Gemini AO Program
Scaling Multi-Conjugate Adaptive
Optics Performance Estimates to
Extremely Large Telescopes
Brent Ellerbroek and Francois Rigaut
Gemini Observatory
March 31, 2000
Ellerbroek/Rigaut [4007-30]
1
Gemini AO Program
Presentation Outline
• MCAO modeling for 8-meter class telescopes
• Extension to ELT’s
– Computational limitations
– Restricting attention to anisoplanatism
• Mathematical formulation
• Cases considered
• Sample results
– Normalized
– Numerical
• Summary and plans
March 31, 2000
Ellerbroek/Rigaut [4007-30]
2
Gemini AO Program
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
March 31, 2000
Ellerbroek/Rigaut [4007-30]
3
Gemini AO Program
Sample Gemini MCAO Results
• Strehl vs LGS signal
level, wavelength, and
field offset
• 5 LGS, 162 subapertures
• 4 NGS, 22 subapertures
• 3 DM’s
– 0, 4.5, 9.0 km
conjugates
– 17 actuators across
pupil
• Median CP seeing
March 31, 2000
Ellerbroek/Rigaut [4007-30]
4
Gemini AO Program
Modeling Limitations for ELT’s
• 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 D=32/64/96 m
• Computation requirements scale as D6
– Factors of 4096/262144/2985984
• Simpler, less comprehensive approaches necessary
for initial trade studies
March 31, 2000
Ellerbroek/Rigaut [4007-30]
5
Gemini AO Program
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
March 31, 2000
Ellerbroek/Rigaut [4007-30]
6
Gemini AO Program
Problem Formulation
• Aperture- and FOV-averaged mean-square phase error
s2 = N-1||T(x-HEy)||2
Where
x: phase profile(s) to be corrected
N=dim(x)
T: piston removal operator
y: WFS measurement vector
H: DM-to-phase influence matrix
E: DM command estimation matrix
March 31, 2000
Ellerbroek/Rigaut [4007-30]
7
Gemini AO Program
Analysis Summary
• Goal: Determine
s*2 = minE < s2 >
E* = arg minE < s2 >
<…> denotes averaging over turbulence statistics
• Solution
s*2 = N-1 trace[TA-C -1 (HTTB)T(HTTH)-1(HTTB)]
E* = (HTTH)-1HTTBC-1
Where
A = <xxT>
B = <xyT>
C = <yyT>
March 31, 2000
Ellerbroek/Rigaut [4007-30]
8
Gemini AO Program
FOV/Aperture Scaling for
Kolmogorov Turbulence
Cone
MCAO
Effect
(General
(Focus
Anisoplanatism)
Anisoplanatism)
Scaling
5/3 with2 k=k(C 2(h),h )
=k(D/r
s*2=k(D/rs0*)25/3
with
0) k=k(C
n dm,qf/D,q
b
n (h),hb,h
b/D)
March 31, 2000
Ellerbroek/Rigaut [4007-30]
9
Gemini AO Program
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
March 31, 2000
Ellerbroek/Rigaut [4007-30]
10
Gemini AO Program
Guide Star and FOV Geometries
qf
qb
Evaluation
points in
field-ofview
qb
5 higherorder guide
stars (NGS
or LGS)
qb
9 higherorder guide
stars (NGS
or LGS)
March 31, 2000
Ellerbroek/Rigaut [4007-30]
Auxilliary
tip/tilt or loworder NGS
with LGS
11
Gemini AO Program
Aperture Sampling
q
h2
h1
h0=0
D,n
March 31, 2000
• 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
Ellerbroek/Rigaut [4007-30]
12
Gemini AO Program
Sample Normalized Results
• CP turbulence
• 3 DM’s
• 5 higher-order
guide stars
• Solid: LGS,
with different
auxilliary NGS
options
• Dashed: NGS,
with different
r=qb/qf values
March 31, 2000
Ellerbroek/Rigaut [4007-30]
13
Gemini AO Program
Observations on Normalized
Results
• Normalized phase variance (s*2/(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)
March 31, 2000
Ellerbroek/Rigaut [4007-30]
14
Gemini AO Program
Sample Numerical Results
(CP Turbulence, 3 DM’s)
March 31, 2000
Ellerbroek/Rigaut [4007-30]
15
Gemini AO Program
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 qf=1’, 5 m < D < 12.5 m
– s about 0.17 mm for qf=1.5’, 7.5 m < D < 18.75 m
– Tempting to scale curves to larger apertures
• NGS MCAO
– Modestly superior to LGS MCAO when r=qb/qf=1
– Performance degrades rapidly with increasing r
– What values of r are consistent with guide star
models?
March 31, 2000
Ellerbroek/Rigaut [4007-30]
16
Gemini AO Program
Summary and Plans
• Summary
– Anisoplanatic errors evaluated analytically for
MCAO on ELT’s
– 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
March 31, 2000
Ellerbroek/Rigaut [4007-30]
17