R.Ramlau, Von adaptiver Optik zur PSF Rekonstruktion

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1 Von adaptiver Optik zur PSF Rekonstruktion Ronny Ramlau Günter Auzinger, Andreas Obereder, Stefan Raffetseder, Daniela Saxenhuber, Iuliia Shatokhina, Mykhaylo Yudytskiy, Roland Wagner Johann Radon Institute for Computational and Applied Mathematics (RICAM) Österreichische Akademie der Wissenschaften (ÖAW) Linz, Austria Wien, 14. Dezember, 2015

2 Outline E-ELT, MICADO, METIS and AO Atmospheric Tomography PSF reconstruction Application

3 Johann Radon Institute for Computational and Applied Mathematics European Extremely Large Telescope European Southern Observatory (ESO) build and operate astronomical telescopes, e.g, in the Atacama desert, Chile 2008: Austria joins ESO Dec 4, 2014: Final decision to build the E-ELT Very Large Telescope (VLT, 8m) Linz scientific contribution: Mathematical Algorithms and Software Principles of Adaptive Optics Atmospheric Tomography PSF reconstruction

4 Johann Radon Institute for Computational and Applied Mathematics European Extremely Large Telescope European Southern Observatory (ESO) build and operate astronomical telescopes, e.g, in the Atacama desert, Chile 2008: Austria joins ESO Dec 4, 2014: Final decision to build the E-ELT European Extremely Large Telescope (E-ELT, 39m) Linz scientific contribution: Mathematical Algorithms and Software Principles of Adaptive Optics Atmospheric Tomography PSF reconstruction

5 Johann Radon Institute for Computational and Applied Mathematics European Extremely Large Telescope E-ELT vs. Stephansdom Principles of Adaptive Optics Atmospheric Tomography PSF reconstruction

6 MICADO and METIS Multi-AO Imaging Camera for Deep Observations Mid-infrared E-ELT Imager and Spectrometer First light instruments of the E-ELT Certain Adaptive Optics modes High contrast & resolution imaging Source: MICADO Consortium

7 Image formation on a telescope Observed image I T is degraded by the point spread function (psf): I T (x) = I (y) PSF T (x y) dy PSF without atmosphere: PSF 0 = F(χ T ) 2 the larger the telescope, the better approximates PSF T the delta distribution: PSF of the VLT (8m) PSF of the E-ELT (40m)

8 Impact of turbulent atmosphere PSF with atmosphere: PSF A = F(χ T exp(iϕ)) 2, ϕ turbulence PSF with atmosphere PSF with atmosphere, AO corrected ϕ and thus PSF is time (and directional) dependent: N I T = I (t i ) PSF A (t i ) t [0.3ms 2ms], N i=1

9 An Adaptive Optics System (Source: ESO) Adaptive optics: hardware based real-time deblurring Computation of mirror deformation from wavefront measurements: = inverse problem Speed requirements: turbulence of the atmosphere changes rapidly reconstruction must be computed about 500 times per second

10 An Adaptive Optics System

11 Turbulence in the Atmosphere

12

13 Goals of Adaptive Optics Systems (Source: ESO) Guide stars DMs Good quality Classical AO 1 1 in the vicinity of the star Tomography n 1 inside the field of view Multi Conjugate n m uniform in the field of view Adaptive Optics

14 Wavefront reconstruction: CuReD Cumulative Reconstructor with Domain Decomposition (Zhariy, Rosensteiner, Neubauer, R.) Reconstructions for an 8m telescope, sensor size 84x84

15 Atmospheric Tomography Systems Multi Object Adaptive Optics (MOAO) Multi Conjugate Adaptive Optics (MCAO) (Source: ESO)

16 The tomography problem Input: reconstructed incoming wavefronts ϕ αg on Ω D (aperture) from LGS g = 1,..., G and NGS g = G + 1,..., G + N Goal: fast reconstruction of turbulence layers Φ (l) on Ω l, l = 1,..., L ill-posed inverse problem = requires regularization.

17 Standard approach discretize atmosphere into a finite number of layers set up system matrix A that maps sensor measurements to mirror commands A : (dim WFS) 2 (#WFS) (dim DM) 2 (#DMs) E ELT Rec. time 2ms, Drawbacks: ill cond. system 1 high computational cost 2 new system matrix needed for each guide star configuration 3 speedup needs transformation to different bases 4 approach does not use specific properties of the subproblems

18 3-Step-Approach WFS measurements s x and s y turbulent layers Wavefront Reconst. incoming wavefront Atm.Tom. Projection step incoming screen DM shape residual

19 Projection Step: Shape of deformable mirror projection of reconstructed layers into direction of interest dir (application of A dir ) here: zenith (center direction) additional gain control possible: input (for LGS and NGS separately) and/or output gain

20 A Wavelet Approach for Atmospheric Tomography Wavelet-based approach: Concept: Use wavelets to represent the turbulence layers. Why wavelets? approximative properties: less coefficients DWT is O(n) fast decay in frequency domain: efficient turbulence statistics representation Wavelets of choice: Daubechies 3

21 Speed results: MCAO with Wavelet System configuration: Intel(R) Xeon(R) CPU 2.67GHz 12 Cores (dual hexacore) MVM Finite Element Wavelet 3-layer, PCG 4 iter 92 ms 3.0 ms 7 cores used: 6 WFS + 1 core for TTS computation

22 Reasons for the need of PSF reconstruction quality evaluation for the AO system time delay higher order aberrations non common path aberrations coarse grid of the sensor direction dependent PSF in different AO modes wavelength dependent image improvement in post processing

23 PSF reconstruction for MCAO Use tomographic reconstruction of the atmosphere from measured data (intermediate result of gradient-based method) Project through the atmosphere to get PSFs for each desired direction using A dir (as in gradient-based method) pseudo-wavefronts used for calculations Simulate higher order terms not seen by WFS as before. Combine the three parts

24 PSF reconstruction for MCAO

25 Deconvolution

26 Future Work Spiders in the telescope aperture obstruction of aperture by spiders non-connected segments on WFS piston in nullspace advanced algorithms for DM control needed Optimization of reconstruction layer profiles Development of algorithms for positioning the reconstruction layers fitting to a given atmosphere model (compression) and optimization of such profiles.

27 Future Work The Gaia Project From measurements of the light spectra of probe stars (ESA space probe Gaia ), the distribution of the galactic interstellar matter (ISM) has to be reconstructed. Tomography, severely ill-posed

28 Literature [1] M. Zhariy, A. Neubauer, M. Rosensteiner and R. Ramlau: Cumulative Wavefront Reconstruction for the Shack-Hartmann Sensor, Inv. Prob. Imag. 4(5), p (2011) [2] Matthias Rosensteiner: Cumulative Reconstructor: Fast wavefront reconstruction algorithm for Extremely Large Telescopes, J. Opt. Soc. Am. A 28, (2011) [3] R. Ramlau, M. Rosensteiner, A. Obereder, D. Saxenhuber.: Efficient iterative Tip/Tilt Reconstruction for Atmospheric Tomography, Inverse Problems in Science and Engineering, doi: / , [4] T. Helin and M. Yudytskiy, Wavelet methods in multi conjugate adaptive optics, Inverse Problems, 29(8):085003, [5] M. Yudytskiy, T. Helin, R. Ramlau, A finite element - wavelet hybrid algorithm for atmospheric tomography, Journal of the Optical Society of America A Vol. 31 (3): , [6] D. Saxenhuber, R. Ramlau, A Gradient Based Method for Atmospheric Tomography, Austrian In-Kind Contribution - AO, ESO,2013.

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