Adaptive Optics Nicholas Devaney GTC project, Instituto de Astrofisica de Canarias

1
Adaptive OpticsNicholas DevaneyGTC project,
Instituto de Astrofisica de Canarias

• 1. Principles
• 2. Multi-conjugate
• 3. Performance challenges

2
Anisoplanatic Error

3
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

4
Single-conjugate correction
Ref Véran, JOSA A, 17, p1325 (2000)
5
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

6
Multi-Conjugate AO

• MCAO is an extension of the idea of conjugating
  to turbulence to N deformable mirrors. In
  proposed systems N2-3.

7
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 ?

8
Optimal altitudes for deformable mirrors

• Tokovinin (JOSA A17,1819) has shown that for very
  large apertures
• 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

9
?M for 2 deformable mirrorsLa Palma turbulence
profiles

• Optimal altitude DM10, DM2 13km
• Optimal altitudes similar for all profiles
• Smooth decrease in isoplanatic angle as
• move away from optimal

10
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

11
Star Oriented MCAO

• Single Star WFS architecture
• Global Reconstruction
• n GS, n WFS, m DM,
• 1 RTC

The correction applied at each DM is computed
using all the input data. The correction across
the FoV can be optimised for specified directions.
12
Layer Oriented MCAO

• Layer Oriented WFS architecture
• Local Reconstruction
• x GS, n WFS, n DM,
• n RTC

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.
13
MCAO wavefront sensing

• Star-oriented systems plan to use multiple
  Shack-Hartmann 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.

14
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)
P is a projection matrix (This is similar to
sub-aperture testing of aspheres)
15
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)
• where
• for G guide stars (g1...G)

16
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.

17
Wavefront sensing for MCAO

• Whichever approach is employed, there are (of
  course) some limitations.
• Aliasing

GS1
GS2
This looks the same to both GS
H
?
This also looks the same to both GS
18
Wavefront sensing for MCAO

• Aliasing occurs between layers separated by H for
  frequencies higher than fc
• trade-off between field of view and degree of
  correction (unless increase the number of guide
  stars)

19
Gaps in the meta-pupil
Meta-pupil
Guide star beam footprints at altitude H
20
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

21
MCAO Simulations
3 NGS FoV1.5 arcmin
Average SR drops and variation over FoV increases
as FoV is increased
Ref Femenía Devaney, in preparation
22
Optimal altitude of DM2 ?
23
Sky Coverage
Stars per square degree using Guide Star
Catalogue II
There are 1326 stars deg-2 brighter than mR17.5
?0.95 in FOV2
p (n?3) 7 in 2 2 in 1.5
Does not take geometry into account
24
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.....

25
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 ??

26
Quadratic errors and tip-tilt anisoplanatism
S2 a1x2
?
h
S1 a0x2
Anisoplanatic tilt
27
Measuring with LGS
H
h
x
28
Measuring with LGS
H
a1x2
?
if a0 ? -a1 (1-h/H)2 then dont see anything !!
h
a0x2
29
Measuring with LGS
H
H
null if a0 ? -a1 (1-h/H)2
a1x2
?
h
a0x2
30
Possible hybrid approaches...

• Na laser guide stars (H90km) plus NGS (H?)
• Na laser guide stars plus Rayleigh guide star
  (Hlt30km) plus NGS (for global tip-tilt).
• Na laser guide stars plus Rayleigh guide stars at
  different ranges plus NGS
• ........

31
Results using 4 LGS 1NGS
SR at 2.2 ?m 3 LGS FoV1 arcmin
FOV 1.5 arcmin
32
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.

33
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 fov2 conjugate to ground
• 1 sensor with fov2 conjugate to high altitude
• The ground layer will have a residual of high
  altitude turbulence

34
Multi-fov layer oriented wavefront sensing
2
DM at altitude
Telescope pupil
35
Gemini South MCAO
Courtesy Eric James Brent Ellerbroek, Gemini
Observatory
36
ESO MAD Bench Optical design
Courtesy of E.Marchetti, N. Hubin ESO
37
Global Reconstruction SH WFS

• Three movable SH WFS

• Three Fast read-out CCD

• XY tables fixed axes
• direction

• Acquisition camera

Courtesy of E.Marchetti, N. Hubin ESO
38
Layer Oriented WFS

• Multi Pyramid WFS, up to eight pyramids
• Two CCD cameras for ground and high altitude
  conjugations

Courtesy of E.Marchetti, N. Hubin ESO