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# Lecture16.2008 by liaoxiuli

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```									          Lecture 16

The applications of tomography:
MCAO, MOAO, GLAO

Claire Max
AY 289C
UC Santa Cruz
March 6, 2008
Page 1
Next week (the last week of class!)

• Tuesday March 11th lecture:
– AO for imaging the living human retina.
– Jason Porter, Univ. of Houston

• Thursday March 13th lecture:
– Extreme AO for imaging planets around nearby stars
– Bruce Macintosh, Lawrence Livermore National Lab

• Final exam: take-home, open-book
– Distributed at lecture Thursday March 13th
– Due in my office (or my computer) on or before
Thurs March 20th at noon. This is a hard deadline.
Page 2
The final homework assignment

• Will be on web by end of this week

• Due Thurs March 13

and get ready for the exam

• What approaches have you found useful in reviewing
classes like this? What makes the material “stick” ?

Page 3
Outline of lecture

• Review of AO tomography concepts

• AO applications of tomography
– Ground-layer AO (GLAO)

Page 4
What is Tomography ?
1. Cone effect

90 km

“Missing” Data

Credit: Rigaut, MCAO for Dummies                    Page 5
What is Tomography ?
2. Wider field of view, no cone effect

Tomography lets
you reconstruct
90 km

turbulence in the
entire cylinder of
air above the
telescope mirror

Credit: Rigaut, MCAO for Dummies                         Page 6
Ragazzoni’s Tomography Cartoon

Credit: Ragazzoni, Nature 403, 2000   Page 7
Concept of a metapupil

• Can be made larger than
“real” telescope pupil

• Increased field of view due to
overlap of fields toward
multiple guide stars

Page 8
How tomography works: from Don Gavel

kZ

k z         1
kx           
          z

kX

k x   N k x ,k x 


 x    n x   z, z dz
0

Fourier slice theorem in tomography
(Kak, Computer Aided Tomography, 1988)
• Each wavefront sensor measures the integral of index variation along the ray lines
• The line integral along z determines the kz=0 Fourier spatial frequency component
• Projections at several angles sample the kx,ky,kz volume
9
How tomography works: from Don Gavel

kZ

k z         1
kx           
          z

kX

k x   N k x ,k x 


 x    n x   z, z dz
0

• The larger the telescope’s primary mirror, the wider the range of
angles accessible for measurement
• In Fourier space, this means that the “bow-tie” becomes wider
telescope
10
How tomography works: some math

y  Ax
• where
y = vector of all WFS measurements          x
x = value of dOPD) at each voxel in
turbulent volume above telescope                         y

A is a forward propagator (entries = 0 or
1)
• Assume we measure   y with our wavefront sensors
• Want to solve for x = value of dOPD)

• The equations are underdetermined – there are more unknown voxel
values than measured phases  blind modes. Need a few natural guide
stars to determine these.                                      Page 11
Solve for the full turbulence above the
telescope using the back-propagator

xA y   T

x
y = vector of all WFS measurements
x = value of dOPD) at each voxel in       y
turbulent volume above telescope

AT is a back propagator along
rays back toward the guidestars

x
Use iterative algorithms to converge
on the solution.                            y
Page 12
LGS Related Problems: Null modes

• Tilt Anisoplanatism :
Low order modes (e.g.
focus) > Tip-Tilt at
altitude
 Dynamic Plate
Scale changes                       QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.

• Five “Null Modes” are not
seen by LGS (Tilt
indetermination problem)
NGSs to control these
modes
Credit: Rigaut, MCAO for Dummies                                     Page 13
Outline of lecture

• Review of AO tomography concepts

• AO applications of tomography
– Ground-layer AO (GLAO)

Page 14
What is multiconjugate AO?

Turbulence Layers

Deformable mirror

Credit: Rigaut, MCAO for Dummies                   Page 15
What is multiconjugate AO?

Deformable mirrors                 Turbulence Layers

Credit: Rigaut, MCAO for Dummies                   Page 16
The multi-conjugate AO concept

Turb. Layers        Telescope                WFS
#2              #1               DM1   DM2

Atmosphere
UP

Credit: Rigaut, MCAO for Dummies                                Page 17
“Star Oriented” MCAO

Guide Stars
• Each WFS looks at one star
• Global Reconstruction
High Altitude Layer
• n GS, n WFS, m DMs
• 1 Real Time Controller
Ground Layer
• The correction applied at           Telescope
each DM is computed using    DM2
all the input data.
DM1
WFC

WFSs

Credit: N. Devaney                              Page 18
Layer Oriented MCAO

• Layer Oriented WFS architecture                   Guide Stars

• Local Reconstruction

• x GS, n WFS, n DMs                            High Alt. Layer

• n RTCs

• Wavefront is reconstructed at               Ground Layer
each altitude independently.                 Telescope

