Optical observations by ground‐based astronomers have long been limited by the distorting effects of the Earth's atmosphere. Primary mirrors have been polished to exquisite accuracy for telescopes with apertures as large as 10 meters, but at optical wavelengths these can deliver an angular resolution typically no better than that of a 25‐cm telescope, as atmospheric turbulence deforms the image on a millisecond time scale. One (highly expensive) approach to overcome this problem has been to loft instruments such as the Hubble Space Telescope above the atmosphere. Another approach, pursued by instrument builders in the astronomy community and their counterparts in the military, has been to design electro‐optical systems that measure and undo the effects of clear‐air turbulence in real time. (See figure 1.) A number of such adaptive optic devices have already been built and operated on large ground‐based telescopes, delivering near‐diffraction‐limited performance at infrared and visible wavelengths. With th...

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Adaptive Optics in Astronomy

Adaptive Optics is a prime example of how progress in observational astronomy can be driven by technological developments. At many observatories it is now considered to be part of a standard instrumentation suite, enabling ground-based telescopes to reach the diffraction limit and thus providing spatial resolution superior to that achievable from space with current or planned satellites. In this review we consider adaptive optics from the astrophysical perspective. We show that adaptive optics has led to important advances in our understanding of a multitude of astrophysical processes, and describe how the requirements from science applications are now driving the development of the next generation of novel adaptive optics techniques.

Adaptive Optics for Astronomy

A general formulation is given for the derivation of theoretical temporal power spectra of quantities related to turbulent wave-front phase. These temporal power spectra and their asymptotic power laws and cutoff frequencies are presented for various quantities of interest in the field of interferometry (differential piston), wave-front sensing (Shack–Hartmann and curvature sensor), adaptive optics (Zernike polynomials), and seeing monitoring (differential angle of arrival). We show that the differential piston spectrum has two cutoff frequencies and exhibits a very steep decrease at high frequencies. The curvature sensor is shown to be much less sensitive than the Shack–Hartmann sensor to the low temporal frequencies. A study of the Zernike temporal power spectra shows that their cutoff frequencies increase with the polynomial radial degree. Both single-layer and multilayer plane and spherical waves are considered. The effect of wind direction is also taken into account. We point out the influence of the cone effect on the temporal power spectra when Rayleigh or sodium laser guide stars are used for wave-front sensing. The cone effect results in a temporal decorrelation between natural and laser guide star wave fronts. Finally, we demonstrate that in adaptive optics systems low-order modes require higher servoloop bandwidths than do high-order modes in order for the residual variance to be balanced between the corrected modes. The same conclusion applies to fringe tracking in large telescope interferometers equipped with adaptive optics systems.

Wave-front temporal spectra in high-resolution imaging through turbulence

Deconvolution is a necessary tool for the exploitation of a number of imaging instruments. We describe a deconvolution method developed in a Bayesian framework in the context of imaging through turbulence with adaptive optics. This method uses a noise model that accounts for both photonic and detector noises. It additionally contains a regularization term that is appropriate for objects that are a mix of sharp edges and smooth areas. Finally, it reckons with an imperfect knowledge of the point-spread function (PSF) by estimating the PSF jointly with the object under soft constraints rather than blindly (i.e., without constraints). These constraints are designed to embody our knowledge of the PSF. The implementation of this method is called Mistral. It is validated by simulations, and its effectiveness is illustrated by deconvolution results on experimental data taken on various adaptive optics systems and telescopes. Some of these deconvolutions have already been used to derive published astrophysical interpretations.

