Laboratory demonstration of accurate and efficient nanometer-level wavefront control for extreme adaptive optics

A 32 x 32 microelectricalmechanical systems mirror is controlled in a closed-loop adaptive optics test bed with a spatially filtered wavefront sensor (WFS), Fourier transform wavefront reconstruction, and calibration of references with a high-precision interferometer. When correcting the inherent aberration of the mirror, 0.7 nm rms phase error in the controllable band is achieved. When correcting an etched phase plate with atmospheric statistics, a dark hole 10(3) deeper than the uncontrollable phase is produced in the phase power spectral density. Compensation of the mirror's influence function is done with a Fourier filter, which results in improved loop convergence. Use of the spatial filter is shown to reduce the gain variability of the WFS in a quadcell configuration.     

Exploiting the spatiotemporal correlation in adaptive optics using data-driven H2-optimal control

A recently proposed data-driven H2-optimal control approach is demonstrated on a laboratory setup. Most adaptive optics (AO) systems are based on a control law that neglects the temporal evolution of the wavefront. The proposed control approach is able to exploit the spatiotemporal correlation in the wavefront without assuming any form of decoupling. By analyzing the dynamic behavior of the wavefront sensor (WFS), it is shown that if the wavefront correction device can be considered static, the transfer function from control input to WFS output reduces to a two-tap impulse response and an integer number of samples delay. Considering this model structure, a data-driven identification procedure is developed to estimate the relevant parameters from measurement data. The specific structure allows for an analytical expression of the optimal controller in terms of the system matrices of the minimum-phase spectral factor of the atmospheric disturbance model. The performance of the optimal controller is compared with that of the standard AO control law. An analysis of the dominant error sources shows that optimal control may reduce the temporal error.     

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.     

On-sky performances of an optical phasing sensor based on a cylindrical lenslet array for segmented telescopes

New optical phasing sensor technologies have been studied with a test bench experiment, called Active Phasing Experiment, on-sky at the European Southern Observatory Very Large Telescope. One of the sensors was of the Shack-Hartmann type using cylindrical lenslets across the segment borders for the measurement of the phasing errors. With bright stars, the precision of the measurement of piston steps at a single border was better than 9 nm wavefront RMS, and the precision of the closed-loop correction of the piston errors of the segments across the whole mirror was better than 10 nm wavefront RMS. With dimmer stars of magnitude up to 14.5, precisions of the order of 22 nm wavefront RMS were obtained.     

Alignment algorithm for three-mirror anastigmatic telescopes based on nodal aberration theory

For most of the alignment algorithms, alignment errors and figure errors cannot be separated due to the coupling effect among optical elements. We present an alignment algorithm for TMA telescopes on the framework of nodal aberration theory (NAT). Based on NAT, we firstly determine the axial misalignments of secondary (SM) and tertiary (TM) mirrors. Then we decouple the lateral misalignments and angular misalignments of SM and TM. Finally, we decouple the figure errors of primary mirror (PM) from the alignment errors of SM and TM. To validate the algorithm, a TMA telescope is designed for simulation. In the simulation, modulation transfer function (MTF) is chosen to evaluate the telescope before and after correction. It is found that the algorithm presented in this paper maintains high precision. In the end, a Monte Carlo simulation is conducted to further demonstrate the accuracy of the presented alignment algorithm even in poor conditions.     

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.     

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.     

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.     

Comparison between a model-based and a conventional pyramid sensor reconstructor

A model of a non-modulated pyramid wavefront sensor (P-WFS) based on Fourier optics has been presented. Linearizations of the model represented as Jacobian matrices are used to improve the P-WFS phase estimates. It has been shown in simulations that a linear approximation of the P-WFS is sufficient in closed-loop adaptive optics. Also a method to compute model-based synthetic P-WFS command matrices is shown, and its performance is compared to the conventional calibration. It was observed that in poor visibility the new calibration is better than the conventional.     

Mean-square residual error of a wavefront after propagation through atmospheric turbulence and after correction with Zernike polynomials

The root-mean-square (rms) of the residual wavefront, after propagation through atmospheric turbulence and corrected from Zernike polynomials, has been derived for the von Kármán turbulence model. The rms for any location in the telescope pupil and the pupil average rms have been calculated. It is shown that the residual rms on the edge of the pupil can be up to 35% larger than the pupil average residual rms. The results are useful to estimate the required rms stroke of deformable mirror (DM) actuators when they are used as a second stage of correction either in a tip-tilt, single-DM configuration or in a tip-tilt, two-DM (woofer-tweeter) setup.     

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.     

环形阵列微变形镜两种设计准则的分析比较

在波前校正中,环形阵列的分立式微变形镜充分利用了各个单元。环形阵列的分立式微变形镜有等单元面积和等单元宽度两种设计准则,以37单元环形阵列微变形镜为例,从校正波前适配误差和校正后剩余波前的Strehl比两方面对两种设计准则进行比较。结果表明,采用等单元面积设计的环形微变形镜校正畸变波前的性能更好。特别是波前畸变严重时,这种效果更加明显。     

Wavefront error measurement of high-numerical-aperture optics with a Shack-Hartmann sensor and a point source

We developed a new, to the best of our knowledge, test method to measure the wavefront error of the high-NA optics that is used to read the information on the high-capacity optical data storage devices. The main components are a pinhole point source and a Shack-Hartmann sensor. A pinhole generates the high-NA reference spherical wave, and a Shack-Hartmann sensor constructs the wavefront error of the target optics. Due to simplicity of the setup, it is easy to use several different wavelengths without significant changes of the optical elements in the test setup. To reduce the systematic errors in the system, a simple calibration method was developed. In this manner, we could measure the wavefront error of the NA 0.9 objective with the repeatability of 0.003 lambda rms (lambda = 632.8 nm) and the accuracy of 0.01 lambda rms.     

