1. Adaptive Optics in the VLT and ELT era Beyond Basic AO
François Wildi
Observatoire de Genève

2. Adaptive Optics wavefront errors reminder
The residual wavefront error is the quality criterion in AO
The wavefront error depends on:
The number of degrees do freedom (i.e. +/- nb of actuators) of the deformable mirror.
The lag (delay) in the control system
The noise in the wavefront sensor which depends on the guide star magnitude
The size of the field of view
Side effects like WFS non-ideality, NCPA, disturbances like vibrations

3. Dependence of Strehl on l and number of DM degrees of freedom
Assume bright natural guide star
No meas’t error or iso-planatism or bandwidth error
Deformable mirror fitting error only

4. Decreasing fitting error
Reminder #1: Dependence of Strehl on l and number of DM degrees of freedom (fitting)
Decreasing fitting error
Assume bright natural guide star
No meas’t error or iso-planatism or bandwidth error
Deformable mirror fitting error only

5. Basics of wavefront sensing
Measure phase by measuring intensity variations
Difference between various wavefront sensor schemes is the way in which phase differences are turned into intensity differences
General box diagram:
Wavefront sensor
Guide
star
Turbulence
Telescope
Optics
Detector
Recon-structor
Computer
Transforms aberrations into intensity variations

6. Types of wavefront sensors
“Direct” in pupil plane: split pupil up into subapertures in some way, then use intensity in each subaperture to deduce phase of wavefront. REAL TIME
Slope sensing: Shack-Hartmann, pyramid sensing
Curvature sensing
“Indirect” in focal plane: wavefront properties are deduced from whole-aperture intensity measurements made at or near the focal plane. Iterative methods - take a lot of time.
Image sharpening, multi-dither
Phase diversity

7. Shack-Hartmann wavefront sensor concept - measure subaperture tilts
Pupil plane
Image plane
CCD
CCD

8. WFS implementation
Compact
Time-invariant

9. How to reconstruct wavefront from measurements of local “tilt”

10. Effect of guide star magnitude (measurement error)
Because of the photons statistics, some noise is associated with the read-out of the Shack-Hartmann spots intensities
Assumes no fitting error or other error terms

11. Effect of guide star magnitude (measurement error)
Assumes no fitting error or other error terms
bright star
Decreaing measurement error
dim star

12. Reminder #3: Strehl vs l and guide star angular separation (anisoplanatism)

13. Reminder #3: Strehl vs l and guide star angular separation (anisoplanatism)

14. Anisoplanatism side effect:
Because correction quality falls off rapidly looking sideways from the guide star AND because faint stars cannot be used as guide stars, Only a very small part of the sky is accessible to natural guide star AO systems!

15. Sky coverage accounting for guide star densities
LGS coverage ~80 %
Tip/tilt sensor magnitude limit
Hartmann sensor magnitude limit
Galactic latitude
NGS coverage 0.1 %
Isokinetic angle qk
Isoplanatic angle q0

16. (Temporary) conclusion on isoplanatism:
With 0.1% sky coverage, classical AO is of limited use for general astronomy.
This is perticularly true for extra-galactic astronomy, where the science object is diffuse, often faint and cannot be used for wavefront sensing.

17. High precision Wide field MOAO AO’s great divide ExAO
LTAO (high coverage)
GLAO
MCAO
MOAO

18. Like classical AO but more of the same
ExAO in a nutshell
Like classical AO but more of the same
The wavefront error minimized on axis
Large number of degrees do freedom (i.e. +/- nb of actuators) of the deformable mirror.
Minimal lag (delay) in the control system
Low noise in the wavefront sensor: Bright guide star
“No” field of view
WFS non-ideality fought with spatial filter, NCPA measured and corrected, disturbances like vibrations countered with advanced signal processing

