Shack-Hartmann tomographic wavefront reconstruction using LGS:

Analysis of spot elongation and fratricide effect

Clélia Robert1, Jean-Marc Conan1, Damien Gratadour2,

Thierry Fusco1,Cyril Petit1, Jean-François Sauvage1, Nicolas Muller1

11 ONERA, ONERA, 22 Obs. Meudon (LESIA) Obs. Meudon (LESIA)

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Expected Noise for LGS-HO-WFS

Turbulence

Sodium ~10 km

~20 km

~90 km

• Backscattering of the laser in the Sodium layer at an altitude of ~90 km

• Laser emission:10 km thickness• Paralax effect on ELT

Spot elongation ~ 10 " @ 42 m• Anisoplanatism effects• Non-uniformity of the Na density profile• Rayleigh scattering

Sodium layer

Detector plane

Pupil plane

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Outline

• Modal wavefront tomography & model description

• Central/Edge LGS launching

• Impact of fratricide effect

• Number of reconstructed layers

• Up to 32 m telescope

• Conclusion & perspectives

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Multi-LGS wavefront reconstruction

• Model of measurements:

errorswavefront

Wavefront sensor(Shack-Hartmann)

Covariance of the errors (centred)

• Minimum Variance (=MAP): Covariance of the wavefront

• Propagation of multi-LGS slope noise

• Modal matrix-based simulation tool for {tomography + noise} wavefront error (WFE)

Errors correlated on x and y

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Principle of tomographic simulations

The atmosphere is not scaled vertically!

1:2 scaling

ELT, 42m

6 Sodium LGS: altitude 90km

Science target

21m

6 LGS altitude : 45 km

• Telescope diameter 21 m, 42x42 sous-pupilles, central occultation factor 0.3• No distorsion of Sodium profile•Images = elongated Gaussian, subap. FoV 10x10 arcsec^2, pixscale=0.75 “• Modal (KL) matrix-based MAP wavefront reconstruction with analytical WCoG • Tip/tilt LGS measurement, plane waves (!)

Sketches courtesy R. Myers

10 km LGS thickness -> 5 km,

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Downscaled simulation (1:2)•Telescope = 21m & 0.5 m subap

•6 LGS on 1 min ring (MAORY-like) •Medium LGS flux:

500 photons/subap/frame & 3 e- RON

Tomographic performance M1 ≡ M2

about 59 nmEven a small gain for edge launching

Edge launching gives more uniform propagation onto modes !

Impact of launching scheme: Central (M2) vs edge (M1)

[no fratricide effect]

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Spot elongation: launch from M1 side… why does it work?

Lowest elongation where the layer is seen only once

Courtesy M. Tallon & al.

Information redundancyfor large elongated spots

Side launchCentral launch

Schematic sketch with 3 LGSs

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performed by D. Gratadour (LESIA) based on Gemini code

code has been validated with experimental data (Gemini...)

common activity for MAORY / ATLAS / EAGLE studies

– Currently used for LGS tomography analysis (see next slides) – Will be used for Optimal LGS WFS algorithm definition & WFS design (correlation)

Modeling of fratricide background

Examples of fratricide effects21 m / 6 LGS (launch behind M2)

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MAORY-like case with fratricide

Downscaled simulation • Telescope = 21m & 0.5 m subap

• 6 LGS on 1 min ring •Medium LGS flux:

500 photons/subap/frame & 3 e- RON

rms error 20% smaller with edge launching

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Summary of fratricide effect impact

LGS

constellation ring diameter xx

MAORY

1 arcmin

ATLAS

2.1 arcmin

EAGLE

3.6 arcmin

Low

LGS flux

RON=0 e-

+ 47 nm

[+ 15 nm]

+46 nm

[+13 nm]

+47 nm

[+12 nm]

Medium LGS flux

RON=3 e-+37 nm

[+11 nm]

+38 nm

[+10 nm]

+36 nm

[+ 8 nm]

Downscaled simulation • Telescope = 21m & 0.5 m subaperure

• 6 LGS on xx arcmin ring

Quite uniform and moderate impact for each LGS asterism (in quadratic difference)Quite uniform and moderate impact for each LGS asterism (in quadratic difference)

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Impact of the number of reconstructed layers

ATLAS project

LGS asterism 4.2 arcmin

WFE (nm) 3 layers 5 layers

Centre with elongation

60 58

Edge with elongation

59 56

Without elongation

42 39

WFE stable with 10 reconstructed layers in a 10 m telescope simulation Impact of Cn2 profile uncertainties in altitude and strength ??

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Up to 32 m telescope simulation

• Fast & memory efficient developments for 42m simulations • Modal KL matrix-based MAP reconstruction, sparse matrices multiplication and storage• WFE still grows up in a 32 m telescope case: More unseen modes up to 2600 KL involved

Medium LGS flux, 2 reconstructed layers, with spider

Telescope diameter

10 m 16 m 21 m 32 m

Center 41 53 56 69

Edge 42 56 55 71

Not ellong. 31 39 38 49

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1. Development of a of a fast & memory efficient modal matrix-based MAPMAP reconstructor using “analytical” WCoG [1,2]

[1] Sandrine Thomas et al, MNRAS 2008, [2] Laura Schreiber et al, MNRAS 2009

2. Edge launching is better than central launchingRMS error 20% smaller when fratricide effect is accounted for

warning: LGS spot anisoplanatism neglected…

3. WFS noise model: “slope equivalent uniform noise”factor 2 reduction in noise variance wrt simplistic single LGS channel + not regularized reconstruction

even with relaxed requirement on photon flux (typically 500 ph/subap/frame with 3 e- RON)

Confirmed on 32m case

4. Pupil segmentation (spider, fratricide effect) has limited effect with regularized reconstruction (MAP)

Conclusion

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• Fast modal reconstructor development

• Spherical versus plane waves tomography & comparison with zonal E2E tool & Fourier codes (Cyril Petit presentation)

• LGS tomography activity gives updated “slope equiv. uniform noise” for

Fourier code update of MAORY / ATLAS / EAGLE projects (presentations of Diolaiti, Fusco, Rousset)

• Analysis of LGS spot anisoplanatism (phase and scintillation)[3] Scintillation and phase anisoplanatism in Shack-Hartmann wavefront sensing. Clélia Robert et al. JOSA A, Vol. 23, Issue 3, pp. 613-624 (2006).

Impact through tomographic reconstruction: see Nicolas Muller’s Poster

• Impact of Cn2 profile uncertainties in altitude and strength (presentations of Conan, Fusco)

Perspectives