Development of AO

7/31/2019 Development of AO

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Click to edit Master subtitle style

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

Development of AO

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