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)

AO4ELT Paris, June 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 ~ m Anisoplanatism effects Non-uniformity of the Na density profile Rayleigh scattering Sodium layer Detector plane Pupil plane

AO4ELT Paris, June 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

AO4ELT Paris, June Multi-LGS wavefront reconstruction Model of measurements: errors wavefront 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

5 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,

AO4ELT Paris, June 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 nm Even 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]

AO4ELT Paris, June Spot elongation: launch from M1 side… why does it work? Lowest elongation where the layer is seen only once Courtesy M. Tallon & al. Information redundancy for large elongated spots Side launch Central launch Schematic sketch with 3 LGSs

AO4ELT Paris, June 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 effects 21 m / 6 LGS (launch behind M2)

AO4ELT Paris, June 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

AO4ELT Paris, June 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 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)

AO4ELT Paris, June 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 ??

AO4ELT Paris, June 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 m16 m21 m32 m Center Edge Not ellong

AO4ELT Paris, June of a MAP 1.Development of a fast & memory efficient modal matrix-based MAP reconstructor using “analytical” WCoG [1,2] [1] Sandrine Thomas et al, MNRAS 2008, [2] Laura Schreiber et al, MNRAS Edge launching is better than central launching RMS error 20% smaller when fratricide effect is accounted for warning: LGS spot anisoplanatism neglected… 3. 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. 4.Pupil segmentation (spider, fratricide effect) has limited effect with regularized reconstruction (MAP) Conclusion

AO4ELT Paris, June 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 (2006). Impact through tomographic reconstruction: see Nicolas Muller’s Poster Impact of Cn2 profile uncertainties in altitude and strength (presentations of Conan, Fusco) Perspectives

AO4ELT Paris, June Calculation of the LGS spot elongation When focalised at 90 km height and with 10 km thickness LGS lauched at 21m with 2 arcmin from optical axis has a spot elongation of 5 arcsec in the telescope focal plane 1 h 2 h h2h2 1  e =  2 -  1 h2h2 h2.h2. h 1. h1h1 h1h1 ~ r r + r

AO4ELT Paris, June What do we want to learn ? Is LS estimator sufficient ? Errors non uniform Is WLS estimator better ? Errors non uniform Correlation on the errors Kolmogorov a priori useful? MAP (MMSE) Use of multi-LGS ? GLAO, MCAO, MOAO, LTAO Errors correlated on x and y x y

AO4ELT Paris, June Pure wavefront reconstruction methods Model of measurements: Least Squares: errors wavefront Wavefront sensor (Shack-Hartmann, Fried ?geometry, …) Matrix to invert Weighted Least Squares: covariance of the errors (centred) Minimum Variance (=MAP): Covariance of the wavefront

AO4ELT Paris, June Phase estimators: LS, WLS, uniform noise MAP, & MAP Telescope diameter: from 4,2 m to 42m cases subap FoV = 10", seeing = 1.2", OPD without elongation: 1 rad nm Estimation of WFE (nm) in SFoV directions (bias^2 + noise_variance) 3 LGS Validation OK in a “GLAO” configuration as Tallon (SPIE 08) alias multi-LGS with pupil-only turbulence! (no anisoplanatism) 3 LGS Propagation of multi-LGS slope noise

AO4ELT Paris, June WFE + 15 nm : 80 nm compared to 65 nm Impact of fratricide effect Downscaled E2E simulation Telescope = 21m & 0.5 m subap 6 LGS on 1 min ring (MAORY-like) low LGS flux: 250 photons/subap/frame & 0 e- RON

AO4ELT Paris, June Summary of fratricide effect impact LGS constellation ring diameter xx MAORY 1 arcmin ATLAS 1.5 arcmin ATLAS 2.1 arcmin EAGLE 3.6 arcmin Low LGS flux RON=0 e nm+14 nm+13 nm+12 nm Medium LGS flux RON=3 e- +11 nm+10 nm +8 nm Downscaled E2E simulation Telescope = 21m & 0.5 m subaperure 6 LGS on xx arcmin ring

AO4ELT Paris, June Medium LGS flux, WFE + 2 nm Downscaled E2E simulation Telescope = 21 m & 0.5 m subap 6 LGS on 1 arcmin ring (MAORY-like) homothetic spider Thickness respected ~1 sub-aperture Impact of pupil segmentation [no fratricide effect] 8-arms spider

AO4ELT Paris, June MAORY-like case with fratricide & spider effects Downscaled E2E simulation Telescope = 21 m & 0.5 m subap 6 LGS on 1 min ring Medium LGS flux: 500 photons/subap/frame & 3 e- RON homothetic spider Thickness respected ~1 sub-ap 3 reconstructed layers rms error 30% smaller with edge launching Absolute error value estimated in 32 m telescope case Uniform performance in MAORY FoV

AO4ELT Paris, June Estimation of WFS error through tomographic reconstruction Impact of 3D phase and scintillation anisoplanatism [synergy with Nicolas Muller Onera] Analytical expression exists for 2D object [3] Scintillation and phase anisoplanatism in Shack-Hartmann wavefront sensing. Clélia Robert et al. JOSA A, Vol. 23, Issue 3, pp (2006). => estimation at sub-aperture level for largest elongations (worst case) Account for 3D shape of the spot through propagation code (PILOT) on downscaled cases : no difference with 2D object First results show that it is not negligible on very elongated spots in edge launching. So serious? these data are also almost discarded because of poor SNR… Impact through tomographic reconstruction: see Poster [unit = nm rms of sub-ap edge OPD along elongated axis] central launching = 30 nm ; edge launching = 93 nm

AO4ELT Paris, June Estimation of WFS error through tomographic reconstruction Impact of LGS noise signature on modal tomographic reconstruction Account for spot elongation pattern related to the laser launching option Reconstruction using MAP estimator on downscaled cases: 21m, LGS angle and height scaled with D, 3 layers... Various spot position estimators (WCoG) Account for additive fratricide background Account for pupil segmentation (spider) 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 (2006). Impact through tomographic reconstruction: see Nicolas Muller’s Poster

AO4ELT Paris, June Impact of the number of reconstructed layers ATLAS Two LGS asterisms 3 arcmin and 4.2 arcmin 3 and 5 reconstructed layers