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### System Modeling

Brent Ellerbroek

Presentation Outline

- 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

MCAO Preliminary Design Review

Objectives and Approach

- 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

MCAO Preliminary Design Review

SimulationFeatures

- Zonal
- 2nd order Dynamics
- Misregistration

Minimal Variance

- Shack-Hartmann
- Geometric or Wave Optics
- Gain/bias calibration
- 3-D LGS
- Photon + Read Noise
- Misregistration

Science Fields

NGS’s

LGS’s

- Turbulence
- Filtered white noise
- Taylor hypothesis

LGS

Pointing

Tip/Tilt

Offload

Recon-

structor

DM’s

TTM

Common- and

Noncommon

Path Errors

LGS + NGS

WFS’s

Science

Instrument

Strehl Histories

Mean PSF’s

Strehl Budget (H Band, Zenith, r0=0.166 m at 0.5 mm, Bright NGS)

Overall

0.436 (239nm)

Instrument

0.941 (65)

MCAO

0.563(199)

Telescope

0.822 (116)

Primary (60)

Secondary (60)

Alignment (20)

Disturbances

0.606 (186)

Implementation

0.933 (69)

Dome Seeing (50)

AO + Science Folds (58)

Uncorrectable errors (43)

Uncalibrated non-common path errors (41)

Fitting Error (109)

Windshake (34)

Anisoplanatism (133)

Centroid gain (21)

Diffraction, 3d LGS (48)

Servo Lag (26)

DM-WFS registration (24)

LGS Noise (32)

LGS focus (12)

Component Non-

linearites (10)

MCAO Preliminary Design Review

Error Pedigrees

- 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

MCAO Preliminary Design Review

Performance with Median Seeing

- 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:

MCAO Preliminary Design Review

Strehl Nonuniformity over Field

- 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)

MCAO Preliminary Design Review

NGS Limiting Magnitude

- 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

MCAO Preliminary Design Review

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

- Appreciable sky coverage, with margin on limiting magnitude

MCAO Preliminary Design Review

Sensitivity and Trade Studies

- Strehl variations with seeing
- Strehl variations with LGS signal level
- Strehl variations with control bandwidth

MCAO Preliminary Design Review

Strehl Variation with Seeing

1.00

K

H

0.80

J

0.60

Strehl

0.40

0.20

0.05

0.10

0.15

0.20

0.25

- Zenith
- Linear systems analysis
- Turbulence Strehl only

r0 at 0.50 mm

MCAO Preliminary Design Review

Fractional Strehl Variability at Cerro Pachon

0.25

J

H

K

0.20

0.15

Fractional Strehl Change

0.10

0.05

0.00

0.0

0.5

1.0

2.0

1.5

Dt, hours

MCAO Preliminary Design Review

Strehl Variation with LGS Signal Level

1.00

K

0.80

H

Strehl

0.60

J

0.40

DesignPoint

0.20

200

400

600

800

PDE’s per subaperture at 800 Hz

- Zenith
- Linear systems analysis
- Turbulence Strehl only

MCAO Preliminary Design Review

Strehls with a Reduced Laser Complement

- 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

MCAO Preliminary Design Review

Strehl Variation with Control Bandwidth

- 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

MCAO Preliminary Design Review

Pulsed vs. CW Laser Tradeoffs

- 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?”

MCAO Preliminary Design Review

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

MCAO Preliminary Design Review

Pulsed vs. CW: Subvisible Cirrus

- 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)

MCAO Preliminary Design Review

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

Corner WFS

MCAO Preliminary Design Review

How Short a Pulse?

- 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

MCAO Preliminary Design Review

How Short a Pulse?

Rs=Zs sec y

Sodium Return

rs=zs sec y

RR

Fratricidal Rayleigh

Range gate [t1,t2]

Laser pulse rate f, duty cycle d

F is the fraction of sodium return measured within range gate

MCAO Preliminary Design Review

Relative LGS signal with Range Gating to Avoid Fratricide

0 10 20 30 40 50 60

1.0

1.0

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0.0

0.0

0 10 20 30 40 50 60

700 Hz

Relative LGS Signal

DC = 0.00

= 0.20

= 0.25

= 0.30

= 0.40

= 0.50

800 Hz

Zenith Angle, Degrees

MCAO Preliminary Design Review

Pulsed vs. CW: Summary

- 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

MCAO Preliminary Design Review

AO Module Optical Sensitivity Analysis

- 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

MCAO Preliminary Design Review

AO Loop Model for Computing Flexure/Thermal Sensitivities

M2 focus, telescope pointing

On-axis tip/tilt/

focus

Telescope

DM’s

OIWFS

3 by 35 Zernikes

Least

squares fit

- LGS WFS focus
- NGS WFS boresight

NGS

WFS’s

3x

tip/tilt

Pupil mirrors

Pupil alignment

LGS

WFS’s

5 by 35 Zernikes

(tilt removed)

5x tip/tilt

LGS pointing

MCAO Preliminary Design Review

Summary and Plans

- 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-to-WFS misregistration…)

MCAO Preliminary Design Review

Thursday, 5/24

0800 Welcome

0805 Project overview

0830 Science case

0930 Break

0945 System overview

System modeling

1100 AO Module optics

1145 Lunch

1245 AO Module mechanics

1340 AO Module electronics

1400 Break

1415 Beam Transfer Optics

1510 Laser Launch Telescope

Closed committee session

1800 Adjourn

PDR AgendaMCAO Preliminary Design Review

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