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Johann Radon Institute for Computational and Applied Mathematics
Von adaptiver Optik zur PSF Rekonstruktion
Ronny RamlauGunter Auzinger, Andreas Obereder, Stefan Raffetseder, Daniela
Saxenhuber, Iuliia Shatokhina, Mykhaylo Yudytskiy, Roland Wagner
Johann Radon Institute for Computational and Applied Mathematics (RICAM)Osterreichische Akademie der Wissenschaften (OAW)
Linz, Austria
Wien, 14. Dezember, 2015
Principles of Adaptive Optics Atmospheric Tomography PSF reconstruction
www.oeaw.ac.at R.Ramlau, Von adaptiver Optik zur PSF Rekonstruktion
Johann Radon Institute for Computational and Applied Mathematics
Outline
• E-ELT, MICADO, METIS and AO
• Atmospheric Tomography
• PSF reconstruction
• Application
Principles of Adaptive Optics Atmospheric Tomography PSF reconstruction
www.oeaw.ac.at R.Ramlau, Von adaptiver Optik zur PSF Rekonstruktion
Johann Radon Institute for Computational and Applied Mathematics
European Extremely Large Telescope
European SouthernObservatory (ESO)
build and operateastronomical telescopes,e.g, in the Atacamadesert, Chile
2008: Austria joins ESO
Dec 4, 2014: Finaldecision to build theE-ELT
Very Large Telescope(VLT, 8m)
Linz scientific contribution:Mathematical Algorithms and Software
Principles of Adaptive Optics Atmospheric Tomography PSF reconstruction
www.oeaw.ac.at R.Ramlau, Von adaptiver Optik zur PSF Rekonstruktion
Johann Radon Institute for Computational and Applied Mathematics
European Extremely Large Telescope
European SouthernObservatory (ESO)
build and operateastronomical telescopes,e.g, in the Atacamadesert, Chile
2008: Austria joins ESO
Dec 4, 2014: Finaldecision to build theE-ELT
European Extremely LargeTelescope
(E-ELT, 39m)
Linz scientific contribution:Mathematical Algorithms and Software
Principles of Adaptive Optics Atmospheric Tomography PSF reconstruction
www.oeaw.ac.at R.Ramlau, Von adaptiver Optik zur PSF Rekonstruktion
Johann Radon Institute for Computational and Applied Mathematics
European Extremely Large Telescope
E-ELT vs. Stephansdom
Principles of Adaptive Optics Atmospheric Tomography PSF reconstruction
www.oeaw.ac.at R.Ramlau, Von adaptiver Optik zur PSF Rekonstruktion
Johann Radon Institute for Computational and Applied Mathematics
MICADO and METIS
Multi-AO Imaging Camera for Deep ObservationsMid-infrared E-ELT Imager and Spectrometer
Source: MICADO Consortium
• First light instruments of the E-ELT
• Certain Adaptive Optics modes
• High contrast & resolution imaging
Principles of Adaptive Optics Atmospheric Tomography PSF reconstruction
www.oeaw.ac.at R.Ramlau, Von adaptiver Optik zur PSF Rekonstruktion
Johann Radon Institute for Computational and Applied Mathematics
Image formation on a telescope
• Observed image IT is degraded by the point spread function(psf):
IT (x) =
∫I (y) · PSFT (x − y) dy
• PSF without atmosphere: PSF0 = |F(χT
)|2• the larger the telescope, the better approximates PSFT the deltadistribution:
PSF of the VLT (8m) PSF of the E-ELT (40m)
Principles of Adaptive Optics Atmospheric Tomography PSF reconstruction
www.oeaw.ac.at R.Ramlau, Von adaptiver Optik zur PSF Rekonstruktion
Johann Radon Institute for Computational and Applied Mathematics
Impact of turbulent atmosphere
PSF with atmosphere: PSFA = |F(χT· exp(iϕ))|2, ϕ ∼ turbulence
PSF with atmospherePSF with atmosphere,
AO corrected
• ϕ and thus PSF is time (and directional) dependent:
IT =N∑
i=1
I (ti ) ∗ PSFA(ti ) ∆t ∈ [0.3ms − 2ms],N ≈ 60.000
Principles of Adaptive Optics Atmospheric Tomography PSF reconstruction
www.oeaw.ac.at R.Ramlau, Von adaptiver Optik zur PSF Rekonstruktion
Johann Radon Institute for Computational and Applied Mathematics
An Adaptive Optics System
(Source: ESO)
Adaptive optics: hardware based real-time deblurringComputation of mirror deformation from wavefrontmeasurements:
=⇒ inverse problemSpeed requirements:
turbulence of the atmosphere changes rapidlyreconstruction must be computed about 500 times per second
Principles of Adaptive Optics Atmospheric Tomography PSF reconstruction
www.oeaw.ac.at R.Ramlau, Von adaptiver Optik zur PSF Rekonstruktion
Johann Radon Institute for Computational and Applied Mathematics
An Adaptive Optics System
Principles of Adaptive Optics Atmospheric Tomography PSF reconstruction
www.oeaw.ac.at R.Ramlau, Von adaptiver Optik zur PSF Rekonstruktion
Johann Radon Institute for Computational and Applied Mathematics
Turbulence in the Atmosphere
Principles of Adaptive Optics Atmospheric Tomography PSF reconstruction
