FALCON: a concept to extend adaptive optics corrections to cosmological fields

FALCON is an original concept for a next generation spectrograph at ESO VLT or at future ELTs. It is a spectrograph including multiple small integral field units (IFUs) which can be deployed within a large field of view such as that of VLT/GIRAFFE. In FALCON, each IFU features an adaptive optics correction using off-axis natural reference stars in order to combine, in the 0.8-1.8 \mu m wavelength range, spatial and spectral resolutions (0.1-0.15 arcsec and R=10000+/-5000). These conditions are ideally suited for distant galaxy studies, which should be done within fields of view larger than the galaxy clustering scales (4-9 Mpc), i.e. foV > 100 arcmin2. Instead of compensating the whole field, the adaptive correction will be performed locally on each IFU. This implies to use small miniaturized devices both for adaptive optics correction and wavefront sensing. Applications to high latitude fields imply to use atmospheric tomography because the stars required for wavefront sensing will be in most of the cases far outside the isoplanatic patch.Comment: To appear in the Backaskog "Second Workshop on ELT" SPIE proceeding

PSF reconstruction for NAOS-CONICA

Adaptive optics (AO) allows one to derive the point spread function (PSF) simultaneously to the science image, which is a major advantage in post-processing tasks such as astrometry/photometry or deconvolution. Based on the algorithm of \citet{veran97}, PSF reconstruction has been developed for four different AO systems so far: PUEO, ALFA, Lick-AO and Altair. A similar effort is undertaken for NAOS/VLT in a collaboration between the group PHASE (Onera and Observatoire de Paris/LESIA) and ESO. In this paper, we first introduce two new algorithms that prevent the use of the so-called "$U\_{ij}$ functions" to: (1) avoid the storage of a large amount of data (for both new algorithms), (2) shorten the PSF reconstruction computation time (for one of the two) and (3) provide an estimation of the PSF variability (for the other one). We then identify and explain issues in the exploitation of real-time Shack-Hartmann (SH) data for PSF reconstruction, emphasising the large impact of thresholding in the accuracy of the phase residual estimation. Finally, we present the data provided by the NAOS real-time computer (RTC) to reconstruct PSF ({\em (1)} the data presently available, {\em (2)} two NAOS software modifications that would provide new data to increase the accuracy of the PSF reconstruction and {\em (3)} the tests of these modifications) and the PSF reconstruction algorithms we are developing for NAOS on that basis.Comment: 12 pages & 13 figures. To be published in the proceedings of the SPIE conference Advances in Adaptive Optics - Astronomical Telescopes & Instrumentation, 24-31 May 2006, Orland

Analytical model-based analysis of long-exposure images fromground-based telescopes

The search for Earth-like exoplanets requires high-contrast and high-angular resolution instruments, which designs can be very complex: they need an adaptive optics system to compensate for the effect of the atmospheric turbulence on image quality and a coronagraph to reduce the starlight and enable the companion imaging. During the instrument design phase and the error budget process, studies of performance as a function of optical errors are needed and require multiple end-to-end numerical simulations of wavefront errors through the optical system. In particular, the detailed analysis of long-exposure images enables to evaluate the image quality (photon noise level, impact of optical aberrations and of adaptive optics residuals, etc.). Nowadays simulating one long but finite exposure image means drawing several thousands of random frozen phase screens, simulating the image associated with each of them after propagation through the imaging instrument, and averaging all the images. Such a process is time consuming, demands a great deal of computer resources, and limits the number of parametric optimization. We propose an alternative and innovative method to directly express the statistics of ground-based images for long but finite exposure times. It is based on an analytical model, which only requires the statistical properties of the atmospheric turbulence. Such a method can be applied to optimize the design of future instruments such as SPHERE+ (VLT) or the planetary camera and spectrograph (PCS - ELT) or any ground-based instrument.Comment: 7 pages, 0 figur

MODULES DE DRINFELD QUASICRISTALLINS

Dans cet article nous développons la notion de module de Drinfeld quasicristallin, que l'on peut voir comme un analogue en caractéristique zéro des modules de Drinfeld classiques. On prendra garde que l'adjectif se réfère aux quasi-cristaux (au sens de [23]), sans rapport avec la théorie cristalline initiée par A. Grothendieck

