Adaptive Optics and its Application to Astronomy

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1 Adaptive Optics and its Application to Astronomy Francois J. RODDIER Institute for Astronomy, University of Hawaii, 2680 Woodlawn Dr, Honolulu, HI USA (Received November 11, 1998) Adaptive optics is now routinely used on a growing number of optical telescopes for the real-time compensation of atmospherically-induced aberrations. After a brief historical account, current technology is described. The limitations of the technique are reviewed. An example is given of the performance one can now achieve. Astronomical applications are summarized. Key Words: Adaptive optics, Optical telescopes, Astronomy Brief History of Adaptive Optics The concept of using an active optical element for the realtime compensation of atmospherically induced wave-front distortion was first discussed by an astronomer, Horace Babcock, as a means to improve the angular resolution of astronomical images.1) However, the required technologies were not sufficiently advanced at that time. Soon after, the invention of the laser triggered both experimental and theoretical work on optical propagation through the turbulent atmosphere. Researchers working for defense applications started to use segmented mirrors to compensate the effect of the atmosphere in attempts to concentrate laser beams on remote targets. This was done by trial-and-error (multidither technique). As artificial satellites were sent on orbit, a need appeared to make images of these objects for surveillance, and attempts were made to use similar techniques for imaging.2) The first adaptive optics (AO) system able to sharpen two-dimensional images was built at Itek by Hardy and his coworkers.3) A larger version was installed in 1982 at the Air-force Maui Optical Site (AMOS) on Haleakala. By the end of the seventies AO systems were widely developed by industry for defense applications.4) AO systems with more than a thousand degrees-of-freedom have since been built.5) Although the technology was classified, its success transpired, and astronomers became interested in applying AO to astronomy. Unfortunately, most interesting astronomical sources are much dimmer than artificial satellites. Astronomers are used to express the brightness of a star in terms of magnitudes, a logarithmic scale in which an increase of 5 magnitudes describes a decrease in brightness by a factor 100. On a clear dark night, stars up to magnitude 6 are visible to the naked eye. The Maui Airforce adaptive-optics system goes barely beyond. Astronomers often observe stars as faint as mag 20 or beyond. Therefore, they need more sensitive systems. It was soon realized that it is possible to observe in the infrared while sensing the wave front in the visible. This is because wave-front distortions produced by the atmosphere are sufficiently achromatic. For infrared imaging, the compensation requirements are less severe, and one can use a fainter "guide" source to sense the wave-front. In the eighties, great progress was being made in developing InSb and HgCdTe detector arrays for imaging in the near infrared, and infrared astronomy was blooming. Therefore two important astronomical institutions decided to sponsor a development program on AO for infrared astronomy: the European Southern Observatory (ESO) and the US National Optical Astronomy Observatories (NOAO). The NOAO effort was interrupted after 4 years. But the ESO effort, which involved astronomers, defense research experts, and industry, led to the construction of a prototype instrument called"come-on". The first compensated stellar images were obtained in October 1989 with the Haute-Provence-Observatory 1.52-m telescope in France.6) Soon after, the system was operated on the 3.6-m telescope of the European Southern Observatory (ESO) in Chile.7) COME-ON has since been upgraded under the name of "COME -ON-PLUS", and utilized for astronomical observations in Chile.8) The first scientific papers based on these observations appeared in A user-friendly interface has later been added to COME-ON-PLUS which became ADONIS, a user instrument facility at ESO.9) These AO systems are based on a technology similar to that developed for defense applications (Shack-Hartmann stacked-actuator wave-front sensor and continuous facesheet deformable mirror). Compared to that of defense systems, the number of degrees-of-freedom is smaller. It allows these systems to sense the wave-front with fainter"guide" sources, up to mag 13 or 14, but limits their application to the near infrared. Meanwhile, a new technique was developed at the Institute for Astronomy of the University of Hawaii (UH). It involved the development of a new type of wave-front sensor called"curvature sensor", and a new type of deformable mirror called bimorph.10,11) The technique was believed to be more suitable to astronomical observations. An experimental instrument was built and successfully tested at the coude focus of the Canada- France-Hawaii (CFH) telescope on Mauna Kea. In December 1993, the first astronomical observations were performed with this instrument. The first scientific paper appeared in Since then, a Cassegrain-focus visitor instrument has been built. It The Review of Laser Engineering February 1999