www.oeaw.ac.at R.Ramlau, Von adaptiver Optik zur PSF Rekonstruktion
Johann Radon Institute for Computational and Applied Mathematics
Goals of Adaptive Optics Systems
(Source: ESO)
Guide stars DMs Good quality
Classical AO 1 1 in the vicinity of the starTomography n 1 inside the field of view
Multi Conjugate n m uniform in the field of viewAdaptive Optics
Principles of Adaptive Optics Atmospheric Tomography PSF reconstruction
www.oeaw.ac.at R.Ramlau, Von adaptiver Optik zur PSF Rekonstruktion
Johann Radon Institute for Computational and Applied Mathematics
Wavefront reconstruction: CuReD
Cumulative Reconstructor with Domain Decomposition (Zhariy,Rosensteiner, Neubauer, R.)
Reconstructions for an 8m telescope, sensor size 84x84
Principles of Adaptive Optics Atmospheric Tomography PSF reconstruction
www.oeaw.ac.at R.Ramlau, Von adaptiver Optik zur PSF Rekonstruktion
Johann Radon Institute for Computational and Applied Mathematics
Atmospheric Tomography Systems
Multi Object Multi ConjugateAdaptive Optics Adaptive Optics
(MOAO) (MCAO)(Source: ESO)
Principles of Adaptive Optics Atmospheric Tomography PSF reconstruction
www.oeaw.ac.at R.Ramlau, Von adaptiver Optik zur PSF Rekonstruktion
Johann Radon Institute for Computational and Applied Mathematics
The tomography problem
Input:
• reconstructed incomingwavefronts ϕαg on ΩD
(aperture) from LGSg = 1, . . . ,G and NGSg = G + 1, . . . ,G + N
Goal:
• fast reconstruction ofturbulence layers Φ(l)
on Ωl , l = 1, . . . , L
ill-posed inverse problem=⇒ requires regularization.
Principles of Adaptive Optics Atmospheric Tomography PSF reconstruction
www.oeaw.ac.at R.Ramlau, Von adaptiver Optik zur PSF Rekonstruktion
Johann Radon Institute for Computational and Applied Mathematics
Standard approach
• discretize atmosphere into a finite number of layers• set up system matrix A that maps sensor measurements tomirror commands
A : (dim WFS)2 · (#WFS)× (dim DM)2 · (#DMs)
E − ELT ∼ 60.480× 9.296
Rec . time ∼ 2ms,
ill cond . system
• Drawbacks:
1 high computational cost2 new system matrix needed for each guide star configuration3 speedup needs transformation to different bases4 approach does not use specific properties of the subproblems
Principles of Adaptive Optics Atmospheric Tomography PSF reconstruction
www.oeaw.ac.at R.Ramlau, Von adaptiver Optik zur PSF Rekonstruktion
Johann Radon Institute for Computational and Applied Mathematics
3-Step-ApproachWFS measurements sx and sy
↓ Wavefront Reconst.incoming wavefront
Atm.Tom.−−−−−−−→
turbulent layers
Projection stepincoming screen DM shape residual
Principles of Adaptive Optics Atmospheric Tomography PSF reconstruction
www.oeaw.ac.at R.Ramlau, Von adaptiver Optik zur PSF Rekonstruktion
Johann Radon Institute for Computational and Applied Mathematics
Projection Step: Shape of deformable mirror
• projection ofreconstructed layers intodirection of interest dir(application of Adir )
• here: zenith(center direction)
• additional gain controlpossible: input (for LGSand NGS separately)and/or output gain
Principles of Adaptive Optics Atmospheric Tomography PSF reconstruction
www.oeaw.ac.at R.Ramlau, Von adaptiver Optik zur PSF Rekonstruktion
Johann Radon Institute for Computational and Applied Mathematics
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
Principles of Adaptive Optics Atmospheric Tomography PSF reconstruction
www.oeaw.ac.at R.Ramlau, Von adaptiver Optik zur PSF Rekonstruktion
Johann Radon Institute for Computational and Applied Mathematics
Speed results: MCAO with Wavelet
System configuration:
• Intel(R) Xeon(R) CPU X5650 @ 2.67GHz• 12 Cores (dual hexacore)
MVM Finite Element–Wavelet3-layer, PCG 4 iter
92 ms 3.0 ms
7 cores used: 6 WFS + 1 core for TTS computationPrinciples of Adaptive Optics Atmospheric Tomography PSF reconstruction
www.oeaw.ac.at R.Ramlau, Von adaptiver Optik zur PSF Rekonstruktion
Johann Radon Institute for Computational and Applied Mathematics
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
Principles of Adaptive Optics Atmospheric Tomography PSF reconstruction
www.oeaw.ac.at R.Ramlau, Von adaptiver Optik zur PSF Rekonstruktion
Johann Radon Institute for Computational and Applied Mathematics
PSF reconstruction for MCAO
• Use tomographic reconstruction of the atmosphere frommeasured data (intermediate result of gradient-based method)
• Project through the atmosphere to get PSFs for each desireddirection using Adir (as in gradient-based method)→ pseudo-wavefronts used for calculations
• Simulate higher order terms not seen by WFS as before.