• Each WFS is optically coupled to    DM2
all the others.
DM1
• GS light co-added for better SNR.          WFC1      WFC2

WFS1

WFS2
Credit: N. Devaney                                     Page 19
MCAO Performance Predictions
NGS, Mauna Kea Atmospheric Profile

No AO                         Classical AO              MCAO
1 DM / 1 NGS          2 DMs / 5 NGS

165’’
320 stars / K band / 0.7’’ seeing                    Stars magnified for clarity

Credit: Rigaut, MCAO for Dummies                                              Page 21
MCAO Simulations, 3 laser guide stars

Strehl at 2.2 m
3 NGS, FoV = 1 arc min

Strehl at 2.2 m
3 NGS, FoV = 1.5 arc min

Average Strehl drops, variation over FoV
increases as FoV is increased
Credit: N. Devaney                                         Page 22
Results from ESO’s Multiconjugate AO

Single Conjugate     Multi Conjugate

Page 23
Gemini South MCAO
Science Path
NGS WFS Path
LGS WFS Path

DM9
DM0

OAP1       OAP2
WFSBS
TTM
DM4.5

Zoom Focus    LGS WFS
Lens
WFS

Credit: Eric James & Brent Ellerbroek, Gemini Observatory   Page 24
Outline of lecture

• Review of AO tomography concepts

• AO applications of tomography
– Ground-layer AO (GLAO)

Page 25
Distinctions between multi-conjugate
and multi-object AO

?

1-2 arc min

• DMs conjugate to different         • Only one DM per object,
altitudes in the atmosphere          conjugate to ground
• Guide star light is corrected by   • Guide star light doesn’t
DMs before its wavefront is
measured                             bounce off small MEMS DMs in
multi-object spectrograph
Page 26
Science with MOAO: multiple deployable
spatially resolved spectrographs

• A MEMS DM underneath each high-redshift galaxy, feeding a
narrow-field spatially resolved spectrograph (IFU)

• No need to do AO correction on the blank spaces between the
galaxies
Page 27
Why does MOAO work if there is only one
deformable mirror in the science path?

• Tomography lets you
measure the turbulence
throughout the volume
above the telescope
90 km

Page 28
Why does MOAO work if there is only one
deformable mirror in the science path?

• Tomography lets you
measure the turbulence
throughout the volume
above the telescope
90 km

• In the direction to each
galaxy, you can then
project out the
turbulence you need to
cancel out for that galaxy

Page 29
Outline of lecture

• Review of AO tomography concepts

• AO applications of tomography
– Ground-layer AO (GLAO)

Page 30
Ground layer AO: do tomography, but
only use 1 DM (conjugate to ground)

MCAO                              GLAO

single DM
conjugated to
ground layer

GLAO uses 1 ground-conjugated DM, corrects near-ground turbulence

Credit: J-M Conan                                                   Page 31
Correcting just the ground layer gives a
very large isoplanatic angle

• Strehl = 0.38 at  = 0
0 is isoplanatic angle
3 / 5
                                
2.914 k (sec  )  dz CN (z) z 
 0        2        8/3    2      5/3

                   0             

0 is weighted by high-altitude turbulence
(z5/3)

• If turbulence is only at low altitude,
overlap is very high.
Common
• If you only correct the low altitude                             Path
turbulence, the isoplanatic angle will be
large (but the correction will be only
modest)
Telescope Page 32
Ground Layer AO (GLAO) typically decreases
natural “seeing” by a factor of 1.5 to 2

• Example: GLAO
calculation for Giant
Magellan Telescope
(M. Johns)
conjugation at 160 m
above primary mirror.
• Performance goals:
–    > 0.8 m
– Field of view: >10’
– Factor of 1.5-2
reduction in image
size.

Modeled using Cerro Pachon
turbulence profile. (M-L Hart 2003)
Page 33
Many observatories have ambitious
GLAO projects planned

• Near term on medium sized
telescopes: SOAR (4.25m), William
Herschel Telescope (4.2m), MMT
(6.5m)
• Medium term on VLT (8m), LBT
(2x8m)
• Longer term on Giant Magellan
Telescope etc.
• Is it worth the large investment “just”
to decrease “seeing” disk by factor of
1.5 to 2 ?
– Depends on whether existing or
planned large spectrographs can
– Potential improved SNR for
background-limited point sources

Page 34
time

Credit: A.          Page 35
Credit: A.
Tokovinin    Page 36
Summary

• Tomography: a way to measure the full volume of turbulence
above the telescope
• Once you have measured the turbulence and know its height
distribution, there are several ways to do the wavefront correction
to get wider field of view
– Multi-conjugate AO: multiple DMs, each optically conjugate to a
different layer in the atmosphere.
– Multi-object AO: correct many individual objects, each over a
small field.
– Ground-layer AO: correct just the turbulence close to the
ground. Gives very large field of view but only modest
correction. Should work in both the visible and the IR.

Page 37

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