, we extend the direct problem formulation of star-oriented multi-conjugate adaptive optics (MCAO) to model and quantify this error analytically. We show that the turbulence estimation with the least-squares reconstructor is subject to strong generalized aliasing, in particular affecting the badly seen modes, whereas with the minimum-mean-square-error reconstructor the estimation is little affected. Finally, we show that the application of modal gain optimization techniques in closed-loop MCAO systems is jeopardized by the generalized aliasing error.     

Optimization of star-oriented and layer-oriented wavefront sensing concepts for ground layer adaptive optics

Multiconjugate adaptive optics is one of the major challenges in adaptive optics. It requires the measurement of the volumic distribution of the turbulence. Two wavefront sensing (WFS) concepts have been proposed to perform the wavefront analysis for such systems: the star-oriented and layer-oriented approaches. We give a performance analysis and a comparison of these two concepts in the framework of the simplest of the multi-guide-star adaptive optics systems, that is, ground layer adaptive optics. A phase-related criterion is proposed to assess analytically the performance of both concepts. This study highlights the main advantages and drawbacks of each WFS concept and shows how it is possible to optimize the concepts with respect to the signal to noise ratio on the phase measurement. A comparison of their optimized versions is provided and shows that one can expect very similar performance with the two optimized concepts.     

Scintillation and phase anisoplanatism in Shack-Hartmann wavefront sensing

Adaptive optics provides a real-time compensation for atmospheric turbulence that severely limits the resolution of ground-based observation systems. The correction quality relies on a key component, that is, the wavefront sensor (WFS). When observing extended sources, WFS precision is limited by anisoplanatism effects. Anisoplanatism induces a variation of the turbulent phase and of the collected flux in the field of view. We study the effect of this phase and scintillation anisoplanatism on wavefront analysis. An analytical expression of the error induced is given in the Rytov regime. The formalism is applied to a solar and an endoatmospheric observation. Scintillation effects are generally disregarded, especially in astronomical conditions. We shall prove that this approximation is not valid with extended objects.     

Preconditioned conjugate gradient wave-front reconstructors for multiconjugate adaptive optics

Multiconjugate adaptive optics (MCAO) systems with 10(4)-10(5) degrees of freedom have been proposed for future giant telescopes. Using standard matrix methods to compute, optimize, and implement wavefront control algorithms for these systems is impractical, since the number of calculations required to compute and apply the reconstruction matrix scales respectively with the cube and the square of the number of adaptive optics degrees of freedom. We develop scalable open-loop iterative sparse matrix implementations of minimum variance wave-front reconstruction for telescope diameters up to 32 m with more than 10(4) actuators. The basic approach is the preconditioned conjugate gradient method with an efficient preconditioner, whose block structure is defined by the atmospheric turbulent layers very much like the layer-oriented MCAO algorithms of current interest. Two cost-effective preconditioners are investigated: a multigrid solver and a simpler block symmetric Gauss-Seidel (BSGS) sweep. Both options require off-line sparse Cholesky factorizations of the diagonal blocks of the matrix system. The cost to precompute these factors scales approximately as the three-halves power of the number of estimated phase grid points per atmospheric layer, and their average update rate is typically of the order of 10(-2) Hz, i.e., 4-5 orders of magnitude lower than the typical 10(3) Hz temporal sampling rate. All other computations scale almost linearly with the total number of estimated phase grid points. We present numerical simulation results to illustrate algorithm convergence. Convergence rates of both preconditioners are similar, regardless of measurement noise level, indicating that the layer-oriented BSGS sweep is as effective as the more elaborated multiresolution preconditioner.     

Open-loop correction of horizontal turbulence: system design and result

Adaptive optics systems often work in a closed-loop configuration due to the hysteretic and nonlinearity properties of conventional deformable mirrors. Because of the high-precision wavefront generation and nonhysteretic properties of liquid-crystal devices, the open-loop control becomes possible. Open-loop control is a requirement for advanced adaptive optics concepts. We designed an open-loop adaptive optics system with a liquid-crystal-on-silicon wavefront corrector. This system is simple, fast, and can save much more light compared to conventional liquid-crystal-based closed-loop systems. The detailed principle, construction, and operation are discussed. The 500 m horizontal turbulence correction experiment was done using a 250 mm telescope in the laboratory. The whole system can reach a 60 Hz correction frequency. Evaluation of the correction precision was done at closed-loop configuration, which is 0.2 lambda (lambda=0.633 microm) in peak to valley. The dynamic image under open-loop correction got the same resolution compared to closed-loop correction. The whole system reached 0.68 arc sec resolution capability at open-loop correction, which is slightly larger than the system's diffraction-limited resolution of 0.65 arc sec.     

