Spectrometer slit-power-coupling calculations for natural and laser guide-star adaptive optics

We use numerical calculations to examine the relation between adaptive optics (AO) turbulence compensation and power coupled through a spectrometer slit for both laser and natural guide-star AO systems. The AO system and observing parameters used are relevant to the Gemini-North 8-m telescope. For this study, we separate residual tilt from residual higher-order aberrations to isolate their relative effects under a variety of operating conditions. Our results demonstrate that slit-coupled intensity is not uniquely determined by system Strehl alone; we show that this is due to the differing effects of higher-order and tilt aberrations on the shape of the compensated point-spread function. For the Gemini spectrometer and AO system, the wider point-spread function halo associated with an added residual higher-order aberration reduces slit-coupled intensity more rapidly than a broad point-spread function core induced by residual tilt.     

Chromatic effects of the atmosphere on astronomical adaptive optics

The atmosphere introduces chromatic errors that may limit the performance of adaptive optics (AO) systems on large telescopes. Various aspects of this problem have been considered in the literature over the past two decades. It is necessary to revisit this problem in order to examine the effect on currently planned systems, including very high-order AO on current 8-10 m class telescopes and on future 30-42 m extremely large telescopes. We review the literature on chromatic effects and combine an analysis of all effects in one place. We examine implications for AO and point out some effects that should be taken into account in the design of future systems. In particular we show that attention should be paid to chromatic pupil shifts, which may arise in components such as atmospheric dispersion compensators.     

Time-sharing wave-front-sensing adaptive optics

Based on the concept of common-path/common-mode adaptive optics, the time-sharing wave-front-sensing adaptive optics system contains only one Hartmann-Shack (H-S) wave-front sensor, which detects two aberrations in the beam path alternately. After data fusion of the two aberrations, the actuator voltage of the deformable mirror (DM) is obtained. How the disturbances of the slope data and the response matrix influence the DM's actuator voltage in the data fusion methods is discussed, and the effective upper limits are given. Feasible data fusion methods are tested, and experiments verify that the performance of the system is good. The time-sharing technique is limited in sampling rate and is suitable only for corrections of slowly changing phases, because the H-S wave-front sensor's sampling frequency must be adequate for the alternate detection of two aberrations.     

Estimating the effects of structural vibration on adaptive optics system performance

This paper presents analytical tools developed for estimating the effects of structural vibration on closed-loop adaptive optics system image quality. The general equation for the normalized intensity distribution of an image subject to structural vibration is derived. The resulting two-dimensional theoretical point spread function is computed numerically and compared with empirical data obtained on sky at the Multiple Mirror Telescope Observatory. A simplified analytical expression for the normalized intensity distribution is derived for long exposures and used to quantify the effects on Strehl and spot full width at half-maximum as a function of vibration amplitude, telescope diameter, and observation wavelength.     

Durham adaptive optics real-time controller

The Durham adaptive optics (AO) real-time controller was initially a proof of concept design for a generic AO control system. It has since been developed into a modern and powerful central-processing-unit-based real-time control system, capable of using hardware acceleration (including field programmable gate arrays and graphical processing units), based primarily around commercial off-the-shelf hardware. It is powerful enough to be used as the real-time controller for all currently planned 8 m class telescope AO systems. Here we give details of this controller and the concepts behind it, and report on performance, including latency and jitter, which is less than 10 μs for small AO systems.     

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.     

Isoplanatism in a multiconjugate adaptive optics system

Turbulence correction in a large field of view by use of an adaptive optics imaging system with several deformable mirrors (DM's) conjugated to various heights is considered. The residual phase variance is computed for an optimized linear algorithm in which a correction of each turbulent layer is achieved by applying a combination of suitably smoothed and scaled input phase screens to all DM's. Finite turbulence outer scale and finite spatial resolution of the DM's are taken into account. A general expression for the isoplanatic angle thetaM of a system with M mirrors is derived in the limiting case of infinitely large apertures and Kolmogorov turbulence. Like Fried's isoplanatic angle theta0,thetaM is a function only of the turbulence vertical profile, is scalable with wavelength, and is independent of the telescope diameter. Use of angle thetaM permits the gain in the field of view due to the increased number of DM's to be quantified and their optimal conjugate heights to be found. Calculations with real turbulence profiles show that with three DM's a gain of 7-10x is possible, giving the typical and best isoplanatic field-of-view radii of 16 and 30 arcseconds, respectively, at lambda = 0.5 microm. It is shown that in the actual systems the isoplanatic field will be somewhat larger than thetaM owing to the combined effects of finite aperture diameter, finite outer scale, and optimized wave-front spatial filtering. However, this additional gain is not dramatic; it is less than 1.5x for large-aperture telescopes.     

