Tomographic wavefront error using multi-LGS constellation sensed with Shack-Hartmann wavefront sensors

Noise effects induced by laser guide star (LGS) elongation have to be considered globally in a multi-LGS tomographic reconstruction analysis. This allows a fine estimation of performance and the comparison of different launching options. We present a modal analysis of the wavefront error with Shack-Hartmann wavefront sensors based on quasi-analytical matrix formalism. Including spot elongation and the Rayleigh fratricide effect, edge launching produces similar performance to central launching and avoids the risk of possible underestimation of fratricide scatter. Performance improves slightly with an optimized centroid estimator and is not affected by a slight field-of-view truncation of the subapertures. Finally we discuss detector characteristics for a LGS Shack-Hartmann wavefront sensor.     

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.     

Optimal reconstruction for closed-loop ground-layer adaptive optics with elongated spots

The design of the laser-guide-star-based adaptive optics (AO) systems for the Extremely Large Telescopes requires careful study of the issue of elongated spots produced on Shack-Hartmann wavefront sensors. The importance of a correct modeling of the nonuniformity and correlations of the noise induced by this elongation has already been demonstrated for wavefront reconstruction. We report here on the first (to our knowledge) end-to-end simulations of closed-loop ground-layer AO with laser guide stars with such an improved noise model. The results are compared with the level of performance predicted by a classical noise model for the reconstruction. The performance is studied in terms of ensquared energy and confirms that, thanks to the improved noise model, central or side launching of the lasers does not affect the performance with respect to the laser guide stars' flux. These two launching schemes also perform similarly whatever the atmospheric turbulence strength.     

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.     

Comparison of vibration mitigation controllers for adaptive optics systems

Vibrations are detrimental to the performance of modern adaptive optics (AO) systems. In this paper, we describe new methods tested to mitigate the vibrations encountered in some of the instruments of the Gemini South telescope. By implementing a spectral analysis of the slope measurements from several wavefront sensors and an imager, we can determine the frequencies and magnitude of these vibrations. We found a persistent vibration at 55 Hz with others occurring occasionally at 14 and 100 Hz. Two types of AO controllers were designed and implemented, Kalman and H∞, in the multiconjugate AO tip-tilt loop. The first results show a similar performance for these advanced controllers and a clear improvement in vibration rejection and overall performance over the classical integrator scheme. It is shown that the reduction in the standard deviation of the residual slopes (as measured by wavefront sensors) is highly dependent on turbulence, wind speed, and vibration conditions, ranging--in terms of slopes RMS value--from an almost negligible reduction for high speed wind to a factor of 5 for a combination of low wind and strong vibrations.     

Effect of aberrations and scatter on image resolution assessed by adaptive optics retinal section imaging

The effect of increased high-order wavefront aberrations on image resolution was investigated, and the performance of adaptive optics (AO) for correcting wavefront error in the presence of increased light scatter was assessed in a model eye. An AO section imaging system provided an oblique view of a model retina and incorporated a wavefront sensor and deformable mirror for measurement and compensation of wavefront aberrations. Image resolution was quantified by the width of a Lorentzian curve fitted to a laser line image. Wavefront aberrations were significantly reduced with AO, resulting in improvement of image resolution. In the model eye, image resolution was degraded with increased high-order wavefront aberrations (horizontal coma and spherical) and improved with AO correction of wavefront error in the presence of increased light scatter. The findings of the current study suggest that AO imaging systems can potentially improve image resolution in aging eyes with increased aberrations and scatter.     

Measuring the centroid gain of a Shack-Hartmann quad-cell wavefront sensor by using slope discrepancy

Shack-Hartmann wavefront sensors (SH WFS) are used by many adaptive optics (AO) systems to measure the wavefront. In this WFS, the centroid of the spots is proportional to the wavefront slope. If the detectors consist of 2 x 2 quad cells, as is the case in most astronomical AO systems, then the centroid measurement is proportional to the centroid gain. This quantity varies with the strength of the atmospheric turbulence and the angular extent of the beacon. The benefits of knowing the centroid gain and current techniques to measure it are discussed. A new method is presented, which takes advantage of the fact that, in a SH-WFS-based AO system, there are usually more measurements than actuators. Centroids in the null space of the wavefront reconstructor, called slope discrepancy measurements, contain information about the centroid gain. Tests using the W. M. Keck Observatory AO system demonstrate the accuracy of the algorithm.     

