Optimal wave-front reconstruction strategies for multiconjugate adaptive optics

We propose an optimal approach for the phase reconstruction in a large field of view (FOV) for multiconjugate adaptive optics. This optimal approach is based on a minimum-mean-square-error estimator that minimizes the mean residual phase variance in the FOV of interest. It accounts for the C2n profile in order to optimally estimate the correction wave front to be applied to each deformable mirror (DM). This optimal approach also accounts for the fact that the number of DMs will always be smaller than the number of turbulent layers, since the C2n profile is a continuous function of the altitude h. Links between this optimal approach and a tomographic reconstruction of the turbulence volume are established. In particular, it is shown that the optimal approach consists of a full tomographic reconstruction of the turbulence volume followed by a projection onto the DMs accounting for the considered FOV of interest. The case where the turbulent layers are assumed to match the mirror positions [model-approximation (MA) approach], which might be a crude approximation, is also considered for comparison. This MA approach will rely on the notion of equivalent turbulent layers. A comparison between the optimal and MA approaches is proposed. It is shown that the optimal approach provides very good performance even with a small number of DMs (typically, one or two). For instance, good Strehl ratios (greater than 20%) are obtained for a 4-m telescope on a 150-arc sec x 150-arc sec FOV by using only three guide stars and two DMs.     

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.     

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.     

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.     

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.     

基于自适应光学系统闭环数据的大气相干长度的计算

提出了一种计算大气相干长度(r0)的新方法。根据自适应光学系统的控制关系,由闭环数据复原得到开环数据,并计算出系统噪声。大气相干长度由去除系统噪声的开环数据得到。与传统的方法相比较,此方法不需要中断自适应光学系统的工作进行开环数据采集,保证了校正的连续性。而且,用此方法计算得到实时的r0,消除了系统噪声的影响。将此方法应用于61单元的自适应光学系统中,对实测大气相干长度进行了分析。     

Numerical simulations of multiconjugate adaptive optics wave-front reconstruction on giant telescopes

We present sample Monte Carlo simulation results to illustrate the trends in multiconjugate adaptive optics (MCAO) performance as the telescope aperture diameter increases from 8 to 32 m with all other first-order system parameters held constant. The MCAO system considered includes three deformable mirrors, a 1-arc min square field of view, and five wave-front-sensing references consisting of either natural guide stars or laser guide stars at a range of either 30 or 90 km. The rms residual wave-front error decreases slowly with increasing aperture diameter with natural guide stars, whereas performance degrades significantly with increasing aperture diameter for laser guide stars at 30 km if the number of guide stars is held fixed. Performance with laser guide stars at 90 km is a weak function of telescope aperture diameter in the range from 8 to 32 m, with rms wave-front errors no more than 20% greater than the corresponding natural guide-star case for the same level of wave-front sensor's measurement noise.     

Fast wave-front reconstruction in large adaptive optics systems with use of the Fourier transform

Wave-front reconstruction with the use of the fast Fourier transform (FFT) and spatial filtering is shown to be computationally tractable and sufficiently accurate for use in large Shack-Hartmann-based adaptive optics systems (up to at least 10,000 actuators). This method is significantly faster than, and can have noise propagation comparable with that of, traditional vector-matrix-multiply reconstructors. The boundary problem that prevented the accurate reconstruction of phase in circular apertures by means of square-grid Fourier transforms (FTs) is identified and solved. The methods are adapted for use on the Fried geometry. Detailed performance analysis of mean squared error and noise propagation for FT methods is presented with the use of both theory and simulation.     

Large-scale wave-front reconstruction for adaptive optics systems by use of a recursive filtering algorithm

We propose a new recursive filtering algorithm for wave-front reconstruction in a large-scale adaptive optics system. An embedding step is used in this recursive filtering algorithm to permit fast methods to be used for wave-front reconstruction on an annular aperture. This embedding step can be used alone with a direct residual error updating procedure or used with the preconditioned conjugate-gradient method as a preconditioning step. We derive the Hudgin and Fried filters for spectral-domain filtering, using the eigenvalue decomposition method. Using Monte Carlo simulations, we compare the performance of discrete Fourier transform domain filtering, discrete cosine transform domain filtering, multigrid, and alternative-direction-implicit methods in the embedding step of the recursive filtering algorithm. We also simulate the performance of this recursive filtering in a closed-loop adaptive optics system.     

