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Laser guide star(s) for large telescopes: cone effect and astrophysical implications: 

Laser guide star(s) for large telescopes: cone effect and astrophysical implications M. Le Louarn CRAL - Observatoire de Lyon (AIRI) Observatoire Européen Austral - Garching

Plan of the presentation: 

Plan of the presentation Turbulence and Adaptive Optics - Introduction diffraction limit on large telescopes (real time correction) Laser guide star increase the number of observed objects Cone effect and increase of the corrected FOV Access to the visible over a 100'' FOV on an 8m telescope Fundamental limits of MCAO generalized isoplanatic angle Conclusions - future developpments

Atmospheric turbulence: 

Atmospheric turbulence atmospheric turbulence  random variations of the air refractive index  blurred images Cn2(h) = strength of turbulence at altitude h can be measured with balloon soundings for example some discrete layers (ground, 5 km, 10 km) + extended component Short exposure images without AO (K band - 2.2 m, tel. 3.6m): Movement of the center of gravity (“tilt”) and image deformations (higher order aberrations).

Atmospheric parameters: 

Atmospheric parameters Fried parameter correlation time Isoplanatic Angle Seeing: Object 2 Telescope Object 1 Turbulence Turbulence common to the two objects r0  10-20 cm in V, 1.0 m in K 0  2-3'' in V, 20'' in K 0  3-6 ms in V, 25 ms in K k=2/ }  IR

Principle of adaptive optics: 

Principle of adaptive optics

Wavefront sensing: 

Wavefront sensing Shack-Hartmann wavefront sensor local slope of the wavefront  center of gravity of the image at the focus of the micro-lenses. (ex. Fontanella 85)

Errors in AO: 

Errors in AO photon noise + read-out noise + aliasing + fitting + temporal delay Nph: Number of photons / subaperture / integration time ds: size of the subapertures if ds > r0 1 otherwise Rousset 94, Parenti & Sasiela 94

Errors in AO: 

Errors in AO Nph: Number of photons / subaperture / integration time ds: size of the subapertures e: detector read-out noise if ds > r0 1 otherwise Rousset 94, Parenti & Sasiela 94 photon noise + read-out noise + aliasing + fitting + temporal delay

Errors in AO: 

Errors in AO ds: sub-aperture size Rousset 94, Parenti & Sasiela 94 Finite size of the sub-apertures photon noise + read-out noise + aliasing + fitting + temporal delay

Errors in AO: 

Errors in AO ddm: distance between actuators Rousset 94, Parenti & Sasiela 94 Non zero interactuator distance D ddm photon noise + read-out noise + aliasing + fitting + temporal delay

Errors in AO: 

Errors in AO Rousset 94, Parenti & Sasiela 94 gather enough photons to  measurement noise read the detector compute the DM commands  atmosphere has evolved between measurement and command  temporal delay error:  : delay between the beginning of the measurement and the command 0 : correlation time photon noise + read-out noise + aliasing + fitting + temporal delay

AO results: 

AO results S  0.1-0.2

Sky coverage: 

Sky coverage K Band (2.2  m) J Band (1.25 m) Tel. 8m, Paranal, seeing: 0.5’’ Blue: NGS 2 positions in the Galaxy: pole, disk In agreement with Sandler et al. 94 Le Louarn et al. 98

Laser Guide Star: 

Laser Guide Star need a bright reference source within the isoplanatic patch (object, star).  limited sky coverage.  artificial reference with a laser (Foy&Labeyrie 85) in general, use the Na layer at 90 km.

Physical limitations I: tilt: 

Physical limitations I: tilt Tilt indetermination light follows the same path on the way to the Na layer and back (Pilkington 87). LGS is fixed at the focus of the emitter telelescope  NGS tilt Solutions: nearby NGS (!) polychromatic LGS (Foy et al. 95) perspective effect (Ragazzoni et al. 99) LGS real position Atmospheric tilt Apparent position of the LGS Telescope

Physical limitations II: cone effect: 

Physical limitations II: cone effect Caused by the finite altitude of the Na layer All the turbulence is not probed. turbulence is zoomed  biased measurement 8m Telescope “Paranal” atmosphere model red: median model (0.7’’, 0=1.7’’) blue: good model (0.5’’, 0=3.5’’) (20% of the time) d0  3 m - 6 m in V Tyler 94 Le Louarn et al 98.

