Scaling%20Multi-Conjugate%20Adaptive%20Optics%20Performance%20Estimates%20to%20Extremely%20Large%20Telescopes

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Scaling Multi-Conjugate Adaptive Optics
Performance Estimates to Extremely Large
Telescopes

• Brent Ellerbroek and Francois Rigaut
• Gemini Observatory

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Presentation Outline

• MCAO modeling for 8-meter class telescopes
• Extension to ELTs
• Computational limitations
• Restricting attention to anisoplanatism
• Mathematical formulation
• Cases considered
• Sample results
• Normalized
• Numerical
• Summary and plans

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MCAO modeling for 8-meter class telescopes

• Comprehensive analysis/simulation models
  available
• Integrated first-order treatment of
• Anisoplanatic effects (FOV DM conjugates
  LGS/NGS constellation)
• DM/WFS fitting error
• WFS noise
• Time delay and servo control law
• Reconstruction algorithm
• Windshake and non-common path aberrations
• Results in hours to several days with a
  workstation

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Sample Gemini MCAO Results

• Strehl vs LGS signal level, wavelength, and field
  offset
• 5 LGS, 162 subapertures
• 4 NGS, 22 subapertures
• 3 DMs
• 0, 4.5, 9.0 km conjugates
• 17 actuators across pupil
• Median CP seeing

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Modeling Limitations for ELTs

• Assuming
• Fixed DM conjugates and guide star constellation
• Fixed subaperture dimensions and actuator pitch
• Memory requirements scale as D4
• Factors of 256/4096/20736 for D32/64/96 m
• Computation requirements scale as D6
• Factors of 4096/262144/2985984
• Simpler, less comprehensive approaches necessary
  for initial trade studies

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Simplified Modeling Approach

• Evaluate anisoplanatic effects only
• Fundamental error source determining performace
  vs field-of-view, DM conjugates, and NGS/LGS
  guide star constellation
• Area of greatest uncertainty
• Other error terms can be approximated with
  simplified scaling laws
• Computation requirements greatly reduced

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Problem Formulation

• Aperture- and FOV-averaged mean-square phase
  error
• s2 N-1T(x-HEy)2
• Where
• x phase profile(s) to be corrected
• Ndim(x)
• T piston removal operator
• y WFS measurement vector
• H DM-to-phase influence matrix
• E DM command estimation matrix

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Analysis Summary

• Goal Determine
• s2 minE lt s2 gt
• E arg minE lt s2 gt
• ltgt denotes averaging over turbulence statistics
• Solution
• s2 N-1 traceTA-C -1 (HTTB)T(HTTH)-1(HTTB)
• E (HTTH)-1HTTBC-1
• Where
• A ltxxTgt
• B ltxyTgt
• C ltyyTgt

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FOV/Aperture Scaling for Kolmogorov Turbulence
Scaling
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Cases Considered

• Turbulence profiles
• Median Cerro Pachon (r0 0.166m, q0 2.74)
• Median Mauna Kea (r0 0.236m, q0 2.29)
• Deformable mirrors
• 3 conjugate to 0, 4, 8 km
• 4 conjugate to 0, 2.67, 5.33, 8 km
• Guide stars and WFS
• 5 or 9 NGS
• 5 or 9 LGS
• 1 or 4 auxilliary low-order NGS

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Guide Star and FOV Geometries
Evaluation points in field-of-view
5 higher-order guide stars (NGS or LGS)
9 higher-order guide stars (NGS or LGS)
Auxilliary tip/tilt or low-order NGS with LGS
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Aperture Sampling
q

• Minimum points across pupil set by
• h1q/D 1/n
• To avoid interpolation and under sampling of
  turbulence
• n must scale with D to study performance vs
  aperture diameter
• Computations reasonable for n 20

h2
h1
h00
D,n
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Sample Normalized Results

• CP turbulence
• 3 DMs
• 5 higher-order guide stars
• Solid LGS, with different auxilliary NGS
  options
• Dashed NGS, with different rqb/qf values

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Observations on Normalized Results

• Normalized phase variance (s2/(D/r0)5/3)
  decreases with decreasing normalized beam shear
  (h2qf/D)
• For decreasing qf, the phase variance decreases
  proportionately
• For increasing D, the reduction is countered by
  the increase in (D/r0)5/3
• NGS MCAO performance degrades rapidly with
  increasing r qb/qf
• LGS MCAO requires multiple tip/tilt or low order
  NGS
• Best NGS and LGS results proportional over a wide
  range of normalized beam shears (h2q/D)

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Sample Numerical Results(CP Turbulence, 3 DMs)
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Observations on Numerical Results

• Would prefer better sampling of science field
• LGS MCAO with 4 auxilliary NGS
• Performance varies slowly with D for fixed qf
• s about 0.12 mm for qf1, 5 m lt D lt 12.5 m
• s about 0.17 mm for qf1.5, 7.5 m lt D lt 18.75 m
• Tempting to scale curves to larger apertures
• NGS MCAO
• Modestly superior to LGS MCAO when rqb/qf1
• Performance degrades rapidly with increasing r
• What values of r are consistent with guide star
  models?

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Summary and Plans

• Summary
• Anisoplanatic errors evaluated analytically for
  MCAO on ELTs
• LGS results favorable with 3-4 auxilliary NGS
• NGS results favorable for guide stars within
  science field
• Plans
• Limited optimization of DM/guide star geometries
• Accelerate computations for larger apertures by
  exploiting matrix structures
• DM-to-phase influence matrix sparse
• Turbulence statistics shift-invariant