Low order wavefront sensor trade studyLow order wavefront sensor trade study

Richard ClareRichard Clare

NGAO meeting #4NGAO meeting #4

January 22 2007January 22 2007

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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?

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Sodium LGS at 90km

Discrete layers of turbulence, describedby Zernikes, a.

NGS at infinitygenerated with guide star statistics(Bahcall-Soneira, Spagna models)

a(1)

a(3)

a(2)

•Calculate transformation matrices from

LGS, NGS, science points to aperture

naTb nn

aTb LL

aTb ss

Modeling overview

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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

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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)

Asterism LAOS without noise

Sky cov. without noise

LAOS with noise

Sky cov. with noise

Good (equilateral)

71±9 58 115±11 84±2

25th percentile

76±13 86 88±9 119±0

Median 106±16 114 200±15 178±5

75th percentile

192±33 221 480±52 334±4

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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

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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

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Example Cumulative Density Function

Errors are in nm. 1 mas =12.1 nm for a 10m telescope

Field Galaxies science caseJ band

30th percentile=107nm

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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

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Spectral BandErrors are in nm. 1 mas =12.1 nm for a 10m telescope

Tip/tilt error (nm)

Spectral band

10th percentile Median 90th percentile

V 198 326 1140*

J 80 131 221

H 78 127 212

K 99 161 261

For field galaxies science case and 1 TTFA + 2TT sensors

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NGS Patrol Field Diameter

For field galaxies science case, J band, and 1 TTFA + 2TT sensors

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LOWFS number & order

Tip/tilt error (nm)

LOWFS 10th percentile Median 90th percentile

1 TT 152 209 359

1 TTFA 125 215 312

3 TT 90 146 263

1 TTFA + 2TT

80 131 221

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)

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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)

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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)

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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 N 317 284 277

Narrow Field 116 96 94

Field Galaxies

156 131 127

Errors are in nm. 1 mas =12.1 nm for a 10m telescope

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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