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					Computing Challenges in Adaptive Optics for
        the Thirty Meter Telescope

                    Corinne Boyer
 High Performance Computing in Observational Astronomy
                     Pune, India
                   October 13, 2009



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    High Performance Computing in Observational Astronomy - Pune, October 13, 2009
                                   This Talk

Introduction to the Thirty Meter Telescope (TMT)
Adaptive Optics (AO) Basics
TMT first light AO system
–   System architecture
–   Computing challenges
–   Control Algorithms
–   Real time controller hardware architecture:
        Based on Field programmable gate arrays
Future TMT AO challenges



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                    Today’s Large and Extremely Large
                    Optical Infrared Telescope Projects
Ground-based optical infrared projects:
 – Giant Magellan Telescope (GMT) (25m equivalent aperture)
                                                               JWST
 – Thirty Meter Telescope (TMT) (30m aperture)
 – European Extremely Large Telescope (E-ELT) (42m aperture)
 – Sample science cases include: understanding the emergence
   of large scale structure in early universe, how galaxies
   assemble and evolve, where, when and how often planets
   form…
Space project: James Webb Space Telescope (8m aperture)
                                                E-ELT
                   TMT


GMT
          Thirty Meter Telescope Overview
Collaboration of ACURA (Canada),
University of California, Cal Tech and
NAOJ (Japan)
Mauna Kea in Hawai’i
First Light 2018
Ritchey-Chrétien optical design
30 m filled aperture, finely segmented
  – 492 segments, 1.44m across
     corners
f/1 primary
3.1 m convex active secondary
Articulated tertiary
  – Flat elliptical, 2.5m x 3.5m
f/15 output focal ratio
20 arc min FOV (15 unvignetted);
Wavelength 0.31 – 28 µm; Operational
1° thru 65°
Nasmyth-mounted instrumentation
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     Light Collection Increases as D2




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                Adaptive Optics (AO) Further
              Increases Telescope Sensitivity
Historically, the performance of ground-based
telescopes has been limited by atmospheric turbulence
– Large telescopes collected more light in proportion to D2 to
  detect fainter objects, but with no improvement in image quality
AO Systems now allow the removal in real time of much
of the effect of atmospheric turbulence, and gain a
further improvement in sensitivity of ~ D2
TMT is being designed as an end-to-end system to
correct atmospheric disturbances, and approach the
diffraction limited image quality of a 30 meter aperture




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                                                                                                          Lick AO




                                    Sample Images




Gemini AO - Globular cluster M-13            Keck AO - Uranus
                                                                               Keck LGS AO - Image of the
                                                                                     Galactic Center
    MCAO Strehl Uniformity over 2’ FoV (ESO VLT)




       Classical AO                 MCAO                        Gemini - Imaging of Extra-Solar Planets
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                                        AO Basics
                                                                             SH WFS

                                                      Atmospheric turbulence…
                                                      introduces wavefront and image
                                                      quality degradations…
                                                      which can in principal be
                                                      compensated by a wavefront
                                                      corrector…
                                                      provided that they can be measured
                                                      with a wavefront sensor…
                                                      observing a suitable reference star
                                                      (sufficiently bright)
                                                      This method is called “Natural Guide
Wavefront
corrector                                             Star (NGS) AO”
                                                      Two major limitations:
                                                    – Only a small fraction of sky can be
                                                       observed nearby NGS
   Real Time                                        – Small field of view over which AO
   Controller                                          correction is good (anisoplantism) 8
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                 Increasing Sky Coverage with Laser
                          Guide Stars (LGS) Keck
Use of laser beam to generate an artificial reference
star. Two solutions:
 – Rayleigh guide stars: propagation of a near-UV laser
   and detection of backscatter at altitudes between 5-
   25km
 – Sodium guide stars: laser lights at 589nm to excite          Gemini
   sodium atoms in the mesosphere at ~90km
      Better correction of higher altitude turbulence
Main limitations/issues:
 – Finite range of LGS induces a “cone effect”
       Multi guide stars required for large telescope
 – Tip/tilt guide stars still required (but much      VLT
   fainter)
 – Sodium layer has nonzero thickness and
   variable structure

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                      Defeating Anisoplanatism via Multi-
                      Conjugate Adaptive Optics (MCAO)
                                                 Telescope          Deformable              Wave
                                                                   Mirrors (DMs)            Front
                                                                                           Sensors




 Multiple
Guide Stars                   Atmospheric
                           Turbulence “Layers”
                                                                                    Processors and
                                                                                   Control Algorithms

   3-d turbulence profile estimated using multiple sensors and guide stars (using
   tomographic algorithms)
   Turbulence compensated in 3-d using multiple deformable mirrors conjugated to
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   various turbulence layer heights in the atmosphere
          High Performance Computing in Observational Astronomy - Pune, October 13, 2009
                             AO Processing Basics

