SAXO, the extreme Adaptive Optics System of SPHERE. Overview and calibration procedure

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1 SAXO, the extreme Adaptive Optics System of SPHERE. Overview and calibration procedure J.-F. Sauvage a,t.fusco a,c.petit a,s.meimon a,e.fedrigo b, M Suarez Valles b,m.kasper b, N. Hubin b, J.-L. Beuzit c, J. Charton c, A. Costille c, P. Rabou c, D. Mouillet c, P. Baudoz d,t. Buey d,a.sevin d, F. Wildi e,k.dohlen f a ONERA, BP 72, Chatillon France, b ESO, Karl-Schwarzschild-Straβe 2, Garching, D Germany, c LAOG, Observatoire de Grenoble, BP 53, F Grenoble, France, d LESIA, Observatoire de Paris, 5 Place Jules Janssen Meudon, France, e HES-SO, 1, rte de Cheseaux CH-1401 Yverdon f LAM,Observatoire de Marseille, BP 8, F Marseille, France, ABSTRACT The direct imaging of exoplanet is a challenging goal of todays astronomy. The light transmitted by exoplanet atmosphere is of a great interest as it may witness for life sign. SPHERE is a second generation instrument for the VLT, dedicated to exoplanet imaging, detection, and characterisation. SPHERE is a global project of an European consortium of 11 institutes from 5 countries. We present here the state of the art of the AIT of the Adaptive Optics part of the instrument. In addition we present fine calibration procedures dedicated to extreme Adaptive Optics systems. First we emphasized on vibration and turbulence identification for optimization of the control law. Then, we describe a procedure able to measure and compensate for NCPA with a coronagraphic system. Keywords: high angular resolution, adaptive optics 1. INTRODUCTION We present here an overview of the high performance adaptive optics system for the SPHERE instrument. 1 More particularly, we present here the problematic of the calibration of the instrument. The main scientific objective of SPHERE is to perform high contrast imaging of extrasolar planets (between 1 and 20 jupiter masses). Imaging of an exoplanet allows a first order characterization of the exoplanet atmosphere (clouds, dust content, methane, water absorption, effective temperature, radius, dust polarization). Moreover, investigating a large target sample allows one to reach statistical distribution, different variety of stellar classes as well as evolutionary trends. The whole instrument is dedicated to high contrast imaging. This requires joint high performance of each part of the instrument. We present in the first section the problematic of the XAO internal calibrations. We propose an identification procedure that can be coupled to the vibration filtering control law, based on a kalman filter scheme. We propose a vibration model identification scheme, including a turbulent model identification. Last, we present the results of an end-to-end simulation of the AO system of SPHERE, SAXO, using the output of our vibration identification method. As detailed before, the AO system for SPHERE, called SAXO (Sphere AO for exoplanet Observation) is a challenging system composed by high performance sub-systems (high order DM, optimized RTC, EMCCD...) A global trade-off from all the points mentioned above (combined with optical design, technological aspect, cost and risk issues) leads to the following AO system main characteristics: Further author information: (Send correspondence to JFS) JFS: jean-francois.sauvage@onera.fr, Telephone: +33 (0) Adaptive Optics Systems II, edited by Brent L. Ellerbroek, Michael Hart, Norbert Hubin, Peter L. Wizinowich, Proc. of SPIE Vol. 7736, 77360F 2010 SPIE CCC code: X/10/$18 doi: / Proc. of SPIE Vol F-1

