1. MCAO System Modeling Brent Ellerbroek

2. MCAO May 24-25, 2001MCAO Preliminary Design Review2 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

3. MCAO May 24-25, 2001MCAO Preliminary Design Review3 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

4. MCAO Science Instrument LGS + NGS WFS’s Turbulence - Filtered white noise - Taylor hypothesis Science Fields LGS’s NGS’s LGS Pointing Tip/Tilt Offload DM’s TTM Recon- structor Common- and Noncommon Path Errors Strehl Histories Mean PSF’s Simulation Features Shack- Hartmann Geometric or Wave Optics Gain/bias calibration 3-D LGS Photon + Read Noise Misregistration Zonal 2 nd order Dynamics Misregistration Minimal Variance

5. MCAO May 24-25, 2001MCAO Preliminary Design Review5 Strehl Budget (H Band, Zenith, r 0 =0.166 m at 0.5  m, Bright NGS) Overall 0.436 (239nm) Telescope 0.822 (116) Instrument 0.941 (65) Disturbances 0.606 (186) Implementation 0.933 (69) MCAO 0.563(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. MCAO May 24-25, 2001MCAO Preliminary Design Review6 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

7. MCAO May 24-25, 2001MCAO Preliminary Design Review7 Performance with Median Seeing Modeling based upon r 0 =0.166 m at =0.50  m Median seeing at CP has r 0 =0.166 m at =0.55  m Correction factors derived from seeing trade study:,  m0.851.251.652.20 Strehl correction factor0.7110.8540.9130.950 Strehl at median seeing0.0310.2010.3980.596

8. MCAO May 24-25, 2001MCAO Preliminary Design Review8 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),  m1.251.652.20 Analysis variability, %14.948.995.23 Simulation variability, %15.118.855.13

9. MCAO May 24-25, 2001MCAO Preliminary Design Review9 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

10. MCAO May 24-25, 2001MCAO Preliminary Design Review10 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 3 by 18.53 by 19.03 by 19.517.5 + 2 by 19.5 30 degrees 0.580.690.770.755 Galactic Pole 0.0850.1350.1850.160 Appreciable sky coverage, with margin on limiting magnitude

11. MCAO May 24-25, 2001MCAO Preliminary Design Review11 Sensitivity and Trade Studies Strehl variations with seeing Strehl variations with LGS signal level Strehl variations with control bandwidth

12. MCAO May 24-25, 2001MCAO Preliminary Design Review12 Strehl Variation with Seeing Zenith Linear systems analysis Turbulence Strehl only r 0 at 0.50  m 0.050.10 0.150.200.25 0.20 0.40 0.60 0.80 1.00 Strehl K H J

13. MCAO May 24-25, 2001MCAO Preliminary Design Review13 Fractional Strehl Variability at Cerro Pachon 0.20 0.25 0.05 0.10 0.15 1.5 2.01.00.5 0.0 0.00 JHKJHK  t, hours Fractional Strehl Change

14. MCAO May 24-25, 2001MCAO Preliminary Design Review14 Strehl Variation with LGS Signal 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 Strehl K H J 800600400 200 Design Point

15. MCAO May 24-25, 2001MCAO Preliminary Design Review15 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 H band Strehl Ratio Laser Config. Center FoVEdge FoVCorner FoV Full0.7030.5980.586 Interim0.6860.5650.545

16. MCAO May 24-25, 2001MCAO Preliminary Design Review16 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 H band Strehl Ratio Sampling Rate, Hz Center FoVEdge FoVCorner FoV 7000.7100.6010.579 8000.7080.5970.574 9000.7060.5930.569

17. MCAO May 24-25, 2001MCAO Preliminary Design Review17 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?”

18. MCAO May 24-25, 2001MCAO Preliminary Design Review18 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 FormatLoop Bandwidth, Hz Phase Margin, Degrees Gain Margin, dB CW34.467.39.5 Pulsed37.675.415.6

19. MCAO May 24-25, 2001MCAO Preliminary Design Review19 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)

20. MCAO May 24-25, 2001MCAO Preliminary Design Review20 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

21. MCAO May 24-25, 2001MCAO Preliminary Design Review21 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. MCAO May 24-25, 2001MCAO Preliminary Design Review22 How Short a Pulse? Range gate [t 1,t 2 ] Laser pulse rate f, duty cycle d F is the fraction of sodium return measured within range gate R Fratricidal Rayleigh Sodium Return r s =z s sec  R s =Z s sec 

23. MCAO May 24-25, 2001MCAO Preliminary Design Review23 Relative LGS signal with Range Gating to Avoid Fratricide 0 10 20 30 40 50 60 1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8 0.6 0.4 0.2 0.0 Zenith Angle, Degrees Relative LGS Signal DC = 0.00 = 0.20 = 0.25 = 0.30 = 0.40 = 0.50 800 Hz 700 Hz

24. MCAO May 24-25, 2001MCAO Preliminary Design Review24 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

25. MCAO May 24-25, 2001MCAO Preliminary Design Review25 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

26. MCAO May 24-25, 2001MCAO Preliminary Design Review26 AO Loop Model for Computing Flexure/Thermal Sensitivities Telescope Least squares fit LGS WFS’s OIWFSDM’s NGS WFS’s M2 focus, telescope pointing On-axis tip/tilt/ focus 3 by 35 Zernikes 3x tip/tilt 5 by 35 Zernikes (tilt removed) Pupil alignment Pupil mirrors 5x tip/tilt LGS pointing LGS WFS focus NGS WFS boresight

27. MCAO May 24-25, 2001MCAO Preliminary Design Review27 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…)

28. MCAO May 24-25, 2001MCAO Preliminary Design Review28 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 1245 AO Module mechanics 1340 AO Module electronics 1400 Break 1415 Beam Transfer Optics 1510 Laser Launch Telescope 1545 Closed committee session 1800 Adjourn