2 was first used in December 1994 at the f/35 Cassegrain focus of the CFH telescope (3.35-m aperture). Compared to the European AO system, the UH system is simpler to build, and easier to operate. Above all, it uses an array of higher performance detectors called avalanche photo-diodes (APDs). It allows the sensing of the wave-front to be performed on fainter guide sources, up to magnitude 16. A consequence is that a larger number of objects are now accessible to wave-front compensation. A user instrument based on this technique has since been built for the CFH telescope (PUEO). Another one has been built in Japan, and will soon operate on the 8-m Subaru telescope on Mauna Kea. Meanwhile, the UH team has built a new AO system called Hokupa'a, to be used as a visitor instrument on the 8- m Gemini telescope on Mauna Kea. Because the brightness of the guide source severely limits the sensing of the wave-front, Foy and Labeyrie proposed to use laser beacons to create artificial sources with light back scattered by the atmosphere.12) We now know that the same idea had been independently proposed a few years earlier by US defense researchers, and was already being developed as classified research. In 1991, after the political changes in Russia, the US National Science Foundation (NSF) convinced government authorities of the importance of the technique to astronomy, and obtained its declassification. As a result, many US groups have actively pursued the development of artificial laser guide sources (LGS), both for defense and astronomical applications (see the January and February 1994 issues of J. Opt. Soc. Am.). However, there are still difficulties. A natural guide star (NGS) is still needed to determine the tip/tilt component of the wave-front aberration, and large telescopes may require the use of several laser beacons to overcome the so-called cone effect due to the finite distance of the source. To date, LGS systems have not yet outperformed NGS systems for astronomical observations. Since 1994, a growing number of observatories have been equipped with AO systems to be used with or without laser beacons. In addition, astronomers obtained access to the Air Force SOR system in New Mexico. The most scientifically productive systems still remain the conventional ESO ADONIS system and the CFHT-UH "curvature type" systems. An extensive review of AO in Astronomy can be found in a book edited by Roddier.13) Hardware and Software An AO system can be described as follows (see diagram on Fig.1). Relay optics is used to form an image of the telescope entrance aperture on a wave-front compensation system, generally a deformable mirror. A beam splitter selects part of the light reflected from the deformable mirror and send it to a wave-front sensor. In most astronomical systems, it is the visible part of the Fig. 1 Diagram of an adaptive optics system. con supported by an array of stacked piezoelectric or electrostrictive actuators. Actuators pull or push on the plate producing local bumps or dips (Fig.2 (a)). This technology was developed for defense applications and is used in the COME- ON type systems.6,8) Bimorph mirrors consist of a pair of piezoelectric wafers glued together with electrodes in-between and outside. The wafers are polarized perpendicular to the surface. When voltages are applied to the electrodes, electric fields are produced inside the wafers so that one wafer contracts whereas the other one expands, locally bending the mirror (Fig.2 (b)). This technology was specifically developed for astronomical applications.14) Compared to continuous facesheet mirrors, bimorph mirrors are easier to fabricate and therefore less expensive. They also scatter less light and generally produce higher quality images. However, unlike continuous facesheet mirrors, their stroke decreases steeply with the spatial frequency of the deformation (as the square of it). Bimorph mirrors better compensate the low-order aberration terms produced not only by turbulence but also by telescope optics. They can even compensate wave-front tip/tilt motion. On the other hand, continuous facesheet mirrors better compensate small scale wave-front errors, but often lack of stroke to compensate low-order aberration terms. They always require the use of an additional fast steering flat mirror for image stabilization. light (below 1 