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.     

自适应光学系统中变形镜和波前传感器共轭位置要求的分析

通过对几何光学和物理光学模型的数值计算,分析了自适应光学系统中小像差畸变波前在空间自由传播时自身的变化情况,进而给出了系统中对变形镜和波前探测器与被校正瞳面之间共轭位置关系的要求和允许范围.结果表明,波前自由传播时的变化程度决定于像差自身的类型和大小、光束的口径以及传播的距离,大口径小像差波前近距离传播时波前变化误差很小.一般来说,变形镜和波前传感器偏离被校正瞳面共轭位置距离满足菲涅尔数大于1000时,对系统校正效果的影响可以忽略.实际应用中,应该根据校正对象的特征来具体计算波前误差随传播距离的变化,从而设计波前传感器和变形镜的位置,以及选择使用4F光学系统.本文的分析可以为自适应光学系统的整体光路设计提供一定理论参考.     

No wavefront sensor adaptive optics system for compensation of primary aberrations by software analysis of a point source image. 1. Methods

Adaptive optics (AO) has been recently used for the development of ophthalmic devices. Its main objective has been to obtain high-resolution images for diagnostic purposes or to estimate high-order eye aberrations. The core of every AO system is an optical device that is able to modify the wavefront shape of the light entering the system; if you know the shape of the incoming wavefront, it is possible to correct the aberrations introduced in the optical path from the source to the image. The aim of this paper is to demonstrate the feasibility, although in a simulated system, of estimating and correcting an aberrated wavefront shape by means of an iterative gradient-descent-like software procedure, acting on a point source image, without expensive wavefront sensors or the burdensome computation of the point-spread-function (PSF) of the optical system. In such a way, it is possible to obtain a speed and repeatability advantage over classical stochastic algorithms. A hierarchy in the aberrations is introduced, in order to reduce the dimensionality of the state space to be searched. The proposed algorithm is tested on a simple optical system that has been simulated with ray-tracing software, with randomly generated aberrations, and compared with a recently proposed algorithm for wavefront sensorless adaptive optics.     

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 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.     

Myopic deconvolution of adaptive optics images by use of object and point-spread function power spectra: reply to comment

Partial correction in adaptive optics (AO) is well understood now. This partial correction is due to the limitations of the AO system performance, which leaves residual phase fluctuations in the instrument pupil. Knowledge of these residuals allows the optical transfer function (OTF) of the high-angular-resolution imaging system to be estimated accurately. Therefore, light scattering by aerosols cannot be invoked to justify the shape of an AO partial-correction OTF in astronomical conditions. The light scattering does not modify the high-angular-resolution OTF but merely contributes to a slight increase of the sky background.     

Calibration and precompensation of noncommon path aberrations for extreme adaptive optics

Noncommon path aberrations (NCPAs) are one of the main limitations of an extreme adaptive optics (AO) system. NCPAs prevent extreme AO systems from achieving their ultimate performance. These static aberrations are unseen by the wavefront sensor and therefore are not corrected in closed loop. We present experimental results validating what we believe to be new procedures of measurement and precompensation of the NCPAs on the AO bench at ONERA (Office National d'Etudes et de Recherches Aérospatiales). The measurement procedure is based on refined algorithms of phase diversity. The precompensation procedure makes use of a pseudo-closed-loop scheme to overcome the AO wavefront-sensor-model uncertainties. Strehl ratio obtained in the images reaches 98.7% at 632.8 nm. This result allows us to be confident of achieving the challenging performance required for direct observation of extrasolar planets.     

