1. Low order modes sensing for LGS MCAO with a single NGS S. Esposito, P. M. Gori, G. Brusa Osservatorio Astrofisico di Arcetri Italy Conf. AO4ELT 23-26 June 2009, Paris. Presented by: S. Esposito

2. Presentation overview The technique concept First numerical simulations The achieved results Low order modes indetermination in LGS MCAO Conf. AO4ELT 23-26 June 2009, Paris.

3. Low Order Modes indetermination The general configuration for an MCAO system assumes to discard the global tip- tilt signal measured by the LGSs. However the global tilt of LGS is generated by the projection of all Zernike modes given on the meta-pupils on Z2 and Z3 of the conical LGS footprints. So, discarding LGS global tilt some information is lost Blue: layer 1.0 km Red: layer 8.0 km Residual rms [rad] Zernike mode # Corrected FoV 2 arcminutes LGS = 4 DM = 2 Layer = 2 (1.0km, 8km) #modes = 50 The atmospheric perturbation is perfectly reconstructed when the tip-tilt of the LGS is correctly measured and included in the MCAO reconstructor. Z4,Z5,Z6 Conf. AO4ELT 23-26 June 2009, Paris. A single realization example

4. The technique principle AO4ELT, 22-26 June, 2009, Paris. 1)Recover the LGSs global tilt information. Using this information the MCAO reconstruction WF residuals affects only low order modes (those having singular eigenvalues). 2) Use measurements from a single NGS placed inside the MCAO FOV to recover low order modes over the various MCAO system metapupils. The talk will be focused on the case of 2 DMs. Initial results for 3 DMs will be described later. In all the work the wavefront sensing is simulated by decomposing the received wavefront into zernike polinomials.

5. LGS upward path c LGS displacement due to layer tilt Layer perturbation over metapupil Including upward tilt in MCAO interaction matrix The MCAO interaction matrix including upward and downward propagation is obtained by subtracting two lines of the upward IM to the MCAO reconstructor (downward IM). Downw ard IM Upward IM Dw-Up IM Conf. AO4ELT 23-26 June 2009, Paris. Atm. layers MCAO example configuration 4 LGS located on xy axis DM = 2 Z4 to Z11 reconstructed Z2 to Z11 measured (LGS) LGS tilt signal can be achieved by taking into account the upward propagation of the LGS in the MCAO reconstructor. T_lgs = T_dw – T_up - =

6. Total MCAO IM MCAO example configuration Corrected FoV 2 arcmin 4 LGS 2 DM Z4 to Z11 reconstructed modes Z2 to Z11 measured (LGS) LGS #1 LGS #2 LGS #3 LGS #4 DM #1DM #2 The IM quantified the effect on the LGS WFS of the Zernike modes 4 to 11 applied on the two metapupils. Zernike 2 & 3 are not applied giving null measurements on the WFS. Applied modes on system metapupils (Z4-Z11) 3 Eigenvalues ≈ 10^-8 Measured modes on WFS #1 (Z2- Z11) Conf. AO4ELT 23-26 June 2009, Paris. Error for modes higher then Z6 is negligible Z modes # Residual rms log scale [rad]

7. 2DM case: recovering Z4,Z5 & Z6 from NGS We use the information from 1 NGS in the FoV to reconstruct Z4,Z5,Z6 on the 2 DM 3 Eigenvalues ≈ 10^-8 Case for LGS reconstructor only (2DM, 2L). Focus combination on the two DMs is badly seen because the ratio between focus and tilt introduced on the LGS footprint by a focus on the metapupil is constant and do not depend on height h of the layer. Using Z4,Z5 and Z6 measurement on NGS having a different footprint geometry permits focus measurement with a different ratio. So, ambiguity is solved. DM 1DM 2  are the coefficients projecting focus on metapupil in focus over LGS and NGS footprint. C_cil(Z4), C_con(Z4) are the contributions to measured Z4 due to all Zs over the metapupils unknowns

8. Iso and aniso-planatic tip-tilt A global tilt on the metapupil generates the same LGS & LGS tip tilt all over the MCAO FoV. It is called isoplanatic tilt. A generic mode on the metapupil generates different global tilts over the MCAO. This is the anisoplanatic tilt components in a tip tilt measurements. Conf. AO4ELT 23-26 June 2009, Paris. wavefront over the metapupil