micron). The infrared part of the spectrum is sent to the instrument (camera or spectrograph). Output signals from Wave-Front Sensors the wave-front sensor are then processed by control electronics and converted into voltages to be applied to the deformable mirror. Because natural guide stars are faint, the sensing of the wavefront must preferably be performed with broad band light, as broad as possible to collect a maximum number of photons. Occasionally, it must be performed on an extended source such 2.1 Deformable Mirrors Several types of deformable mirrors have been developed to compensate wave fronts. These are monolithic, segmented, continuous facesheet, and bimorph mirrors. Only the last two have been used in stellar astronomy and will be described here. Continuous facesheet mirrors consist of a thin plate of glass or sili- as a small nebulosity, a galaxy core, a small planet or an asteroid. In other terms, the sensor must work with incoherent light sources. A consequence is that light from points widely apart on the telescope aperture does not interfere, and the associated wavefront phases cannot be directly compared. One can only measure phase differences over a small distance, that is phase de- Vol. 27, No.2 Adaptive Optics and its Application to 79

3 Fig. 2 Deformable mirrors used in astronomy: (a) continuous facesheet mirror supported by stacked actuators; (b) bimorph mirror. rivatives. Three types of wave-front sensors have been used for AO: shearing interferometers, Shack-Hartmann sensors, and curvature sensors. Because shearing interferometers tend to lose light, only the last two types of sensors are used in astronomy and will be described here. A Shack-Hartmann sensor measures first order phase derivatives, that is local wave-front slopes, along two orthogonal directions. From such measurements, an estimate of the wavefront surface is obtained by integrating wave-front slopes in both directions. It can be shown that a least-square solution is obtained by computing the wave-front Laplacian first. The Laplacian is then integrated by solving a Poisson equation with radial edge slopes as boundary conditions.15) A Shack-Hartmann sensor is a set of small lenses in a plane conjugate to the telescope aperture. Each lenslet forms an image of the guide source on a detector array (Fig.3 (a)). By comparison with a reference plane wave, a distorted wave-front produces shifts in the location of each of these images (Fig.3 (b)). A measure of the shift gives an estimate of the wave-front slope averaged over each lenslet area, or subaperture. The COME-ON series systems use an intensified Reticon array for bright sources and an Electron Bombarded CCD (EBCCD) for faint sources. Fast, low noise CCDs are now used for this application. It avoids the need for an intensifier stage, and has the advantage of the higher quantum efficiency and broader bandwidth of silicon detectors. Readout noise is the main limitation. A curvature sensor measures a combination of first and second order phase derivatives. It directly gives estimates of the wave-front Laplacian and radial edge slopes. This is done by simply comparing the illuminations I1 and I2, in two planes symmetrically defocused (Fig.3 (c)). It can be shown that local differences in illumination are directly related to the local wavefront total curvature or Laplacian, whereas differences in the location of the aperture edge image give a measure of the wavefront radial edge slope. Again, a wave-front surface can be reconstructed by solving a Poisson equation using the estimated edge slopes as boundary conditions. 10) The curvature sensor developed at UH uses a vibrating membrane mirror located in the image plane to sequentially defocus in opposite directions an image of the telescope entrance aperture formed on a detector array (Fig.3 (d)). The membrane oscillates between a concave and a convex shape producing the required signals in the form of a modulation of the detector outputs. A synchronous demodulation is used to detect the signals.14) Compared to the Shack-Hartmann sensor, this technique has several advantages. Firstly, by changing the amplitude of the membrane vibration one can easily change the amount of defocus, hence the sensitivity of the sensor. This sensitivity can be continuously matched to the angular size of the guide source. Secondly, only one detector is required per subaperture. The first experimental UH system consisted of an array of only 13 avalanche photo-diodes. These detectors have the optical band-width and the quantum efficiency of silicon, but are noise-free photon- (a) Fig. 3 Wavefront sensors used in astronomy. Left: Shack-Hartmann sensor. Right: curvature sensor. The Review of Laser Engineering February 1999

