Showing papers by "Éric Thiébaut published in 2010"

Fast minimum variance wavefront reconstruction for extremely large telescopes

Abstract: We present what we believe to be a new algorithm, FRactal Iterative Method (FRiM), 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 that 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, with N being the number of phase samples to estimate. Finally, we propose an effective preconditioning that also scales as O(N) and yields the solution in five to ten conjugate gradient iterations for any N. The resulting algorithm is therefore O(N). As an example, for a 128×128 Shack–Hartmann wavefront sensor, the FRiM appears to be more than 100 times faster than the classical vector-matrix multiplication method.

Image reconstruction in optical interferometry

Abstract: Since the first multitelescope optical interferometer [1], considerable technological improvements have been achieved. Optical (visible/infrared) interferometers are now widely open to the astronomical community and provide the means to obtain unique information from observed objects at very high angular resolution (submilliarcsecond). There are numerous astrophysical applications, such as stellar surfaces, environment of premain sequence or evolved stars, and central regions of active galaxies. See [2]-[4] for comprehensive reviews about optical interferometry and recent astrophysical results. As interferometers do not directly provide images, reconstruction methods are needed to fully exploit these instruments. This article aims at reviewing image reconstruction algorithms in astronomical interferometry using a general framework to formally describe and compare the different methods. The challenging issues in image reconstruction from interferometric data are introduced in the general framework of inverse problem approach. This framework is then used to describe existing image reconstruction algorithms in radio interferometry and the new methods specifically developed for optical interferometry.

Fractal iterative method for fast atmospheric tomography on extremely large telescopes

Abstract: A challenge of adaptive optics (AO) on Extremely Large Telescopes (ELTs) is to overcome the difficulty of solving a huge number of equations in real time, especially when atmospheric tomography is involved. This is particularly the case for multi-conjugate or multi-objects AO systems. In addition, the quality of the wavefront estimation is crucial to optimize the performances of the future systems in a situation where measurements are missing and noises are correlated. The Fractal Iterative Method has been introduced as a fast iterative algorithm for minimum variance wavefront reconstruction and control on ELTs. This method has been successfully tested on Classical Single Conjugate AO systems on Octopus numerical simulator at ESO. But the minimum variance approach is expected to be mostly useful with atmospheric tomography. We present the first results obtained with FrIM in the context of atmospheric tomography. We recall the principle of the algorithm and we summarize the formalism used for modeling the measurements obtained from laser guide stars that entail spot elongation and tip/tilt indetermination, mixed with low order measurements from natural guide stars. We show the respective effects of tip/tilt indetermination, spot elongation, unseen modes on various configurations, as well as the usefulness of priors and correct noise models in the reconstruction. This analysis is essential for balancing the various errors that combine in a quite complex way and to optimize the configuration of the future AO systems for specific science cases and instrument requirements.

Milli-arcsecond images of the Herbig Ae star HD 163296

Abstract: Context. The very close environments of young stars are the hosts of fundamental physical processes, such as planet formation, stardisk interactions, mass accretion, and ejection. The complex morphological structure of these environments has been confirmed by the now quite rich data sets obtained for a few objects by near-infrared long-baseline interferometry. Aims. We gathered numerous interferometric measurements for the young star HD 163296 with various interferometers (VLTI, IOTA, KeckI and CHARA), allowing for the first time an image independent of any a priori model to be reconstructed. Methods. Using the Multi-aperture image Reconstruction Algorithm (MiRA), we reconstruct images of HD 163296 in the H and K bands. We compare these images with reconstructed images obtained from simulated data using a physical model of the environment of HD 163296. Results. We obtain model-independent H and K-band images of the surroundings of HD 163296. The images present several significant features that we can relate to an inclined asymmetric flared disk around HD 163296 with the strongest intensity at about 4-5 mas. Because of the incomplete spatial frequency coverage, we cannot state whether each of them individually is peculiar in any way. Conclusions. For the first time, milli-arcsecond images of the environment of a young star are produced. These images confirm that the morphology of the close environment of young stars is more complex than the simple models used in the literature so far.