Questions on LGSs: 

Questions on LGSs What is the gain brought by the LGS Limits in  (cone) ? Astrophysical gain ?

NGS/LGS Performance: 

NGS/LGS Performance NGS LGS + NGS for tilt Good atmospheric conditions (solid) - dashed: median model (Paranal) observations at zenith, 8m Tel., SH 16x16, 3 e- RON, AO optimized for the IR. Le Louarn et al. 98

NGS/LGS Performance: 

NGS/LGS Performance Le Louarn et al. 98 NGS LGS + NGS for tilt Good atmospheric conditions (solid) - dashed: median model (Paranal) observations at zenith, 8m Tel., SH 16x16, 3 e- RON, AO optimized for the IR.

NGS/LGS Performance: 

NGS/LGS Performance Le Louarn et al. 98 NGS LGS + NGS for tilt Good atmospheric conditions (solid) - dashed: median model (Paranal) observations at zenith, 8m Tel., SH 16x16, 3 e- RON, AO optimized for the IR.

Sky coverage: 

Sky coverage K Band (2.2  m): High sky coverage J Band (1.25 m): Average sky coverage 8m Tel, Paranal, seeing: 0.5’’ red: LGS Blue: NGS 2 positions in the Galaxy: pole, disk Agreement with Sandler et al. 94 Le Louarn et al. 98

Sky coverage (K band): 

Sky coverage (K band) GS: Good seeing MS: Median seeing Catalogues: QSO: Veron-Cetty Mira: GCVS Ref :USNO Le Louarn et al. 98

Sky coverage (J band): 

Sky coverage (J band) Le Louarn et al. 98 GS: Good seeing MS: Median seeing Catalogues: QSO: Veron-Cetty Mira: GCVS Ref :USNO

Answers on LGS: 

Answers on LGS Gain brought by a LGS ? Limits in  (cone) ? Astrophysical gain ? K band, coverage : 0.2 %  10 % (G. poles, S=0.2) J band, coverage : 0.02  0.1 %(G. poles, S=0.2) large number of extragalactic objects: K: 7000 QSO vs 360 (NGS) J: 1000 QSO vs 12 (NGS) J band, with good atmospheric cond. But: non corrected cone effect  LGS limited to the IR anisoplanatism limits the corrected FOV (20'' in K) solution to these problems: 3D mapping

3D mapping of turbulence: 

3D mapping of turbulence measure of the turbulence volume: several LGSs (Tallon & Foy 90) They allow to: Solve the cone effect Increase the corrected FOV, if several DMs conjugated to different heights are used (MCAO) first step in experimental verification: multi-NGS case (Ragazzoni et al. 2000). I will discuss only the LGS case.

MCAO: 

MCAO

MCAO: 

MCAO Geometric limit

OAMC: "history": 

OAMC: "history" Dicke 75: Several DMs increase of the FOV (NGS) Johnston & Welsh 94: MCAO model  "tilt anisoplanatism" Ellerbroek 94, Ellerbroek & Rhoadarmer 97 : hybrid system with LGSs at different altitudes + tilt NGS. Fusco et al. 1999-2000 MCAO on NGSs The correction is not very sensitive to the Cn2 profile. Rigaut et al. 2000 : Model of 5 LGS, 3 DMs, + 3 NGS (tilt). Rigaut et al. 2000: preliminary study to install the system on Gemini-S ( sky in 2004)

Questions on MCAO: 

Questions on MCAO How to "glue" the measurements together ? Effect of tilt indetermination ? What FOV can we reconstruct ? Anisoplanatism effects ? tilt ? residual ? Effects of the turbulence profile ?  anisoplanatism ? How to compute the DM commands