4 counting detectors. Photons are simultaneously counted over Fundamental Limitations half a modulation cycle. The difference in photon counts between the two half cycles gives the sensor signals. A stated disadvantage of curvature sensing is error propagation. When Laplacians are computed from slope measurements, errors are correlated. Errors in slope measurements appear with opposite signs in two adjacent Laplacian estimates. They tend to cancel each other in the estimated wave-front. When Laplacians are measured directly, errors are statistically independent and propagates more rapidly. Hence, for large arrays, slope measurements are expected to give better results. However, when the loop is closed, wave-front distortions shrink and the sensitivity of the curvature sensor can be increased accordingly, whereas that of the Shack-Hartmann cannot. As shown analytically or by computer simulations, it more than offsets the effect of error propagation.16) Control Loop Many sources of errors limit the performance of an AO system. We will review them briefly. The most fundamental limitation is set by the spatial wave-front sampling, that is the finite number N of degrees-of-freedom of the AO system. It determines the accuracy with which one can correct an arbitrary wavefront distortion. The corresponding residual rms error is called the wave-front fitting error. The larger is N, the smaller is the fitting error. For a given N, the error still depends on the statistics of the wave-front perturbations. Random wave-front distortions can be described as linear combinations of statistically independent modes called Karhunen-Loeve modes. It can be shown that the average wave-front fitting error will be a minimum if the first N Karhunen-Loeve modes can be all generated by a linear combination of the system modes. The bimorph mirrors of the UH systems have been optimized to best fit the atmospheric Karhunen-Loeve modes. The second most important limitation is set by the temporal sampling, or loop frequency bandwidth. Wave-front distortions produced by the atmosphere change continuously. An AO system has to follow the time evolution of the wave-front. However, there is a limit to the speed at which the system can follow this evolution. The limit is mainly set by the time needed to compute the voltages one has to apply to the deformable mirror. The error due to the finite temporal bandwidth of the AO system is called the time delay error. The third most important limitation comes from noise in the wave-front sensor measurements. It can be electronic read-out noise, photon shot noise from a faint guide star, or a combination of both. There are also occasional, or less important limitations. The most important occasional limitation occurs when the guide source differs from the object being studied. If their angular distance is sufficiently large, the associated light waves will take a different path through the atmosphere, and will be differently affected. This effect increases with the altitude of the turbulent layers. The resulting error is called the isoplanicity error. The angular distance over which this error becomes important is called the isoplanatic angle. The higher is the degree of compensation, the smaller is the isoplanatic angle. Multiconjugate AO systems have been envisaged to reduce this error The role of the control loop is to convert M signals from the wave-front sensor into P voltages to be applied to the deformable mirror. In most systems, the number M of wave-front measurements is larger than the number P of actuators to be controlled. This is the case for the COME-ON type systems. These systems are said to be over determined, and the accuracy of the compensation is mainly limited by the mirror. However, especially when measurements are noisy, one may wish to minimize the number of wave-front measurements and take M=P. The sensor must then be precisely matched to sense those particular deformations that the mirror can correct. This is the case of the UH "curvature" type systems, where wave-front curvature measurements are used to apply bending moments and create a corresponding curvature in a bimorph mirror. The mirror then behaves as an analog device which solves the Poisson equation and reconstruct the wave-front. One could also envisage underdetermined systems for which M P and chose the minimum mirror deformation that fits the wave-front measurements (minimum norm solution). In this case, the accuracy of the compensation would be essentially limited by the sensor. In practice deformable mirrors are not perfect. Deformable mirrors often introduce additional aberrations one has to correct. To be able to correct these distortions, one needs at least as many measurements as actuators. by using a set of deformable mirrors to compensate different Most AO systems are linear, at least in a small range near the closed-loop operating