Optimal reconstruction for closed-loop ground-layer adaptive optics with elongated spots.

Abstract: The design of the laser-guide-star-based adaptive optics (AO) systems for the Extremely Large Telescopes requires careful study of the issue of elongated spots produced on Shack–Hartmann wavefront sensors. The importance of a correct modeling of the nonuniformity and correlations of the noise induced by this elongation has already been demonstrated for wavefront reconstruction. We report here on the first (to our knowledge) end-to-end simulations of closed-loop ground-layer AO with laser guide stars with such an improved noise model. The results are compared with the level of performance predicted by a classical noise model for the reconstruction. The performance is studied in terms of ensquared energy and confirms that, thanks to the improved noise model, central or side launching of the lasers does not affect the performance with respect to the laser guide stars’ flux. These two launching schemes also perform similarly whatever the atmospheric turbulence strength.

Closed-loop ground layer adaptive optics simulations with elongated spots : impact of modeling noise correlations

Abstract: Laser guide stars on an Extremely Large Telescope (ELT) produce elongated spots on the sub- apertures of the Shack-Hartmann wavefront sensors for adaptive optics (AO) correction. This degrades the mea- surement accuracy and introduces structured correlations in the centroiding errors, depending on the position of the laser launch telescope with respect to the sub-aperture location inside the pupil. Advanced centroiding algorithms are used to improve the measurement accuracy, but closed-loop control methods in adaptive optics usually neglect the structured error correlations. However, properly modeling the noise correlations is expected to improve the correction. We take into account structured errors statistics inside a fast algorithm for wavefront reconstruction and control on a 42-meter telescope. The closed-loop performance of the new algorithm, including a maximum a posteriori reconstruction and a pseudo open-loop control with an integrator is compared to the uni- form and uncorrelated noise model used in classical AO corrections. End-to-end simulations are used to compare the two approaches. A ground layer AO configuration is simulated. The results provide additional information to the discussion about the choice of laser launch telescope positions on an ELT-class telescope.

Development of a high-dynamic range imaging instrument for a single telescope by a pupil remapping system

Abstract: We present the laboratory demonstration of a very high-dynamic range imaging instrument FIRST (Fibered Imager foR Single Telescope). FIRST combines the techniques for aperture masking and a single-mode fiber interferometer to correct wavefront errors, which leads to a very high-dynamic range up to 106 around very near the central object (~ λ/D) at visible to near-infrared wavelengths. Our laboratory experiments successfully demonstrated that the original image can be reconstructed through a pupil remapping system. A first on-sky test will be performed at the Lick Observatory 3- m Shane telescope for operational tests in the summer of 2010.

Probing magnetic fields in volume with multifrequency polarized synchrotron emission

Abstract: We investigate the problem of probing the local spatial structure of the magnetic field of the interstellar medium using multifrequency polarized maps of the synchrotron emission at radio wavelengths. We focus in this paper on the three-dimensional (3D) reconstruction of the largest scales of the magnetic field, relying on the internal depolarization (due to differential Faraday rotation) of the emitting medium as a function of electromagnetic frequency. We argue that multiband spectroscopy in the radio wavelengths, developed in the context of high-redshift extragalactic H i lines, can be a very useful probe of the 3D magnetic field structure of our Galaxy when combined with a maximum a posteriori reconstruction technique. When starting from a fair approximation of the magnetic field, we are able to recover the true one by using a linearized version of the corresponding inverse problem. The spectral analysis of this problem allows us to specify the best sampling strategy in electromagnetic frequency and predicts a spatially anisotropic distribution of posterior errors. The reconstruction method is illustrated for reference fields extracted from realistic magnetohydrodynamical simulations.

