Maximizing GSMT Science Return
with
Scientific Figures of Merit
Maximizing value
• Who are the interested parties?
– Scientist users
– Funding agencies
• What constitutes value to them?
– Scientific return
– Cost
• What gives greatest value?
MAXIMUM SCIENTIFIC RETURN FOR COST
Quantifying value
Components of value
• Performance
– Requirements
– Goals
• Cost
– Build
– Operations
• Schedule
– First light
– Operating life
R
I
$$$
S
Science
K
Science merit function
Science merit function =  ( Wi x FOMi )
• Figure of Merit (FOM)
– For each capability, embodied as instrument + telescope
– Quantitative, with analytical and numerical components
– Function of instrument and telescope properties
• Weight (W)
– Scientific judgment call
Example 1. GSMT spectroscopic capability
Aperture
Field of view
Spatial resolution
Resolved stellar
populations
30 m
2-3 arcmin
10 milliarcsec
Wavelength coverage
Spectral resolution
Instrument type
0.3-1.2 microns
1000’s
OIR multislit
Parameter
Star formation
30 m
< 10 arcmin
15 milliarcsec
0.3-2.2 microns
> 2000
OIR MOS
Example 2: CELT IR AO system emissivity
•
Cryogenic AO system at prime focus
• Ultimate performance for emissivity
• Negative impacts on telescope design, enclosure cost
•
Cryogenic AO system at Nasmyth focus
• Quantifiably almost as good
• Expect lower total observatory cost
•
Warm AO system at Nasmyth focus
• Dramatically reduced performance
• Low cost, maintains spatial resolution advantage
• Trades against space platform sensitivity advantage
What is the science mission?
Type of mission impacts FOM, weights
• Design reference mission
– Total science program specified
• Timely science mission
– Maximize science achieved in initial period
• Scientific capability mission
– Instrument capabilities for wide range of potential science
Example: UKIRT WFCAM program
• WFCAM: widefield 1-2 m camera on 3.8 m telescope
• Several large scale surveys over ~10 years (DRM)
• Quick shallow surveys first (STM)
• Selected deep fields done repeatedly (STM + DRM)
• Instrument permits installation of custom filters (SCM)
http://www.ukidss.org
GSMT sample imaging capabilities
• Enhanced seeing widefield imager
– Gaussian profile
– Tens of arcmin FOV
• Narrow field coronagraph
– Highest possible Strehl and dynamic range
– FOV is arcseconds
• Moderate field, diffraction limited imaging
– Moderate Strehl over arcminute FOV
Imaging FOM inputs: telescope
• D, primary mirror diameter
• TPtel (  ), throughput
•  ( , , t ), delivered image quality
• S ( , , t ) , Strehl ratio
•  (  ) , emissivity
• Etel , operating efficiency
Imaging FOM inputs: instrument
• TPinstrl (  ), throughput
• DQE(  ), detector quantum efficiency
•  , pixel sampling
• , , wavelength coverage and resolution
• R, D, read noise and dark current
• Sc, scattered light susceptibility
• Etel , system efficiency
Imaging FOM inputs: multiplex advantages
• , total solid angle field of view
• n, number of simultaneous spectral channels
Imaging FOM inputs: other science value factors
• Timeliness
• First light
• Other facilities
• Competition
• Access
• To facility
• To data
Enhanced native seeing imager
• Science
– Distribution of high redshift galaxies
– Integrated properties of galaxies
• Programmatic
– Use at wavelengths where diffraction limit can’t be achieved
– Use in less favorable conditions, e.g. thin cirrus
• Implications for FOM
– Slightly extended sources with some central concentration
– Wavelength coverage is   1 m
Enhanced native seeing imager
Background limited, uncrowded field case
Neglect





Emissivity
Strehl ratio
Read noise, dark current
Scattered light
Programmatic terms
Gather terms into a Figure of Merit for (integration time)-1
Enhanced native seeing imager
Background limited, uncrowded field FOM
1/time  [ (D2/2) • TPtel () • Etel] •
Telescope
[ • DQE • TPtinstr() • Etinstr • f(/) • f(n) • f(, ) ]  Instrument
• Track telescope, instrument separately
• Some factors require simulations to determine appropriate formulations
• Some factors may include weighting functions
Formulation of image quality 
Poor
conditions
1.0

arcsec
Good
conditions
0.5
0
10
, arcminutes
20
Delivered image quality vs field angle and conditions
Optimizing /
photometry
Time 
detection
1
/
2
/
3
4
Weighting function for 
weight
1
0
0
MCAO
regime
, arcminutes
20
Tel, atmos
rolloffs
Enhanced native seeing imager trades
Some performance (and cost) trades:
– D, 
– , 
– TPtel () (coatings)
– n (instrument complexity)
–  (optics complexity, coatings choices)
Narrow field coronagraphic imager
• Science
– Discovery and characterization of planetary systems
• Programmatic
– Diffraction limited, very high Strehl at first light
– Use in best seeing conditions
• Implications for FOM
– Wavelength coverage is 1    5 m
– Treatment of systematic effects important
– Independent of telescope design, AO implementation details
Coronagraphic imager FOM additional inputs
• d, subaperture size of primary
• n, number of actuators on deformable mirror
• , residual wavefront rms error
• , speckle lifetime (site characteristic)
• g, gain, ratio of peak intensity to halo level
• R, amplitude reduction of primary core and halo by
coronagraph
Coronagraphic imager FOM
Comparison with enhanced seeing imager:
 Neglect traditional seeing measure 
 Include Strehl ratio S, emissivity 
 Use additional terms to describe AO, coronagraph
impacts
Coronagraphic imager sensitivity FOM
FOM for sensitivity (SNR):
sensitivity  [ D2 • TP • E •  • DQE • -1 • f(/) • f(n) • f(, ) ]½
• [ S / (1-S) ] • [ D / d ]2 • [ 1/R ]
• Includes “traditional” components, Strehl and gain advantages
• Not yet in right units!
• How to account for systematic effects?
Coronagraphic imager systematics
SNR limited by speckle structure in uncorrected halo
– Pointlike
– 100% amplitude modulation
– Persist for time 
Variety of solutions
– Decorrelation (large n, kHz AO update rate)
– Simultaneous differential imaging (NICI)
– PSF engineering, e.g. speckle sweeping
– Data taking and reduction methods
Coronagraphic imager final FOM
• Characterize time – SNR relation by parameter 
•  = 2 for photon noise limited system, less if
residual systematic errors are significant
1/time  ( previous expression ) 
Narrow field coronagraphic imager trades
• Mirror segment size d
• Speckle lifetime  (site characteristics)
• Emissivity  and Strehl ratio S
•  error budget allocations
•  /  with 
• Suppression of systematic error
Wide field – narrow field comparisons

FOV
DIQ
Tel geometry
Tel optics
Secondary
Emissivity
AO system
Wide field
Narrow field
< 1 m
20 arcmin
~0.5 arcsec
uncritical
fast, complex
large
irrelevant
Active secondary
~10E3 actuators
1 – 5 m
2 arcsec
~0.005 arcsec
important
slow, simple
small
important
Ditto + DM w/
~10E4 actuators
Maximizing value, redux
Return to performance, cost, schedule, risk mix:
Is there a similar approach to maximizing value?
Performance-cost index
PCI = Science merit function / total cost (capital + ops)
How to do optimization?
Maximizing value, redux
• Evaluate a few plausible approaches
– Telescope type
– Instruments
• Trade studies for key parameters
– Effect on SMF
– Effect on cost
• Creative tension between Scientist, Engineer, and Manager