2 A 41x41 actuator DM of 180 mm diameter, located in a pupil plane with an inter-actuator stroke > ±1μm (mechanical), a maximum stroke > ±3.5μm (mechanical), plus a 2-axis TTM with a ±0.5 mas resolution. 40x40 Shack-Hartmann WFS, with a spectral range between 0.45 and 0.95 μm, 6x6 pixels per sub-aperture (Shannon 0.65 μm), a focal plane filtering device with variable size (from λ/d to 3λ/d at 0.7μm) and a temporal sampling frequency 1kHz (goal 1.5 khz). The foreseen detector is a 240x240 pixels Electron Multiplication CCD detector with a read-out-noise < 1e and a 1.4 excess photon noise 2 Mixed numerical control law with a Kalman filter law for Tip-Tilt control and an Optimal Modal Gain Integrator law for DM control. The global AO loop delay (including CCD read-out and RTC delays) has to be lower than 1 ms (goal 666 μs) Non-common path aberrations: off-line measurements and on-line compensation using a phase diversity algorithm Auxiliary IR tip-tilt sensor and pupil sensor to measure and correct for optical axis and pupil displacement On the other hand, we present here the calibration of XAO system linked to the scientific instrument itself. This involves the measurement and compensation of NCPA in presence of a coronagraph. 2.AITPLANANDFIRSTRESULT SPHERE instrument is now in Assembly Integration and Test phase (AIT). The Common Path and Infrastructure (CPI) is being integrated in Grenoble LAOG-IPAG institute, while the AO system SAXO is being integrated and characterized in Meudon Observatory. Figure 3 and 4 show picture of both cleanrooms. The Meudon integration will consist in the caracterization of SAXO performance, while Grenoble integration will consist in CPI performance in a first step, and the whole instrument further on. For now, AIT at Meudon observatory consisted in alignment of the old NAOS turbulence simulator redesigned for SPHERE framework, and aligment of Common Path optics comprising the parabola collimating beam on TipTilt mirror and Deformable mirror (DM). Numerical tests of the Real-Time Computer (RTC) have already been performed showing that 1.2 full frame frequency can be achieved with less than 200 μs of pure latency. 3. VIBRATION IDENTIFICATION METHOD One of the key elements in SPHERE performance is to ensure a Tip-Tilt residual less than 3 mas. This could be achieved using a dedicated kalman filter which allows to optimally deal with turbulence while is has also to reduce system and telescope vibration often responsible of most of the residual Tip-Tilt in current AO system. A specific kalman filter has been designed to deal with such kind of vibrations but a critical issue remains the calibration of the vibration in this filter. In what follows, we consider that each signal (turbulence, vibration 1, vibration 2,... ), and each mode are independant and decorrelated. Thus, we can consider only one mode, for instance the tilt. The data is then a time sequence of tilt pseudo open loop measurements. Let us suppose that the incoming vibration is an oscillatory signal, characterized by its damping coefficient k ( related to the vibration bandwidth) and its natural frequency f vib. The sampled version of the vibration, obtained by averaging the signal over one time period [(n 1)T,(n)T ], can suitably be approximated by a scalar second-order Auto-Regressive (AR2) model: 3 x n = a 1 x n 1 + a 2 x n 2 + ξ n, (1) with ξ n a Gaussian white noise of variance σξ 2. Thus, we can link the AR2 model coefficients to more meaningful ones, namely the oscillatory continuous-time parameters k, f vib : a 1 =2e 2kπfvibT cos(2πf vib T 1 k 2 ), a 2 = e 4kπfvibT. (2) Variance σξ 2 behaves as a scaling factor. The identification scheme consists in estimating the k, f vib,σξ 2 of each vibration component, as well as the turbulent parameters, from data which contain both turbulence and vibrations. The first step is to separate vibrations and turbulence. Proc. of SPIE Vol F-2

3 Figure 1. Overview of SPHERE instrument implantation. This mechanical scheme shows fore optics implantation, and instrument localisation. Proc. of SPIE Vol F-3

4 Figure 2. Figure 3. Optical AIT bench in the cleanroom of Meudon Observatory. Basic optics and Turbulence Simulator are being aligned. Proc. of SPIE Vol F-4

