Warm-started wavefront reconstruction for adaptive optics

Future extreme adaptive optics (ExAO) systems have been suggested with up to 10(5) sensors and actuators. We analyze the computational speed of iterative reconstruction algorithms for such large systems. We compare a total of 15 different scalable methods, including multigrid, preconditioned conjugate-gradient, and several new variants of these. Simulations on a 128x128 square sensor/actuator geometry using Taylor frozen-flow dynamics are carried out using both open-loop and closed-loop measurements, and algorithms are compared on a basis of the mean squared error and floating-point multiplications required. We also investigate the use of warm starting, where the most recent estimate is used to initialize the iterative scheme. In open-loop estimation or pseudo-open-loop control, warm starting provides a significant computational speedup; almost every algorithm tested converges in one iteration. In a standard closed-loop implementation, using a single iteration per time step, most algorithms give the minimum error even in cold start, and every algorithm gives the minimum error if warm started. The best algorithm is therefore the one with the smallest computational cost per iteration, not necessarily the one with the best quasi-static performance.     

Laser guide star wavefront sensing for ground-layer adaptive optics on extremely large telescopes

We propose ground-layer adaptive optics (GLAO) to improve the seeing on the 42?m European Extremely Large Telescope. Shack-Hartmann wavefront sensors (WFSs) with laser guide stars (LGSs) will experience significant spot elongation due to off-axis observation. This spot elongation influences the design of the laser launch location, laser power, WFS detector, and centroiding algorithm for LGS GLAO on an extremely large telescope. We show, using end-to-end numerical simulations, that with a noise-weighted matrix-vector-multiply reconstructor, the performance in terms of 50% ensquared energy (EE) of the side and central launch of the lasers is equivalent, the matched filter and weighted center of gravity centroiding algorithms are the most promising, and approximately 10×10 undersampled pixels are optimal. Significant improvement in the 50% EE can be observed with a few tens of photons/subaperture/frame, and no significant gain is seen by adding more than 200 photons/subaperture/frame. The LGS GLAO is not particularly sensitive to the sodium profile present in the mesosphere nor to a short-timescale (less than 100?s) evolution of the sodium profile. The performance of LGS GLAO is, however, sensitive to the atmospheric turbulence profile.     

Predictive wavefront control for adaptive optics with arbitrary control loop delays

We present a modification of the closed-loop state space model for adaptive optics control that allows delays that are a noninteger multiple of the system frame rate. We derive the new forms of the predictive Fourier control Kalman filters for arbitrary delays and show that they are linear combinations of the whole-frame delay terms. This structure of the controller is independent of the delay. System stability margins and residual error variance both transition gracefully between integer-frame delays.     

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.     

Investigation of gaseous light-beam wavefront correctors as adaptive optics elements

The possibility of increasing the rate of variation of the optical parameters of gaseous focusing systems by directing a light beam perpendicular to the gas flow direction is investigated experimentally. It is shown that the rate of vartation of the focal length can reach considerable values close to those of adaptive optics. Academic Scientific Complex “A. V. Luikov Institute of Heat and Mass Transfer of the Academy of Sciences of Belarus”, Minsk, Belarus. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 69, No. 4, pp. 568–572, July–August, 1996.     

Atmospheric turbulence profiling with SLODAR using multiple adaptive optics wavefront sensors

The slope detection and ranging (SLODAR) method recovers atmospheric turbulence profiles from time averaged spatial cross correlations of wavefront slopes measured by Shack-Hartmann wavefront sensors. The Palomar multiple guide star unit (MGSU) was set up to test tomographic multiple guide star adaptive optics and provided an ideal test bed for SLODAR turbulence altitude profiling. We present the data reduction methods and SLODAR results from MGSU observations made in 2006. Wind profiling is also performed using delayed wavefront cross correlations along with SLODAR analysis. The wind profiling analysis is shown to improve the height resolution of the SLODAR method and in addition gives the wind velocities of the turbulent layers.     

Optimization of a predictive controller for closed-loop adaptive optics

For closed-loop adaptive optics systems limited by time delay and measurement noise, we demonstrate that the ideal rejection transfer function is proportional to the frequency signal-to-noise ratio of the wave-front input. We describe a new modal linear predictive controller that approaches this ideal transfer function. Its parameters are optimized by minimization of the residual wave-front error with a modified recursive least-squares algorithm. The optimization can be performed with closed-loop data in the case of evolving turbulent conditions. We present numerical simulations to show the significant improvements brought by the predictor.     

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.     

Optimization of scanning strategy of digital Shack-Hartmann wavefront sensing

In the traditional Shack-Hartmann wavefront sensing (SHWS) system, a lenslet array with a bigger configuration is desired to achieve a higher lateral resolution. However, practical implementation limits the configuration and this parameter is contradicted with the measurement range. We have proposed a digital scanning technique by making use of the high flexibility of a spatial light modulator to sample the reflected wavefront [X. Li, L. P. Zhao, Z. P. Fang, and C. S. Tan, "Improve lateral resolution in wavefront sensing with digital scanning technique," in Asia-Pacific Conference of Transducers and Micro-Nano Technology (2006)]. The lenslet array pattern is programmed to laterally scan the whole aperture. In this paper, the methodology to optimize the scanning step for the purpose of form measurement is proposed. The correctness and effectiveness are demonstrated in numerical simulation and experimental investigation.     