Adaptive control in an adaptive optics experiment

This paper presents results from an adaptive optics experiment in which an adaptive control loop augments a classical adaptive optics feedback loop. Closed-loop wavefront errors measured by a self-referencing interferometer are fed back to the control loops, which drive a membrane deformable mirror to correct the wavefront. The paper introduces new frequency-weighted deformable mirror modes used as the control channels and new wavefront sensor modes for analyzing the performance of the control loops. The corrected laser beam also is imaged by a diagnostic target camera. The experimental results show reduced closed-loop wavefront errors and correspondingly sharper diagnostic target images produced by the adaptive control loop as compared with the classical AO loop.     

Anisoplanatic deconvolution of adaptive optics images

A modified method for maximum-likelihood deconvolution of astronomical adaptive optics images is presented. By parametrizing the anisoplanatic character of the point-spread function (PSF), a simultaneous optimization of the spatially variant PSF and the deconvolved image can be performed. In the ideal case of perfect information, it is shown that the algorithm is able to perfectly cancel the adverse effects of anisoplanatism down to the level of numerical precision. Exploring two different modes of deconvolution (using object bases of pixel values or stellar field parameters), we then quantify the performance of the algorithm in the presence of Poissonian noise for crowded and noncrowded stellar fields.     

Geometric view of adaptive optics control

The objective of an astronomical adaptive optics control system is to minimize the residual wave-front error remaining on the science-object wave fronts after being compensated for atmospheric turbulence and telescope aberrations. Minimizing the mean square wave-front residual maximizes the Strehl ratio and the encircled energy in pointlike images and maximizes the contrast and resolution of extended images. We prove the separation principle of optimal control for application to adaptive optics so as to minimize the mean square wave-front residual. This shows that the residual wave-front error attributable to the control system can be decomposed into three independent terms that can be treated separately in design. The first term depends on the geometry of the wave-front sensor(s), the second term depends on the geometry of the deformable mirror(s), and the third term is a stochastic term that depends on the signal-to-noise ratio. The geometric view comes from understanding that the underlying quantity of interest, the wave-front phase surface, is really an infinite-dimensional vector within a Hilbert space and that this vector space is projected into subspaces we can control and measure by the deformable mirrors and wave-front sensors, respectively. When the control and estimation algorithms are optimal, the residual wave front is in a subspace that is the union of subspaces orthogonal to both of these projections. The method is general in that it applies both to conventional (on-axis, ground-layer conjugate) adaptive optics architectures and to more complicated multi-guide-star- and multiconjugate-layer architectures envisaged for future giant telescopes. We illustrate the approach by using a simple example that has been worked out previously [J. Opt. Soc. Am. A 73, 1171 (1983)] for a single-conjugate, static atmosphere case and follow up with a discussion of how it is extendable to general adaptive optics architectures.     

Deconvolution of adaptive optics retinal images

We quantitatively demonstrate the improvement to adaptively corrected retinal images by using deconvolution to remove the residual wave-front aberrations. Qualitatively, deconvolution improves the contrast of the adaptive optics images. In this work we demonstrate that quantitative information is also increased by investigation of the improvement to cone classification due to the reduction in confusion of adjacent cones because of the extended wings of the point-spread function. The results show that the error in classification between the L and M cones is reduced by a factor of 2, thereby reducing the number of images required by a factor of 4.     

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.     

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.     

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.     

