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Optimisation of
           Multi-Object Spectroscopy
                  in Astronomy
                      Brent Miszalski
                     SALT Research Fellow
                       brent@saao.ac.za



Sunday 18 March 12
Overview

 • Galaxy redshift surveys
 • Multi-object spectroscopy (MOS)
 • MOS field configuration by
        simulated annealing
 • MOS at the Southern African Large
        Telescope (SALT)

    Miszalski et al. 2006, MNRAS, 371,1537
Sunday 18 March 12
NGC 1376
Sunday 18 March 12
M 101
Sunday 18 March 12
Hubble Ultra Deep Field
Sunday 18 March 12
Hubble’s law
        • Expansion of the
               universe produces a
               Doppler-shift in light
               of galaxies towards
               red end of spectrum

        • The ‘redshift’ z=(λ-
               λ0)/λ0 is related to
               recessional velocity
               of each galaxy V~cz
        • V=H        0d
Sunday 18 March 12
Galaxies cluster together




Sunday 18 March 12
Comoving distance
  DC - distance between two galaxies




Density parameters

                       matter

                     dark energy
                      curvature
Sunday 18 March 12
Millenium Simulation (Springel et al. 2005)
Sunday 18 March 12
We need more redshifts

        • Measuring fundamental cosmological
               parameters depends on statistical analysis
               of large scale structure
        • A few thousand galaxies is not enough
        • Need hundreds of thousands or millions
        • Cannot do this one object at a time...
Sunday 18 March 12
Multi-Object Spectroscopy




    • Developed in late 80s/early 90s
    • Highly successful but very complex (more focus on
           getting instrument working, rather than optimising it)
Sunday 18 March 12
2dF: Two-degree Field facility
                         4-m Anglo-Australian
                              Telescope




   Lewis et al. (2002)
Sunday 18 March 12
Sunday 18 March 12
Sunday 18 March 12
Sunday 18 March 12
wavelength




Sunday 18 March 12
wavelength




Sunday 18 March 12
2dFGRS (Colless et al. 2001)




Sunday 18 March 12
N(z)~250,000!




Sunday 18 March 12
wigglez.swin.edu.au
                                              Wigglez
                     Drinkwater et al. 2010




Sunday 18 March 12
wigglez.swin.edu.au
                                                 Wigglez
                     Drinkwater et al. 2010




                                   Blake et al. 2010




Sunday 18 March 12
wigglez.swin.edu.au
                                                 Wigglez
                     Drinkwater et al. 2010




                                   Blake et al. 2010




Sunday 18 March 12
A challenging optimisation problem

 • 400 fibres to match up to N
        targets (up to ~1000)
 • Targets have priorities 1(lowest)
        to 9(highest)
 • Limited fibre reach
 • Fibres and buttons cannot
        collide, but fibre crossover ok
 •      Uniformly sample targets    [no structure imprint]

 • Prefer straighter fibres          [quicker config times]
Sunday 18 March 12
Fibre and target reach




Sunday 18 March 12
Fibre and target reach




Sunday 18 March 12
Sunday 18 March 12
Simulated Annealing
      • Donnelly et al. (1992) first proposed and
             implemented SA for field configuration, but not
             fast enough back then
      • SA simulates slow cooling of physical systems
             (e.g. glass), making small random changes at each
             temperature level
      • Metropolis (1953) algorithm determines whether
             a change is accepted
      • Fewer and fewer “bad” changes are accepted at
             lower temperatures
Sunday 18 March 12
Travelling Salesman Problem
                     Numerical Recipes (Ch. 10)




           (b) large river penalty   (c) negative river penalty!




Sunday 18 March 12
Annealing schedule
     • Start with unallocated fibres, a few hundred targets
            and an initial temperature Ti

     • Slowly cool Ti by multiplication with (1-ΔT)
     • Randomly choose new targets for each fibre,
            multiple times (up to 105 swaps per ΔT)
     • The randomisation of each fibre occurs in four ways
     • Metropolis (1953) algorithm accepts or denies each
            change, depending on global ‘quality’ of field
     • Reach quasi-static equilibrium at each temperature
Sunday 18 March 12
Four randomisation cases
before



   after




Sunday 18 March 12
Metropolis algorithm




Sunday 18 March 12
Metropolis algorithm


                             Boltzmann distribution in
                               statistical mechanics




Sunday 18 March 12
Objective function
                      target    close   straighten
                     priority   pairs     fibres      maximise
                                                       me!




