Transcript Adaptive Optics Nicholas Devaney GTC project, Instituto de

Adaptive Optics
Nicholas Devaney
GTC project, Instituto de Astrofisica de Canarias
1. Principles
2. Multi-conjugate
3. Performance & challenges
Anisoplanatic Error
Guide star
Science object
 iso  0.3
r0
h
Turbulent
layer
Telescope pupil
|
Anisoplanatic Error
• Anisoplanatism limits the AO field of view
– =0.5 m, 0 ~ 2 arcseconds
– 0  r0   6/5
– =2.2 m, 0 ~ 12 arcseconds
• Inside the Field of View the PSF is not constant
• If turbulence were concentrated in a single layer
then a deformable mirror conjugate to that layer
would give isoplanatic correction.
– The DM should be over-sized
– A single reference source requires wavefront
extrapolation
Single-conjugate correction
Deformable mirror
Telescope pupil
DM
Ref: Véran, JOSA A, 17, p1325 (2000)
Guide star footprint
on wavefront sensor
Optimized Single Conjugate Correction
• Real turbulence is distributed in altitude; average
profile of Cn2 is smooth, but during a given
observation has layerd structure.
• Can find an optimal conjugate altitude for the
deformable mirror
• This approach is employed in the Altair system on
Gemini North
Multi-Conjugate AO
• MCAO is an extension of the idea of conjugating
to turbulence to N deformable mirrors. In
proposed systems N=2-3.
Layer 1
Layer 2
Telescope
DM1
DM2
Controller
WFS
Multi-Conjugate AO
– To what altitudes should the deformable mirrors
be made conjugate ?
– What wavefront sensing approach can be used
to control the deformable mirrors ?
– What are the limitations ?
Optimal altitudes for deformable mirrors
• Tokovinin (JOSA A17,1819) has shown that for
very large apertures
 
  
M
2



5
3
• where M is a generalisation of the isoplanatic
angle when M deformable mirrors are employed.
• M depends on the altitudes of the M mirrors and
the turbulence distribution in altitude
• This assumes perfect measurement of all the
turbulence in the volume defined by the field of
view
M for 2 deformable mirrors
La Palma turbulence profiles
•Optimal altitude DM1~0, DM2 ~13km
•Optimal altitudes similar for all profiles
•Smooth decrease in isoplanatic angle as
move away from optimal
Wavefront sensing for MCAO
• We would like to perform ‘tomography’ of the
turbulent volume defined by the telescope pupil
and the field of view. It is not necessary to
reconstruct the turbulent layers; ‘only’ need to
determine the commands for the deformable
mirrors.
• Tomography involves taking images with source
and detector placed in different orientations.
MCAO will employ multiple guide stars for
simultaneous wavefront sensing.
• There are two approaches:
– Star-oriented , sometimes referred to as ‘classical’ (!)
– Layer-oriented
Star Oriented MCAO
Reference Stars
• Single Star WFS
architecture
• Global Reconstruction
• n GS, n WFS, m DM,
1 RTC
High Altitude Layer
Ground Layer
Telescope
DM2
The correction applied at each DM is
computed using all the input data.
The correction across the FoV can be
optimised for specified directions.
DM1
WFC
WFSs
Layer Oriented MCAO
• Layer Oriented WFS
architecture
• Local Reconstruction
• x GS, n WFS, n DM,
n RTC
Reference Stars
High Altitude Layer
Ground Layer
Telescope
The wavefront is reconstructed at each
altitude independently.
Each WFS is optically coupled to all the
others.
GS light is co-added for a better SNR.
DM2
DM1
WFC1
WFS1
WFS2
WFC2
MCAO wavefront sensing
• Star-oriented systems plan to use multiple ShackHartmann sensors
• Layer-oriented systems can use any pupil-plane
wavefront sensor; proposed to use pyramid sensor
• Layer oriented can adapt spatial and temporal
sampling at each layer independently
• As in single-conjugate AO the wavefront
reconstruction can be zonal or modal. Most
theoretical work based on modal approach.
Modal
Tomography
Describe turbulence on each layer
as a Zernike expansion, a(l)
(Unit circle = metapupil)
looking towards GS in direction 
at each layer intercept a circle of
diameter D. Determine phase as
Zernike expansion b(l)
l 

l
b ( , hl )  P( ; hl )a
P is a projection matrix
(This is similar to sub-aperture
testing of aspheres)
Modal Tomography
• The phase at r on the pupil for wavefronts coming
from direction = sum of phase from L layers
along that direction (near-field approximation) ;



