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

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

Extragalactic Fields Optimized for Adaptive Optics

In this paper we present the coordinates of 67 55' x 55' patches of sky which have the rare combination of both high stellar surface density (>0.5 arcmin^{-2} with 13<R<16.5 mag) and low extinction (E(B-V)<0.1). These fields are ideal for adaptive-optics based follow-up of extragalactic targets. One region of sky, situated near Baade's Window, contains most of the patches we have identified. Our optimal field, centered at RA: 7h24m3s, Dec: -1deg27'15", has an additional advantage of being accessible from both hemispheres. We propose a figure of merit for quantifying real-world adaptive optics performance, and use this to analyze the performance of multi-conjugate adaptive optics in these fields. We also compare our results to those that would be obtained in existing deep fields. In some cases adaptive optics observations undertaken in the fields given in this paper would be orders of magnitude more efficient than equivalent observations undertaken in existing deep fields.Comment: 28 pages, 15 figures, 1 table; accepted for publication in PAS

Laser Tomography Adaptive Optics (LTAO): A performance study

We present an analytical derivation of the on-axis performance of Adaptive Optics systems using a given number of guide stars of arbitrary altitude, distributed at arbitrary angular positions in the sky. The expressions of the residual error are given for cases of both continuous and discrete turbulent atmospheric profiles. Assuming Shack-Hartmann wavefront sensing with circular apertures, we demonstrate that the error is formally described by integrals of products of three Bessel functions. We compare the performance of Adaptive Optics correction when using natural, Sodium or Rayleigh laser guide stars. For small diameter class telescopes (~5m), we show that a few number of Rayleigh beacons can provide similar performance to that of a single Sodium laser, for a lower overall cost of the instrument. For bigger apertures, using Rayleigh stars may not be such a suitable alternative because of the too severe cone effect that drastically degrades the quality of the correction.Comment: accepted for publication in JOS

Ground-based adaptive optics coronagraphic performance under closed-loop predictive control

The discovery of the exoplanet Proxima b highlights the potential for the coming generation of giant segmented mirror telescopes (GSMTs) to characterize terrestrial --- potentially habitable --- planets orbiting nearby stars with direct imaging. This will require continued development and implementation of optimized adaptive optics systems feeding coronagraphs on the GSMTs. Such development should proceed with an understanding of the fundamental limits imposed by atmospheric turbulence. Here we seek to address this question with a semi-analytic framework for calculating the post-coronagraph contrast in a closed-loop AO system. We do this starting with the temporal power spectra of the Fourier basis calculated assuming frozen flow turbulence, and then apply closed-loop transfer functions. We include the benefits of a simple predictive controller, which we show could provide over a factor of 1400 gain in raw PSF contrast at 1 $\lambda/D$ on bright stars, and more than a factor of 30 gain on an I = 7.5 mag star such as Proxima. More sophisticated predictive control can be expected to improve this even further. Assuming a photon noise limited observing technique such as High Dispersion Coronagraphy, these gains in raw contrast will decrease integration times by the same large factors. Predictive control of atmospheric turbulence should therefore be seen as one of the key technologies which will enable ground-based telescopes to characterize terrrestrial planets.Comment: Accepted to JATI

Study of a MEMS-based Shack-Hartmann wavefront sensor with adjustable pupil sampling for astronomical adaptive optics

We introduce a Shack-Hartmann wavefront sensor for adaptive optics that enables dynamic control of the spatial sampling of an incoming wavefront using a segmented mirror microelectrical mechanical systems (MEMS) device. Unlike a conventional lenslet array, subapertures are defined by either segments or groups of segments of a mirror array, with the ability to change spatial pupil sampling arbitrarily by redefining the segment grouping. Control over the spatial sampling of the wavefront allows for the minimization of wavefront reconstruction error for different intensities of guide source and different atmospheric conditions, which in turn maximizes an adaptive optics system's delivered Strehl ratio. Requirements for the MEMS devices needed in this Shack-Hartmann wavefront sensor are also presented

Optical Design and Active Optics Methods in Astronomy

Optical designs for astronomy involve implementation of active optics and adaptive optics from X-ray to the infrared. Developments and results of active optics methods for telescopes, spectrographs and coronagraph planet finders are presented. The high accuracy and remarkable smoothness of surfaces generated by active optics methods also allow elaborating new optical design types with high aspheric and/or non-axisymmetric surfaces. Depending on the goal and performance requested for a deformable optical surface analytical investigations are carried out with one of the various facets of elasticity theory: small deformation thin plate theory, large deformation thin plate theory, shallow spherical shell theory, weakly conical shell theory. The resulting thickness distribution and associated bending force boundaries can be refined further with finite element analysis. Keywords: active optics, optical design, elasticity theory, astronomical optics, diffractive optics, X-ray optic

Adaptive Optics for Astronomy

Adaptive Optics is a prime example of how progress in observational astronomy can be driven by technological developments. At many observatories it is now considered to be part of a standard instrumentation suite, enabling ground-based telescopes to reach the diffraction limit and thus providing spatial resolution superior to that achievable from space with current or planned satellites. In this review we consider adaptive optics from the astrophysical perspective. We show that adaptive optics has led to important advances in our understanding of a multitude of astrophysical processes, and describe how the requirements from science applications are now driving the development of the next generation of novel adaptive optics techniques.Comment: to appear in ARA&A vol 50, 201