                                 WFS
WFS pixels         WFS         gradients      Wavefront    DM errors                    DM commands
                                                                          DM control
                processing                  reconstruction




      3 main steps:
         WFS processing: compute centroids from WFS pixels
         Wavefront reconstruction: compute DM error signals from WFS
         centroids. Conventional approach is a simple matrix vector multiply.
         DM control: compute DM actuator commands from DM error signals
         (apply a temporal filter)




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      AO Challenges for Large Telescopes

High-order deformable mirrors (DM) and tip/tilt mirror with large
stroke, low hysteresis and high bandwidth
High-order low noise wavefront sensors (WFS)
Sodium lasers with high coupling efficiency coefficient
Real time controllers solving very high-order problems at very high
bandwidth
 – For example, the TMT first light AO system must solve a 35k x 7k
   control problem at 800Hz
 – Size of problem is at least 2 orders of magnitude greater than the most
   challenging near-term AO systems
 – Conventional matrix multiply approach is impractical on account of
   memory requirement and need to update the algorithm in real time
 – Computationally efficient algorithms and innovative hardware
   implementations provide effective solutions

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           The TMT first light AO Architecture
MCAO LGS AO System:
- Feeds 3 instruments
- 60x60 order system
- 2 DMs, 6 LGS WFS,
3 low-order NGS WFS
- 800Hz

                                                                       Laser Guide Star Facility:
                                                                       - Up to 9 LGS
                                                                       - Center-launch design
                                                                       - Conventional optics
                                                                       - 25W Lasers




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          Real Time Computing Requirements
                 for TMT First Light AO
Process outputs from a suite of wavefront sensors (WFS) including six 60x60
order LGS WFS and three low-order NGS WFS.
Compute and apply commands to two high order deformable mirrors (DM) with
a total of ~7500 actuators and one tip/tilt stage using computationally efficient
algorithms
Operate at a 800Hz sampling rate with 1000µs end-to-end latency (strong goal
of 400µs)
Update and optimize the control algorithms in real time as the observing
parameters and atmospheric conditions change
Also…
 – Offload persistent, low spatial frequency components of the deformable mirrors and
   tip/tilt stage commands to the telescope
 – Compute commands for the Laser Guide Star Facility fast steering mirrors to
   stabilize the pointing of the LGS on the sky
 – Store up to one night of circular buffer data for diagnostic purposes or PSF post
   processing reconstruction
          Up to 90TB; ~<5GB/s
          PSF: Essential tool for data reduction of science observations


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  TMT First Light AO LGS Real Time
     Computing Block Diagram




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        Wavefront Sensor Processing




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                   LGS WFS Processing:
                    Pixels to Gradients
6 Shack Hartmann LGS WFS, each has 60x60 sub-apertures with
sub-aperture size varying from 6x6 to 6x15 pixels:
– ~205,000 pixels per WFS
– ~5,800 gradients per WFS
Use a constrained matched filter algorithm to compute the gradients at
800Hz sampling rate
– Noise optimal algorithm
– Simple matrix-vector multiplication performed synchronously with the
  digitization of the pixels intensities (500µs); final sub-aperture gradient
  computed within 10µs after final pixels have been provided.
– Updated in real time at 1Hz to account for changes in seeing, sodium
  laser profile and laser beam quality:
       By dithering the LGS fast steering mirrors located in the Laser Guide
       Star Facility
Reference vector (calibration purpose) is subtracted
Gradients are used as inputs for the wavefront reconstruction process
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        Low order NGS WFS Processing:
              Pixels to Gradients
3 low-order WFS working in the IR:
 –   Either 2x2 or 1x1 Shack Hartmann WFS
 –   Tip/tilt for fast guiding
 –   Focus for LGS WFS
 –   Tilt anisoplanatism for high-order wavefront control
 –   Processing sampling rate depends upon the signal level of the NGS
 –   Very small number of pixel to process in comparison to LGS WFS
     (~3,000 pixels)
Use a matched filter algorithm to compute the gradients
 – Updated in real time at rate of 0.1Hz based upon variations in seeing
   and AO system performance
Gradients are used as inputs for the wavefront reconstruction
process



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            Wavefront Reconstruction




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     Wavefront Reconstruction: Gradients
             to DM error signals
Wavefront reconstruction consists of two steps:
– 3-D turbulence profile estimated with tomographic algorithm
– Projection to various DM with DM fitting algorithm
Minimum variance algorithms to solve both steps
– Computationally efficient algorithms
NGS wavefront reconstruction is performed separately
using standard modal least-square reconstructor:
– Split tomography
     Better control of low-order modes
     Reduce coupling between LGS and NGS modes