Mistral: a myopic edge-preserving image restoration method, with application to astronomical adaptive-optics-corrected long-exposure images

The complexity of computing conventional matrix multiply wave-front reconstructors scales as O(n3) for most adaptive optical (AO) systems, where n is the number of deformable mirror (DM) actuators. This is impractical for proposed systems with extremely large n. It is known that sparse matrix methods improve this scaling for least-squares reconstructors, but sparse techniques are not immediately applicable to the minimum-variance reconstructors now favored for multiconjugate adaptive optical (MCAO) systems with multiple wave-front sensors (WFSs) and DMs. Complications arise from the nonsparse statistics of atmospheric turbulence, and the global tip/tilt WFS measurement errors associated with laser guide star (LGS) position uncertainty. A description is given of how sparse matrix methods can still be applied by use of a sparse approximation for turbulence statistics and by recognizing that the nonsparse matrix terms arising from LGS position uncertainty are low-rank adjustments that can be evaluated by using the matrix inversion lemma. Sample numerical results for AO and MCAO systems illustrate that the approximation made to turbulence statistics has negligible effect on estimation accuracy, the time to compute the sparse minimum-variance reconstructor for a conventional natural guide star AO system scales as O(n3/2) and is only a few seconds for n = 3500, and sparse techniques reduce the reconstructor computations by a factor of 8 for sample MCAO systems with 2417 DM actuators and 4280 WFS subapertures. With extrapolation to 9700 actuators and 17,120 subapertures, a reduction by a factor of approximately 30 or 40 to 1 is predicted.

Efficient computation of minimum-variance wave-front reconstructors with sparse matrix techniques.

An adaptive optics prototype system has been tested at the 1.52 m telescope of the Observatoire de Haute Provence, resulting in diffraction-limited images at near infrared wavelengths (2.2 to 5 microns). This paper presents the first results and a short analysis, which demonstrate the considerable gain in resolution and sensitivity achieved by this technique. Single stars, close binary stars, and a satellite have been resolved. In some cases another star several arcseconds apart has been used as reference for the wavefront sensing.

First diffraction-limited astronomical images with adaptive optics

The results of the first observations made on a large (3.6-m) telescope with the adaptive optics prototype, named COME-ON, conceived to explore the application of this technique for the European Very Large Telescope, are presented. The wavefront is studied, after its correction by the servo-system, using a Zernike polynomial expansion. The analysis of uncorrected and corrected images in the near infrared (≤5 μm) leads to a detailed evaluation of the system performance in terms of improvement of angular resolution, reaching nearly the ideal diffraction profiles down to 2.2 μm, and Strehl ratio, approaching 0.6 to 0.8 at 3.8 μm

Adaptive optics on a 3.6-m telescope : results and performance

Les premieres observations astronomiques realisees avec un systeme d'optique adaptative, basees au sol, sont presentees

Adaptive optics can be used to improve the quality of optical imaging instruments otherwise limited in resolution by atmospheric turbulence. To achieve a given level of resolution improvement at the lowest cost, design of adaptive mirrors must be carefully optimized. We have calculated the mean value of the optical transfer function (OTF) of an instrument corrected by adaptive optics using the OTF as a criterion for resolution optimization and describing perturbations through their phase structure function. A four-parameter numerical program has been written to compute the OTF. Assuming that the optics diameter and the perturbation Fried's parameter are known, it then becomes possible to optimize the system by a proper choice of the number of actuators and of the influence diameter, a parameter which characterizes the size of the required corrections.

Adaptive optics for optimization of image resolution.

This paper is a presentation of the so-called COME-ON adaptive optics prototype system developed jointly by four
European institutions. This system has been tested on the 1.52m telescope of the Observatoire de Haute Provence on
October 12 to 23 and November 13 to 24, 1989. Diffration-limited infrared imaging has been achieved during these first
tests. The adaptive optics system consists of a 19 actuator deformable mirror and a Hartmann-Shack type wavefront
sensor. In this instrument the wavefront sensing is performed at visible wavelengths while the correction is performed for
near infrared imaging (1 .2 to 5 .tm). Specialized computers drive the deformable mirror and a tip-tilt mirror. The
bandwidth of the servo-loop is 9 Hz at 0 dB point in open-loop. The results obtained with this instrument will be very
useful for the design of the future adaptive optics system for the ESO Very Large Telescope (VLT).

Jean-Paul Gaffard

Papers

First diffraction-limited astronomical images with adaptive optics

Adaptive optics on a 3.6-m telescope : results and performance

First diffraction-limited astronomical images with adaptive optics

Adaptive optics for optimization of image resolution.

Adaptive optics prototype system for infrared astronomy: I. System description