Research on error control and compensation in magnetorheological finishing

Although magnetorheological finishing (MRF) is a deterministic finishing technology, the machining results always fall short of simulation precision in the actual process, and it cannot meet the precision requirements just through a single treatment but after several iterations. We investigate the reasons for this problem through simulations and experiments. Through controlling and compensating the chief errors in the manufacturing procedure, such as removal function calculation error, positioning error of the removal function, and dynamic performance limitation of the CNC machine, the residual error convergence ratio (ratio of figure error before and after processing) in a single process is obviously increased, and higher figure precision is achieved. Finally, an improved technical process is presented based on these researches, and the verification experiment is accomplished on the experimental device we developed. The part is a circular plane mirror of fused silica material, and the surface figure error is improved from the initial λ/5 [peak-to-valley (PV) λ=632.8 nm], λ/30 [root-mean-square (rms)] to the final λ/40 (PV), λ/330 (rms) just through one iteration in 4.4 min. Results show that a higher convergence ratio and processing precision can be obtained by adopting error control and compensation techniques in MRF.     

Lateral Support of Very Large Telescope Mirrors by Edge Forces Only

Abstract

Until now a diameter of about 4 m seemed to be the upper-size limit of telescope mirrors that still permitted cost-saving designs of lateral supports by edge forces alone. In some designs, the supporting edge forces comprised not only basic push-pull action normal to the edge but also a specific, moderate amount of tangential shear. However, this was a by-product of design economy rather than the result of understanding the potential of tangential support forces as a means of reducing mirror flexure systematically, down to residuals in the 1% region. The surprising possibility of extending the usefulness of pure edge supports is demonstrated by the example of the 8-m mirror of the European Southern Observatory's Very Large Telescope. Fitted with a lateral support at the outer edge alone, this thin mirror will exhibit a wavefront aberration with a calculated rms value of only 18 nm, without taking into account possible active control.     

Prediction of wave-front sensor slope measurements with artificial neural networks

For adaptive optical systems to compensate for atmospheric turbulence effects, the wave-front perturbation must be measured with a wave-front sensor (WFS) and corrected with a deformable mirror. One limitation in this process is the time delay between the measurement of the aberrated wave front and implementation of the proper correction. Statistical techniques exist for predicting the atmospheric aberrations at the time of correction based on the present and past measured wave fronts. However, for the statistical techniques to be effective, key parameters of the atmosphere and the adaptive optical system must be known. These parameters include the Fried coherence length r(0), the atmospheric wind-speed profile, and the WFS slope measurement error. Neural networks provide nonlinear solutions to adaptive optical problems while offering the possibility to function under changing seeing conditions without actual knowledge of the current state of the key parameters. We address the use of neural networks for WFS slope measurement prediction with only the noisy WFS measurements as inputs. Where appropriate, we compare with classical statistical-based methods to determine if neural networks offer true benefits in performance.     

Wide-field Fizeau imaging telescope: experimental results

A nine-aperture, wide-field Fizeau imaging telescope has been built at the Lockheed-Martin Advanced Technology Center. The telescope consists of nine, 125 mm diameter collector telescopes coherently phased and combined to form a diffraction-limited image with a resolution that is consistent with the 610 mm diameter of the telescope. The phased field of view of the array is 1 murad. The measured rms wavefront error is 0.08 waves rms at 635 nm. The telescope is actively controlled to correct for tilt and phasing errors. The control sensing technique is the method known as phase diversity, which extracts wavefront information from a pair of focused and defocused images. The optical design of the telescope and typical performance results are described.     

微机械薄膜变形镜的闭环校正模型

介绍了微机械薄膜变形镜(MMDM)面形影响函数的意义,并测量了Oko公司37通道MMDM的面形影响函数矩阵,实验验证了镜面形变和单个驱动电极电压平方之间的线性关系,分析了变形镜的校正能力,建立了自适应光学系统闭环校正的模型.搭建基于MMDM的自适应光学实验系统,采用人眼出射波前作为原始波前进行实验,结果表明,模型能快速有效的对动态畸变波前进行校正,为基于MMDM的自适应光学系统提供了算法支持.     

Lithographic characterization of the spherical error in an extreme-ultraviolet optic by use of a programmable pupil-fill illuminator

Extreme-ultraviolet (EUV) lithography remains a leading contender for use in the mass production of nanoelectronics at the 32 nm node. Great progress has been made in all areas of EUV lithography, including the crucial issue of fabrication of diffraction-limited optics. To gain an accurate understanding of the projection optic wavefront error in a completed lithography tool requires lithography-based aberration measurements; however, making such measurements in EUV systems can be challenging. We describe the quantitative lithographic measurement of spherical aberration in a 0.3 numerical aperture. EUV microfield optic. The measurement method is based on use of the unique properties of a programmable coherence illuminator. The results show the optic to have 1 nm rms spherical error, whereas interferometric measurements performed during the alignment of the optic indicated a spherical error of less than 0.1 nm rms.