Transcript MCAO System Modeling Brent Ellerbroek Presentation Outline MCAO • Modeling objectives and approach • Updated baseline performance – Strehl and Strehl uniformity – NGS limiting magnitude and.

MCAO
System Modeling
Brent Ellerbroek
Presentation Outline
MCAO
• Modeling objectives and approach
• Updated baseline performance
– Strehl and Strehl uniformity
– NGS limiting magnitude and sky coverage
• Sensitivity and trade studies
– Seeing
– Laser power
– Control loop bandwidth
• Pulsed vs. CW lasers
• AO Module tolerance analysis
• Summary and detailed design phase plans
May 24-25, 2001
MCAO Preliminary Design Review
2
Objectives and Approach
MCAO
• Determine realistically feasible MCAO performance
– Higher-order effects
• Diffraction effects in the atmosphere, optics, and WFS
• Extended, three-dimensional LGS with pointing jitter
• Variable seeing and LGS signal levels
– Implementation error sources
• Static/dynamic DM-to-WFS misregistration
• Non-common path errors
• Etc….
• Approach
– Linear systems analysis for first-order effects
– Propagation simulation for higher-order error sources
– AO loop modeling included in AO module tolerance analysis
May 24-25, 2001
MCAO Preliminary Design Review
3
MCAO
NGS’s
Simulation
Features
LGS’s
Turbulence
- Filtered white noise
- Taylor hypothesis
LGS
Pointing
Tip/Tilt
Offload
Minimal Variance
ShackHartmann
• Geometric or
Wave Optics
• Gain/bias
calibration
• 3-D LGS
• Photon + Read
Noise
• Misregistration
•
Science Fields
Reconstructor
LGS + NGS
WFS’s
DM’s
TTM
• Zonal
• 2nd order Dynamics
• Misregistration
Common- and
Noncommon
Path Errors
Science
Instrument
Strehl Histories
Mean PSF’s
Strehl Budget (H Band, Zenith,
r0=0.166 m at 0.5 mm, Bright NGS)
MCAO
Overall
0.436 (239nm)
Telescope
0.822 (116)
Primary (60)
Secondary (60)
Alignment (20)
Dome Seeing (50)
AO + Science Folds (58)
Fitting Error (109)
Anisoplanatism (133)
Servo Lag (26)
Instrument
0.941 (65)
MCAO
0.563(199)
Disturbances
0.606 (186)
Implementation
0.933 (69)
Windshake (34)
Diffraction, 3d LGS (48)
LGS Noise (32)
May 24-25, 2001
MCAO Preliminary Design Review
Uncorrectable errors (43)
Uncalibrated noncommon path errors (41)
Centroid gain (21)
DM-WFS registration (24)
LGS focus (12)
Component Nonlinearites (10)
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Error Pedigrees
MCAO
• Fitting error, anisoplanatism, servo lag
– Linear systems analysis
• LGS noise, diffraction, 3-d LGS: Simulation
• Windshake: Placeholder from Altair analysis
• Uncorrectable and non-common path errors:
– AO Module tolerance analysis (not final design)
• Centroid gain: AOM analysis + estimates of seeing variability
• DM-WFS misregistration
– Simulations using misregistration magnitudes from AOM tolerance
analysis (not final design)
• LGS focus drift: La Palma measurements + servo analysis
• Component nonlinearities: Allocation
May 24-25, 2001
MCAO Preliminary Design Review
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Performance with Median Seeing
MCAO
• Modeling based upon r0=0.166 m at l=0.50 mm
• Median seeing at CP has r0=0.166 m at l=0.55 mm
• Correction factors derived from seeing trade study:
l, mm
0.85
1.25
1.65
Strehl correction factor
0.711
0.854
0.913 0.950
Strehl at median seeing
0.031
0.201
0.398 0.596
May 24-25, 2001
MCAO Preliminary Design Review
2.20
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Strehl Nonuniformity over Field
MCAO
• Estimates still based upon linear systems analysis
– Presented at CoDR
– Neglect diffraction, 3-d LGS, implementation errors
• First simulation results confirm linear systems
analysis
– Only 3 points in field (center, edge, corner)
• Nonuniformity over entire field smaller by factor of 2
– Includes diffraction, 3-d LGS, representative DM-WFS
misregistration (but not non-common path errors)
l, mm
1.25
1.65
Analysis variability, %
14.94
8.99 5.23
Simulation variability, %
15.11
8.85 5.13
May 24-25, 2001
MCAO Preliminary Design Review
2.20
8
NGS Limiting Magnitude
MCAO
• Defined relative to a 50% field-averaged Strehl in
H band
• Four refinements/changes in analysis since CoDR
– Optical transmittance to NGS WFS now 0.4, not 0.5
– Field of view width now 80”, not 60”
– Closed-loop AO sharpens NGS PSF and improves gain by
factor of 1.8
– Wave front errors in NGS WFS optics are ~120 nm RMS
(small compared with uncompensated turbulence)
• Magnitude limits slightly improved by net effect
– New limits are magnitude 19.6, 19.5, and 19.2 for dark sky,
50% sky, and 80% sky
May 24-25, 2001
MCAO Preliminary Design Review