Modules de Drinfeld Quasicristallins

In this article we develop the notion of quasicrystalline Drinfeld module, which one may view as an analog in characteristic zero of classical Drinfeld modules. We point out that the adjective refers to quasicrystals in the sense of Y. Meyer, and has no relation with the crystalline theory developed by A. Grothendieck. ----- Dans cet article nous d\'eveloppons la notion de module de Drinfeld quasicristallin, que l'on peut voir comme un analogue en caract\'eristique z\'ero des modules de Drinfeld classiques. On prendra garde que l'adjectif se r\'ef\`ere aux quasi-cristaux (au sens de Y. Meyer), sans rapport avec la th\'eorie cristalline initi\'ee par A. Grothendieck.Comment: 40 pages, 1 figure, in Frenc

Fast minimum variance wavefront reconstruction for extremely large telescopes

We present a new algorithm, FRiM (FRactal Iterative Method), aiming at the reconstruction of the optical wavefront from measurements provided by a wavefront sensor. As our application is adaptive optics on extremely large telescopes, our algorithm was designed with speed and best quality in mind. The latter is achieved thanks to a regularization which enforces prior statistics. To solve the regularized problem, we use the conjugate gradient method which takes advantage of the sparsity of the wavefront sensor model matrix and avoids the storage and inversion of a huge matrix. The prior covariance matrix is however non-sparse and we derive a fractal approximation to the Karhunen-Loeve basis thanks to which the regularization by Kolmogorov statistics can be computed in O(N) operations, N being the number of phase samples to estimate. Finally, we propose an effective preconditioning which also scales as O(N) and yields the solution in 5-10 conjugate gradient iterations for any N. The resulting algorithm is therefore O(N). As an example, for a 128 x 128 Shack-Hartmann wavefront sensor, FRiM appears to be more than 100 times faster than the classical vector-matrix multiplication method.Comment: to appear in the Journal of the Optical Society of America

Near-infrared wavefront sensing for the VLT interferometer

The very large telescope (VLT) interferometer (VLTI) in its current operating state is equipped with high-order adaptive optics (MACAO) working in the visible spectrum. A low-order near-infrared wavefront sensor (IRIS) is available to measure non-common path tilt aberrations downstream the high-order deformable mirror. For the next generation of VLTI instrumentation, in particular for the designated GRAVITY instrument, we have examined various designs of a four channel high-order near-infrared wavefront sensor. Particular objectives of our study were the specification of the near-infrared detector in combination with a standard wavefront sensing system. In this paper we present the preliminary design of a Shack-Hartmann wavefront sensor operating in the near-infrared wavelength range, which is capable of measuring the wavefronts of four telescopes simultaneously. We further present results of our design study, which aimed at providing a first instrumental concept for GRAVITY.Comment: 10 pages, 7 figures, to appear in "Ground-based and Airborne Instrumentation for Astronomy II" SPIE conference, Marseille, 23-28 June 200

Frequency and isostericity of RNA base pairs

Most of the hairpin, internal and junction loops that appear single-stranded in standard RNA secondary structures form recurrent 3D motifs, where non-Watson–Crick base pairs play a central role. Non-Watson–Crick base pairs also play crucial roles in tertiary contacts in structured RNA molecules. We previously classified RNA base pairs geometrically so as to group together those base pairs that are structurally similar (isosteric) and therefore able to substitute for each other by mutation without disrupting the 3D structure. Here, we introduce a quantitative measure of base pair isostericity, the IsoDiscrepancy Index (IDI), to more accurately determine which base pair substitutions can potentially occur in conserved motifs. We extract and classify base pairs from a reduced-redundancy set of RNA 3D structures from the Protein Data Bank (PDB) and calculate centroids (exemplars) for each base combination and geometric base pair type (family). We use the exemplars and IDI values to update our online Basepair Catalog and the Isostericity Matrices (IM) for each base pair family. From the database of base pairs observed in 3D structures we derive base pair occurrence frequencies for each of the 12 geometric base pair families. In order to improve the statistics from the 3D structures, we also derive base pair occurrence frequencies from rRNA sequence alignments