5 Figure 4. Optical AIT bench in the cleanroom of LAOG institute. 3.1 Signal separation To perform source separation, namely turbulence on one hand and several vibrations on the other hand, prior information is mandatory. We will consider the following prior: The vibration signal is the sum of AR2 processes; Each AR2 process is sharp, i.e. its damping coefficient K verifies 0 <K<0.05; The range whithin which all the natural frequencies f vib of the vibration set are is within [f s /60,f s /3.], with glob f s the sampling frequency of ˆφ n time sequence. Of course, this is an arbitrary setting, which has to be adapted to the pratical case adressed. Only, the lower bound has to be below the AO loop cutoff frequency, so that the AO overshoot region is included. Also, the upper bound has to be below half the sampling frequency, so that a vibration-free high frequency region is available for turbulent spectrum estimation. The first step consists in building a new time sequence from the in which only the turbulent part is present. Using the prior information, we first build a model periodogram P m, equal to the experimental periodogram outside [f s /60,f s /3.], and linear in a log-log representation whithin this range. Then we modify the time sequence so that its periodogram is close to P m. If we consider that the signal is the output of an AR filter, it is possible to fit the AR parameters on the time series. Among the various methods that estimate AR coefficients (knowing the order) from a time sequence, we use an IDL built-in library TS_COEF, using an iterative scheme. This estimation method was tested on various cases and provides reliable results. It is certainly not optimal, but simple, fast and robust. ˆφ glob n Proc. of SPIE Vol F-5

6 3.2 Vibration parameters estimation At this stage, we have a periodogram P glob glob of ˆφ n, and an estimated turbulent PSD Ŝtur. We consider that the turbulence and vibration signals are decorrelated, so: P glob = P (φ tur )+P (φ vib,1 )+P (φ vib,2 )+... A periodogram is a noisy PSD Power Spectrum Density, with a signal to noise ratio (SNR) close to 1, i.e. : σ( P S ) S The fittting error of the TS_COEF library is negligible compared to the periodogram noise, so we gather: We form the residual periodogram We apply Equation 3 : σ( P Ŝ ) Ŝ (3) P glob Ŝtur = P (φ vib,1 )+P (φ vib,2 )+...+ P (φ tur ) Ŝtur (4) σ(p (φ tur ) Ŝtur ) Ŝtur and suppose that this noise is 0 mean Gaussian, wich yields the following classical χ 2 data-likelihood in φ vib : J(φ vib,1 P glob )= Ŝtur P (φ vib,1 ) We then compute the parameters of the AR2 process which minimizes J. This AR2 process should be the strongest component in the vibration set. From these AR2 parameters, we compute the analytical PSD Ŝvib,1. For the next step, we form the criterion Ŝ tur J(φ vib,2 P glob )= Ŝtur Ŝvib,1 P (φ vib,2 ) Ŝ tur + Ŝvib,1 We use this procedure iteratively to identify one by one the vibration signals. At each step, the last identified vibration is subtracted from the current residual spectrum. 4. VALIDATION ON SIMULATED AND EXPERIMENTAL DATA 4.1 Validation on NAOS experimental data In this section, we use the identification procedure on NAOS experimental reconstructed open-loop tip-tilt measurements. Data are courtesy of Yann Clenet. Figure 5 shows the data periodogram and the estimated vibration and turbulent total PSD. Our identification software identified 7 AR2 vibration components, in addition to the turbulent signal. Both vibration and turbulence components are successfully fitted. It confirms the efficiency of the method, and the relevance of AR2 representation for vibrations and turbulence. The identified vibration model is certainly sub-optimal, and the signal could probably be described by a smaller number of AR2 processes, say 5, with the same accuracy. However, although the state space description with seven AR2 vibration modes is heavier than with five, the overall performance of the loop should be the same. In what follows, we try to assess the efficiency of the identification process through the overall AO loop performance. 2 2 Proc. of SPIE Vol F-6