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MCAO
Sky Coverage
• Computed via Monte Carlo Simulation
– Bahcall-Soneira model
– Guide field diameter of 2.2’ (slight vignetting permitted)
– Field must contain 3 widely spaced NGS
• NGS define triangle with area > 0.5 square arc minute OR
• Triangle contains field center, and area > 0.25 square arc
minute
• Science field may be shifted +/- 15 arc seconds
Magnitudes
30 degrees
Galactic Pole
3 by 18.5 3 by 19.0 3 by 19.5 17.5 + 2 by 19.5
0.58
0.69
0.77
0.755
0.085
0.135
0.185
0.160
• Appreciable sky coverage, with margin on limiting
magnitude
May 24-25, 2001
MCAO Preliminary Design Review
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Sensitivity and Trade Studies
MCAO
• Strehl variations with seeing
• Strehl variations with LGS signal level
• Strehl variations with control bandwidth
May 24-25, 2001
MCAO Preliminary Design Review
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MCAO
Strehl Variation with Seeing
1.00
K
H
0.80
J
Strehl
• Zenith
• Linear
systems
analysis
• Turbulence
Strehl only
0.60
0.40
0.20
0.05
May 24-25, 2001
0.10
0.15
0.20
r0 at 0.50 mm
MCAO Preliminary Design Review
0.25
12
Fractional Strehl Variability at
Cerro Pachon
MCAO
Fractional Strehl Change
0.25
0.20
J
H
K
0.15
0.10
0.05
0.00
0.0
0.5
1.0
1.5
2.0
Dt, hours
May 24-25, 2001
MCAO Preliminary Design Review
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Strehl Variation with LGS Signal
Level
1.00
0.80
Strehl
• Zenith
• Linear
systems
analysis
• Turbulence
Strehl only
MCAO
K
H
0.60
J
0.40
0.20
May 24-25, 2001
Design Point
200
400
600
800
PDE’s per subaperture at 800 Hz
MCAO Preliminary Design Review
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Strehls with a Reduced Laser
Complement
MCAO
• Initial MCAO laser configuration may be descoped
due to reasons of schedule or cost
• Growth path to the full laser system should be
maintained
• One possible interim laser configuration:
– 60% nominal laser power, split into
– 1 full power and 4 half power laser guide stars
H band Strehl Ratio
Laser
Config.
Center FoV
Edge FoV
Corner FoV
Full
0.703
0.598
0.586
Interim
0.686
0.565
0.545
May 24-25, 2001
MCAO Preliminary Design Review
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Strehl Variation with Control
Bandwidth
MCAO
• 800 Hz sampling rate previously selected to
optimize conventional LGS AO performance
• CoDR committee recommended study of MCAO
performance variations with bandwidth
• Strehl variations near 800 Hz are very gradual
– Noise and servo lag effects nearly cancel
H band Strehl Ratio
Sampling
Rate, Hz
Center FoV Edge FoV
Corner FoV
700
0.710
0.601
0.579
800
0.708
0.597
0.574
900
0.706
0.593
0.569
May 24-25, 2001
MCAO Preliminary Design Review
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Pulsed vs. CW Laser Tradeoffs
MCAO
• Control loop error rejection and stability
– Reduced latency with pulsed lasers
• Operation with thin/subvisible cirrus
• Rayleigh backscatter interference
– How short a pulse is needed to avoid “fratricide?”
May 24-25, 2001
MCAO Preliminary Design Review
17
MCAO
Pulsed vs. CW: Servo Characteristics
• Baseline control law used for analysis
– c(n+1) = 0.5 c(n) + 0.5 c(n-1) + 0.5 e(n-1)
– 34 Hz closed loop bandwidth for 800 frame rate
– Conservative; simple impulse response function due to
choice of coefficients
– Reflects latency due to CW laser and LGS WFS readout
time
• Pulsed laser would reduced latency from 2 cycles to
(about) 1.1 and improve servo performance
Pulse Format
Loop
Phase Margin,
Bandwidth, Hz
Degrees
Gain Margin,
dB
CW
34.4
67.3
9.5
Pulsed
37.6
75.4
15.6
May 24-25, 2001
MCAO Preliminary Design Review
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Pulsed vs. CW: Subvisible Cirrus
MCAO
• Backscatter due to subvisible cirrus will be strong
and highly variable on timescales of seconds
• With a pulsed laser, low altitude backscatter can be
suppressed by range-gating the LGS WFS
• MCAO operation with CW lasers not possible
– Conventional LGS AO with a single beacon still feasible
• Resulting increase in total MCAO downtime is about
8% (absolute)
May 24-25, 2001
MCAO Preliminary Design Review
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MCAO
Pulsed vs. CW: Rayleigh Backscatter
• Increased background for certain subapertures
• SNR reduced from 16.8-1 to 9.5-1 due to
background photon noise
• Background fluctuations due to turbulence and laser
pointing jitter TBD
On-axis WFS
May 24-25, 2001
Corner WFS
MCAO Preliminary Design Review
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How Short a Pulse?