19. High contrast imaging XAO, S~90% Coronagraph Differential Methods
visible
coronagraph
infrared
Diff. Pol.
IFS
SDI
Highest contrast observations require multiple correction stages to correct for
Atmospheric turbulence
Diffraction Pattern
Quasi-static instrumental aberrations
XAO, S~90%
Coronagraph
Differential Methods

20. NCPA compensation
Use of phase diversity for NCPA correction on Vis. path
Strong improvement of bench internal SR (45 -> 85 in Vis)
various optimisations still to be performed 11

21. NCPA compensation for IR path
Ghosts
NCPA compensation
320 modes estimated, 220 corrected
No compensation

22. Implementation CPI ZIMPOL IFS IRDIS ITTM PTTM DM DTTS WFS DTTP Focus 1
De-rotator
HWP2
ITTM
HWP1
PTTM
Polar Cal
Focus 2 DM
Focus 4
NIR ADC
VIS ADC
DTTS
VIS corono
Focus 3
ZIMPOL
WFS
NIR corono
DTTP
IFS
IRDIS

23. Sky coverage and Wide field in a nutshell
To circumvent the sky coverage problem, several ways have been devised and are actively pursued:
Laser Tomography Adaptive Optics (LTAO) Laser guide stars are used to probe the atmosphere and project it in the science object direction
Ground Layer Adaptive Optics (GLAO) Laser guide stars are used to probe the atmosphere but only the ground layer is corrected
Multi-Conjugate Adaptive Optics (MCAO) Laser guide stars are used to probe the atmosphere and turbulence is projected and corrected in several layers
Multi Object Adaptive Optics (MOAO) Laser guide stars are used to probe the atmosphere and turbulence is projected in several directions. Each direction has one (or several DM’s)

24. Laser tomography AO
In LTAO, the atmosphere is probed by multiple Wave Front Sensors to form a model of the atmosphere. This model is used to compute the wavefront distorsion in a perticular direction and therefore calculate a correction in that direction.
It allows a good correction in a direction that lacks a good natural guide star at the expense of system complexity
Field is not increased!

25. Proper use of the system requires several wavefront sensors to perform Tomography
Altitude Layer (phase aberration = +)
Ground Layer = Pupil (phase aberration = O)
Inversion process
describe figure
Altitude of aberration proportional to shear at WFS -> retrieve altitude from 2D wfs info. Tomography = stereoscopy
In MCAO case: Restricted problem -> limited number of DM. Treated as a whole. Similarly to AO were one does not explicitely reconstruct the phase, in MCAO the 3D phase distribution is not reconstructed, and then projected to the DMs. The system computes directly the DM commands that will minimize the error as measured by the WFS.
More stable.
Tomography = Stereoscopy
WFS#1
WFS#2

26. WFS Set-up and LTAO reconstruction
Turb. Layers
Telescope #2 #1
DM corrects #1 + #2 in red direction
WFS
Usual stuff
Atmosphere UP

27. Ground layer AO
In GLAO, the atmosphere is probed by multiple Wave Front Sensors to form a model of the atmosphere. Only the ground layer is extracted form the model and used to feed back a correction mirror conjugated to the ground.
It allows a correction of the atmospheric wavefront error that happens in the common path of all objects at the expense of system complexity
Field is very large but performance is limited

28. Performance expected from GLAO (Gemini)

29. WFS Set-up and GLAO reconstruction
Turb. Layers #2 #1
Telescope
WFS
DM corrects #1
Usual stuff
Atmosphere UP

30. Laser guide stars vs natural guide stars
Tomography can also be performed with natural guide stars BUT:
Requires planning the NGS for each observation
Quality is not constant due to NGS geometry and flux distribution
Requires movable wave front sensors
Solution unanimously discarded today

31. Multi Conjugate Adaptive Optics
To increase the isoplanatic patch, the idea is to design an adaptive optical system with several deformable mirrors (DM), each correcting for one of the turbulent layer Each DM is located at an image of the corresponding layer in the optical system. (By definition, the layer and the DM are called conjugated  by the optical system).