 (r )    r   xh 
L
(l )


(l )
l
l 1

 2r 
  bn ( ) Z n  
D
n2

N
where

L

bn ( )   b ( , hl )
l 1
(l )
n
for G guide stars (g=1...G)
L
L
 


 (l )
(l )
bg ( g )   bg ( g , hl )   P( g , hl )a
l 1
l 1
Modal Tomography
• So there is a linear relation between the phase
measured at the pupil for G guide stars and the
phase on L metapupils
• This is inverted to give a
• In practice measure slopes (or curvatures), but
these are also linearly related to the pupil phase.
Wavefront sensing for MCAO
• Whichever approach is employed, there are (of
course) some limitations.
• Aliasing:
GS1
H
GS2
This looks
the same to both GS

This also
looks the same to
both GS
Wavefront sensing for MCAO
• Aliasing occurs between layers separated by H for
frequencies higher than fc
1
fc 
H
• trade-off between field of view and degree of
correction (unless increase the number of guide
stars)
Gaps in the ‘meta-pupil’
‘Meta-pupil’
Guide star beam
footprints at altitude H

Telescope
Pupil for
field
position 
MCAO Numerical Simulations
• Use numerical simulations to determine the
performance of a dual-conjugate system suitable for
use on a 10m telescope on La Palma (e.g. the GTC).
• Want to determine performance as a function of
guide star configuration and DM2 conjugate altitude
(DM1 will be conjugate to the pupil).
• Use a 7-layer approximation to balloon
measurements of vertical distribution of turbulence;
simulate 7 Kolmogorov screens for each ‘frame’.
• Geometric propagation
• Shack-Hartmann wavefront sensing (16x16 subaps)
• Zernike deformable mirrors
• No noise
MCAO Simulations
SR at 2.2 m
3 NGS FoV=1 arcmin
3 NGS FoV=1.5 arcmin
Average SR drops and variation over FoV increases as FoV is
increased
Ref: Femenía & Devaney, in preparation
Optimal altitude of DM2 ?
Sky Coverage
Stars per square degree
using Guide Star Catalogue II
There are 1326 stars deg-2
brighter than mR=17.5
=0.95 in FOV=2´
P ( n) 
p(n  3)  1   p(0)  p(1)  p(2)

 1  exp( ) 1     2
p (n3) = 7% in 2´
= 2% in 1.5´
 n exp(  )
n!

Does not take geometry
into account
Sky coverage...
• The probability of finding ‘constellations’
of bright, nicely distributed natural guide
stars is very small. The obvious solution is
to use multiple laser guide stars.
• Besides the sky coverage, a major
advantage is the stability of the system
calibration
– (roughly) constant guide star flux
– constant configuration
• The cone effect is not a problem
• However.....
LGS in MCAO
• Recall cannot determine tip-tilt from LGS
• When using multiple LGS the result is tip-tilt
anisoplanatism. Unless corrected, this will
severely limit the MCAO performance
• How to correct ?
– polychromatic LGS or other scheme to measure
LGS tip-tilt
– measure tip-tilt on several NGS in the field
– make quadratic wavefront measurements on
guide stars at different ranges ..... huh ??
Quadratic errors and tip-tilt anisoplanatism
S2 = a1x2

h
S1 = a0x2
 ( x)  a1 ( x  h)  a0 x
2
2
 a1 x  a1 h   2a1 xh  a0 x
2
2
Anisoplanatic
tilt
2
Measuring with LGS