Sunday 18 March 12
Objective function




                           Temperature




Sunday 18 March 12
A sample run


                     E




                             Temperature

Sunday 18 March 12
Simulations
  • Both uniform and clustered fields
  • Also use actual cosmological
         simulations (mock catalogues)
  • Different priority distributions
  • Fields with close pairs
  • LOTS of trial and error in
         selecting best algorithm
         parameters
  • Usually configure 1000 fields each
Sunday 18 March 12
Total target yield




Sunday 18 March 12
Total target yield




Sunday 18 March 12
Target priorities




                     lowest               highest
Sunday 18 March 12
Target priorities




                     lowest               highest
Sunday 18 March 12
Target priorities




Sunday 18 March 12
Target priorities




Sunday 18 March 12
Target priorities




Sunday 18 March 12
Uniformity
Oxford




      SA




Sunday 18 March 12
OLD
             (Oxford)




Sunday 18 March 12
NEW
             (Annealing)




Sunday 18 March 12
Fibre straightness




                     γ=0.0     γ=0.125    γ=2.0




Sunday 18 March 12
Fibre straightness




                     γ=0.0     γ=0.125    γ=2.0




Sunday 18 March 12
Algorithm summary
     • Power is in contained in the objective function
     • Performance far exceeds previous algorithms
     • Both in raw target yield and flexibility
     • Routinely used by astronomers at AAT since 2006
     • Routinely used by several large galaxy redshift surveys
     • Generic algorithm suitable to many other MOS
            instruments
     • Opportune time to apply it to MOS masks at SALT!
Sunday 18 March 12
SALT
  • Biggest single telescope in Southern Hemisphere!
  • 11.1m x 9.8m optical mirror
  • Refurbished instrumentation: April 2011
  • Second science semester starts in May 2012
  • Multi-object capability: instead of fibres, use slit-masks
  • MOS is currently being tested/commissioned
  • Perfect time to explore optimisation of mask design
photo: Lisa Crause
Sunday 18 March 12
Sunday 18 March 12
Sunday 18 March 12
MOS masks

      • Cheaper than developing a robot + fibre system
      • Use laser to cut slits in carbon fibre mask
      • Mask is placed in focal plane of telescope
      • Each slit produces a spectrum
      • Challenge is to ‘pack in’ the best arrangement of
             slits in one mask
      • A unique set of constraints c.f. fibre optimisation
Sunday 18 March 12
Laser mask cutter   MOS @ SALT
                            Slit mask cutter software GUI




Sunday 18 March 12
courtesy
                                           David
                                          Gilbank
 ~1/2 degree




                     IMACS on Magellan
                       6.5-m telescope
                            Chile
Sunday 18 March 12
courtesy
                                           David
                                          Gilbank
 ~1/2 degree




                     IMACS on Magellan
                       6.5-m telescope
                            Chile
Sunday 18 March 12
courtesy
           David
          Gilbank


                     slits




Sunday 18 March 12
courtesy
                 David
                Gilbank




Sunday 18 March 12
AIMS project
   • An exploratory study for a new mask design algorithm
   • Dr Brent Miszalski (SAAO/SALT)
   • Dr David Gilbank (SAAO)
   • Prof Bruce Bassett (AIMS/SAAO/UCT)
   • Design clear guidelines necessary for algorithm
          development to start
   • Identify most efficient and clever ways to conduct basic
          operations needed in a mask algorithm
Sunday 18 March 12
MOS mask design issues
      • What data structures to use in algorithm?
       • Hashes, vectors, lists, etc. Best choices == faster
      • How to tilt slits to capture > 1 target in field?
      • What randomisation steps to choose?
       • Shifting slit centres, extending slit size??
       • Shuffling groups of slits? Adding new slits?
      • How do we best define a “good” mask design?
       • Quantify completeness? Ensemble designs?
Sunday 18 March 12
MOS mask design issues
      • What is the best way to explore the parameter
             space of the problem?
      • Monte carlo simulations, statistics on real input data
      • Review previous MOS algorithms (especially mask
             design algorithms)
      • Most algorithms in the literature could be
             considerably improved
      • Your work could be used routinely at SALT!
Sunday 18 March 12
Applications

      • An improved MOS algorithm has multiple
             applications
      • Not just cosmological surveys (most of which are
             done on smaller telescopes with larger fields)
      • Globular clusters - spectroscopy of individual stars
      • Galaxy clusters - studying cluster properties as a
             function of redshift to bring new insights into galaxy
             formation and evolution, cosmology.