9. Recovering isoplanatic tip tilt over the metapupils - Z2 and Z3 applied on the system metapupils, are not seen by the LGS. -Z2 & Z3 are recovered using tip tilt measurements of the same NGS used for Z4,Z5 & Z6. - NGS and LGS tilt contains isoplanatic and anisoplanatic tilt components. Conf. AO4ELT 23-26 June 2009, Paris. Only the tip tilt sum on both layers is recovered but this is not relevant because of tilt isoplanaticity. The recovered isoplanatic Tip / Tilt are then applied on the DM’s together with the high order commands found directly from MCAO reconstructor. The anisoplanatic ones are recovered by simulating a cylindrical propagation in the MCAO estimated atmosphere. This estimate is good because corrected already for Z4,Z5,Z6 ambiguity. NGS measured tip tilt

10. Numerical simulations Main simulation parameters: - r0 total = 0.12m @ 500 nm - 2 Atm.Layers h = 1.0 km, r0 = 0.14m h = 8.0 km, r0 = 0.30m - 2 DM’s@ 1.0 km & 8 km; - 50 Zernike modes for generating Atmosphere - 50 Zernike modes reconstructed 45 through MCAO Rec Z2,Z3,Z4,Z5,Z6 with 1 NGS and MCAO Rec - Corrected FOV = 120 arcsec - ELT = 42 m - No central obscuration - 4 LGS - LGS proj. = 3m diam (launched from telescope optics) Conf. AO4ELT 23-26 June 2009, Paris. Computations done using Mathematica to obtain a formal solution for a function projecting Zernike modes on metapupil to stars footprints at a given layer. Green disks: LGS launching Red disk: EELT obstruction Red circle: EELT pupil (42m) LGS geometry

11. 2DM, 2 Layers results MCAO performance: the NGS wf is estimated using a cylindrical propagation in the reconstructed atmosphere. This estimated wf is compared with the actual wf. This is done for all the directions in the MCAO FoV. Blue: Input atm. Red: residual Yellow: “closed loop” Layer 1, 1.0km Layer 2, 8.0km Up+Dw propagation for MCAO REC. LGS global tilts measured. 1 NGS to measure: Z2,Z3,Z4,Z5,Z6 as outlined All rms is given at LGS wavelength. The mean phase residual in the considered 2 arcmin diameter FoV is 0.19 rad coming from Z4-Z6, input rms is 137 rad (red dots) All other modes have a negligible residual. Zernike mode # Residual rms [rad]

12. 2DMs: results vs # of modes Conf. AO4ELT 23-26 June 2009, Paris. # of Zernike modes Total residual rms over FoV Reconstruction with 50 modes and NGS measuring Z2,Z3,Z4,Z5,Z6 Phase rms between atm & cilindrical estimate in the MCAO FoV Single iteration (open loop) 2 iterations (closed loop) All rms is given at LGS wavelength.

13. more layers and DMs……. Briefly……. 1) 2DM 3 Layer 2) 3DM 3Layer 3 layers at 0.1km, 6.0km,8.5km r0 0.156m, 0.296m, 0.390m r0 total 0.119m 2DMS at 0.1km, 6.0km Residual rms over FoV 1.75 rad 3 layers at 0.1km, 6.0km,8.5km r0 0.16m, 0.30m, 0.39m r0 total 0.12m 3DMS at 0.1km, 6.0km, 8.5km Residual rms over FoV 1.3 rad No optimization of MCAO reconstructors…… -7 eigenvalues 10^-8 removed from reconstructor -3DM require three different object types to solve the ambiguity (LGS & NGS for 2DMs). -Work in progress on this case to generalize the methods to 3 DMs Z2,Z3,Z4,Z5,Z6) Conf. AO4ELT 23-26 June 2009, Paris. All rms is given at LGS wavelength.

14. Summary A technique to overcome the problem of the low order modes indetermination in LGS MCAO has been presented. The technique consider LGS upward propagation in the IM to be able to use the LGSs global tilt informations. In such a way all modes except Z2,Z3,Z4,Z5,Z6 are correctly reconstructed for 2DMs case. Then a solution is presented to use a single NGS in the FoV is to determine Z2,Z3,Z4,Z4,Z5 over the metapupils. The phase residual rms over the whole FoV is found 0.19 rad in the case of 2 DMs – 2 Layers. This results shows that using the considered technique the sky coverage of a 2DM MCAO system is highly increased, as it depends on the presence of only one NGS in the whole Patrol Field. Work is ongoing to evaluate the technique performance in the 3DMs case. Conf. AO4ELT 23-26 June 2009, Paris.