conditions. In this range, the response of the sensor to each actuator is described by a P x M interaction matrix. A singular value decomposition of the interaction matrix gives a set of singular values. The number N of non-zero singular values is the number of degrees-of-freedom of the system, that is the number of linearly independent parameters one can control to compensate the wave-front distortions. As shown below, it strongly determines the compensation performance of the AO system. The matrix which converts the sensor signals into actuator voltages is called the control matrix. It is usually taken as the generalized inverse of the mirror-sensor interaction matrix. Its eigen modes are called system modes. Its eigen values are the loop gains for each mode. All the modes are not equally sensitive to noise. When noisy signals come from a faint guide source, it is possible to optimize the compensation performance by decreasing the gain of the most noisy modes. This technique called modal control has been developed for the atmospheric layers in different conjugate planes. Another occasional error occurs when imaging and sensing are done at different wavelengths. This is the case for most astronomical systems. The error, called chromatic error is generally small unless observations are made far from zenith. A final limitation comes from stellar scintillation. Atmospheric turbulence not only produces wave-front phase errors but also amplitude errors. These fluctuations of the illumination are due to light diffracted by high altitude turbulent layers. They may affect the sensing of the wave-front. They also affect image quality without being compensated by the AO system. A multi-conjugate AO system would compensate them. The minimization of all these sources of errors is called system optimization. There are two stages of system optimization. The first stage is during the system design. A system must be designed to achieve a given goal. Different goals may lead to different technical solutions. AO systems developed for defense applications were designed for optimal compensation of bright COME-ON systems.17,18) visible light sources using relatively small telescopes under relatively poor seeing conditions. The UH astronomical system was Vol. 27, No.2 Adaptive Optics and its Application to 81

5 designed for optimal compensation of near-infrared images with a large astronomical telescope under good seeing conditions with very faint stellar guide sources. temporal sampling requirements It led to different spatial and as well as different detector requirements. An optimization tool widely used in AO system design is the computation of a wave-front error budget. Approximate analytic expressions are used to estimate the above described contributions to the residual wave-front error, and errors are added quadratically. Parameters are chosen which minimize the total mean square wave-front error. This is equivalent to maximizing the Strehl ratio of a point source image (ratio of the maximum intensity to that of a diffraction-limited point source). Once an AO system is well defined, computer simulations can be used to fine tune the optimization. Random wavefront are numerically generated, simulating the effect of the atmosphere. For each wave-front, the response of the system is calculated. This is repeated many times until a good estimate is obtained for the average illumination in the image plane. Although the computations are lengthy, they are now widely used. Such simulations have been made to compare the performance of the UH approach to that of the conventional COME-ON approach in view of designing the AO system of the future Gemini telescope on Mauna Kea. The second stage of optimization is during its operation. An astronomical AO system has to operate not only under highly variable seeing conditions, but also with a wide variety of guide sources (angular diameter and brightness). In each case, the operator has to fine tune the loop parameters to get the best possible compensation. For a COME-ON type system, the operator has first to chose the sensor (Reticon or EBCCD). He must then chose a threshold above which a centroid will be determined on each sub-image of the Shack-Hartmann sensor. He must then record open-loop wave-front sensor data, determine the noise level, and compute the power spectrum of the various modes. For each mode he will determine the optimum loop gain to apply. This used to take a significant amount of time before each observation. The ADONIS system now uses an automatic procedure to do this. The UH system is simpler. The operator has only two parameters to play with, the amplitude of the membrane vibration and the total loop gain. This is done by minimizing the closed-loop error signals. Current Performance characteristic of the system, but