多层共轭自适应光学的进展与展望

该文论述了多层共轭自适应光学的原理和主要模式，波前畸变的探测与重构是多层共轭自适应光学的研究核心，文中分析了层析、定向层和多视场定向层等实现波前畸变探测与重构的方法；介绍了系统中导星的使用：总结并分析了近年来国内外在理论及实践中的研究进展和取得的成果．提出多层共轭自适应光学的发展前景．     

Tomography approach for multi-object adaptive optics

Multi-object adaptive optics (MOAO) is a solution developed to perform a correction by adaptive optics (AO) in a science large field of view. As in many wide-field AO schemes, a tomographic reconstruction of the turbulence volume is required in order to compute the MOAO corrections to be applied in the dedicated directions of the observed very faint targets. The specificity of MOAO is the open-loop control of the deformable mirrors by a number of wavefront sensors (WFSs) that are coupled to bright guide stars in different directions. MOAO calls for new procedures both for the cross registration of all the channels and for the computation of the tomographic reconstructor. We propose a new approach, called "Learn and Apply (L&A)", that allows us to retrieve the tomographic reconstructor using the on-sky wavefront measurements from an MOAO instrument. This method is also used to calibrate the registrations between the off-axis wavefront sensors and the deformable mirrors placed in the science optical paths. We propose a procedure linking the WFSs in the different directions and measuring directly on-sky the required covariance matrices needed for the reconstructor. We present the theoretical expressions of the turbulence spatial covariance of wavefront slopes allowing one to derive any turbulent covariance matrix between two wavefront sensors. Finally, we discuss the convergence issue on the measured covariance matrices, we propose the fitting of the data based on the theoretical slope covariance using a reduced number of turbulence parameters, and we present the computation of a fully modeled reconstructor.     

Adaptive optics technique to overcome the turbulence in a large-aperture collimator

A collimator with a long focal length and large aperture is a very important apparatus for testing large-aperture optical systems. But it suffers from internal air turbulence, which may limit its performance and reduce the testing accuracy. To overcome this problem, an adaptive optics system is introduced to compensate for the turbulence. This system includes a liquid crystal on silicon device as a wavefront corrector and a Shack-Hartmann wavefront sensor. After correction, we can get a plane wavefront with rms of about 0.017 lambda (lambda=0.6328 microm) emitted out of a larger than 500 mm diameter aperture. The whole system reaches diffraction-limited resolution.     

弱光61单元自适应光学系统的控制优化

在自适应光学系统中,波前校正残误差主要由未完全补偿湍流所引起的误差和系统闭环噪声组成。基于一阶比例－积分控制器分析了弱光６１单元适应光学系统的控制特性。在此基础上风云地非Ｋｏｌｍｏｇｏｒｏｖ湍流情况,提出一种根据实际测量的大气湍流波前扰动功率谱来确定系统,针对非Ｋｏｌｍｏｇｏｒｏｖ湍流情况,提出一根据实际测量的大气湍流波前扰动功率谱来确定系统最优控制带宽的新方法。应用这种方法对弱光６１单元自适应光     

Optimal control law for classical and multiconjugate adaptive optics

Classical adaptive optics (AO) is now a widespread technique for high-resolution imaging with astronomical ground-based telescopes. It generally uses simple and efficient control algorithms. Multiconjugate adaptive optics (MCAO) is a more recent and very promising technique that should extend the corrected field of view. This technique has not yet been experimentally validated, but simulations already show its high potential. The importance for MCAO of an optimal reconstruction using turbulence spatial statistics has already been demonstrated through open-loop simulations. We propose an optimal closed-loop control law that accounts for both spatial and temporal statistics. The prior information on the turbulence, as well as on the wave-front sensing noise, is expressed in a state-space model. The optimal phase estimation is then given by a Kalman filter. The equations describing the system are given and the underlying assumptions explained. The control law is then derived. The gain brought by this approach is demonstrated through MCAO numerical simulations representative of astronomical observation on a 8-m-class telescope in the near infrared. We also discuss the application of this control approach to classical AO. Even in classical AO, the technique could be relevant especially for future extreme AO systems.     

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.     

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.     