32. What is multiconjugate? Case without
Turbulence Layers
Deformable mirror

33. What is multiconjugate? Case with it
Deformable mirrors
Turbulence Layers

34. Multiconjugate AO Set-up
Turb. Layers
Telescope
WFS #2 #1
DM#2
DM#1
Usual stuff
Atmosphere UP

35. Effectiveness of MCAO: no correction
Numerical simulations:
5 Natural guide stars
5 Wavefront sensors
2 mirrors
8 turbulence layers
MK turbulence profile
Field of view ~ 1.2’
H band
Numerical simulation tools written at Gemini
here I present results obtained with a Monte Carlo based simulation, with the parameter listed here.
What you see is a seeing limited image of a stellar field.
Note speckle boiling (uncorrelated from one corner to the next) and global image motion.
Close the loop with single centered guide star -> good compensation in small centered fov. Anisoplanatism of high order modes -> speckle boiling. Aniso of tilt -> image motion off axis. Image motion mostly radial because of the better correlation of tangential tilt component
Add 4 stars in 4 corners, and one DM -> MCAO system

36. Effectiveness of MCAO: classical AO
Numerical simulations:
5 Natural guide stars
5 Wavefront sensors
2 mirrors
8 turbulence layers
MK turbulence profile
Field of view ~ 1.2’
H band
Numerical simulation tools written at Gemini
here I present results obtained with a Monte Carlo based simulation, with the parameter listed here.
What you see is a seeing limited image of a stellar field.
Note speckle boiling (uncorrelated from one corner to the next) and global image motion.
Close the loop with single centered guide star -> good compensation in small centered fov. Anisoplanatism of high order modes -> speckle boiling. Aniso of tilt -> image motion off axis. Image motion mostly radial because of the better correlation of tangential tilt component
Add 4 stars in 4 corners, and one DM -> MCAO system

37. Effectiveness of MCAO: MCAO proper
Numerical simulations:
5 Natural guide stars
5 Wavefront sensors
2 mirrors
8 turbulence layers
MK turbulence profile
Field of view ~ 1.2’
H band
Numerical simulation tools written at Gemini
here I present results obtained with a Monte Carlo based simulation, with the parameter listed here.
What you see is a seeing limited image of a stellar field.
Note speckle boiling (uncorrelated from one corner to the next) and global image motion.
Close the loop with single centered guide star -> good compensation in small centered fov. Anisoplanatism of high order modes -> speckle boiling. Aniso of tilt -> image motion off axis. Image motion mostly radial because of the better correlation of tangential tilt component
Add 4 stars in 4 corners, and one DM -> MCAO system

38. MCAO Performance Summary Early NGS results, MK Profile
Classical AO
MCAO
No AO
1 DM / 1 NGS
2 DMs / 5 NGS
Long exposure images.
Pros of MCAO
Enlargement of the field
PSF uniformity across the field -> data reduction impacts
165’’
320 stars / K band / 0.7’’ seeing
Stars magnified for clarity

39. The reality…: GEMINI MCAO Module
NGS source
simulator
LGS source
Science ADC
Beamsplitter
Diagnostic WFS
NGS
WFS
LGS zoom corrector
ADC
shutters
DMs
TTM
LGS WFS
This is a schematic showing the components of the AOM and the light path through them.
The light from the telescope enters the system at the top RHS and is directed onto the 3 deformable mirrors. These are the mirrors which are conjugated to different heights in the atmosphere. The beam then reflects off a tip-tilt mirror and onto a beamsplitter. At this point, part of the beam is directed down to another beamsplitter where the laser light is split from the natural star light, probably by use of a filter at the sodium wavelength. The laser light is directed onto the LGS WFS’s while the natural star light is directed to an array of Avalanche Photo Diodes. The APD’s are used to obtain Tip/Tilt information while the LGS WFS’s are used to obtain higher order corrections for abberations such as coma, astigmatism, trefoil, etc.
The remaining star light, not picked off by the first beamsplitter carries on into the telescope instrument being used for the observation.

