1. Low order wavefront sensor trade study Richard Clare NGAO meeting #4 January 22 2007

2. 2 Outline Background on sky coverage simulator Assumptions and parameter set chosen for NGAO What spectral band should we use for the LOWFS? How many LOWFS do we need? What modes should the LOWFS measure? What is the sky coverage for different science cases? What is the effect of the LGS asterism radius on partial correction and sky coverage?

3. 3 Sodium LGS at 90km Discrete layers of turbulence, described by Zernikes, a. NGS at infinity generated with guide star statistics (Bahcall-Soneira, Spagna models) a(1) a(3) a(2) Calculate transformation matrices from LGS, NGS, science points to aperture Modeling overview

4. 4 Simulator methodology Calculate atmospheric tip/tilt error with minimum variance estimator from transformation matrices and covariance matrices of atmosphere & noise Optimize sampling frequency to balance servo lag and noise Choose combination of NGS that gives lowest total error Monte Carlo over many NGS constellations Generate cumulative density functions of performance

5. 5 Checking against an AO Simulation Compare to LAOS for 4 asterisms for an 8m telescope with no windshake, no sodium tracking error, integrator control, and 10 phase screens for each asterism –Generally good agreement, but LAOS results somewhat poorer with noise Median tip/tilt error (nm) AsterismLAOS without noise Sky cov. without noise LAOS with noise Sky cov. with noise Good (equilateral) 71±958115±1184±2 25 th percentile 76±138688±9119±0 Median106±16114200±15178±5 75 th percentile 192±33221480±52334±4

6. 6 Simulation Parameters/Assumptions Finite outer scale (75m) Mauna Kea (7 layer) turbulence and velocity profile First 6 Zernike orders considered, only tip/tilt errors are evaluated Detector pixels are seeing-limited in V band (0.5 arc sec) and diffraction-limited in J/H/K bands (λ /D rads) NGS are partially corrected in J/H/K bands. Not in V band. Integral control with g=0.5 7 LGS asterism (1 on-axis, 6 in a ring) = Ralf’s asterism 7a LGS measurements are noise-free Limiting magnitude is chosen to be 19 for all spectral bands At zenith Read noise = 10 e Run over 500 NGS constellations

7. 7 Median Field of View J=16.4 Field Galaxies case: Latitude=30 deg J=17.1 J=19.0 J=17.4 J=18.7 J=16.6

8. 8 Example Cumulative Density Function Errors are in nm. 1 mas =12.1 nm for a 10m telescope Field Galaxies science case J band 30 th percentile=107nm

9. 9 Choice of Spectral Band Trade-off between: 1.Partial correction 2.Sky background 3.Zeropoint (number of photons) 4.Spot size As λ increases, tip/tilt estimate

10. 10 Spectral Band Errors are in nm. 1 mas =12.1 nm for a 10m telescope Tip/tilt error (nm) Spectral band 10 th percentileMedian90 th percentile V1983261140* J80131221 H78127212 K99161261 For field galaxies science case and 1 TTFA + 2TT sensors

11. 11 NGS Patrol Field Diameter For field galaxies science case, J band, and 1 TTFA + 2TT sensors

12. 12 LOWFS number & order Tip/tilt error (nm) LOWFS10 th percentileMedian90 th percentile 1 TT152209359 1 TTFA125215312 3 TT90146263 1 TTFA + 2TT 80131221 Errors are in nm. 1 mas =12.1 nm for a 10m telescope For field galaxies science case, and J band TT=tip/tilt (ie 1x1), TTFA=tip/tilt/focus/astigmatism (2x2)

13. 13 Different science cases Three science cases chosen from NGAO proposal Science cases have different higher order error, galactic latitude and science field size 1.Goods N (218 nm, 45 deg, 1.09 arc min) 2.Narrow Field (86 nm, 10 deg, 0.178 arc min) 3.Field Galaxies (173nm, 30 deg, 0.7 arc min)

14. 14 Degree of partial correction Partial correction depends on LGS asterism radius and higher order error from science case Goods N (218nm)Field galaxies (173nm) Narrow Field (86nm)

15. 15 Median results for science cases/asterisms Median tip/tilt error (nm) Science Case LGS radius =7”.2 LGS radius =21”.6 LGS radius =35”.9 Goods N317284277 Narrow Field1169694 Field Galaxies 156131127 Errors are in nm. 1 mas =12.1 nm for a 10m telescope

16. 16 Conclusions IR WFS (either J or H) is preferable to visible Multiple NGS WFS significantly improve tip/tilt estimate Measuring focus with 1 of the tilt sensors also helps A wider LGS asterism improves partial correction over the field and hence sky coverage