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                         LGS Tomography (1)
    Minimum variance algorithm:                      s = Gx + n
           (G C
              T   "1
                  NG + CX ) x = G T CN s
                        "1           "1
                                             with   CX = xx T
                   A                b               CN = nn T
                                         !
    System to solve has the form A x = b
!                                   !
     – A is the block-structured tomography operator (sparse and low-rank)
     – x is the tomography vector of unknowns (OPD)
                                    !
     – b is the right hand side tomography vector computed from the pseudo open loop
       LGS gradients
    Several options have been developed for the tomography step as
    alternatives to the standard (and impractical) matrix-vector-multiply solution
     –    Iterative solutions
     –    Grid-based computations
     –    Warm restart used to accelerate convergence
     –    For all solutions, study impact on AO performance
    Solvers perform matrix-vector multiplications
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                   LGS Tomography (2)
2 System-oriented solvers:
 – CG30: 30 iterations of Conjugate Gradient (no preconditioning)
   operating on the whole tomography system
 – FD3: 3 iterations of Fourier Domain Preconditioned Conjugate Gradient
   operating on the whole tomography system
2 Layer-oriented solvers (block generalization of the Gauss-Seidel
iteration):
 – BGS-CG20: Block Gauss-Seidel with 20 iterations of Conjugate
   Gradient for each atmospheric layer
 – BGS-CBS: Block Gauss-Seidel with Cholesky back-substitutions for
   each atmospheric layer




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                              DM Fitting
DM fitting matrix system has also the form A x =b
– A is the block-structured fitting operator (sparse)
– x is the DM actuator vector of unknowns
– b is the fitting right hand side vector
Proposed solver: 4 iterations of Conjugate Gradient
(CG4).




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        Wavefront Correctors Control




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          Wavefront Correctors Control :
         DM error signals to DM commands
Simple integrator with adjustable gain applied to the DM
error signals computed by wavefront reconstruction
process.
Woofer/tweeter algorithm implemented for control of tip/tilt
modes:
– TTP commands obtained by applying additional proportional-
  integrator to tip/tilt components of filtered ground-layer DM
  commands.
Filtered DM and TTP commands clipped to avoid
saturation
Integrator windup is preventing by subtracting clipping
adjustments from inputs of temporal filters.
Invisible mode removal is taken into account by pseudo
open loop control and has been removed from the
wavefront corrector control algorithm
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                 Computation and Memory
                     Requirements

                                             Memory                 Number of
                                              (MB)              operations GMAC/s
                                                                 (1000µs latency)
LGS WFS processing                               10                        7.2
LGS wavefront reconstruction
       BGS-CBS                                   50                         80
       BGS-CG20                                   2                        280
       CG30                                       2                        245
       FD3                                       40                        250




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                Hardware Implementation
Hardware architecture depends upon choice of tomographic algorithm
– Which impacts processing requirement and memory requirement
Hardware implementation impacts the latency
– Appropriate processor for each task (Field Programmable Gate Arrays,
  Digital Signal Processor, Graphic Processing Unit, others…)
     Floating point versus fixed point
– Parallelization efficiency including inter-processor communication and bus
  contingencies
– On-chip memory is limited
      Multiply the number of processors
      Add external memory
TMT has supported two competitive studies for the conceptual design of
the first light TMT AO system real time controller:
– DRAO (Dominion Radio Astrophysical Observatory) and tOSC (the Optical
  Science Company)
– Both companies have demonstrated the feasibility of developing the TMT
  real time controller using today’s Xilinx’s Virtex-5 FPGA technology.
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              TMT Real Time Controller
                Conceptual Studies




Credit to DRAO and tOSC
For more information: http://ao4elt.lesia.obspm.fr/

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        Future Computing Challenges for TMT

Building the real time controller for the TMT first light AO system is the
first computing challenge for TMT AO in terms of:
 – Algorithm complexity,
 – Processing requirements,
 – But is feasible with today’s technology.
Other challenges will follow:
 – Adaptive Optics Secondary
        Synchronization of various real time systems
 – First light MCAO system upgrade
        Will implement 120x120 order wavefront sensors and deformable
       mirrors to improve the AO performance and provide diffraction limited
       images
       At least a factor 4 in terms of processing and memory requirements
 – Multi-Object Adaptive Optics (MOAO) System may also be very challenging:
       8 LGS and up to 20 60x60 order DMs (one per science object)
Stay tuned…
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Questions?




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                          Acknowledgements

  The authors gratefully acknowledge the support of the TMT partner
institutions
  They are:
    – the Association of Canadian Universities for Research in Astronomy (ACURA)
    – the California Institute of Technology
    – and the University of California
 This work was supported as well by:
    –   the Gordon and Betty Moore Foundation
    –   the Canada Foundation for Innovation
    –   the Ontario Ministry of Research and Innovation
    –   the National Research Council of Canada
    –   the Natural Sciences and Engineering Research Council of Canada
    –   the British Columbia Knowledge Development Fund
    –   the Association of Universities for Research in Astronomy (AURA)
    –   and the U.S. National Science Foundation.



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