hi 
x
H



 ( x )   S i 1 
i
 ( x; )   Si hi  1 
i

H
hi  
x 
H  
h
x
Measuring with LGS
2
h
h


 ( x; )  a0 x  a1 1   x 2  a1 h2  2a1hx1  
 H
 H
2
a1
x2
piston
if a0  -a1 (1-h/H)2 then don’t
see anything !!
a0x2
H
tilt so can’t measure

h
Measuring with LGS
2
h
h


 ( x; )  a0 x  a1 1   x 2  a1 h2  2a1hx1  
 H
 H
2
2
h 

 ( x; )  a0 x  a1 1  '  x 2
 H 
2
2
null if a0  -a1 (1-h/H´)
a1x2
H´ H

h
a0x2
Possible hybrid approaches...
• Na laser guide stars (H=90km) plus NGS (H=)
• Na laser guide stars plus Rayleigh guide star
(H<30km) plus NGS (for global tip-tilt).
• Na laser guide stars plus Rayleigh guide stars at
different ranges plus NGS
• ........
Results using 4 LGS + 1NGS
SR at 2.2 m
3 LGS FoV=1 arcmin
FOV =1.5 arcmin
Is there an alternative ?
• In principle, layer-oriented wavefront
sensing can use multiple faint guide stars.
• Implementation with pyramid sensors can
be complicated if need dynamic
modulation.
• An extension to give better sky coverage is
‘multi-fov’ layer oriented.
Multi-fov layer oriented wavefront sensing
• Layers near the pupil can be corrected with large
field of view
• High-layer field of view should be limited since
correction of non-conjugate layers degrades as
1/HFOV ,where H is distance of layer from DM
• Example:
– 1 sensor with annular fov = 2-6´ conjugate to
ground layer
– 1 sensor with fov=2´ conjugate to ground
– 1 sensor with fov=2´ conjugate to high altitude
• The ground layer will have a residual of high
altitude turbulence
Multi-fov layer oriented wavefront sensing
2´
DM at altitude
6´
Telescope pupil
Gemini South MCAO
Science
Path
NGS
WFS
Path
LGS
Other
WFS
Stuff
Path
DM0
DM9
SCIBS
ADC
Source
Simulators
• f/33.4 output
• Focal- and pupil plane
WFSBS OAP1
locations preserved
TTM
• Standard
optical bench
DM4.5
design with space frame
support
• In-plane packaging with
adequate room ADC
for
WFS
electronics
OAP2
Diagnostic
WFS and
Imaging
Camera
Zoom Focus
OAP3
Lens
LGS WFS
Courtesy: Eric James & Brent Ellerbroek, Gemini Observatory
ESO MAD Bench Optical design
14:45:32
To WFS 2’
0.45-0.95m
WFS
Re-imaging
objective
MACAO-SINFONI
DM 60 mm
0 Km conj.
wavefront sensor
objective
1st deformable mirror
F/15 Nasmyth
focus
Nasmyth
focus
Telecentric
F/20 focus
MACAO-VLTI
DM
100 mmmirror
2nd
deformable
8.5 Km conj.
To IR Camera
1-2.5m
collimator
dichroic
derotator
to IR imaging
camera
Dichroic
IR/Vis
Courtesy of E.Marchetti, N. Hubin ESO
Scale:
250.00
MM
derotator
+/- 1’ FoV
ESO 05-Mar-02
Collimator
F=900 mm
0.10
Global Reconstruction SH WFS
• Three movable SH WFS
• Three Fast read-out CCD
• XY tables fixed axes
direction
Lenslet
Array
Pick-Up
Mirror
• Acquisition camera
Acquisition
Camera
FoV 2'
Fast Read-Out
CCD
XY Table
Courtesy of E.Marchetti, N. Hubin ESO
Pupil
Reimaging
Lens
200mm
Layer Oriented WFS
• Multi Pyramid WFS, up to eight pyramids
• Two CCD cameras for ground and high altitude conjugations
Ground
Conjugated CCD
Pupil re-imaging
objective
Motions
Higher altitude
conjugated
CCD
Pyramid
Star enlargers
F/20 focal
plane
Courtesy of E.Marchetti, N. Hubin ESO