A new calibration strategy for adaptive telescopes with pyramid WFS

MNRAS 481, 2829–2840 (2018) doi:10.1093/mnras/sty2485 Advance Access publication 2018 September 11 A new calibration strategy for adaptive telescopes with pyramid WFS C. T. Heritier,1,2,3,4‹ S. Esposito,3 T. Fusco,1,2 B. Neichel,1 S. Oberti,4 R. Briguglio,3 G. Agapito,3 A. Puglisi,3 E. Pinna3 and P.-Y. Madec4 1 Aix Marseille Univ, CNRS, CNES, LAM, Marseille, France DOTA, Unité HRA, 29 avenue de la division Leclerc, F-92322 Chatillon, France 3 INAF – Osservatorio Astrofisico di Arcetri Largo E. Fermi 5, I-50125 Firenze, Italy 4 European Southern Observatory, Karl-Schwarzschild-str-2, D-85748 Garching, Germany 2 ONERA, ABSTRACT Several telescopes include large deformable mirrors (DM) located directly inside the telescope. These adaptive telescopes trigger new constraints for the calibration of the adaptive optics (AO) systems as they usually offer no access to an artificial calibration source for the interaction matrix measurement. Moreover, the optical propagation between the DM and the wavefront sensor (WFS) may evolve during the operation, resulting in misregistrations that highly affect the AO performance and thus the scientific observation. They have to be measured and compensated, for instance by updating the calibration. A new strategy consists of estimating the misregistrations and injecting them into synthetic models to generate noise-free interaction matrices. This pseudo-synthetic approach is the baseline for the adaptive optics facility working with a Shack–Hartmann WFS and seems particularly suited for the future Extremely Large Telescope as the calibration will have to be regularly updated, for a large numbers of actuators. In this paper, the feasibility of a pseudo-synthetic calibration with pyramid WFS at the Large Binocular Telescope (LBT) is investigated. A synthetic model of the LBT AO systems is developed, and the procedure to adjust the misregistrations parameters is introduced, extracting them from an experimental interaction matrix. We successfully tested an interaction matrix generated from the model on the real system in high-order AO mode. We recorded a slightly better performance with respect to the experimental one. This work demonstrates that a highaccuracy calibration can be obtained using the pseudo-synthetic approach with pyramid WFS. Key words: instrumentation: adaptive optics – telescopes. 1 I N T RO D U C T I O N Adaptive optics (AO) is now commonly spread on large aperture optical telescope facilities to compensate in real time the variations of optical index in the atmosphere and retrieve the full angular resolution of the telescope (Babcock 1953). The principle of a classical AO system is the following: a wavefront sensor (WFS) measures a signal relative to the phase and sends it to a real-time computer (RTC) that computes the corresponding commands to apply on a deformable mirror (DM). This system is usually operated in a feedback loop at a higher frequency than the temporal evolution of the turbulence (typically, a few hundred Hz). However, to provide a good correction (e.g. to be able to apply the correct shape on the DM at the right time), the AO loop has to be properly calibrated before the operations. This is achieved by measuring the interaction  E-mail: matrix of the system which consists of recording the WFS signals corresponding to a specific command of the DM actuators. Recent developments in telescope designs and DM technology have led to consider DM located directly into the telescope (turning them from active-to-adaptive telescopes) to reduce the number of optics and increase the numbers of photons available for the instruments. This concept was first validated on the MMT (Wildi et al. 2003) and is now used on two of the largest ground-based optical telescopes, the Large Binocular Telescope (LBT), with its two adaptive secondary mirrors (ASMs) (Riccardi et al. 2003; Esposito et al. 2010a) of 672 actuators, and the Unit Telescope 4 of the Very Large Telescope, recently upgraded to become the adaptive optics facility (AOF) (Stroebele et al. 2006; Arsenault et al. 2008) with its deformable secondary mirror (DSM) of 1170 actuators. The next generation telescopes, the Extremely Large Telescope (ELT) (Gilmozzi & Spyromilio 2007) and Giant Magellan Telescope (GMT) (Johns 2006), will also include large adaptive mirrors in their design with, respectively, 4356 and 4702 actuators (Hinz et al. 2010; Vernet et al. 2012). The Thirty Meter Telescope (TMT)  C 2018 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society Accepted 2018 September 6. Received 2018 September 6; in original form 2018 August 27 2830 C. T. Heritier et al. 1 Relative shifts, rotation, magnification, or higher order pupil distortion between the DM actuators and WFS subapertures. MNRAS 481, 2829–2840 (2018) modal gains during the operations will improve the closed loop performance (Korkiakoski, Vérinaud & Le Louarn 2008; Esposito et al. 2012; Esposito et al. 2015; Bond et al. 2018; Deo et al. 2018). Considering that all of the first light instruments of the ELT will include a pyramid WFS in their design (Brandl et al. 2016; Clénet et al. 2016; Neichel et al. 2016) it is necessary to identify the key elements and the accuracy requirements to reproduce the behaviour of an AO system with pyramid WFS with the overall goal to generate calibration data that can be used on a real system. After a short introduction of the classical and new calibration methods in the context of the adaptive telescopes (Section 2), this paper will introduce the development of a synthetic model, reproducing the FLAO-LBT systems (Esposito et al. 2010b), focusing on the model definition and sensitivity (Section 3). Section 4 details the adjustment procedure for the misregistrations parameters that have been thoroughly verified in simulation. Section 5 presents the results of day-time validation at the LBT. 2 AO C A L I B R AT I O N O F A N A DA P T I V E TELESCOPE This section aims to present the calibration procedure for a classical AO system and provides a short summary of the different calibration strategies in the frame of the future ELT. 2.1 General case Mathematically, the interaction matrix of an AO system is the transfer matrix between the DM and the WFS space. Following the notations introduced in Meimon, Petit & Fusco (2015), the interaction matrix D of an AO system is: D = MWFS .MDM , (1) where MDM is the conversion matrix between the DM commands and the optical phase deformations and MWFS the corresponding WFS measurement matrix. This matrix is then inverted to provide the reconstructor R that is used in closed loop. R = D† . (2) The most common inversion method consists of using a truncated singular values decomposition (SVD), filtering the modes badly seen by the WFS for stability (Boyer, Michau & Rousset 1990 but using a generalized SVD adding priors on the noise and turbulence statistics provides a gain in (...truncated)