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With the aim of paving the road for future accurate astrometry with MICADO at the European-ELT, we performed an astrometric study using two different but complementary approaches to investigate two critical components that contribute to the total astrometric accuracy. First, we tested the predicted improvement in the astrometric measurements with the use of an atmospheric dispersion corrector (ADC) by simulating realistic images of a crowded Galactic globular cluster. We found that the positional measurement accuracy should be improved by up to ~2 mas with the ADC, making this component fundamental for high-precision astrometry. Second, we analysed observations of a globular cluster taken with the only currently available Multi-Conjugate Adaptive Optics assisted camera, GeMS/GSAOI at Gemini South. Making use of previously measured proper motions of stars in the field of view, we were able to model the distortions affecting the stellar positions. We found that they can be as large as ~200 mas, and that our best model corrects them to an accuracy of ~1 mas. We conclude that future astrometric studies with MICADO requires both an ADC and an accurate modelling of distortions to the field of view, either through an a-priori calibration or an a-posteriori correction.
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We present in this study a first analysis of the astrometric error budget of absolute astrometry relative to background galaxies using adaptive optics. We use for this analysis multi-conjugated adaptive optics (MCAO) images obtained with GeMS/GSAOI at Gemini South. We find that it is possible to obtain 0.3 mas reference precision in a random field with 1 hour on source using faint background galaxies. Systematic errors are correctable below that level, such that the overall error is approximately 0.4 mas. Because the reference sources are extended, we find it necessary to correct for the dependency of the PSF centroid on the used aperture size, which would otherwise cause an important bias. This effect needs also to be considered for Extremely Large Telescopes (ELTs). When this effect is corrected, ELTs have the potential to measure proper motions of dwarfs galaxies around M31 with 10 km/s accuracy over a baseline of 5 years.
Astrometric detection and mass determination of Earth-mass exoplanets requires sub-microarcsec accuracy, which is theoretically possible with an imaging space telescope using field stars as an astrometric reference. The measurement must however overcome astrometric distortions which are much larger than the photon noise limit. To address this issue, we propose to generate faint stellar diffraction spikes using a two-dimensional grid of regularly spaced small dark spots added to the surface of the primary mirror (PM). Accurate astrometric motion of the host star is obtained by comparing the position of the spikes to the background field stars. The spikes do not contribute to scattered light in the central part of the field and therefore allow unperturbed coronagraphic observation of the stars immediate surrounding. Because the diffraction spikes are created on the PM and imaged on the same focal plane detector as the background stars, astrometric distortions affect equally the diffraction spikes and the background stars, and are therefore calibrated. We describe the technique, detail how the data collected by the wide-field camera are used to derive astrometric motion, and identify the main sources of astrometric error using numerical simulations and analytical derivations. We find that the 1.4 m diameter telescope, 0.3 sq.deg field we adopt as a baseline design achieves 0.2 microarcsec single measurement astrometric accuracy. The diffractive pupil concept thus enables sub-microarcsec astrometry without relying on the accurate pointing, external metrology or high stability hardware required with previously proposed high precision astrometry concepts.
Context: Exoplanet science has made staggering progress in the last two decades, due to the relentless exploration of new detection methods and refinement of existing ones. Yet astrometry offers a unique and untapped potential of discovery of habitable-zone low-mass planets around all the solar-like stars of the solar neighborhood. To fulfill this goal, astrometry must be paired with high precision calibration of the detector. Aims: We present a way to calibrate a detector for high accuracy astrometry. An experimental testbed combining an astrometric simulator and an interferometric calibration system is used to validate both the hardware needed for the calibration and the signal processing methods. The objective is an accuracy of 5e-6 pixel on the location of a Nyquist sampled polychromatic point spread function. Methods: The interferometric calibration system produced modulated Young fringes on the detector. The Young fringes were parametrized as products of time and space dependent functions, based on various pixel parameters. The minimization of func- tion parameters was done iteratively, until convergence was obtained, revealing the pixel information needed for the calibration of astrometric measurements. Results: The calibration system yielded the pixel positions to an accuracy estimated at 4e-4 pixel. After including the pixel position information, an astrometric accuracy of 6e-5 pixel was obtained, for a PSF motion over more than five pixels. In the static mode (small jitter motion of less than 1e-3 pixel), a photon noise limited precision of 3e-5 pixel was reached.
In this article we identify and discuss various statistical and systematic effects influencing the astrometric accuracy achievable with MICADO, the near-infrared imaging camera proposed for the 42-metre European Extremely Large Telescope (E-ELT). These effects are instrumental (e.g. geometric distortion), atmospheric (e.g. chromatic differential refraction), and astronomical (reference source selection). We find that there are several phenomena having impact on ~100 micro-arcsec scales, meaning they can be substantially larger than the theoretical statistical astrometric accuracy of an optical/NIR 42m-telescope. Depending on type, these effects need to be controlled via dedicated instrumental design properties or via dedicated calibration procedures. We conclude that if this is done properly, astrometric accuracies of 40 micro-arcsec or better - with 40 micro-arcsec/year in proper motions corresponding to ~20 km/s at 100 kpc distance - can be achieved in one epoch of actual observations
Adaptive optics (AO) systems deliver high-resolution images that may be ideal for precisely measuring positions of stars (i.e. astrometry) if the system has stable and well-calibrated geometric optical distortions. A calibration unit, equipped with back-illuminated pinhole mask, can be utilized to measure instrumental optical distortions. AO systems on the largest ground-based telescopes, such as the W. M. Keck Observatory and the Thirty Meter Telescope require pinhole positions known to 20 nm to achieve an astrometric precision of 0.001 of a resolution element. We characterize a photo-lithographic pinhole mask and explore the systematic errors that result from different experimental setups. We characterized the nonlinear geometric distortion of a simple imaging system using the mask; and we measured 857 nm RMS of optical distortion with a final residual of 39 nm (equivalent to 20 {mu}as for TMT). We use a sixth order bivariate Legendre polynomial to model the optical distortion and allow the reference positions of the individual pinholes to vary. The nonlinear deviations in the pinhole pattern with respect to the manufacturing design of a square pattern are 47.2 nm +/- 4.5 nm (random) +/- 10.8 nm (systematic) over an area of 1788 mm$^2$. These deviations reflect the additional error induced when assuming the pinhole mask is manufactured perfectly square. We also find that ordered mask distortions are significantly more difficult to characterize than random mask distortions as the ordered distortions can alias into optical camera distortion. Future design simulations for astrometric calibration units should include ordered mask distortions. We conclude that photo-lithographic pinhole masks are >10 times better than the pinhole masks deployed in first generation AO systems and are sufficient to meet the distortion calibration requirements for the upcoming thirty meter class telescopes.
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