ShackHartmann tomographic wavefront reconstruction using LGS Analysis of

Shack-Hartmann tomographic wavefront reconstruction using LGS: Analysis of spot elongation and fratricide effect Clélia Robert 1, Jean-Marc Conan 1, Damien Gratadour 2, Thierry Fusco 1, Cyril Petit 1, Jean-François Sauvage 1, Nicolas Muller 1 1 ONERA, 2 Obs. Meudon (LESIA)

Expected Noise for LGS-HO-WFS • • • Sodium ~10 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 AO 4 ELT Paris, June 22 -26 2009 ~90 km 2 Turbulence ~20 km Pupil plane Detector plane

AO 4 ELT Paris, June 22 -26 2009 Outline 3 • Modal wavefront tomography & model description • Central/Edge LGS launching • Impact of fratricide effect • Number of reconstructed layers • Up to 32 m telescope • Conclusion & perspectives

Multi-LGS wavefront reconstruction wavefront • errors Model of measurements: Wavefront sensor (Shack-Hartmann) • Minimum Variance (=MAP): AO 4 ELT Paris, June 22 -26 2009 Errors correlated on x and y 4 Covariance of the wavefront Covariance of the errors (centred) • Propagation of multi-LGS slope noise • Modal matrix-based simulation tool for {tomography + noise} wavefront error (WFE)

Principle of tomographic simulations Science target 10 km LGS thickness -> 5 km, 6 LGS altitude : 45 km 6 Sodium LGS: altitude 90 km 1: 2 scaling The atmosphere is not scaled vertically! 21 m Sketches courtesy R. Myers ELT, 42 m • Telescope diameter 21 m, 42 x 42 sous-pupilles, central occultation factor 0. 3 • No distorsion of Sodium profile • Images = elongated Gaussian, subap. Fo. V 10 x 10 arcsec^2, pixscale=0. 75 “ • Modal (KL) matrix-based MAP wavefront reconstruction with analytical WCo. G • Tip/tilt LGS measurement, plane waves (!) 5

Impact of launching scheme: Central (M 2) vs edge (M 1) AO 4 ELT Paris, June 22 -26 2009 Downscaled simulation (1: 2) • Telescope = 21 m & 0. 5 m subap • 6 LGS on 1 min ring (MAORY-like) • Medium LGS flux: 500 photons/subap/frame & 3 e- RON 6 [no fratricide effect] Tomographic performance M 1 ≡ M 2 about 59 nm Even a small gain for edge launching Edge launching gives more uniform propagation onto modes !

Spot elongation: launch from M 1 side… why does it work? AO 4 ELT Paris, June 22 -26 2009 Central launch 7 Side launch Lowest elongation where the layer is seen only once Schematic sketch with 3 LGSs Courtesy M. Tallon & al. Information redundancy for large elongated spots

Modeling of fratricide background performed by D. Gratadour (LESIA) based on Gemini code has been validated with experimental data (Gemini. . . ) common activity for MAORY / ATLAS / EAGLE studies AO 4 ELT Paris, June 22 -26 2009 Examples of fratricide effects 21 m / 6 LGS (launch behind M 2) 8 – Currently used for LGS tomography analysis (see next slides) – Will be used for Optimal LGS WFS algorithm definition & WFS design (correlation)

MAORY-like case with fratricide AO 4 ELT Paris, June 22 -26 2009 Downscaled simulation • Telescope = 21 m & 0. 5 m subap • 6 LGS on 1 min ring • Medium LGS flux: 500 photons/subap/frame & 3 e- RON 9 rms error 20% smaller with edge launching

Summary of fratricide effect impact AO 4 ELT Paris, June 22 -26 2009 Downscaled simulation • Telescope = 21 m & 0. 5 m subaperure • 6 LGS on xx arcmin ring 10 LGS constellation ring diameter xx MAORY ATLAS EAGLE 1 arcmin 2. 1 arcmin 3. 6 arcmin Low LGS flux RON=0 e- + 47 nm +46 nm +47 nm [+ 15 nm] [+13 nm] [+12 nm] Medium LGS flux RON=3 e- +37 nm +38 nm +36 nm [+11 nm] [+10 nm] [+ 8 nm] Quite uniform and moderate impact for each LGS asterism (in quadratic difference)

Impact of the number of reconstructed layers AO 4 ELT Paris, June 22 -26 2009 ATLAS project LGS asterism 4. 2 arcmin 11 WFE stable with 10 reconstructed layers in a 10 m telescope simulation Impact of Cn 2 profile uncertainties in altitude and strength ? ?

Up to 32 m telescope simulation • • AO 4 ELT Paris, June 22 -26 2009 • 12 Fast & memory efficient developments for 42 m 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

Conclusion 1. 2. Development of a fast & memory efficient modal matrix-based MAP reconstructor using “analytical” WCo. G [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… 3. WFS noise model: “slope equivalent uniform noise” AO 4 ELT Paris, June 22 -26 2009 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) 13 Confirmed on 32 m case 4. Pupil segmentation (spider, fratricide effect) has limited effect with regularized reconstruction (MAP)

Perspectives • Fast modal reconstructor development • Spherical versus plane waves tomography & comparison with zonal E 2 E 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) AO 4 ELT Paris, June 22 -26 2009 • 14 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 Cn 2 profile uncertainties in altitude and strength (presentations of Conan, Fusco) •