• Combine the three parts
Principles of Adaptive Optics Atmospheric Tomography PSF reconstruction
www.oeaw.ac.at R.Ramlau, Von adaptiver Optik zur PSF Rekonstruktion
Johann Radon Institute for Computational and Applied Mathematics
PSF reconstruction for MCAO
Principles of Adaptive Optics Atmospheric Tomography PSF reconstruction
www.oeaw.ac.at R.Ramlau, Von adaptiver Optik zur PSF Rekonstruktion
Johann Radon Institute for Computational and Applied Mathematics
Deconvolution
Principles of Adaptive Optics Atmospheric Tomography PSF reconstruction
www.oeaw.ac.at R.Ramlau, Von adaptiver Optik zur PSF Rekonstruktion
Johann Radon Institute for Computational and Applied Mathematics
Future Work
Spiders in the telescope aperture
obstruction of aperture by ”spiders”
non-connected segments on WFS →piston in nullspace
advanced algorithms for DM controlneeded
Optimization of reconstruction layer profiles
Development of algorithms for positioning the reconstruction layersfitting to a given atmosphere model (compression) andoptimization of such profiles.
Principles of Adaptive Optics Atmospheric Tomography PSF reconstruction
www.oeaw.ac.at R.Ramlau, Von adaptiver Optik zur PSF Rekonstruktion
Johann Radon Institute for Computational and Applied Mathematics
Future Work
The Gaia Project
From measurements of the light spectra ofprobe stars (ESA space probe ”Gaia”), thedistribution of the galactic interstellar matter(ISM) has to be reconstructed.→ Tomography, severely ill-posed
Principles of Adaptive Optics Atmospheric Tomography PSF reconstruction
www.oeaw.ac.at R.Ramlau, Von adaptiver Optik zur PSF Rekonstruktion
Johann Radon Institute for Computational and Applied Mathematics
Literature
[1] M. Zhariy, A. Neubauer, M. Rosensteiner and R. Ramlau: Cumulative WavefrontReconstruction for the Shack-Hartmann Sensor, Inv. Prob. Imag. 4(5), p. 893-913(2011)
[2] Matthias Rosensteiner: Cumulative Reconstructor: Fast wavefront reconstructionalgorithm for Extremely Large Telescopes, J. Opt. Soc. Am. A 28, 2132-2138 (2011)
[3] R. Ramlau, M. Rosensteiner, A. Obereder, D. Saxenhuber.: Efficient iterativeTip/Tilt Reconstruction for Atmospheric Tomography, Inverse Problems in Scienceand Engineering, doi: 10.1080/17415977.2013.873534, 2014.
[4] T. Helin and M. Yudytskiy, Wavelet methods in multi–conjugate adaptive optics,Inverse Problems, 29(8):085003, 2013.
[5] M. Yudytskiy, T. Helin, R. Ramlau, A finite element - wavelet hybrid algorithm foratmospheric tomography, Journal of the Optical Society of America A Vol. 31 (3):550-560, 2014.
[6] D. Saxenhuber, R. Ramlau, A Gradient–Based Method for AtmosphericTomography, Austrian In-Kind Contribution - AO, ESO,2013.
Principles of Adaptive Optics Atmospheric Tomography PSF reconstruction
www.oeaw.ac.at R.Ramlau, Von adaptiver Optik zur PSF Rekonstruktion
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