7 Figure 5. Estimated PSD on NAOS experimental Tilt slopes. 4.2 Closedloopspheresimulations Results presented below have been obtained thanks to an end-to-end numerical simulator of the full SAXO system. This simulator has been cross-checked with the analytical code used during SAXO phase A studies. It is based on the following modules: a multi-layer atmosphere simulator, a filtered Shack-Hartmann Wave-Front Sensor (WFS) module, a Tip-Tilt and Deformable Mirror (DM) module, control laws module, imaging module with coronagraphic imaging. For vibration and turbulence identification, only the tip-tilt mirror is considered, and the turbulence is projected onto the tip and tilt modes. The average windspeed is 12.4m.s 1, the seeing is worth 0.85 arcseconds at 0.5 μm. The flux is photons/sub-aperture/frame. The sampling frequency is 1200 Hz. The vibration model is made of three AR2 processes. First, we simulate a 4000 samples time sequence of pseudo-open loop tilt measurements, with no vibration correction. This corresponds to a state space representation without vibration components. The turbulence dynamic model fed to the controler is perfect, i.e. identical to the model used to simulate the data. We denote this simulation case case 0. As expected, turbulence is well compensated, whereas vibration signal is not mitigated at all. From this simulation case, we build pseudo-open loop measurements on which we perform a turbulence and vibration identification. Now, with the same simulation tool, we generate a new 4000 samples time sequence of pseudo-open loop tilt measurements. The open-loop signal is roughly the same, except that the random noise realization is different. We considere the control low case, where both turbulent and vibrations have been identified by the model. The Open-loop and closed-loop tilt PSD are given in fig. 6. In this result, vibration peak wings are less mitigated. We probably overestimated the turbulent commponent, which, following Bode s theorem, is paid in a less accurate vibration rejection. The vibration variance rejection ratio between the two cases is higher than 90%. Moreover, we can see that the wings of the vibration peaks are not totally compensated for. Bode s integral theorem? justifies the fact that even with a perfect model, the optimal control balances turbulence and vibration correction: a more efficient vibration peak wings correction woul be paid in a less accurate turbulence compensation. We have proposed a simple vibration identification scheme, including a preliminary turbulence model identification. This method makes use of pseudo open loop measurements, so it does not need any specific setup or calibration. It performed successfully on synthetic simulated data and on NAOS experimental data. Finally, a first attempt to assess the vibration variance rejection in an LQG control scheme led to a 90% rejection rate. Proc. of SPIE Vol F-7

8 Figure 6. Open and Closed loop tilt DSP However, although the practical cases processed are representative of the expected experimental conditions, an exhaustive performance evaluation, including a large variety of tests, is yet to be done. Although successful and encouraging, the results presented here are only a first test of our method. 5. INTERACTION BETWEEN XAO SYSTEM AND THE REST OF INSTRUMENT Non-Common Path Aberrations are one of the main limitations to reach the high performance required by exoplanet detection. The static or quasi static aberrations are actualy differential aberrations, between the aberrations of the analysis path that are introducted on the imaging path, and the imaging path aberrations thereselves. Their measurement and compensation in the case of a classical AO system has already been proposed in, 4 with the Pseudo-Closed Loop procedure (PCL). This procedure consists in using a focal plane sensor in order to measure the NCPA down to the imaging camera itself, id est comprising the aberrations of the whole optical path. The focal plane sensing is performed by a phase diversity method. It consists in using two focal and extrafocal images in order to estimate the aberrations. The Figure 7 reminds the performance of the PCL in a classical scheme. The aberrations are decomposed on the 74 firsts coefficients. The 33 firsts ones (from defocus to Z36) are well compensated by the PCL procedure. The limit of the procedure relies in two points, first the capacity of Phase Diversity to measure aberrations, mainly limited by noise in the images. Then, the number of actuators of the DM. this second point is the most limitation. As shown on Figure 7, only the 33 firsts modes have been compensated with a 8x8 actuators DM. The measurement of NCPA in a coronagraphic system can not be directly achieved by focal plane technique as the image formation model assumed by phase diversity does not account for coronagraphic mask or Lyot Stop. Moreover, only the aberrations upstream of the coronagraphic mask realy impact on the final detectivity performance. As the SPHERE instrument is based on coronagraphic imaging, we propose here a differential method able to measure NCPA in a coronagraphic system. The method is discribed with the optical scheme of SPHERE on Figure 8. First, the whole calibration has to be done without the coronagraphic mask in order to make phase diversity measurement relevant. Two focal plane positions are designed to be accessible by a fibered source. The first one is in the entrance of the bench. This position denoted as source cal1 allows to calibrate the aberrations of the whole optical path from entrance down to imaging camera. The aberrations calibrated are therefore upstream and downstream cumulated. The second position is precisely at coroangraphic mask. The phase diversity measurement is then done on the downstream aberrations alone. The difference between the two gives the aberrations upstream of the coronagraphic mask, that can be compensated by the XAO system. In the second focal plane position, the diversity phase has to be applied differently from the global measurement, as the DM is not comprised in the focal path. We proposed a slight axial move of the fibered source in order Proc. of SPIE Vol F-8