End-to-end model for the Polychromatic Laser Guide Star project (ELP-OA)

Abstract: In order to optimize parameters for the ELP-OA project, we have developped an end-to-end model from the laser emission to the computation of the tip-tilt Strehl ratio. ELP-OA aims at measuring the wavefront tip-tilt from the laser guide star alone, without any natural source. It relies on 2-photon excitation of mesospheric sodium, achieved by two laser chains (at 569nm and 589nm) deliv- ering 34W average power each. The modeled twin laser beam is launched with a three aperture interferometer that produces an interferometric pattern in the mesosphere after the passage through a Kolmogorov phase screen. The backscattered flux is computed with an optical Bloch equations code (1). The result of this excitation is an emission at di erent wavelengths. The wavelengths retained are 330nm, 569nm and 589nm. An image of this polychromatic LGS (PLGS) is computed, as it will be observed at the 1.52m telescope at the Observatoire de Haute-Provence (OHP), through a Kolmogorov phase screen again. Then we simulate the adap- tive optics device (adapted from ONERA's BOA AO) at the telescope except for tip-tilt. Air refraction index variations due to atmospheric turbulence create a dispersion between 330nm and 569nm, and the tip-tilt value is derived from this dispersion. This dispersion between 330nm and 569nm is measured using a correlation method and a sub-pixel interpolation. The calculation of the relative position between two simultaneous images at 330nm and 569nm gives a position error, from which the Strehl ratio for tip-tilt is deduced. At this time, we have got Strehl ratios up to approximatively 35% at 550nm, for tilt corrected r0 = 10cm and a projector baseline of 70cm.

Setting up ELP-OA: the polychromatic laser guide star demonstrator

Abstract: ELP-OA ('Etoile Laser Polychromatique pour l'Optique Adaptative) aims at demonstrating the tip-tilt is measurable with a Laser Guide Star (LGS) without any natural guide star. This allows a full sky coverage down to visible wavelengths. ELP-OA is being setup at Observatoire de Haute-Provence (OHP). To create a polychromatic LGS, we use two pulsed dye lasers (at 569nm and 589nm) to produce a two-photons excitation of sodium atoms in the mesosphere. The chromatism of the refractive index of the air yields a difference of the LGS direction at different wavelengths. The position differences is proportionnal to the tip-tilt. Since the LGS isn't sharp enough to give us a small enough error in the differential tip-tilt, we use an interferometric projector to improve the high spatial information in the laser spot. It requires an adaptive optics working down to 330nm. This one is done by post-processing algorithms. Two two aperture projectors are used. Each one creates a fringe-modulated LGS, and a better RMS error in the LGS position is obtained by measuring the information in a normal direction with respect to the fringes. By using a two aperture projector, we also strongly decrease the negative effect of the laser star elongation in the mesosphere, and the Rayleigh contribution near the LGS. We propose a new optimal algorithm to retrieve the tip-tilt from simultaneous images at different wavelengths. To enhance the RMS error of the measurements, we extend this algorithm to exploit the temporal correlation of the turbulence.

Comparison of Reconstruction and Control algorithms on the ESO end-to-end simulator OCTOPUS

Abstract: Extremely Large Telescopes are very challenging concerning their Adaptive Optics requirements. Their diameters, the specifications demanded by the science for which they are being designed for, and the planned use of Extreme Adaptive Optics systems, imply a huge increment in the number of degrees of freedom in the deformable mirrors. It is necessary to study new reconstruction algorithms to implement the real time control in Adaptive Optics at the required speed. We have studied the performance, applied to the case of the European ELT, of three different algorithms: the matrix-vector multiplication (MVM) algorithm, considered as a reference; the Fractal Iterative Method (FrIM); and the Fourier Transform Reconstructor (FTR). The algorithms have been tested on ESO’s OCTOPUS software, which simulates the atmosphere, the deformable mirror, the sensor and the closed-loop control. The MVM is the default reconstruction and control method implemented in OCTOPUS, but it scales in O (N 2 ) operations per loop so it is not considered as a fast algorithm for wave-front reconstruction and control on an Extremely Large Telescope. The two other methods are the fast algorithms studied in the E-ELT Design Study. The performance, as well as their response in the presence of noise and with various atmospheric conditions, has been compared using a Single Conjugate Adaptive Optics configuration for a 42 m diameter ELT, with a total amount of 5402 actuators. Those comparisons made on a common simulator allow to enhance the pros and cons of the various methods, and give us a better understanding of the type of reconstruction algorithm that an ELT demands.