Optimization of sensing parameters for a confocal signal-based wavefront corrector in microscopy

The accuracy of a confocal signal-based wavefront corrector depends on several parameters such as spatial variation of optical properties within the specimen, aberration magnitude and composition, time required for the correction, etc. Here, a numerical analysis has been performed with the aim to improve system performance. The goal of the search algorithm in a confocal signal-based wavefront corrector is to estimate the Zernike coefficients of the aberrations. High-magnitude aberrations show low Strehl ratios. Repeating the correction process results in higher Strehl ratios, but at the cost of increased time. An in-focus on-axis specimen results in higher Strehl ratio compared to an out-of-focus and off-optical-axis specimen. For all cases, the wavefront correction accuracy is better, when the diameter of the pinhole is chosen to be equal to that of the Airy disk. The lower limit on the pinhole size for detecting small magnitude aberrations is set by noise.     

自适应光学技术在星地激光通信地面站上的应用

综述了自适应光学技术在星地激光通信地面站上应用的最新进展。针对星地链路中湍流效应导致的相干度退化和可用度降低的问题,自适应光学技术成为美国和欧洲等国正在研制的中继卫星至地光通信系统解决上述问题的主导手段。这些项目计划开展的自适应光学技术、白天和夜晚多地面站接收技术和相干通信技术等关键技术验证表明,星地激光通信正向高速相干和全天时高可用度的工程化推进。国内成功进行了多次星地光通信试验,高可用度的相干激光通信技术的验证正在积极开展,自适应光学技术已应用到多个地面站并取得了较好的初步试验效果,相关技术进展与国外水平保持一致。

     

High-diffractive-efficiency defocus grating for wavefront curvature sensing

The optimum phase defocus grating for wavefront curvature sensing is proposed. It features an equidistantly quantized, binary-phase-step defocus grating with a phase-step height of pi. The diffractive efficiency of the phase defocus grating is theoretically computed. The optical transfer function is obtained. The optimum phase defocus grating is fabricated. The high diffractive efficiencies of the +/-1 diffraction orders are verified experimentally, the average values of which are 38.08% and 40.36%, respectively.     

Properties of coherence-gated wavefront sensing

Coherence-gated wavefront sensing (CGWS) allows the determination of wavefront aberrations in strongly scattering tissue and their correction by adaptive optics. This allows, e.g., the restoration of the diffraction limit in light microscopy. Here, we develop a model, based on ray tracing of ballistic light scattered from a set of discrete scatterers, to characterize CGWS performance as it depends on coherence length, scatterer density, coherence-gate position, and polarization. The model is evaluated by using Monte Carlo simulation and verified against experimental measurements. We show, in particular, that all aberrations needed for adaptive wavefront restoration are correctly sensed if circularly polarized light is used.     

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.     

Layer-oriented adaptive optics for solar telescopes

First multiconjugate adaptive-optical (MCAO) systems are currently being installed on solar telescopes. The aim of these systems is to increase the corrected field of view with respect to conventional adaptive optics. However, this first generation is based on a star-oriented approach, and it is then difficult to increase the size of the field of view beyond 60-80?arc sec in diameter. We propose to implement the layer-oriented approach in solar MCAO systems by use of wide-field Shack-Hartmann wavefront sensors conjugated to the strongest turbulent layers. The wavefront distortions are averaged over a wide field: the signal from distant turbulence is attenuated and the tomographic reconstruction is thus done optically. The system consists of independent correction loops, which only need to account for local turbulence: the subapertures can be enlarged and the correction frequency reduced. Most importantly, a star-oriented MCAO system becomes more complex with increasing field size, while the layer-oriented approach benefits from larger fields and will therefore be an attractive solution for the future generation of solar MCAO systems.     

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.     

Real-time modal control implementation for adaptive optics

The electronics, computing hardware, and computing used to provide real-time modal control for a laser guide-star adaptive optics system are presented. This approach offers advantages in the control of unobserved modes, the elimination of unwanted modes (e.g., tip and tilt), and automatic handling of the case of low-resolution lens arrays. In our two-step modal implementation, the input vector of gradients is first decomposed into a Zernike polynomial mode by a least-squares estimate. The number of modes is assumed to be less than or equal to the number of actuators. The mode coefficients are then available for collection and analysis or for the application of modal weights. Thus the modal weights may be changed quickly without recalculating the full matrix. The control-loop integrators are at this point in the algorithm. To calculate the deformable-mirror drive signals, the mode coefficients are converted to the zonal signals by a matrix multiply. When the number of gradients measured is less than the number of actuators, the integration in the control loop will be done on the lower-resolution grid to avoid growth of unobserved modes. These low-resolution data will then be effectively interpolated to yield the deformable-mirror drive signals.     

Low-order adaptive optics for free-space optoelectronic interconnects

The concept of adaptive optics for improving the cost-performance of free-space optoelectronic interconnects is discussed. Adaptive optics as a design option for optical interconnect systems is presented and discussed. A practical demonstrator that performs low-order correction was built and tested. Slowly varying misalignments, including thermal effects, were compensated for in a 622-Mbit/s free-space optical data link.     

Approach for reconstructing anisoplanatic adaptive optics images

Atmospheric turbulence corrupts astronomical images formed by ground-based telescopes. Adaptive optics systems allow the effects of turbulence-induced aberrations to be reduced for a narrow field of view corresponding approximately to the isoplanatic angle theta(0). For field angles larger than theta(0), the point spread function (PSF) gradually degrades as the field angle increases. We present a technique to estimate the PSF of an adaptive optics telescope as function of the field angle, and use this information in a space-varying image reconstruction technique. Simulated anisoplanatic intensity images of a star field are reconstructed by means of a block-processing method using the predicted local PSF. Two methods for image recovery are used: matrix inversion with Tikhonov regularization, and the Lucy-Richardson algorithm. Image reconstruction results obtained using the space-varying predicted PSF are compared to space invariant deconvolution results obtained using the on-axis PSF. The anisoplanatic reconstruction technique using the predicted PSF provides a significant improvement of the mean squared error between the reconstructed image and the object compared to the deconvolution performed using the on-axis PSF.     

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.