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Lecture16.2008

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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

• Will be intended to help you review the whole course
  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
   – Multi-conjugate adaptive optics (MCAO)
   – Multi-object adaptive optics (MOAO)
   – 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
• More information about the full volume of turbulence above the
  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)
     Need 3 well spread
      NGSs to control these
      modes
Credit: Rigaut, MCAO for Dummies                                     Page 13
 Outline of lecture


• Review of AO tomography concepts

• AO applications of tomography
   – Multi-conjugate adaptive optics (MCAO)
   – Multi-object adaptive optics (MOAO)
   – 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
Demonstrator (MAD)




   Single Conjugate     Multi Conjugate



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


         DM9
  DM0

                    SCIBS      ADC




                      OAP1       OAP2
             WFSBS
 TTM
           DM4.5



                             Zoom Focus    LGS WFS
                ADC            OAP3
                                Lens
WFS


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


• Review of AO tomography concepts

• AO applications of tomography
   – Multi-conjugate adaptive optics (MCAO)
   – Multi-object adaptive optics (MOAO)
   – 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
   – Multi-conjugate adaptive optics (MCAO)
   – Multi-object adaptive optics (MOAO)
   – 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)
• Adaptive secondary
  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
       take advantage of smaller image
    – 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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