ELP-OA: status report of the setup of the demonstrator of the Polychromatic Laser Guide Star at Observatoire de Haute-Provence

Abstract: We report the status of ELP-OA (Etoile Laser polychromatique pour l’Optique Adaptative), the full demonstrator which we are building at OHP 1.52m telescope. The goal is to open adaptive optics to the domain of visible wavelengths at large telescopes, which is almost not feasible today because of the tiny isoplanatic patch. ELP-OA relies on the 2-photon excitation of sodium in the mesosphere, through 589 and 569 nm transitions. We use 2 pulsed dye lasers (on loan from CEA) pumped with NdYAGs. The average power at the mesosphere will be 2 × 22W. The twin laser beams are projected to the mesosphere by a 3-aperture interferometer. The backscattered ´ spots in NaI lines at 330, 569 and 589nm are oberved through an adaptive optics at the telescope coude focus, derived from the ONERA’s BOA device. The differential tilt measurement channel is equipped with an EMCCD. We use a correlation algorithm to extract it. From our end to end model we expect tilt Strehl ratios of 35% at 550nm (see Meilard et al in this conference). First lasers launches are planned early 2010, with the full experiment running 2011.

Comparison between closure phase and phase referenced interferometric image reconstructions

Abstract: We compare the quality of interferometric image reconstructions for two different sets of data: square of the visibility plus closure phase (e.g. AMBER like case) and square of the visibility plus visibility phase (e.g. PRIMA+AMBER or GRAVITY like cases). We used the Multi-aperture image Reconstruction Algorithm for reconstructions of test cases under different signal-to-noise ratios and noisy data (squared visibilities and phases). Our study takes into account noise models based on the statistics of visibility, phase and closure phase. We incorporate the works developed by Tatulli and Chelly (2005) on the noise of the power-spectrum and closure phase in the read-out and photon noise regimes,1 and by Colavita (1999) on the signal-to-noise ratio of the visibility phase.2 The final images were then compared to the original one by means of positions and fluxes, computing the astrometry and the photometry. For the astrometry, the precision was typically of tens of microarcseconds, while for the photometry, it was typically of a few percent. Although both cases are suitable for image restorations of real interferometric observations, the results indicate a better performance of phase referencing (V 2 + visibility phase) in a low signal-to-noise ratio scenario.

Image reconstruction in optical interferometry: application to the inner regions of protoplanetary disks

Abstract: Planets are believed to form in circumstellar disks around newly born stars at distances ranging from 0.1 to 10 AUs. This location corresponds to milli-arcsecond scales at the distance of the closest star forming regions and to temperatures ranging from a few hundred to a few thousand Kelvin. To conduct observations of close environments of such disks at the milli-arcsecond scale, infrared interferometry is a suitable tool that can be employed to observe T Tauri, FU Ori and Herbig Ae/Be stars. However, the data obtained so far consist of a small number of measurements which can only constrain theoretical models. With the advent of recent multi-aperture interferometers, the interferometric data can be used to reconstruct images independently of any parametric model, as is routinely done in the radio frequency range. On the other hand, in the optical range, not enough measurements are available to univocally reconstruct an image and some a priori must be introduced. In this contribution, we present systematic tests performed on the MiRA algorithm (an image reconstruction algorithm developed for optical interferometry) in order to evaluate the feasibility of the technique. The methodology allows deriving some practical rules for the user and has been applied to an YSO (HD 163296). I present the results of the image reconstruction, providing the first images of a complex YSO.