Adaptive Optics

Adaptive Optics

Joel  Johansson  

November  8th,  2010  

(1/28)  

Outline

•  Background

– Limitations of telescopes – Atmospheric blurring

•  Adaptive Optics

– Deformable mirrors – Wavefront sensors – Guide stars

•  Before&After

(2/28)  

Resolving power of a telescope

•  Light gathering power

•  Angular resolution (ideally…)

(Rayleigh’s criterion – ”diffraction limit”)

€

θ = 1.22(λ ^/D)€

∝ D²

Airy disc – best focussed spot through circular aperture

(3/28)  

The atmosphere

Turbulence

•  occurs mainly in the troposphere

•  is highly variable (daily/seasonally)

•  occurs in defined layers (ground, jet-streams)

Wind  shear  

Kelvin-­‐Helmholz  instability   ConvecCon  

(4/28)  

Atmospheric turbulence

e atmospheric coherence radius:

”Fried parameter” - largest size on telescope over which phase of incoming wave is correlated (σ² = 1)

€

r₀ ∝ C_N² dh

0

∞

⎛

∫

⎝ ⎜ ⎞

⎠ ⎟

−3 / 5

∝ λ^{6 / 5}

Refractive index structure constant (Random turbulence - Kolmogorov statistics)

(5/28)  

Atmospheric blurring

Without atmosphere (or with adaptive optics) at the diffraction limit

Short exposure image (many speckles at

diffraction limit of the telescope)

Long exposure image (”seeing disc” )

€

θ ≈ λ^{/ D}

D = 1 m D = 2 m D = 8 m

€

θ ≈ λ / r₀ ≈ 1"

(6/28)  

SimulaCons:  Nick  Kaiser  

Turbulence summary

Impact of turbulence on telescope depends on wavelength of interest!

•  Coherence length:

r₀≈10 cm @ V-band (500 nm)

r₀≈70 cm @ K-band (2.2 microns)

•  Atmospheric time constant:

(Averaged wind speed v≈15m/s) τ₀≈2.5ms @ V-band (500 nm) τ₀≈15ms @ K (2.2 microns)

€

r₀ ∝ λ^{6 / 5}

€

τ₀ ∝ r₀ v

⎛

⎝ ⎜ ⎞

⎠ ⎟

(7/28)  

Deformable Mirrors

•  Number of subapertures: (D/r₀)²

r₀ = 12 cm / 70 cm (4000 / 130 actuators)

•  Temporal response: faster than coherence time (τ₀ = few millisconds)

•  Dynamic range (”stroke”): several µm

(8/28)  

Deformable Mirror types

Segmented / Continous face-sheet

•  Change shape of reflecting surface

•  Actuators:

–  Piezoelectric

–  voice coil (electro-magnetic)

Bimorph mirrors

•  Changes curvature of mirror

•  2 layers of Piezoelectric ceramics

(10/28)  

Segmented mirrors

William Herschel Telescope, La Palma

•  76 element segmented mirror

•  Each square mirror is mounted on 3 piezos (piston, tip & tilt)

(11/28)  

Continous face-sheet DM’s

Number  of  actuators   100  -­‐  1500     Inter-­‐actuator  spacing   2-­‐10  mm       Voltage         few  hundred  V     Stroke         few  microns     Resonant  frequency   few  kHz    

Cost           high    

Keck @ Hawaii. 146mm diameter, 349 actuators, 7 mm spacing

(12/28)  

Bimorph Mirrors

Number  of  zones     13  -­‐  85    

DM  size         30-­‐200  mm     Electrode  geometry   radial/circular   Voltage         few  hundred  V     Resonant  frequency   more  than  500  Hz     Cost           moderate    

Gemini North Telescope @ Hawaii

•  85 element mirror

(13/28)  

Deformable Secondary Mirrors

Telescope     Diameter     #  Actuators   MMT     64cm       336  

LBT         91cm       672   VLT         112cm       1170     (E-­‐ELT     250cm     5000)  

Including the DM as part of the telescopes reduces the background added by the AO system.

MMT,  Arizona  

VLT,  Chile  

(14/28)  

Wave Front Sensors

•  Measure slopes of wavefront (1st derivative)

•  Spot displacement proportional to wavefront tilt

Schack-Hartmann

Distorted  wavefront   Lenslet  array  

CCD  

(15/28)  

 Wavefront Sensors

Curvature sensors

•  Measure curvatue of wavefront (2nd derivative)

•  Use oscillating membrane mirror (2

kHz!) to vibrate rapidly between I+ and I- extrafocal positions

• Measure intensity in each subaperture with an “avalanche photodiode” (= ”1 pixel”)

Avalanche Phododiode (APD)

•  ”Semiconductor photomultiplier”

•  Lower QE than CCD, but faster read-out and no noise

(16/28)  

PSF of an AO star

Intensity"

x"

Strehl ratio:

€

R = I_obs(0) I_Diff.lim.(0)

(17/28)  

Laser Guide Stars

William  Herschel  Telescope,  La  Palma   ESO  Very  Large  Telescope,  Chile  

Rayleigh  Laser  Beacon   Sodium  Laser  Beacon  

Laser Guide Stars (LGS)

•  Natural guide stars: not enough bright stars in FOV

•  Rayleigh guide stars: rayleigh back scattering by air molecules @ h≈10km

•  Sodium guide stars: excite atoms in ”sodium layer @ h≈100km

(19/28)  

Some issues…

AO  performance  decreases   quickly  off-­‐axis  

VariaCons  in  sodium  layer  

ElongaCon  of  spot  

Time  (min)  

Height  (km)  

Turbulence above (Rayleigh) guide star?

”Cone effect”

(20/28)  

MultiConjugate Adaptive Optics

Strehl maps

1  star  &  1  DM  

3  stars  &  2  DMs  

(21/28)  

Before and after…

(22/28)  

Black Hole @ Galactic Center

(23/28)  

Space- or ground based telescopes?

HST    (400s)                            ESO  VLT  NAOS/NACO  (300s)    

(24/28)  

Solar physics…

Dunn  Solar  Telescope   Swedish  Solar  Telescope  (with  AO)  

(without  AO)  

(with  AO)  

(25/28)  

Some neighbours…

Neptune  

(26/28)  

Exoplanets

The  HR  8799  system  as  seen  by  the  Keck  Telescope  in  2008.  The  central  messy  region  is   where  the  star  has  been  masked  out.  

(27/28)  

Reference material

•  Lecture notes, Chris Lidman

(http://www.aao.gov.au/local/www/clidman/AO/)

•  Lecture notes, Clair Max

(http://www.ucolick.org/~max/289C/)

•  CTIO tutorial

(http://www.ctio.noao.edu/~atokovin/tutorial/intro.html)

•  CfAO, Summer School on Adaptive Optics

(http://www.cfao.ucolick.org/aosummer/2009/presentations)

•  ”Diffraction-Limited Imaging with Large and Moderate Telescopes”, S.K. Saha

(28/28)  

Extra: Other techniques

Lucky imaging / Shift-and-add algorithms

Take many short exposures - select best quality images – shift and stack

HST,  2.4  m   Palomar,  5.1  m,  0.65’’   Palomar  +  lucky  imaging  

Speckle interferometry

Analyse speckle pattern using Fourier analysis