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.     

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.     

Closed-loop control of a woofer-tweeter adaptive optics system using wavelet-based phase reconstruction

A novel closed-loop control technique for adaptive optics (AO) systems based on a wavelet-based phase reconstruction technique and a woofer-tweeter controller is presented. The wavelet-based reconstruction technique is based on obtaining a Haar decomposition of the phase screen directly from gradient measurements and has been extended here with the use of a Poisson solver to improve performance. This method is O(N) (i.e., a linear computation cost as number of actuators increases) and is the fastest of the known O(N) reconstruction techniques. The controller configuration is based on the woofer-tweeter controller to control low- and high-spatial-frequency aberrations, respectively. The separation of the woofer and tweeter signals is done using a computationally efficient method that is based on the availability of a low-spatial-resolution reconstruction during the wavelet synthesis process. The performance of the proposed technique is evaluated using a simulated AO system and phase screens generated to reflect atmospheric turbulence with various dynamic characteristics. Results indicate that the combination of the wavelet-based phase reconstruction and woofer-tweeter controller leads to very good results with respect to speed and accuracy.     

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.     

Tip-tilt reconstruction with a single dim natural guide star in multiconjugate adaptive optics with laser guide stars

A solution to the problem of detecting the tip-tilt modes in multiconjugate adaptive optics (MCAO) with laser guide stars (LGS) is presented. This solution requires the presence of only a single relatively dim natural guide star (NGS) within the reconstructed field of view (FoV). The dim NGS is used for the reconstruction of the tip-tilt modes on the entire FoV, while the tomographic reconstruction of second-order and higher-order modes is made possible by having an LGS constellation with LGSs at different heights. Due to the relatively low brightness required for the tip-tilt NGS and the large corrected FoV (as compared with the case of conventional adaptive optics) the presented solution provides a means to achieve near-diffraction-limited performance of a 10-m-class telescope in the near infrared over a large portion of the sky. Sky coverage calculations assuming median seeing conditions indicate that this technique could be applied to 75% (95%) of the sky, achieving corrections with an average Strehl ratio approximately 0.42(approximately 0.33) in the 2.2 microm K band across the 1.5' reconstructed FoV.     

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.     

Double-deformable-mirror adaptive optics system for phase compensation

Two kinds of algorithm for an adaptive optics (AO) system that uses two deformable mirrors (DMs), one with large stroke and the other with high spatial frequency, to correct different aberrations are described. The algorithms are based on modal method and direction-gradient method, respectively. Numerical simulations for the algorithms have been made. The simulation results indicate that the two DMs in the AO system can correct different aberrations with different characteristics, and the closed-loop performance of a double-DM AO system will be almost the same as that of an AO system that uses a single DM with an ideal stroke.     

Accommodation with higher-order monochromatic aberrations corrected with adaptive optics

Higher-order monochromatic aberrations in the human eye cause a difference in the appearance of stimuli at distances nearer and farther from best focus that could serve as a signed error signal for accommodation. We explored whether higher-order monochromatic aberrations affect the accommodative response to 0.5 D step changes in vergence in experiments in which these aberrations were either present as they normally are or removed with adaptive optics. Of six subjects, one could not accommodate at all for steps in either condition. One subject clearly required higher-order aberrations to accommodate at all. The remaining four subjects could accommodate in the correct direction even when higher-order aberrations were removed. No subjects improved their accommodation when higher-order aberrations were corrected, indicating that the corresponding decrease in the depth of field of the eye did not improve the accommodative response. These results are consistent with previous findings of large individual differences in the ability to accommodate in impoverished conditions. These results suggest that at least some subjects can use monochromatic higher-order aberrations to guide accommodation. They also show that some subjects can accommodate correctly when higher-order monochromatic aberrations as well as established cues to accommodation are greatly reduced.