MCAO
• To avoid Rayleigh fratricide, laser pulses must be
short enough so that
– Rayleigh backscatter from trailing edge of pulse finishes
before sodium backscatter from leading edge begins
– Sodium backscatter from trailing edge ends before next
pulse begins
• LGS Signal will otherwise be lost due to range gating
• Fractional signal loss computed for
–
–
–
–
Uniform sodium return from 90 to 105 km altitude
Uniform laser pulse intensity
Rayleigh backscatter fratricide ending at 15 km range
700 and 800 Hz frame rates, 0 – 60 degree zenith angle
May 24-25, 2001
MCAO Preliminary Design Review
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MCAO
How Short a Pulse?
d 2 RR
t1  
f
c
1
t2 
f
s(t )  [ 0,d / f ] * [ 2 rs / c , 2 Rs / c ]
t2
rs=zs sec y

F   s(t )dt /  s(t )dt
t1
Sodium Return
Rs=Zs sec y
Fratricidal Rayleigh
RR
0
Range gate [t1,t2]
Laser pulse rate f, duty cycle d
F is the fraction of sodium return measured within range gate
May 24-25, 2001
MCAO Preliminary Design Review
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700 Hz
1.0
0.8
0.6
0.4
0.2
0.0
0
800 Hz
Relative LGS Signal
Relative LGS signal with Range
Gating to Avoid Fratricide
MCAO
1.0
0.8
0.6
0.4
0.2
0.0
20
30
40
50
60
50
60
DC = 0.00
= 0.20
= 0.25
= 0.30
= 0.40
= 0.50
0
May 24-25, 2001
10
10
20
30
40
Zenith Angle, Degrees
MCAO Preliminary Design Review
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Pulsed vs. CW: Summary
MCAO
• Pulsed format preferred
– 8% advantage (absolute) in MCAO time lost due to cirrus
– Very modest advantage in servo performance
• CW performance degradation due to fratricide TBD
– Moderate photon noise due to Rayleigh background
– Background variability due to turbulence, laser jitter TBD
– Possible subject for CTIO sodium measurement campaign
• Maximum pulse duty cycle is 30-40% for effective
range gating
– Range gating below 45-50 degrees difficult in any case
– 700 Hz pulse rate preferred if this is important
May 24-25, 2001
MCAO Preliminary Design Review
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AO Module Optical Sensitivity
Analysis
MCAO
• Optical fabrication and alignment sensitivities
computed
• Modeling accounts for partial compensation of
errors by the AO control loops
– Initial alignment in the lab
– Flexure/thermal errors during closed-loop operation
• Sensitivities computed for
–
–
–
–
Higher order wave front errors (science, NGS, LGS paths)
Pupil alignment/distortion (science, LGS paths)
Boresight (tip/tilt) errors (science, LGS paths)
DM adjustments to compensate errors
May 24-25, 2001
MCAO Preliminary Design Review
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AO Loop Model for Computing
Flexure/Thermal Sensitivities
MCAO
M2 focus, telescope pointing
Telescope
On-axis tip/tilt/
focus
DM’s
OIWFS
3 by 35 Zernikes
Least
squares fit
LGS WFS focus
• NGS WFS boresight
•
NGS
WFS’s
3x
tip/tilt
Pupil mirrors
5 by 35 Zernikes
(tilt removed)
LGS
WFS’s
Pupil alignment
5x tip/tilt
LGS pointing
May 24-25, 2001
MCAO Preliminary Design Review
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Summary and Plans
MCAO
• Modeling tools developed
– Linear systems model and wave optics simulation
– AO Module sensitivity analysis
• System performance evaluated
–
–
–
–
–
Baseline Strehls and Strehl nonuniformity
Baseline NGS magnitude limits and sky coverage
Sensitivity studies for seeing, LGS signal, control bandwidth
Pulsed vs. CW laser format
AO Module sensitivity analysis
• Plans for detailed design phase
– Further treatment of implementation errors (laser beam
quality, DM hysteresis, non common path errors, DM-toWFS misregistration…)
May 24-25, 2001
MCAO Preliminary Design Review
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MCAO
PDR Agenda
Thursday, 5/24
0800 Welcome
0805 Project overview
0830 Science case
0930 Break
0945 System overview
1015 System modeling
1100 AO Module optics
1145 Lunch
May 24-25, 2001
1245 AO Module mechanics
1340 AO Module electronics
1400 Break
1415 Beam Transfer Optics
1510 Laser Launch Telescope
1545 Closed committee session
1800 Adjourn
MCAO Preliminary Design Review
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