Abstract
The secondary mirror unit of the European Extremely Large Telescope (ELT) is supported by six 50-cm wide spiders, providing the necessary stiffness to the structure while minimising the obstruction of the beam. The deformable quaternary mirror (M4) contains over 5000 actuators on a nearly hexagonal pattern. The reflective surface of M4 itself is composed of a segmented thin shell made of 6 discontinuous petals. This segmentation of the telescope pupil will create areas of phase isolated by the width of the spiders on the wavefront sensor (WFS) detector, breaking the spatial continuity of the wavefront data. The poor sensitivity of the Pyramid WFS (PWFS) to differential piston (or of any WFS sensitive to the derivative of the wavefront such as the Shack-Hartmann) will lead to badly seen and therefore uncontrollable differential pistons between these areas. In close loop operation, differential pistons between segments will settle around integer values of the average sensing wavelength lambda. The differential pistons typically range from one to tens of time the sensing wavelength and vary rapidly over time, leading to extremely poor performance. In addition, aberrations created by atmospheric turbulence will naturally contain some differential piston between the segments. This differential piston is typically a relatively large multiple of the sensing wavelength, especially for 40 m class telescopes. Trying to directly remove the entire piston contribution over each of the DM segments will undoubtedly lead to poor performance. In an attempt to reduce the impact of unwanted differential pistons that are injected by the AO correction, we compare three different approaches. A first step is to try to limit ourselves to use only the information measured by the PWFS, in particular by reducing the modulation. We show that using this information sensibly is important but it is only a prerequisite and will not be sufficient. We discuss possible ways of improvement by removing the unwanted differential pistons from the DM commands while still trying to maintain the atmospheric segment-piston contribution by using prior information. A second approach is based on phase closure of the DM commands and assumes the continuity of the correction wavefront over the entire unsegmented pupil. The last approach is based on the pair-wise slaving of edge actuators and shows the best results. We compare the performance of these methods using realistic end-to-end simulations. We find that pair-wise slaving leads to a small increase of the total wavefront error, only adding between 20-45 nm RMS in quadrature for seeing conditions between 0.45"-0.85". Finally, we discuss the possibility of combining the different proposed solutions to increase robustness.

Abstract
Context. Canary is the multi-object adaptive optics (MOAO) on-sky pathfinder developed in the perspective of multi-object spectrograph on extremely large telescopes (ELTs). In 2013, Canary was operated on-sky at the William Herschel telescope (WHT), using three off-axis natural guide stars (NGS) and four off-axis Rayleigh laser guide stars (LGS), in open-loop, with the on-axis compensated turbulence observed with a H-band imaging camera and a Truth wave-front sensor (TS) for diagnostic purposes. Aims. Our purpose is to establish a reliable and accurate wave-front error breakdown for LGS MOAO. This will enable a comprehensive analysis of Canary on-sky results and provide tools for validating simulations of MOAO systems for ELTs. Methods. To evaluate the MOAO performance, we compared the Canary on-sky results running in MOAO, in single conjugated adaptive optics (SCAO) and in ground layer adaptive optics (GLAO) modes, over a large set of data acquired in 2013. We provide a statistical study of the seeing. We also evaluated the wave-front error breakdown from both analytic computations, one based on a MOAO system modelling and the other on the measurements from the Canary TS. We have focussed especially on the tomographic error and we detail its vertical error decomposition. Results. We show that Canary obtained 30.1%, 21.4% and 17.1% H-band Strehl ratios in SCAO, MOAO and GLAO respectively, for median seeing conditions with 0.66? of total seeing including 0.59? at the ground. Moreover, we get 99% of correlation over 4500 samples, for any AO modes, between two analytic computations of residual phase variance. Based on these variances, we obtain a reasonable Strehl-ratio (SR) estimation when compared to the measured IR image SR. We evaluate the gain in compensation for the altitude turbulence brought by MOAO when compared to GLAO.