Ion-beam machining of millimeter scale optics

An ion-beam microcontouring process is developed and implemented for figuring millimeter scale optics. Ion figuring is a noncontact machining technique in which a beam of high-energy ions is directed toward a target substrate to remove material in a predetermined and controlled fashion. Owing to this noncontact mode of material removal, problems associated with tool wear and edge effects, which are common in conventional machining processes, are avoided. Ion-beam figuring is presented as an alternative for the final figuring of small (<1-mm) optical components. The depth of the material removed by an ion beam is a convolution between the ion-beam shape and an ion-beam dwell function, defined over a two-dimensional area of interest. Therefore determination of the beam dwell function from a desired material removal map and a known steady beam shape is a deconvolution process. A wavelet-based algorithm has been developed to model the deconvolution process in which the desired removal contours and ion-beam shapes are synthesized numerically as wavelet expansions. We then mathematically combined these expansions to compute the dwell function or the tool path for controlling the figuring process. Various models have been developed to test the stability of the algorithm and to understand the critical parameters of the figuring process. The figuring system primarily consists of a duo-plasmatron ion source that ionizes argon to generate a focused (~200-mum FWHM) ion beam. This beam is rastered over the removal surface with a perpendicular set of electrostatic plates controlled by a computer guidance system. Experimental confirmation of ion figuring is demonstrated by machining a one-dimensional sinusoidal depth profile in a prepolished silicon substrate. This profile was figured to within a rms error of 25 nm in one iteration.     

Advanced vibration suppression algorithms in adaptive optics systems

Vibration suppression in astronomical adaptive optics (AO) systems has gathered great attention in the context of next-generation instrumentation for current telescopes and future Extremely Large Telescopes. Laser tomographic AO systems require natural guide stars to measure the low-order modes such as tip-tilt (TT) and TT-anisoplanatism. To increase the sky coverage, the guide stars are often faint, thus requiring lower temporal sampling frequencies to work on a more favorable signal-to-noise regime. Such sampling frequencies can be of the order of, or even lower than, the range of frequencies where vibrations are likely to appear. Ideally, vibrations affecting the low-order modes could be corrected at the higher laser loop frame rate using an upsampling procedure. This paper compares the most relevant solutions proposed hitherto to a novel multirate algorithm using the linear-quadratic-Gaussian (LQG) approach capable of upsampling the correction to further reduce the impact of vibrations. Results from numerical Monte Carlo simulations span a large range of parameters from pure sinusoids to relatively broad peak vibrations, covering the likely-to-be signals in a realistic AO system. The improvement is shown at sampling frequencies from 20 to 800 Hz, including below the vibration itself, in the example of 29.5 Hz on a Thirty Meter Telescope-like scenario. The multirate LQG ensures the least residual for both faint and bright stars for all the peak widths considered based on telemetry from the Keck Observatory.     

Hysteresis correction in the curvature adaptive optics system

An enhancing Coleman-Hodgdon model is introduced to describe the hysteresis curves of the bimorph deformable mirror (DM). Hysteresis curves are measured from a bimorph DM and then experiment is set up for the correction of hysteresis. Finally, step response and transfer functions of a curvature adaptive optics (AO) system are compared in three cases: with DM hysteresis, without hysteresis, and with hysteresis but corrected. Simulation results show that the bandwidth of a curvature AO system is improved significantly under different loop gains after hysteresis of the DM is corrected.     

Minimum-variance control for woofer-tweeter systems in adaptive optics

The woofer-tweeter concept in adaptive optics consists in correcting for the turbulent wavefront disturbance with a combination of two deformable mirrors (DMs). The woofer corrects for temporally slow-evolving, spatially low-frequency, large-amplitude disturbances, whereas the tweeter is generally its complement, i.e., corrects for faster higher-order modes with lower amplitude. A special feature is that in general both are able to engender a common correction space. In this contribution a minimum-variance solution for the double stage woofer-tweeter concept in adaptive optics systems is addressed using a linear-quadratic-Gaussian approach. An analytical model is built upon previous developments on a single DM with temporal dynamics that accommodates a double-stage woofer-tweeter DM. Monte Carlo simulations are run for a system featuring an 8×8 actuator DM (considered infinitely fast), mounted on a steering tip/tilt platform (considered slow). Results show that it is essential to take into account temporal dynamics on the estimation step. Besides, unlike the other control strategies considered, the optimal solution is always stable.     

Study on the effects of monochromatic aberrations in the accommodation response by using adaptive optics

The effect of asymmetric monochromatic aberrations in the accommodation response was studied by using an adaptive optics (AO) system. This approach permits the precise modification of ocular aberrations during accommodation. The AO system is composed of a real-time Hartmann-Shack wavefront sensor and a membrane deformable mirror with 37 independent actuators. The accommodation response was measured in two subjects with their normal aberrations and with the asymmetric aberrations terms corrected. We found a significant and systematic increase in the response accommodation time, and a reduction in the peak velocity, in both subjects when the aberrations were corrected in real time. However, neither the latency time nor the precision of the accommodation were affected. These results may indicate that the monochromatic aberrations play a role in driving the accommodation response.     

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.