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Adaptive Optics for DAG
Telescope Onur Keskin
02 February 2015
2/30 02 Feb 2015
Ground Based Telescopes
• Advantages: Low cost to built and operate.
• Disadvantages: Low resolution (because of turbulence).
Hubble Space Telescope
• Advantages: High resolution.
• Disadvantages: Extremely high cost to built, launch and operate, small
aperture size.
Ground Based Telescopes with AO Systems
• Advantages: High resolution, larger aperture, moderate cost.
• Disadvantages: Partial correction & LGS requirement for 100% sky coverage
a) Conventional Telescope b) Hubble Space Telescope c) Telescope with AO
Titan - CFAO Image Gallery (Keck & Hubble Telescopes)
Adaptive Optics Systems Introduction
3/30 02 Feb 2015
Optical Turbulence
• How fast is the optical turbulence?
Turbulent layer wind speed is ≈ 10-20 m/s
It takes about 0.01 s for the turbulent layer to move a distance r0
Optical turbulence time scale is ~ 1-10 ms, and this is the typical rate
at which AO system must operate
FWHM = λ/D(1+(D/r0)2)1/2
PSF Width:
No turbulence – diffraction limited
telescope D=4m, at 500 nm, FWHM = 0.026"
With turbulence
typical value r0=0.1 m at 500 nm
FWHM=1.04" – 40 times larger
4/30 02 Feb 2015
Adaptive Optics: Basic Concept
Adaptive Optics refers to optical systems which adapt to compensate for
optical effects introduced by the medium and its image
Curtesy of GEMİNİ
5/30 02 Feb 2015
AO System Dimensioning AO System Design Depends on the Science Program:
• for extreme correction one needs brights stars,
• for wide field correction one needs several stars with limited
correction
• Multi-parameter optimization:
WFS lenslet pitch
WFS integration time
• WFS lenset pitch selection (projected in telescope pupil)
Spatial frequency correction cut-off on the wavefront is higher in
case of using a lower pitch...
Tradeoff: lower the photon counts, noise goes up
An optimal lenslet pitch calculation exists:
σ2φ,res = 0.274 (d/r0) 5/3
6/30 02 Feb 2015
AO System Performance Improvement
7/30 02 Feb 2015
Image Formation through Adaptive Optics
Image plane Object plane
The relation between the object and the image
( )O ( )I
( ) ( )
PSF can be defined as the response of an imaging system to a point source of light
( ) ( ) ( )I O PSF
In Fourier domain
In Spatial domain
( ) ( ) . ( )I f O f OTF f
8/30 02 Feb 2015
Importance of PSF Reconstruction in AO
• PSF reconstruction is used in calibrating image analysis techniques for
astrometry, and in the deconvolution of images to enhance their contrast.
• Why do we need PSF reconstruction?
The optical effects of atmospheric turbulence.
The partial correction by the AO system.
Anisoplanatism.
9/30 02 Feb 2015
φAni=φturbulence(θ)- φDM
Target
Object
Atmospheric
turbulence (0)
φP
φO
φcorrected
Guide
Star
φPε
φO
φuncorrected
Atmospheric
turbulence (θ)
φturbulence(θ)
AO
System
φturbulence(0)
On and Off-Axis PSF Reconstruction from
DAG AO Systems
( ) ( ) (0) (0) (0)tot turbulence turbulence P O
10/30 02 Feb 2015
a) The target object, or objects without AO correction. b) The AO system running in closed-loop. c) The improvement by the PSF deconvolution
(CFHT telescope image Gallery)
PSF Reconstruction from Performance from
DAG AO Systems
11/30 02 Feb 2015
Conclusions
AO system development at Işık University
• DPT application for building of an AO laboratory has been
finalized to gain local experience (via a scaled down experiment
for instance)
• Apply this knowledge to the DAG AO systems
• Classical AO
• Ground Layer AO (GLAO)
• Testing new & sophisticated control algorithms for different AO
schemes to be implemented
• PSF reconstruction tools for improving performance
and deliver turn key AO systems for DAG
12/30 02 Feb 2015
• Assist. Prof. Dr. Onur Keskin
• Isik University
• Department of Mechanical Engineering
• Kumbaba Mevkii, 34980 Sile, Istanbul, Turkey
• Phone: +90 (216) 528 7142
• Fax: +90 (216) 712 1472
• E-mail: [email protected]
13/30 02 Feb 2015
Estimation of the Orthogonal Phase (φO)
The orthogonal component is estimated from Kolmogorov’s atmospheric turbulence theory:
• The AoA experiment is used to determine the Fried coherence length (r0); • Phase screens are generated by Monte-Carlo simulation from the extracted r0; • The parallel component of the phase (DM phase) is removed from the generated phase screens; and
• The structure function of the orthogonal component of the phase is computed.
The determination of the OTF also leads to the determination of the estimated
long-exposure PSF via a single discrete Fourier transform
14/30 02 Feb 2015
Estimation of the Parallel Phase (φPε)
1 1 1
( , ) ( ) ( ) ( ) ( ) ( ) ( )TT mirror woofer tweeter
N N N
P i i tt mirror i i woofer i i tweeter
i i i
r t t M r t M r t M r
total tt mirror woofer tweeteri i i iM M M M and Ntotal = NTTmirror + Nwoofer + Ntweeter
2( , ) ( , ) ( , )
P P PD r r t r t
1 1
( , ) ( ) ( ) ( ) ( )total total
P total total total total
N N
i j i i j j
i j
D r M r M r M r M r
1 1
( ) ( )total total
P
N N
i j ij
i j
D U
1
21
2Re ( ) *( ) ( ) ( )( )
( ( ) )
i j i j
ij
F al F M M P F P F M P F M PU
F F P
15/30 02 Feb 2015
( , ) ( , ) . ( , ) . ( , )Total Anisoplanatic AO TELOTF OTF OTF OTF
1
( , ) exp ( )2 AniAnisoplanaticOTF D
1 2 1 2 1 2
1 1 2 2 1 2 2 1
( , ) ( , ) ( , )
2 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
tot Ani AO
Ani AO Ani AO Ani AO Ani AO
D r r D r r D r r
r r r r r r r r
2 5/ 3
1 2
5/ 3 5/ 3 5/ 35/ 32
1 2 1 2 1 2
0
( , ) 2
2 2 2( ) 2 2 ( ) 2 ( ) 2 ( )
Ani
N
D r r k D
C z dz r r r r r rD D D
2( )
zz
D
Off-Axis PSF Reconstruction