Real-time turbulence profiling with a pair of laser guide star Shack-Hartmann wavefront sensors for wide-field adaptive optics systems on large to extremely large telescopes

Real-time turbulence profiling is necessary to tune tomographic wavefront reconstruction algorithms for wide-field adaptive optics (AO) systems on large to extremely large telescopes, and to perform a variety of image post-processing tasks involving point-spread function reconstruction. This paper describes a computationally efficient and accurate numerical technique inspired by the slope detection and ranging (SLODAR) method to perform this task in real time from properly selected Shack-Hartmann wavefront sensor measurements accumulated over a few hundred frames from a pair of laser guide stars, thus eliminating the need for an additional instrument. The algorithm is introduced, followed by a theoretical influence function analysis illustrating its impulse response to high-resolution turbulence profiles. Finally, its performance is assessed in the context of the Thirty Meter Telescope multi-conjugate adaptive optics system via end-to-end wave optics Monte Carlo simulations.     

System design considerations to improve isoplanatism for adaptive optics retinal imaging

Adaptive optics (AO) retinal images are limited by anisoplanatism; wavefront shape varies across the field of view such that only a limited area can achieve diffraction-limited image quality at one time. We explored three alternative AO modalities designed to reduce this effect, drawn from work in astronomy. Optical design analysis and computer modeling was undertaken to predict the benefit of each modality for various schematic eyes and various complexities of the imaging system. Off-axis performance was found to be limited by system parameters and not by the eye itself, due to the inherent off-axis characteristics of the eye's gradient index lens. This rendered the alternative AO modalities ineffectual compared with conventional AO but did suggest several methods by which anisoplanatism may be reduced by altering the design of conventional AO systems. Several of these design possibilities were explored with further modeling. The best-performing method involved the replacement of system lenses with gradient index versions inspired by the human eye lens. Mirror-based relay optics also demonstrated good off-axis performance, but their advantage was lost in regions of the system suffering from uncorrected higher-order aberration. Incorporating "off-the-plane" beam deviations ameliorated this loss substantially. In this work we also show, to our knowledge for the first time, that the ideal location of a single AO corrector need not lie in the pupil plane.     

Impact of nano- and mesoscale particles on the performance of microcantilever-based sensors

Microcantilever-based sensors comprise an emerging class of chemomechanical sensors. The crucial challenge for every new and promising sensing platform lies in its performance in complex mixtures. Since most biofluids are rich in particulates, we assessed the impact of particles in the liquid stream on the performance of microcantilever sensors operated in both deflection and resonance modes. For both detection modes, sensor response depends on the particle diameter, concentration, and velocity as well as the composition of a thin-film coating. The presence of particles in the fluid stream produce substantial scattering of the laser beam used to measure cantilever deflection. Thus, prior removal of particulate matter from biofluids is required for optimal performance of microcantilever-based biosensors.     

Requirements for discrete actuator and segmented wavefront correctors for aberration compensation in two large populations of human eyes

Numerous types of wavefront correctors have been employed in adaptive optics (AO) systems for correcting the ocular wavefront aberration. While all have improved image quality, none have yielded diffraction-limited imaging for large pupils (>/=6 mm), where the aberrations are most severe and the benefit of AO the greatest. To this end, we modeled the performance of discrete actuator, segmented piston-only, and segmented piston/tip/tilt wavefront correctors in conjunction with wavefront aberrations measured on normal human eyes in two large populations. The wavefront error was found to be as large as 53 microm, depending heavily on the pupil diameter (2-7.5 mm) and the particular refractive state. The required actuator number for diffraction-limited imaging was determined for three pupil sizes (4.5, 6, and 7.5 mm), three second-order aberration states, and four imaging wavelengths (0.4, 0.6, 0.8, and 1.0 microm). The number across the pupil varied from only a few actuators in the discrete case to greater than 100 for the piston-only corrector. The results presented will help guide the development of wavefront correctors for the next generation of ophthalmic instrumentation.     

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.