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: onur.keskin@isikun.edu.tr

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