von adaptiver optik zur psf rekonstruktion · von adaptiver optik zur psf rekonstruktion ronny...

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


Outline

• E-ELT, MICADO, METIS and AO

• Atmospheric Tomography

• PSF reconstruction

• Application




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





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





E-ELT vs. Stephansdom




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




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)




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




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




An Adaptive Optics System




Turbulence in the Atmosphere




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




Wavefront reconstruction: CuReD

Cumulative Reconstructor with Domain Decomposition (Zhariy,Rosensteiner, Neubauer, R.)

Reconstructions for an 8m telescope, sensor size 84x84




Atmospheric Tomography Systems

Multi Object Multi ConjugateAdaptive Optics Adaptive Optics

(MOAO) (MCAO)(Source: ESO)




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.




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




3-Step-ApproachWFS measurements sx and sy

↓ Wavefront Reconst.incoming wavefront

Atm.Tom.−−−−−−−→

turbulent layers

Projection stepincoming screen DM shape residual




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




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




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



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




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




PSF reconstruction for MCAO




Deconvolution




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.




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




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.



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