the wavelength at which the maximum occurs depends upon both the telescope diameter and the seeing conditions. For a theoretically ideal zonal compensation system, the maximum gain in Strehl ratio is by a factor 1.6 times the number N of actuators.19) By comparison, one can express the maximum gain of a real system as 1.6 q N, where q is a measure of the system compensation efficiency. Typical efficiencies are of the order of for curvature systems and 0.3 or less for conventional Shack-Hartmann systems. High order Shack-Hartmann systems tend to have very low efficiencies. Figure 4 shows a three-dimensional plot of the intensity distribution in stellar images. These are 30-second exposures on a magnitude 9.5 star (SAO 12442) taken at the f/35 focus of the CFH telescope (3.35-m aperture) through a narrow-band filter centered at micron. The image on the left was taken with the control loop open (no compensation). Its full width at half maximum (fwhm) is 0.6 arcsecond and its Strehl ratio is The image on the right was taken with the control loop closed. Its fwhm is arcsec and its Strehl ratio is The gain in Strehl ratio is by a factor 32, which is about the maximum achievable with the 36-actuator Hokupa' a system. It is a good example of the performance one can now achieve with an astronomical AO system. Although the performance is highly wavelength dependent, AO systems can still be used over a wide wavelength range, as long as one is prepared to apply post-detection processing techniques. Experience shows that diffraction-limited images can be easily obtained by processing images with Strehl ratios as small as 0.1. This is done by means of deconvolution techniques. This is a situation similar to, and actually better than that of the Hubble Space Telescope before refurbishment, where images were successfully restored with a Strehl ratio of about 0.1. The point spread function (PSF) is recorded soon after or before the object, under similar conditions. For bright guide sources, an estimation of the PSF can even be obtained from the control error signals.20) 5. Astronomical Applications The use of AO on astronomical telescopes has already produced significant advances in several fields of astronomy and is likely to continue to do so. Because observations are made in The performance of an AO system varies widely with seeing conditions. It also varies with the stellar magnitude and angular extent of the guide source used to sense the wave-front. Moreover, for a given wave-front compensation performance, the improvement in image quality highly depends on the wave-length of the image. The gain can be expressed in terms of an increase in Strehl ratio. It can be shown that the gain is a maximum at some particular wavelength. At long wavelengths (2 to 5 microns) on a 3.6-m telescope, uncompensated images are already good, and it requires only a small gain (a factor less than 10 in Strehl ratio) to produce diffraction-limited images. At shorter wavelengths (1 to 2 microns) larger gains are observed (by a factor larger than 10 with current systems), but compensated images have no longer a Strehl ratio close to unity. At maximum gain (typically around 1 micron), the Strehl ratio of the compensated image is only 0.3. Down to the visible, the gain decreases and compensated images have even smaller Strehl ratios. The maximum gain achievable by an AO system is a Fig.4 Plot of the intensity distribution in an uncompensated (left) and a compensated (right) stellar image. Data were obtained on a 9.5 magnitude star with the 36- actuator Hokupa' a AO system mounted at the f/35 focus of the CFH telescope on Mauna Kea. The Review of Laser Engineering February 1999

6 the infrared with larger telescope apertures, AO observations complement rather than compete with those made with the Hubble Space Telescope (HST). We briefly review here the main astronomical applications of AO. AO has been used to produce images of solar system objects, particularly those with a small angular size. These include planets such as Pluto and Charon, Neptune and Uranus, satellites of Jupiter and Saturn such as Io and Titan, and asteroids such as Vesta. Until recently, space probes as well as the HST itself were not equipped with cryogenic infrared cameras. These AO observations provided the first high angular resolution images of these objects in the near infrared. Particularly successful were -observations of Saturn's rings made in 1995 as the Earth was crossing the ring plane. For these observations Saturn's bright satellites Dione and Tethys were used as guide sources. Results obtained in planetary sciences with the UH AO systems have recently been reviewed by Roddier.21) In stellar astronomy AO has also been used to observe star clusters. For these observations, the brightest sources in the cluster