optimization of multi-object spectroscopy in astronomy
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Optimisation of Multi-Object Spectroscopy
in AstronomyBrent Miszalski
SALT Research Fellowbrent@saao.ac.za
Sunday 18 March 12
• Galaxy redshift surveys
• Multi-object spectroscopy (MOS)
• MOS field configuration by simulated annealing
• MOS at the Southern African Large Telescope (SALT)
Overview
Miszalski et al. 2006, MNRAS, 371,1537Sunday 18 March 12
NGC 1376Sunday 18 March 12
M 101Sunday 18 March 12
Hubble Ultra Deep FieldSunday 18 March 12
• 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=H0 d
Hubble’s law
Sunday 18 March 12
Galaxies cluster together
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Comoving distance
Density parameters
matter
dark energy
curvature
DC - distance between two galaxies
Sunday 18 March 12
Millenium Simulation (Springel et al. 2005)Sunday 18 March 12
• 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...
We need more redshifts
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)
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2dF: Two-degree Field facility4-m Anglo-Australian
Telescope
Lewis et al. (2002)Sunday 18 March 12
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wavelength
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wavelength
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2dFGRS (Colless et al. 2001)
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N(z)~250,000!
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WigglezDrinkwater et al. 2010
wigglez.swin.edu.au
Sunday 18 March 12
WigglezDrinkwater et al. 2010
Blake et al. 2010
wigglez.swin.edu.au
Sunday 18 March 12
WigglezDrinkwater et al. 2010
Blake et al. 2010
wigglez.swin.edu.au
Sunday 18 March 12
• 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
• Prefer straighter fibres
A challenging optimisation problem
[quicker config times]
[no structure imprint]
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Fibre and target reach
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Fibre and target reach
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• 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
Simulated Annealing
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Travelling Salesman ProblemNumerical Recipes (Ch. 10)
(b) large river penalty (c) negative river penalty!
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• 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
Annealing schedule
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Four randomisation cases
before
after
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Metropolis algorithm
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Metropolis algorithm
Boltzmann distribution instatistical mechanics
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Objective functionclose pairs
targetpriority
straightenfibres maximise
me!
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Objective function
Temperature
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A sample run
Temperature
E
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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 eachSunday 18 March 12
Total target yield
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Total target yield
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Target priorities
highestlowestSunday 18 March 12
Target priorities
highestlowestSunday 18 March 12
Target priorities
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Target priorities
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Target priorities
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Uniformity
Oxford
SA
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OLD(Oxford)
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NEW(Annealing)
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Fibre straightness
γ=0.0 γ=0.125 γ=2.0
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Fibre straightness
γ=0.0 γ=0.125 γ=2.0
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• 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!
Algorithm summary
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• 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
SALT
photo: Lisa CrauseSunday 18 March 12
Sunday 18 March 12
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• 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
MOS masks
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MOS @ SALTLaser mask cutter
Slit mask cutter software GUI
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~1/
2 de
gree
IMACS on Magellan 6.5-m telescope
Chile
courtesyDavid
Gilbank
Sunday 18 March 12
~1/
2 de
gree
IMACS on Magellan 6.5-m telescope
Chile
courtesyDavid
Gilbank
Sunday 18 March 12
slits
courtesyDavid
Gilbank
Sunday 18 March 12
courtesyDavid
Gilbank
Sunday 18 March 12
• 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
AIMS project
Sunday 18 March 12
• 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?
MOS mask design issues
Sunday 18 March 12
• 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!
MOS mask design issues
Sunday 18 March 12
• 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.
Applications
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Omega Centauri (ESO)
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Über cluster (D. Gilbank)z~0.7
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