MCAO System Modeling Brent Ellerbroek. MCAO May 24-25, 2001MCAO Preliminary Design Review2 Presentation Outline Modeling objectives and approach Updated

MCAOMCAO

System ModelingSystem Modeling

Brent Ellerbroek

May 24-25, 2001 MCAO Preliminary Design Review

2

MCAOMCAO

Presentation OutlinePresentation 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


3

MCAOMCAO

Objectives and ApproachObjectives 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

MCAOMCAO

ScienceInstrument

LGS + NGSWFS’s

Turbulence- Filtered white noise- Taylor hypothesis

Science FieldsLGS’s

NGS’s

LGSPointing

Tip/TiltOffload

DM’sTTM

Recon-structor

Common- andNoncommonPath Errors

Strehl HistoriesMean PSF’s

SimulatiSimulationonFeaturesFeatures

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

• Zonal• 2nd order Dynamics• Misregistration

Minimal Variance


5

MCAOMCAOStrehl Budget (H Band, Zenith, Strehl Budget (H Band, Zenith, rr00=0.166 m at 0.5 =0.166 m at 0.5 m, Bright m, Bright NGS)NGS)

Overall0.436 (239nm)

Telescope0.822 (116)

Instrument0.941 (65)

Disturbances0.606 (186)

Implementation0.933 (69)

MCAO0.563(199)

Fitting Error (109)

Anisoplanatism (133)

LGS Noise (32)

Diffraction, 3d LGS (48)

Windshake (34)Uncalibrated non-common path errors (41)Centroid gain (21)DM-WFS registration (24)

Primary (60)Secondary (60)Alignment (20)Dome Seeing (50)AO + Science Folds (58)

Component Non-linearites (10)

LGS focus (12)

Uncorrectable errors (43)

Servo Lag (26)


6

MCAOMCAO

Error PedigreesError 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


7

MCAOMCAOPerformance with Median Performance with Median SeeingSeeing

• Modeling based upon r0=0.166 m at =0.50 m

• Median seeing at CP has r0=0.166 m at =0.55 m

• Correction factors derived from seeing trade study:

, m 0.85 1.25 1.65 2.20

Strehl correction factor 0.711 0.854 0.913

0.950

Strehl at median seeing

0.031 0.201 0.398

0.596


8

MCAOMCAOStrehl Nonuniformity over Strehl Nonuniformity over FieldField

• 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), m 1.25 1.65 2.20

Analysis variability, % 14.94 8.99 5.23

Simulation variability, % 15.11 8.85 5.13


9

MCAOMCAO

NGS Limiting MagnitudeNGS 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


10

MCAOMCAO

Sky CoverageSky 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 3 by 18.5

3 by 19.0

3 by 19.5

17.5 + 2 by 19.5

30 degrees 0.58 0.69 0.77 0.755

Galactic Pole

0.085 0.135 0.185 0.160• Appreciable sky coverage, with margin on limiting magnitude


11

MCAOMCAOSensitivity and Trade Sensitivity and Trade StudiesStudies

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


12

MCAOMCAO

Strehl Variation with SeeingStrehl Variation with Seeing

• Zenith• Linear

systems analysis

• Turbulence Strehl only

r0 at 0.50 m

0.05 0.10 0.15 0.20 0.25

0.20

0.40

0.60

0.80

1.00

Str

ehl

KH

J


13

MCAOMCAOFractional Strehl Variability Fractional Strehl Variability at Cerro Pachonat Cerro Pachon

0.20

0.25

0.05

0.10

0.15

1.5 2.01.00.50.00.00

JHK

t, hours

Fra

ctio

nal S

treh

l Cha

nge


14

MCAOMCAOStrehl Variation with LGS Strehl Variation with LGS Signal LevelSignal Level

• Zenith• Linear

systems analysis

• Turbulence Strehl only

PDE’s per subaperture at 800 Hz

0.20

0.40

0.60

0.80

1.00

Str

ehl

K

H

J

800600400200

Design Point


15

MCAOMCAOStrehls with a Reduced Laser Strehls with a Reduced Laser ComplementComplement

• 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

Corner FoV

Edge FoVCenter FoV

Laser Config.

0.5860.5980.703Full

0.5450.5650.686Interim


16

MCAOMCAOStrehl Variation with Control Strehl Variation with Control BandwidthBandwidth

• 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


17

MCAOMCAOPulsed vs. CW Laser Pulsed vs. CW Laser TradeoffsTradeoffs

• 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?”


18

MCAOMCAOPulsed vs. CW: Servo Pulsed vs. CW: Servo CharacteristicsCharacteristics

• 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 performancePulse

FormatLoop

Bandwidth, Hz

Phase Margin, Degrees

Gain Margin, dB

CW 34.4 67.3 9.5

Pulsed 37.6 75.4 15.6


19

MCAOMCAOPulsed vs. CW: Subvisible Pulsed vs. CW: Subvisible CirrusCirrus

• 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)


20

MCAOMCAOPulsed vs. CW: Rayleigh Pulsed vs. CW: Rayleigh BackscatterBackscatter

• 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


21

MCAOMCAO

How Short a Pulse?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


22

MCAOMCAO

How Short a Pulse?How Short a Pulse?

2

1 0

]/2,/2[]/,0[

2

1

)(/)(

*)(

1

2

t

t

cRcrfd

R

dttsdttsF

ts

ft

c

R

f

dt

ss

Range gate [t1,t2]Laser pulse rate f, duty cycle dF is the fraction of sodium return measured within range gate

RRFratricidal Rayleigh

Sodium Returnrs=zs sec

Rs=Zs sec


23

MCAOMCAORelative LGS signal with Relative LGS signal with Range Gating to Avoid Range Gating to Avoid FratricideFratricide

0 10 20 30 40 50 60

0 10 20 30 40 50 60

1.0

0.80.60.4

0.20.0

1.0

0.80.60.4

0.20.0

Zenith Angle, Degrees

Rel

ativ

e L

GS

Sig

nal

DC = 0.00 = 0.20 = 0.25 = 0.30 = 0.40 = 0.50

800

Hz

700

Hz


24

MCAOMCAO

Pulsed vs. CW: SummaryPulsed 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


25

MCAOMCAOAO Module Optical AO Module Optical Sensitivity AnalysisSensitivity 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


26

MCAOMCAOAO Loop Model for AO Loop Model for Computing Flexure/Thermal Computing Flexure/Thermal SensitivitiesSensitivities

Telescope

Leastsquares fit

LGSWFS’s

OIWFSDM’s

NGSWFS’s

M2 focus, telescope pointing

On-axis tip/tilt/focus

3 by 35 Zernikes

3xtip/tilt

5 by 35 Zernikes(tilt removed)

Pupil alignment

Pupil mirrors

5x tip/tilt

LGS pointing

• LGS WFS focus• NGS WFS boresight


27

MCAOMCAO

Summary and PlansSummary 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…)


28

MCAOMCAO

PDR AgendaPDR Agenda

Thursday, 5/240800 Welcome 0805 Project overview 0830 Science case0930 Break0945 System overview1015 System modeling1100 AO Module optics1145 Lunch

1245 AO Module mechanics1340 AO Module electronics1400 Break1415 Beam Transfer Optics1510 Laser Launch

Telescope1545 Closed committee

session1800 Adjourn

Documents

MCAO System Modeling Brent Ellerbroek. MCAO May 24-25, 2001MCAO Preliminary Design Review2 Presentation Outline Modeling objectives and approach Updated