Sunday 18 March 12
Omega Centauri (ESO)




Sunday 18 March 12
Über cluster (D. Gilbank)
                              z~0.7




Sunday 18 March 12
Thank you!




        brent@saao.ac.za
Sunday 18 March 12
Sunday 18 March 12

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Optimization of Multi-Object Spectroscopy in Astronomy

  • 1. Optimisation of Multi-Object Spectroscopy in Astronomy Brent Miszalski SALT Research Fellow brent@saao.ac.za Sunday 18 March 12
  • 2. Overview • Galaxy redshift surveys • Multi-object spectroscopy (MOS) • MOS field configuration by simulated annealing • MOS at the Southern African Large Telescope (SALT) Miszalski et al. 2006, MNRAS, 371,1537 Sunday 18 March 12
  • 4. M 101 Sunday 18 March 12
  • 5. Hubble Ultra Deep Field Sunday 18 March 12
  • 6. Hubble’s law • Expansion of the universe produces a Doppler-shift in light of galaxies towards red end of spectrum • The ‘redshift’ z=(λ- λ0)/λ0 is related to recessional velocity of each galaxy V~cz • V=H 0d Sunday 18 March 12
  • 8. Comoving distance DC - distance between two galaxies Density parameters matter dark energy curvature Sunday 18 March 12
  • 9. Millenium Simulation (Springel et al. 2005) Sunday 18 March 12
  • 10. We need more redshifts • Measuring fundamental cosmological parameters depends on statistical analysis of large scale structure • A few thousand galaxies is not enough • Need hundreds of thousands or millions • Cannot do this one object at a time... Sunday 18 March 12
  • 11. Multi-Object Spectroscopy • Developed in late 80s/early 90s • Highly successful but very complex (more focus on getting instrument working, rather than optimising it) Sunday 18 March 12
  • 12. 2dF: Two-degree Field facility 4-m Anglo-Australian Telescope Lewis et al. (2002) Sunday 18 March 12
  • 18. 2dFGRS (Colless et al. 2001) Sunday 18 March 12
  • 20. wigglez.swin.edu.au Wigglez Drinkwater et al. 2010 Sunday 18 March 12
  • 21. wigglez.swin.edu.au Wigglez Drinkwater et al. 2010 Blake et al. 2010 Sunday 18 March 12
  • 22. wigglez.swin.edu.au Wigglez Drinkwater et al. 2010 Blake et al. 2010 Sunday 18 March 12
  • 23. A challenging optimisation problem • 400 fibres to match up to N targets (up to ~1000) • Targets have priorities 1(lowest) to 9(highest) • Limited fibre reach • Fibres and buttons cannot collide, but fibre crossover ok • Uniformly sample targets [no structure imprint] • Prefer straighter fibres [quicker config times] Sunday 18 March 12
  • 24. Fibre and target reach Sunday 18 March 12
  • 25. Fibre and target reach Sunday 18 March 12
  • 27. Simulated Annealing • Donnelly et al. (1992) first proposed and implemented SA for field configuration, but not fast enough back then • SA simulates slow cooling of physical systems (e.g. glass), making small random changes at each temperature level • Metropolis (1953) algorithm determines whether a change is accepted • Fewer and fewer “bad” changes are accepted at lower temperatures Sunday 18 March 12
  • 28. Travelling Salesman Problem Numerical Recipes (Ch. 10) (b) large river penalty (c) negative river penalty! Sunday 18 March 12
  • 29. Annealing schedule • Start with unallocated fibres, a few hundred targets and an initial temperature Ti • Slowly cool Ti by multiplication with (1-ΔT) • Randomly choose new targets for each fibre, multiple times (up to 105 swaps per ΔT) • The randomisation of each fibre occurs in four ways • Metropolis (1953) algorithm accepts or denies each change, depending on global ‘quality’ of field • Reach quasi-static equilibrium at each temperature Sunday 18 March 12
  • 30. Four randomisation cases before after Sunday 18 March 12
  • 32. Metropolis algorithm Boltzmann distribution in statistical mechanics Sunday 18 March 12
  • 33. Objective function target close straighten priority pairs fibres maximise me! Sunday 18 March 12
  • 34. Objective function Temperature Sunday 18 March 12