40. Example of MCAO Performance
13x13 actuators system
K Band
5 LGSs in X of 1 arcmin on a side
Cerro Pachon turbulence profile
200 PDE/sub/ms for H.Order WFS
Four R=18 TT GS 30” off axis (MCAO)
One R=18 TT GS on axis(AO)
Get more quantitative info. Plot of Strehl, FWHM, 50%EE and Slit coupling versus distance to the central GS.
Medium order system. Computations done for the Gemini south system. 5 guide stars, 3 DM. Noise included both on LGS and NGSs. 4 NGS because of symmetry reasons to speed up results evaluation. Demonstrate later that only 3 needed, and adding a fourth only marginally improve the results. Classical LGS AO: one R=18 GS on axis
Comment results

41. MCAO Performance Classical LGS AO MCAO 1 Strehl
Surface plots of Strehl ratio over a 1.5 arc min FoV.
13x13 actuator system, K band, CP turbulence.

42. Other nice features of MCAO
Average Strehl (triangles) 1 .5 +
Strehl St. dev across FoV % (+) 2 4
Profile number
Robustness
Robustness
Sensitivity to noise is fairly better than with AO
Prop noise AO / Prop noise MCAO  sqrt( NGS )
Predictive algorithms possible ?
Robustness
Sensitivity to noise is fairly better than with AO
Prop noise AO / Prop noise MCAO  sqrt( NGS )
Other aspects of MCAO:
Robustness (smooth and forgiving dependence upon DM altitude)
Noise sensitivity (need sqrt(N_GS) times less photons per GS (Gemini case studies)
Slicing up the atmosphere -> Taylor ok ? predictive algorithms

43. Generalized Fitting (Finite number of DMs)
dact
Geometry of the problem
Gen Fitting. Finite # of DMs. Sketch of the geometry
Image sharp bump in layer -> impossible to correct in *all direction* -> filtered out of the command
Command act as a spatial low pass filter of width theta.dh
Simple model check: Using simulation code written at Gemini, we have simulated 2 DMs and 3 DMs system (0,4,13), (0,13), (4,13)
- extrema found where expected
- addition of 0 km DM does not modify perf between 4 and 13
- steep degradation of S > 0-13
- simple model seems to fit good.
Compute error vs regular fitting error -> behavior in 5/3 power of theta.dh

44. Generalized Anisoplanatism (Finite number of Guide Star)
Additional error terms are necessary to represent laser guide star MCAO. Tomography error arises from the finite number and placement of guide stars on the sky. Generalized anisoplanatism error results from the correction of the continuous atmosphere at only a finite number of conjugate layer
altitudes.

45. Generalized Fitting (Finite number of DMs)
Error [rd2]  (.h)5/3
Design Criteria e.g. Error balanced  hmax(,dact)
DM Spacing = 2 x hmax

46. Generalized Anisoplanatism (Finite number of Guide Star)
Turbulence altitude estimation error
OK toward GS, but error in between GS: Strehl “dips”
Maximum FoV depends upon DM pitch.
Example for 7x7 system
FoV = 70”
FoV = 100”

47. Generalized Anisoplanatism goes down with increasing apertures
2D info only
3D info
2D info only
3D info
Aperture

48. MCAO Pros and Cons PROS: Enlarged Field of View
PSF variability problem drastically reduced
Cone-effect solved
Gain in SNR (less sensitive to noise, predictive algorithms)
Marginally enlarged Sky Coverage (LGS systems)
CONS
Complexity: Multiple Guide stars and DMs
Other limitations: Generalized Fitting, anisoplanatism, aliasing

49. Multi objects adaptive optics

50. In certain case, the user does not want to (or need to) have a fully corrected image. He/she might be satisfied with having only specific locations (i.e.) objects corrected in the field.
An AO system designed to provide this kind of correction is called a Multi Objects Adaptive Optics system
MOAO are the systems of choice to feed spectrographs and Integral Field Units in the ELT era.