9 Figure 7. Performance of PCL in a classical AO system. 36 of the 74 firsts Zernike modes have been corrrected down to a level of 3nm. Figure 8. Coronagraph implementation in SPHERE instrument. Two positions are used for source calibration, giving the differential measurement. Proc. of SPIE Vol F-9

10 to provide the expected value of defocus. A validation of the procedure in simulation (indluding error model and noise) has demonstrated a NCPA correction at the level of coronagraphic mask down to a few nanometers RMS. 6. CONCLUSION The AO system (SAXO) for SPHERE, the Planet Finder instrument on the VLT, represents a large step forward both in terms of system components and calibration procedures, nevertheless a complete analysis (with a detailed error budget) has shown that a AO system fulfilling all the requirement mandatory for the direct detection of hot Jupiter like planet is feasible in a reasonable time scale (5 years) with well-known and well tested technologies. After more than four years of preliminary studies, the main components of the AO system have been designed and the integration phase of the whole instrument has begun with an expected first light before the end of REFERENCES [1] Beuzit, J.-L., Feldt, M., Dohlen, K., Mouillet, D., Puget, P., Antici, J., Baudoz, P., Boccaletti, A., Carbillet, M., Charton, J., Claudi, R., Fusco, T., Gratton, R., Henning, T., Hubin, N., Joos, F., Kasper, M., Langlois, M., Moutou, C., Pragt, J., Rabou, P., Saisse, M., Schmid, H. M., Turatto, M., Udry, S., Vakili, F., Waters, R., and Wildi, F., SPHERE: A Planet Finder Instrument for the VLT, in [Proceedings of the conference In the Spirit of Bernard Lyot: The Direct Detection of Planets and Circumstellar Disks in the 21st Century.], Kalas, P., ed., University of California (June 2007). [2] Fusco, T., Nicolle, M., Rousset, G., Michau, V., Beuzit, J.-L., and Mouillet, D., Optimisation of Shack- Hartmann-based wavefront sensor for XAO system, in [Advancements in Adaptive Optics], 5490, Proc. Soc. Photo-Opt. Instrum. Eng. (2004). Date conférence : June 2004, Glasgow, UK. [3] Petit, C., Conan, J.-M., Kulcsár, C., Raynaud, H.-F., and Fusco, T., First laboratory validation of vibration filtering with LQG control law for Adaptive Optics, Optics Express 16(1), (2008). [4] Sauvage, J.-F., Fusco, T., Rousset, G., and Petit, C., Calibration and Pre-Compensation of Non-Common Path Aberrations for extreme Adaptive Optics, J. Opt. Soc. Am. A 24, (Aug. 2007). Proc. of SPIE Vol F-10