Gerard Rousset

A star in a 15.2-year orbit around the supermassive black hole at the centre of the Milky Way

Many galaxies are thought to have supermassive black holes at their centres—more than a million times the mass of the Sun. Measurements of stellar velocities and the discovery of variable X-ray emission have provided strong evidence in favour of such a black hole at the centre of the Milky Way, but have hitherto been unable to rule out conclusively the presence of alternative concentrations of mass. Here we report ten years of high-resolution astrometric imaging that allows us to trace two-thirds of the orbit of the star currently closest to the compact radio source (and massive black-hole candidate) Sagittarius A*. The observations, which include both pericentre and apocentre passages, show that the star is on a bound, highly elliptical keplerian orbit around Sgr A*, with an orbital period of 15.2 years and a pericentre distance of only 17 light hours. The orbit with the best fit to the observations requires a central point mass of (3.7 ± 1.5) × 106 solar masses (M[circdot]). The data no longer allow for a central mass composed of a dense cluster of dark stellar objects or a ball of massive, degenerate fermions.

NAOS, the first AO system of the VLT: on-sky performance

NAOS is the first adaptive optics system installed at the VLT 8m telescopes. It was designed, manufactured and tested by a french Consortium under an ESO contract, to provide compensated images to the high angular resolution IR spectro-imaging camera (CONICA) in the 1 to 5 μm spectral range. It is equipped with a 185 actuator deformable mirror, a tip/tilt mirror and two wavefront sensors, one in the visible and one in the near IR spectral range. It has been installed in November at the Nasmyth focus B of the VLT UT4. During the first light run in December 2001, NAOS has delivered a Strehl ratio of 50 under average seeing conditions for bright guide stars. The diffraction limit of the telescope has been achieved at 2.2 μm. The closed loop operation has been very robust under bad seeing conditions. It was also possible to obtain a substantial correction with mV=17.6 and mK=13.1 reference stars. The on-sky acceptance tests of NAOS-CONICA were completed in May 2002 and the instrument will be made available to the European astronomical community in October by ESO. This paper describes the system and present the on-sky performance in terms of Strehl ratio, seeing conditions and guide star magnitude.

Deconvolution from wave-front sensing: a new technique for compensating turbulence-degraded images

A new technique of high-resolution imaging through atmospheric turbulence is described. As in speckle interferometry, short-exposure images are recorded, but in addition the associated wave fronts are measured by a Hartmann–Shack wave-front sensor. The wave front is used to calculate the point-spread function. The object is then estimated from the correlation of images and point-spread functions by a deconvolution process. An experimental setup is described, and the first laboratory results, which prove the capabilities of the method, are presented. A signal-to-noise-ratio calculation, permitting a first comparison with the speckle interferometry, is also presented.

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

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.

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.

High-order adaptive optics requirements for direct detection of extrasolar planets: Application to the SPHERE instrument

The detection of extrasolar planets implies an extremely high-contrast, long-exposure imaging capability at near infrared and probably visible wavelengths. We present here the core of any Planet Finder instrument, that is, the extreme adaptive optics (XAO) subsystem. The level of AO correction directly impacts the exposure time required for planet detection. In addition, the capacity of the AO system to calibrate all the instrument static defects ultimately limits detectivity. Hence, the extreme AO system has to adjust for the perturbations induced by the atmospheric turbulence, as well as for the internal aberrations of the instrument itself. We propose a feasibility study for an extreme AO system in the frame of the SPHERE (Spectro-Polarimetry High-contrast Exoplanet Research) instrument, which is currently under design and should equip one of the four VLT 8-m telescopes in 2010.

MOAO first on-sky demonstration with CANARY

Context. A new challenging adaptive optics (AO) system, called multi-object adaptive optics (MOAO), has been successfully demonstrated on-sky for the first time at the 4.2 m William Herschel Telescope, Canary Islands, Spain, at the end of September 2010. Aims. This system, called CANARY, is aimed at demonstrating the feasibility of MOAO in preparation of a future multi-object near infra-red (IR) integral field unit spectrograph to equip extremely large telescopes for analysing the morphology and dynamics of high-z galaxies. Methods. CANARY compensates for the atmospheric turbulence with a deformable mirror driven in open-loop and controlled through a tomographic reconstruction by three widely separated off-axis natural guide star (NGS) wavefront sensors, which are in open loop too. We compared the performance of conventional closed-loop AO, MOAO, and ground-layer adaptive optics (GLAO) by analysing both IR images and simultaneous wave-front measurements. Results. In H-band, Strehl ratios of 0.20 are measured with MOAO while achieving 0.25 with closed-loop AO in fairly similar seeing conditions (r 0 ≈ 15 cm at 0.5 μm). As expected, MOAO has performed at an intermediate level between GLAO and closed-loop AO.

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

Adaptive optics systems provide a real-time compensation for atmospheric turbulence. However, the correction is often only partial, and a deconvolution is required for reaching the diffraction limit. The need for a regularized deconvolution is discussed, and such a deconvolution technique is presented. This technique incorporates a positivity constraint and some a priori knowledge of the object (an estimate of its local mean and a model for its power spectral density). This method is then extended to the case of an unknown point-spread function, still taking advantage of similar a priori information on the point-spread function. Deconvolution results are presented for both simulated and experimental data.

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.

Calibration of NAOS and CONICA static aberrations Application of the phase diversity technique

Wedescribe and evaluate the performance of a phase diversity wavefront sensor used to measure the staticaberrations of the VLT instrument NAOS-CONICA. The main limitations of this phase diversity technique are compiled. We investigate the systematic errors due to the experimental implementation and the design restrictions. Further error sources stem from the imperfect knowledge of the system, and from limitations of the algorithm. The influence of these errors on the wavefront estimation is evaluated on numerical and experimental data. This study highlights the essential verifications and calibrations needed to obtain accurate results and gives a practical guideline for the application of a phase diversity wavefront sensor. The comprehensive calibration results and the final gain in optical performance are presented and discussed in a complementary paper (Hartung et al. 2003).