Abstract
The chemical abundances for five metal-poor stars in and towards the Galactic bulge have been determined from the H-band infrared spectroscopy taken with the RAVEN multi-object adaptive optics science demonstrator and the Infrared Camera and Spectrograph at the Subaru 8.2-m telescope. Three of these stars are in the Galactic bulge and have metallicities between -2.1<[Fe/H] < -1.5, and high [a/Fe]~+0.3, typical of Galactic disc and bulge stars in this metallicity range; [Al/Fe] and [N/Fe] are also high, whereas [C/Fe] < +0.3. An examination of their orbits suggests that two of these stars may be confined to the Galactic bulge and one is a halo trespasser, though proper motion values used to calculate orbits are quite uncertain. An additional two stars in the globular cluster M22 show [Fe/H] values consistent to within 1s, although one of these two stars has [Fe/H] = -2.01 ± 0.09, which is on the low end for this cluster. The [a/Fe] and [Ni/Fe] values differ by 2s, with the most metal-poor star showing significantly higher values for these elements. M22 is known to show element abundance variations, consistent with a multipopulation scenario though our results cannot discriminate this clearly given our abundance uncertainties. This is the first science demonstration of multiobject adaptive optics with high-resolution infrared spectroscopy, and we also discuss the feasibility of this technique for use in the upcoming era of 30-m class telescope facilities.

Abstract
Prior statistical knowledge of atmospheric turbulence is essential for designing, optimizing and evaluating tomographic adaptive optics systems. We present the statistics of the vertical profiles of CN2 and the outer scale at Maunakea estimated using a SLOpe Detection And Ranging (SLODAR) method from on-sky telemetry taken by a multi-object adaptive optics (MOAO) demonstrator, called RAVEN, on the Subaru telescope. In our SLODAR method, the profiles are estimated by fitting the theoretical autocorrelations and cross-correlations of measurements from multiple Shack-Haltmann wavefront sensors to the observed correlations via the non-linear Levenberg-Marquardt Algorithm (LMA). The analytical derivatives of the spatial phase structure function with respect to its parameters for the LMA are also developed. From a total of 12 nights in the summer season, a large ground CN2 fraction of 54.3 per cent is found, with median estimated seeing of 0.460 arcsec. This median seeing value is below the results for Maunakea from the literature (0.6-0.7 arcsec). The average CN2 profile is in good agreement with results from the literature, except for the ground layer. The median value of the outer scale is 25.5 m and the outer scale is larger at higher altitudes; these trends of the outer scale are consistent with findings in the literature.

Abstract
The use of Fourier methods in wave-front reconstruction can significantly reduce the computation time for large telescopes with a high number of degrees of freedom. However, Fourier algorithms for discrete data require a rectangular data set which conform to specific boundary requirements, whereas wave-front sensor data is typically defined over a circular domain (the telescope pupil). Here we present an iterative Gerchberg routine modified for the purposes of discrete wave-front reconstruction which adapts the measurement data (wave-front sensor slopes) for Fourier analysis, fulfilling the requirements of the fast Fourier transform (FFT) and providing accurate reconstruction. The routine is used in the adaptation step only and can be coupled to any other Wiener-like or least-squares method. We compare simulations using this method with previous Fourier methods and show an increase in performance in terms of Strehl ratio and a reduction in noise propagation for a 40x40 SPHERE-like adaptive optics system. For closed loop operation with minimal iterations the Gerchberg method provides an improvement in Strehl, from 95.4% to 96.9% in K-band. This corresponds to ~ 40 nm improvement in rms, and avoids the high spatial frequency errors present in other methods, providing an increase in contrast towards the edge of the correctable band.

Abstract
We propose and apply two methods to estimate pupil plane phase discontinuities for two realistic scenarios on the very large telescope (VLT) and Keck. The methods use both phase diversity and a form of image sharpening. For the case of VLT, we simulate the "low wind effect" (LWE) that is responsible for focal plane errors in the spectro-polarimetric high contrast exoplanet research (SPHERE) system in low wind and good seeing conditions. We successfully estimate the simulated LWE using both methods and show that they are complimentary to one another. We also demonstrate that single image phase diversity (also known as phase retrieval with diversity) is also capable of estimating the simulated LWE when using the natural defocus on the SPHERE/differential tip tilt sensor (DTTS) imager. We demonstrate that phase diversity can estimate the LWE to within 30-nm root mean square wavefront error (RMS WFE), which is within the allowable tolerances to achieve a target SPHERE contrast of 10-6. Finally, we simulate 153-nm RMS of piston errors on the mirror segments of Keck and produce NIRC2 images subject to these effects. We show that a single, diverse image with 1.5 waves (peak-to-valley) of focus can be used to estimate this error to within 29-nm RMS WFE, and a perfect correction of our estimation would increase the Strehl ratio of an NIRC2 image by 12%.