Aims. For the first time the astrometric capabilities of the Gemini Multi-Conjugate Adaptive Optics System (GeMS) facility at the Gemini South Adaptive Optics Imager (GSAOI) camera on Gemini-South are tested to quantify the accuracy in determining stellar proper motions in the Galactic globular cluster NGC 6681. Methods. Proper motions from the Hubble Space Telescope (HST) for a sample of its stars are already available, allowing us to construct a distortion-free reference at the epoch of GeMS observations that is used to measure and correct the temporally changing distortions for each GeMS exposure. In this way, we are able to compare the corrected GeMS images with a first-epoch of HST-Advanced Camera for Survey (ACS) images to recover the relative proper motion of the Sagittarius dwarf spheroidal galaxy with respect to NGC 6681. Results. We find this to be (µ α cos δ, µ δ ) = (4.09, −3.41) mas yr −1 , which matches previous HST/ACS measurements with a very good accuracy of 0.03 mas yr −1 and with a comparable precision (rms of 0.43 mas yr −1 ). Conclusions. This study successfully demonstrates that high-quality proper motions can be measured for relatively large fields of view (85 × 85 ) with MCAO-assisted, ground-based cameras and provides a first, successful test of the performances of GeMS on multi-epoch data.

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Multi-object adaptive optics (MOAO) systems are still in their infancy: their complex optical designs for tomographic, wide-field wavefront sensing, coupled with open-loop (OL) correction, make their calibration a challenge. The correction of a discrete number of specific directions in the field allows for streamlined application of a general class of spatio-angular algorithms, initially proposed in Whiteley et al. [J. Opt. Soc. Am. A15, 2097 (1998)], which is compatible with partial on-line calibration. The recent Learn & Apply algorithm from Vidal et al. [J. Opt. Soc. Am. A27, A253 (2010)] can then be reinterpreted in a broader framework of tomographic algorithms and is shown to be a special case that exploits the particulars of OL and aperture-plane phase conjugation. An extension to embed a temporal prediction step to tackle sky-coverage limitations is discussed. The trade-off between lengthening the camera integration period, therefore increasing system lag error, and the resulting improvement in SNR can be shifted to higher guide-star magnitudes by introducing temporal prediction. The derivation of the optimal predictor and a comparison to suboptimal autoregressive models is provided using temporal structure functions. It is shown using end-to-end simulations of Raven, the MOAO science, and technology demonstrator for the 8 m Subaru telescope that prediction allows by itself the use of 1-magnitude-fainter guide stars.

We use a theoretical frame-work to analytically assess temporal prediction error functions on von-Kármán turbulence when a zonal representation of wave-fronts is assumed. Linear prediction models analysed include auto-regressive of order up to three, bilinear interpolation functions and a minimum mean square error predictor.This is an extension of the authors' previously published work [2] in which the efficacy of various temporal prediction models was established. Here we examine the tolerance of these algorithms to specific forms of model errors, thus defining the expected change in behaviour of the previous results under less ideal conditions. Results show that ±100% wind-speed error and ±50 deg are tolerable before the best linear predictor delivers poorer performance than the no-prediction case. Temporal prediction of the atmosphere is a much debated topic. The purpose of prediction is to reduce the error due to servo lag since the turbulence profile changes rapidly (on timescales of a few milliseconds) during the time that it takes to gather sensor information and to compute corrections.Unlike single-conjugated AO systems, in tomographic AO direct access to an estimate of the layered wavefront (WF) is provided at the end of the tomographic step. With turbulence estimated in a discrete number of layers, the frozen-flow approximation can now be called upon with a higher degree of fidelity [1].Temporal prediction is useful for both MultiConjugate AO (MCAO) and Multi-Object AO (MOAO) as a means to increase the sky-coverage [2, 3]. Allowing for greater integration times whilst compensating for the lag error by applying a predictive algorithm enables the system to guide on fainter sources [2]. Provided information on the dynamics of the atmospheric turbulence is available or can be construed, one should be able to obtain a more accurate estimate of the WF at the time a set of commands is applied to the deformable mirror (DM) and therefore improve performance. Lag errors are also considered a serious limitation in high-contrast imaging systems where the broadening of the PSF along * Corresponding author: katjac@uvic.ca the main axis of wind-blown turbulence severely limits contrast at small separations [4].In this letter we discuss alternatives for timeprogressing the atmospheric wave-fronts namely a nearMarkovian model, auto-regressive models and spatial shifting under frozen-flow [2, 5, 6]. The main goal of our work is to provide insight into the accuracy and robustness bounds of such models in view of a contemporary application to the Raven science and technology demonstrator installed on the Subaru Telescope [7].Under the hypothesis that the turbulent atmosphere is a sum of L thin layers located at a discrete number of different altitudes h l , the aperture-plane phase φ(ρ, θ, t) indexed by the bi-dimensional spatial coordinate vectorwhere ϕ l (ρ, t) is the l th -layer wave-front, ω l is the l th layer strength and H θ is a propagation operator in the near-field approximation that relates the aperture-plane ...