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7/12/12
Narsireddy AnuguRoll No: 97/AIM/101006
Under the Guidance ofDr.J.P.Lancelot & Prof.
A.K.Saxena
Development of Adaptive Optics system
at laboratory
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Contents
Introduction
Simulation of Kolmogorov turbulence numerically andexperimentally its characterization
Simulation of SHWFS
Studies of SHWFS in the presence of turbulence
Using turbulent simulator closed loop correction at lab
Analysis of the results
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Kolmogrov Theory of Turbulence in aNutshell
Big whorls have littlewhorls,
Which feed on their
velocity;Little whorls have smaller
Outer scale L0
ground
Inner scalel
hconvection
solar
h
Wind shear
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Kolmogrov Theory of Turbulence : Eddy Cascade
Assume energy is added to system at largest scales -outer scale L0
Then energy cascades from larger to smaller scales(turbulent eddies break down into smaller and smaller
structures). Size scales where this takes place: Inertial range.
Finally, eddy size becomes so small that it is subject todissipation from viscosity. Inner scale l0
L0 ranges from 10s to 100s of meters; l0 is a few mm
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Wave Propagation in Turbulentmedium
For monochromatic planewaves arriving from a distant
point source with wave-vectork, we have
The Turbulent layer1. Scatters light2. Perturbs Phase of the
wave3. Causes fractional
Amplitude changewith effect:
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Atmospheric terms
Atmospheric
coherence
radius : (ro )
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Images with Seeing
Image = Object Point Spread Function
I = O PSF( ) ( ) ( )I u O u P u v dv=
.effective Telescope Atm osphereO TF O TF O TF =
( ) ( ). ( )I f O f P f=
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Overcoming atmospheric seeing
Speckle imaging : which allows bright objects to be observed
with very high resolution.
Working outside the Atmosphere : Hubble Space Telescopeand thus not have any seeing problems
Adaptive optics : Systems that partially solve the seeing
problem. Observations are usually limited to a small region ofthe sky surrounding relatively bright stars.
Lucky Imaging :The technique relies on the fact that every sooften the effects of the atmosphere will be negligible, and henceby recording large numbers of images in real-time, a 'lucky'
excellent image can be picked out. This technique canoutperform adaptive optics in many cases and is evenaccessible to amateurs. It does, however, require very muchlonger observation times than adaptive optics for imaging fainttargets, and is limited in its maximum resolution.
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Generation of Kolmogorov Phasescreen
Motivation : To study astronomical objects propagation throughatmosphere and analyze AO algorithms and system.
Atmosphere can be simulated by different methods numerically
Van Karman Power spectral density
Where,
phase screen related to spectrum
Discrete Fourier transform of the square root of the PSD * random
numbers.
2 25 / 3
0 2 2 11/ 6
0
exp( / )
( ) 0.023( / )( )
i
N D r
=+
0
0
2
L
=
05 .9 2 /
il =
( ) ( ) ikrNf r e dk
=
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Continued..
FourierTransform
method
-
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Analysis and discussion of simulationresults :
Phase structure function:
2 (5/3)
( )
0
( ( 1) ( 1 ) 6.88( )r
rD r r r
r =< +>=
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Study of point source in turbulence
AtD/r0 = 1 & 5
D/r0=10 & 15
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Corresponding PSF
AtD/r0 = 1& 10
D/r0=5& 15
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Different turbulentstrengths
This OTF iscalculatedfor long
exposureimages.
For this 100
shortexposures(1millisecond) imagesadded u
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Adaptive Optics system
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wave-front sensor
Requirements of WFS: WFS must work on white light incoherent sources.
WFS must use the photons very efficiently.
The WFS must be linear over the full range of
atmospheric distortions.
WFS must be fast.
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Continued
Shack HartmannShearinginterferometry
Pyramid wavefront
sensor
Curvature wavefront
sensor
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Shack Hartmann sensor simulated results with WCOGat D/ro=5
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Centroid algorithms
COG
WCOG Weighting function chosen is Gaussian
2 2 2 2
,
,
,
2
,
2
,
( , ) (1/2 ) ( (( ) ( ) )/2 )
( , ) ( , )
( , ) ( , )
( , ) ( , )
( , ) ( , )
( , ) ( , )
/
/
(1/ ) * * * *
c c
x y
x y
x y
x y
x y
W x y exp x x y y
Sw I x y wx y
Sx xI x y W x y
Sy yI x y W x y
Sxx x I x y W x y
Syy y I x y W x y
Xc Sx Sw
Yc Sy Sw
Sw Sxx Sw Sx Sx Syy Sw Sy Sy
= +
=
=
=
=
=
=
=
= +
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Spot realization
Airydisk
Sinc2function
2
10
2 ( )( )
J uP u u
=
Gaussian
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Different noise simulation
Photon noise , turbulent noise
(D/ro=8), read out noise & total
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Centroid calculation with WCOG atD/r0 =3 and 5
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Comparison of Centroid algorithms
Atdifferent S/Nratio
At differentturbulentstrengths
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Continued.
At different subaperturesampling of spot
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The spot pattern at the focal plane of a S-H sensor
Gaussian spot array (10 x 10) Airy disk array(10 x 10)
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Random noise affected spot array
Gaussian spotarray (10 x 10)
Airy diskarray (10 x 10)
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Array pattern at different turbulence strengthsD/ro=1 D/ro=5
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Phase reconstruction
WCOG algorithm has been using for the centroid calculation
phase reconstruction : Model Approach ( ZernikePolynomial )
Zernike polynomials are orthogonal polynomials defined
over unit radius of circle.
Expression of Wavefront: and
The derivatives of the Zernike polynomials can beexpressed as a linear combination of Zernike polynomial
(Noll, 1976)
In Matrix notation
= ^
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Shack Hartmann sensor simulated results with WCOGat D/ro=15
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Low costturbulence
simulator in lab Fabrication
of phasescreens by
sprayingmultiplelayers ofordinaryhair sprayonto a glasssubstrate
Hair s ra
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Experimental setup used for phase screencharacterization
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Phase screens obtained at lab and numericalsimulation
AtD/r0 = 9
AtD/r0 =3
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Characterization of phase screens
Characterization has been done by measuring ro value withtwo methods
1.The model representation ( Zernike approach)
2.OTF method
2 5/6
0
*( ) ( )
*( )
i ii
i i
W r aZ r
Da N
r
=
< >=
5/3
0
( ) exp( 3.44( ) )OTFr =
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Summary of the results
Modal
approach
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Experimental setup for SHWFS
Distortedwavefront
At D/r0=9
Reference
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Comparison of Phase variance with theoretic model
2 5/6
0
*( )i i
Da N
r< > =
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Schematic and experimental layout for closed loopAO
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Lenslet Spots
Reference
At turbulentstrength(D/r0=20)
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Wavefront constructed
NoTurbulence
Turbulence
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Zernike Coefficients
Noturbulence
Turbulence
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When closed loop Adaptive optics system is on
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Closed loop AO Demonstration
AO off (D/r0=20)
AO on
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Summery
Project was carried out in three phases
Study of Atmospheric turbulence experimentally andnumerically
Study on Shack-Hartman sensor
Closed loop correction with AO kit in the presence ofturbulence simulator
Numerical simulation has been done with Matlab-2010awith AMD Athlon 2.7GHz computer . Airy disk spots are
used for Shack Hartmann wavefront sensor study. Centroidcalculation with IWCoG. For phase reconstruction 21 Zernikemodes has been used.
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THANK YOU
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