Split atmospheric tomography using laser and natural guide stars

Laser guide star (LGS) atmospheric tomography is described in the literature as integrated minimum-variance tomographic wavefront reconstruction from a concatenated wavefront-sensor measurement vector consisting of many high-order, tip/tilt (TT)-removed LGS measurements, supplemented by a few low-order natural guide star (NGS) components essential to estimating the TT and tilt anisoplanatism (TA) modes undetectable by the TT-removed LGS wavefront sensors (WFSs). The practical integration of these NGS WFS measurements into the tomography problem is the main subject of this paper. A split control architecture implementing two separate control loops driven independently by closed-loop LGS and NGS measurements is proposed in this context. Its performance is evaluated in extensive wave optics Monte Carlo simulations for the Thirty Meter Telescope (TMT) LGS multiconjugate adaptive optics (MCAO) system, against the delivered performance of the integrated control architecture. Three iterative algorithms are analyzed for atmospheric tomography in both cases: a previously proposed Fourier domain preconditioned conjugate gradient (FDPCG) algorithm, a simple conjugate gradient (CG) algorithm without preconditioning, and a novel layer-oriented block Gauss-Seidel conjugate gradient algorithm (BGS-CG). Provided that enough iterations are performed, all three algorithms yield essentially identical closed-loop residual RMS wavefront errors for both control architectures, with the caveat that a somewhat smaller number of iterations are required by the CG and BGS-CG algorithms for the split approach. These results demonstrate that the split control approach benefits from (i) a simpler formulation of minimum-variance atmospheric tomography allowing for algorithms with reduced computational complexity and cost (processing requirements), (ii) a simpler, more flexible control of the NGS-controlled modes, and (iii) a reduced coupling between the LGS- and NGS-controlled modes. Computation and memory requirements for all three algorithms are also given for the split control approach for the TMT LGS AO system and appear feasible in relation to the performance specifications of current hardware technology.     

Open-loop control of liquid-crystal spatial light modulators for vertical atmospheric turbulence wavefront correction

We present an open-loop adaptive optics (AO) system based on two liquid-crystal spatial light modulators (LCSLMs) that profit from high precision wavefront generation and good repeatability. A wide optical bandwidth of 300 nm is designed for the system, and a new open-loop optical layout is invented to conveniently switch between the open and closed loop. The corresponding control algorithm is introduced with a loop frequency (the reciprocal of the total time delay of a correction loop) of 103 Hz. The system was mounted onto a 2.16 m telescope for vertical atmospheric turbulence correction. The full width at half-maximum of the image of the star α Boo reached 0.636 arc sec after the open-loop correction, while it was 2.12 arc sec before the correction. The result indicates that the open-loop AO system based on LCSLMs potentially has the ability to be used for general astronomical applications.     

Effect of wavefront corrugations on fringe motion in an astronomical interferometer with spatial filters

Numerical simulations of atmospheric turbulence and adaptive optics (AO) wavefront correction are performed to investigate the time scale for fringe motion in optical interferometers with spatial filters. These simulations focus especially on partial AO correction, where only a finite number of Zernike modes are compensated. The fringe motion is found to depend strongly on both the aperture diameter and the level of AO correction used. In all the simulations the coherence time scale for interference fringes is found to decrease dramatically when the Strehl ratio provided by the AO correction is < or = 30%. For AO systems that give perfect compensation of a limited number of Zernike modes, the aperture size that gives the optimum signal for fringe phase tracking is calculated. For AO systems that provide noisy compensation of Zernike modes (but are perfectly piston neutral), the noise properties of the AO system determine the coherence time scale of the fringes when the Strehl ratio is < or = 30%.     

Correctability limitations imposed by plane-wave scintillation in multiconjugate adaptive optics

Plane-wave scintillation is shown to impose multiconjugate adaptive optics (MCAO) correctability limitations that are independent of wavefront sensing and reconstruction. Residual phase and log-amplitude variances induced by scintillation in weak turbulence are derived using linear (diffraction-based) diffractive MCAO spatial filters or (diffraction-ignorant) geometric MCAO proportional gains as open-loop control parameters. In the case of Kolmogorov turbulence, expressions involving the Rytov variance and/or weighted C(2)(n) integrals apply. Differences in performance between diffractive MCAO and geometric MCAO resemble chromatic errors. Optimal corrections based on least squares imply irreducible performance limits that are validated by wave-optic simulations.     