are used as guide sources. Images have been obtained of star forming regions. In the infrared one can see deeper inside condensing clouds. With the enhanced detectivity brought by AO, many new sources have been discovered allowing statistically significant studies to be made of the frequency of binary stars. Several sources previously considered as super-massive objects were resolved into multiple components. High stellar velocities were observed in the center of our Galaxy, supporting the existence of a massive black hole. AO was found to be particularly fruitful for the study of circumstellar material. It has helped studying the mechanism by which evolved stars, which have burned out most of their hydrogen, eject material and ultimately form a nebula called"planetary" because of its planet-like appearance. High angular resolution images have been obtained of the early evolution stages where a"proto-planetary" nebula forms. AO has also been used to study nebulosities around very young stars. Stars form by gravitational collapse of a cloud of gas and dust. The dust eventually condenses into a circumstellar disk in which planets are expected to form. AO observations have brought invaluable information on these early stages of stellar evolution. They have confirmed the existence of disks and have shown us how the original solar nebula probably looked like. There is now a growing use of AO for extra-galactic researches. In some cases galactic nuclei are bright enough to serve as a guide source. This is the case for the brightest quasars or active galactic nuclei. In other cases, a foreground star must be use to sense the wave-front when available. Adaptive optics systems are expected to be soon used on the new generation of large telescopes such as the Keck telescopes, Subaru, Gemini and the European VLT array. It will have two advantages. On one hand, one can keep the same number of subapertures that are currently used on 3.6-m telescopes but observe at longer wavelengths. This will allow astronomers to use fainter natural guide stars, and observe almost all of the sky without even having to use laser beacons. This will boost extragalactic observations such as that of active and non active galactic nuclei, gravitational lensing, and high red shift galaxies. On the other hand, one can increase the number of subapertures of the AO system in proportion to the telescope aperture area, and make the same observations that are now made with 3.6-m telescopes, but with more than twice the angular resolution. Hence, one can expect to see soon the technique applied even more widely to astronomy, especially on very large telescopes. References 1) H. W. Babcock: Pub. Astr. Soc. Pac. 65 (1953), ) A. Buffington, F. S. Crawford, R. A. Muller, and C. D. Orth: J. Opt. Soc. Am. 67 (1977) ) J. W. Hardy, J. E. Lefebvre and C. L. Koliopoulos: J. Opt. Soc. Am. 67 (1977), ) J. E. Pearson, R. H. Freeman, and H. C. Reynolds Jr.: Applied Optics and Optical Engineering (1979), Academic Press, Vol. VII, Chapter 8, ) L. Cuellar, P. Johnson, and D. G. Sandler: Proc. SPIE Conf (1991), M. Ealey, edit., ) G. Rousset, J.-C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Lena, C. Boyer, P. Jagourel, J.-P. Gaffard, and F. Merkle: Astron. Astrophys. 230 (1990) L29. 7) F. Rigaut, G. Rousset, P. Kern, J.-C. Fontanella, J.-P. Gaffard, F. Merkle, and P. Lena: Astron. Astrophys. 250 (1991) ) G. Rousset, J.-L. Beuzit, N. Hubin, E. Gendron, C. Boyer, P.-Y. Madec, P. Gigan, J.-C. Richard, M. Vittot, J.-P. Gaffard, F. Rigaut, and P. Lena: Proc. ESO Conf. 48 (1993), F. Merkle, edit., 65. 9) J.-L. Beuzit, N. Hubin, L. D ly, E. Gendron, P. Gigan, F. Lacombe, D. Rouan, F. Chazallet, D. Rabaud, P.-Y. Madec, G. Rousset, P. Feautrier, H. Geoffray, F. Eisenhauer, R. Hofmann, D. Bonaccini, and E. Prieto: Proc. ESO Conf. 54 (1995), M. Cullum, edit., ) F. Roddier: Applied Optics 27 (1988) ) F. Roddier, M. Northcott, and J. E. Graves: Pub. Astr. Soc. Pac. 103 (1991) ) R. Foy and A. Labeyrie: Astron. Astrophys. 152 (1985) L29. 13) F. Roddier (edit.): Adaptive Optics in Astronomy (1999) Cambridge University Press, in press. 14) F. Roddier, J. Anuskiewicz, M. J. Northcott, and C. Roddier: Proc. SPIE Conf (1994), M. A. Ealey, edit., 2. 15) R. H. Hudgin: J. Opt. Soc. Am. 67 (1977) ) F. Roddier: Optics Commun. 113 (1995) ) E. Gendron and P. Lena: Astron. Astrophys. 291 (1994) ) E. Gendron and P. Lena: Astron. Astrophys. Suppl. Ser. 111 (1995) ) F. Roddier: Pub. Astr. Soc. Pac. 110 (1998) ) J.-P. Veran, F. Rigaut, H. Maitre, and D. Rouan: J. Opt. Soc. Am. A 14 (1997) ) F. Roddier, C. Roddier, L. Close, C. Dumas, J. E. Graves, O. Guyon, B. Han, M. J. Northcott, T. Owen, D. Tholen, and A. Brahic: Proc. ESO Conf. held in Sonthofen (1998), D. Bonaccini, edit., in press. Vol. 27, No.2 Adaptive Optics and its Application to 83