52. MOAO
Up to 20 IFUs each with a DM
8-9 LGS
3-5 TTS

53. MOAO for TiPi (TMT) MEMS-DMs Flat 3-axis steering mirrors OAPs Tiled
focal-plane
4 of 16 d-IFU
spectrograph units
Flat 3-axis
steering mirrors
OAPs
MEMS-DMs

54. Key Design Points for AO
Key points:
30x30 piezo DM placed at M6, providing partial turbulence compensation over the 5’ field.
All LGS picked off by a dichroic and directed back to fixed LGS WFS behind M7. Dichroic moves to accommodate variable LGS range.
The OSM is used to select TT NGS and PSF reference targets.
MEMS devices placed downstream of the OSM to provide independent compensation for each object: 16 science targets, 3 TT NGS, PSF reference targets.

55. Laser guide stars

56. Laser guide star AO needs to use a faint tip-tilt star to stabilize laser spot on sky
from A. Tokovinin

57. Effective isoplanatic angle for image motion: “isokinetic angle”
Image motion is due to low order modes of turbulence
Measurement is integrated over whole telescope aperture, so only modes with the largest wavelengths contribute (others are averaged out)
Low order modes change more slowly in both time and in angle on the sky
“Isokinetic angle”
Analogue of isoplanatic angle, but for tip-tilt only
Typical values in infrared: of order 1 arc min

58. Sky coverage is determined by distribution of (faint) tip-tilt stars
Keck: >18th magnitude 1
271 degrees of freedom
5 W cw laser
Galactic latitude = 90°
Galactic latitude = 30°
From Keck AO book

59. LGS Related Problems: Null modes
Tilt Anisoplanatism : Low order modes > Tip-Tilt at altitude
 Dynamic Plate Scale changes
Within these modes, 5 “Null Modes” not seen by LGS (Tilt indetermination problem)
 Need 3 well spread NGSs to control these modes
Detailed Sky Coverage calculations (null modes modal control, stellar statistics) lead to approximately 15% at GP and 80% at b=30o

61. Additional error terms are necessary to represent laser guide star MCAO. Tomography error arises
from the finite number and placement of guide stars on the sky. Generalized anisoplanatism error results from the correction of the continuous atmosphere at only a finite number of conjugate layer altitudes

62. LGS WFS Subsystem needs constant refocussing!
Trombone design accomodates LGS altitudes between km (Zenith to 65 degrees)
Astigmatism corrector present / Will study Coma corrector
TMT.IAO.PRE REL02

63. TMT MIRES (proposal) Concept Overview LGS trombone system
TMT.INS.PRE DRF01

64. 3. NGS WFS
Radial+Linear stages with encoders offer flexile design with min. vignetting
6 probe arms operating in “Meatlocker” just before focal plane
2x2 lenslets
6” FOV - 60x60 0.1” pix
EEV CCD60
Flexible design - minimize vignetting
Radial + linear stages
Similar to OIWFS for F2 and GMOS
TMT.IAO.PRE REL02
Flamingos2 OIWFS

65. Issues for designer of AO systems
Performance goals:
Sky coverage fraction, observing wavelength, degree of compensation needed for science program
Parameters of the observatory:
Turbulence characteristics (mean and variability), telescope and instrument optical errors, availability of laser guide stars
AO parameters chosen in the design phase:
Number of actuators, wavefront sensor type and sample rate, servo bandwidth, laser characteristics

66. Effects of laser guide star on overall AO error budget
The good news:
Laser is brighter than your average natural guide star
Reduces measurement error
Can point it right at your target
Reduces anisoplanatism
The bad news:
Still have tilt anisoplanatism stilt2 = (  / tilt )5/3
New: focus anisoplanatism sFA2 = ( D / d0 )5/3
Laser spot larger than NGS smeas2 ~ ( b / SNR )2