Clélia Robert 1 , Jean-Marc Conan 1 , Damien Gratadour 2 ,

1. 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 1 ONERA, 2 Obs. Meudon (LESIA)

2. 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 Pupil plane Detector plane Expected Noise for LGS-HO-WFS ~10 km Sodium ~90 km ~20 km Turbulence

3. 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

4. Multi-LGS wavefront reconstruction wavefront errors Covariance of the wavefront • Model of measurements: Wavefront sensor(Shack-Hartmann) • Minimum Variance (=MAP): Errors correlated on x and y Covariance of the errors (centred) • Propagation of multi-LGS slope noise • Modal matrix-based simulation tool for {tomography + noise} wavefront error (WFE)

5. Science target 6 Sodium LGS: altitude 90km ELT, 42m Principle of tomographic simulations 10 km LGS thickness -> 5 km, 6 LGS altitude : 45 km 1:2 scaling • The atmosphere • is not scaled vertically! 21m Sketches courtesy R. Myers • 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 (!)

6. Impact of launching scheme: Central (M2) vs edge (M1) • 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 [no fratricide effect] Tomographic performance M1 ≡ M2 about 59 nm Even a small gain for edge launching Edge launching gives more uniform propagation onto modes !

7. Spot elongation: launch from M1 side… why does it work? Centrallaunch Side launch Lowest elongation where the layer is seen only once Information redundancy for large elongated spots Schematic sketch with 3 LGSs Courtesy M. Tallon & al.

8. Modeling of fratricide background • 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 LGSWFS algorithm definition & WFS design (correlation) Examples of fratricide effects 21 m / 6 LGS (launch behind M2)

9. 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

10. Summary of fratricide effect impact • 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)

11. Impact of the number of reconstructed layers ATLAS project LGS asterism 4.2 arcmin WFE stable with 10 reconstructed layers in a 10 m telescope simulation Impact of Cn2 profile uncertainties in altitude and strength ??

12. 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

13. Conclusion • Development of a fast & memory efficient modalmatrix-basedMAPreconstructor using “analytical” WCoG [1,2] • [1] Sandrine Thomas et al, MNRAS 2008, [2] Laura Schreiber et al, MNRAS 2009 • Edge launching is better than central launching • RMS error 20% smaller when fratricide effect is accounted for • warning: LGS spot anisoplanatism neglected… • 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 • Pupil segmentation (spider, fratricide effect) has limited effect with regularized reconstruction (MAP)

14. Perspectives • 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)