  • 35. A sample run E Temperature Sunday 18 March 12
  • 36. Simulations • Both uniform and clustered fields • Also use actual cosmological simulations (mock catalogues) • Different priority distributions • Fields with close pairs • LOTS of trial and error in selecting best algorithm parameters • Usually configure 1000 fields each Sunday 18 March 12
  • 39. Target priorities lowest highest Sunday 18 March 12
  • 40. Target priorities lowest highest Sunday 18 March 12
  • 44. Uniformity Oxford SA Sunday 18 March 12
  • 45. OLD (Oxford) Sunday 18 March 12
  • 46. NEW (Annealing) Sunday 18 March 12
  • 47. Fibre straightness γ=0.0 γ=0.125 γ=2.0 Sunday 18 March 12
  • 48. Fibre straightness γ=0.0 γ=0.125 γ=2.0 Sunday 18 March 12
  • 49. Algorithm summary • Power is in contained in the objective function • Performance far exceeds previous algorithms • Both in raw target yield and flexibility • Routinely used by astronomers at AAT since 2006 • Routinely used by several large galaxy redshift surveys • Generic algorithm suitable to many other MOS instruments • Opportune time to apply it to MOS masks at SALT! Sunday 18 March 12
  • 50. SALT • Biggest single telescope in Southern Hemisphere! • 11.1m x 9.8m optical mirror • Refurbished instrumentation: April 2011 • Second science semester starts in May 2012 • Multi-object capability: instead of fibres, use slit-masks • MOS is currently being tested/commissioned • Perfect time to explore optimisation of mask design photo: Lisa Crause Sunday 18 March 12
  • 53. MOS masks • Cheaper than developing a robot + fibre system • Use laser to cut slits in carbon fibre mask • Mask is placed in focal plane of telescope • Each slit produces a spectrum • Challenge is to ‘pack in’ the best arrangement of slits in one mask • A unique set of constraints c.f. fibre optimisation Sunday 18 March 12
  • 54. Laser mask cutter MOS @ SALT Slit mask cutter software GUI Sunday 18 March 12
  • 55. courtesy David Gilbank ~1/2 degree IMACS on Magellan 6.5-m telescope Chile Sunday 18 March 12
  • 56. courtesy David Gilbank ~1/2 degree IMACS on Magellan 6.5-m telescope Chile Sunday 18 March 12
  • 57. courtesy David Gilbank slits Sunday 18 March 12
  • 58. courtesy David Gilbank Sunday 18 March 12
  • 59. AIMS project • An exploratory study for a new mask design algorithm • Dr Brent Miszalski (SAAO/SALT) • Dr David Gilbank (SAAO) • Prof Bruce Bassett (AIMS/SAAO/UCT) • Design clear guidelines necessary for algorithm development to start • Identify most efficient and clever ways to conduct basic operations needed in a mask algorithm Sunday 18 March 12
  • 60. MOS mask design issues • What data structures to use in algorithm? • Hashes, vectors, lists, etc. Best choices == faster • How to tilt slits to capture > 1 target in field? • What randomisation steps to choose? • Shifting slit centres, extending slit size?? • Shuffling groups of slits? Adding new slits? • How do we best define a “good” mask design? • Quantify completeness? Ensemble designs? Sunday 18 March 12
  • 61. MOS mask design issues • What is the best way to explore the parameter space of the problem? • Monte carlo simulations, statistics on real input data • Review previous MOS algorithms (especially mask design algorithms) • Most algorithms in the literature could be considerably improved • Your work could be used routinely at SALT! Sunday 18 March 12
  • 62. Applications • An improved MOS algorithm has multiple applications • Not just cosmological surveys (most of which are done on smaller telescopes with larger fields) • Globular clusters - spectroscopy of individual stars • Galaxy clusters - studying cluster properties as a function of redshift to bring new insights into galaxy formation and evolution, cosmology. Sunday 18 March 12
  • 64. Über cluster (D. Gilbank) z~0.7 Sunday 18 March 12
  • 65. Thank you! brent@saao.ac.za Sunday 18 March 12