Impact of sodium laser guide star fratricide on multi-conjugate adaptive optics systems

Laser beams projected from the ground to form sodium layer laser guide stars (LGSs) for adaptive optics (AO) systems experience scattering and absorption that reduce their intensity as they propagate upward through the atmosphere. Some fraction of the scattered light will be collected by the other wavefront sensors and causes additional background in parts of the pupil. This cross-talk between different LGS wavefront sensors is referred to as the fratricide effect. In this paper we quantify the magnitude of four different sources of scattering/absorption and backscattering, and we evaluate their impact on performance with various zenith angles and turbulence profiles for one particular AO system. The resulting wavefront error for the Thirty Meter Telescope (TMT) multi-conjugate AO (MCAO) system, NFIRAOS, is on the order of 5 to 20 nm RMS, provided that the mean background from the fratricide effect can be calibrated and subtracted with an accuracy of 80%. We also present the impact on system performance of momentary variations in LGS signal levels due to variations in cirrus absorption or laser power, and we show that this affects the performance more than does an equal variation in the level of the fratricide.     

Shack-Hartmann wavefront estimation with extended sources: anisoplanatism influence

Anisoplanatism limits the correction field of adaptive optics (AO). In the case of Shack-Hartmann measurement performed on extended sources it may also strongly affect wavefront estimation accuracy. An analytical formalism has been previously proposed to quantify anisoplanatism slope measurement error. It is exploited here to derive the most relevant quantity in AO, the wavefront error. Analytical and end-to-end simulation results are compared in three cases: solar observation, weakly perturbed near-to-ground observation, and strongly perturbed near-to-ground observation. In every case, anisoplanatism wavefront error takes significant values. The accuracy of the analytical model is investigated in detail. Three contributions to the slope error previously identified are considered: phase anisoplanatism, scintillation anisoplanatism, and coupling between scintillation and phase anisoplanatism. The influence of both scintillation and coupling contributions to the wavefront error is confirmed here.     

Aperture size effect on ultrasonic wavefront distortion correction

The influences of aperture size on wavefront distortion correction are investigated both theoretically and numerically. A multilayer, phase-screen model is assumed to be the underlying, distorting medium. Numerical simulations were performed using three wavefront distortion correction methods: time-shift compensation (TSC), backpropagation followed by time-shift compensation (BP+TSC), and the previously proposed, multilayer, phase-screen compensation (MPSC) method. The distorted wavefronts were generated by propagating a planar wavefront through a multilayer, phase-screen model constructed with a two-dimensional (2-D) scanned map of a real abdominal slice. Performances were evaluated by L2 errors between the corrected wavefronts and the undistorted planar wavefront. Point spread functions also were calculated to evaluate the relative image quality. Theoretical analysis shows L2 error will decrease as aperture size grows when exact phase compensation (EPC) is applied, although finite errors will always exist along the edges of the corrected wavefront. Three different aperture sizes, 14.24 mm (64 elements), 28.48 mm (128 elements), and 56.96 mm (256 elements) are considered in this study. Numerical results show that the quality of wavefront with EPC is essentially limited by the aperture size, and the correction methods considered are relatively robust against the aperture size. It also shows that, for low aberration, results with MPSC and EPC are comparable. However, for high aberration, MPSC significantly outperforms EPC in suppression of L2 error and sidelobes. This study suggests that, for most medical ultrasound imaging systems, the exact structure of the distorting medium may not be necessary to be known a priori for optimal distortion correction because of the limitation imposed by finite aperture size.     

两步式灵敏度矩阵法在卡塞格林望远镜装调中的应用

为了调节视场较大的卡塞格林望远镜的次镜位置,提出了两步式灵敏度矩阵模型的计算机辅助装调方法。在分析了传统的二次模型灵敏度矩阵法的缺陷的基础上,根据灵敏度矩阵的特点加入了精调步骤,对传统的灵敏度矩阵法进行了改进。针对卡塞格林系统,分析了各项泽尼克系数与失调量之间的关系,并对300mm口径,0.6°视场的卡塞格林系统进行了校正仿真。仿真结果显示,传统的灵敏度矩阵法校正后沿x、y、z轴偏移及绕x、y轴倾斜的失调量的均值分别为:-0.0684 mm、-0.0892 mm、0.0015 mm、0.0498°和-0.0444°,全视场波像差RMS均小于0.1λ(λ=632.8nm);两步式灵敏度矩阵法校正后的均值分别为-0.0018 mm、-0.0012 mm、0.0002 mm、0.0008°和-0.0012°,全视场RMS均小于0.03λ,明显优于传统的灵敏度矩阵法。