Interaction matrix in MCAO: 

Interaction matrix in MCAO Move one actuator on the deformable mirror response DM  influence function measure of the WFS response ( b ) store b in the interaction matrix as many rows as measurements and columns as actuators Invert that matrix (+ filter  piston)  command matrix: M+  command c of the DM = multiplication between the command matrix and the measurement vector: (eg. Boyer et al. 90)

IM model in MCAO: 

IM model in MCAO Assume weak turbulence  phase additivity (astronomical site) Conjugation heights of the square DMs: 0 km and 10 km The LGS limit the probed volume. The DMs cover the whole corrected FOV The influence function are propagated from the DMs to the (square) pupil: shift + magnification (cone effect + off-axis LGSs) sub-aperture size = inter-actuator distance between the two DMs. WFS: measures the mean phase over a sub-aperture  allows to understand the effect of the tilt WFS response  column of the interaction matrix.

Slide34: 

Mean over each subaperture = column of the IM

Interaction matrix: 

Interaction matrix 2 DMs (5x5, 7x7) 4 LGS at the edge of the FOV 8m tel LGS 1 LGS 2 LGS 3 LGS 4 DM 1 DM 2 Measurements

Modal analysis: 

Modal analysis Interaction matrix Eigenmodes Filtering Inversion Command matrix classic AO: piston = non measured mode Ill-conditioned modes Ill conditioned = singular modes with low or zero eigenvalues. These modes are poorly or not at all measured.

Eigenmodes of the IM: 

Eigenmodes of the IM Eigenmode = combinaison of a deformation on one DM and another deformation on the other. independants of Cn2 Can be decomposed into 2 families: Even modes the deformation has the same sign on both DMs eg.: Even modes have a deformation of opposite sign and a lower eigenvalue (i.e. less well sensed): or

Unmeasurable modes: 

Unmeasurable modes 5x5 actuators on DM 1 - 7x7 actuators on DM2 Piston + Tilt measured from the LGS If one can measure the phase from the LGSs, only even piston modes ("waffle") cannot be measured. Deformation DM1 Deformation DM2 Le Louarn & Tallon 2000

Unmeasurable modes: 

Unmeasurable modes Piston not measured from LGS If piston cannot be measured, then even tilts cannot be measured either Le Louarn & Tallon 2000 5x5 actuators on DM 1 - 7x7 actuators on DM2

Unmeasurable modes: 

Unmeasurable modes The tilt cannot be measured from LGSs. therefore some higher order modes cannot be sensed. Le Louarn & Tallon 2000 5x5 actuators on DM 1 - 7x7 actuators on DM2

Zero eigenvalue modes: 

Zero eigenvalue modes DM 1 DM 2 piston not measured

Zero eigenvalue modes: 

Zero eigenvalue modes DM 1 DM 2 piston not measured tilt not measured

Correct these modes ?: 

Correct these modes ? These modes produce a zero measurement on each LGS (0 EV). The propagation is different for LGSs and NGSs  These modes produce a non zero deformation for NGSs.  Must be corrected other correction varies in the FOV (cf. Johnston + Welsh) LGS

Correct invisible modes: 

Correct invisible modes How can we measure these modes ? Construct a hybrid interaction matrix: 1 NGS : anywhere in the corrected FOV measure only tilts, defocus and astigmatisms. 4 LGS : mesure all modes, execpt piston and tilts. eigenmodes of the system  the modes are seen ! Solution 2: other LGSs at different altitudes (but the tilt is not measured) (Ellerbroek et al.). Solution 3: several NGSs, measuring only tilt (Rigaut & Ellerbroek).

Eigenvalues: 4LGS vs 4LGS+1NGS: 

Eigenvalues: 4LGS vs 4LGS+1NGS dash: 4 LGS only solid: 4 LGSs + 1 NGS 5x5 et 7x7 actuators on the DMs there are 74 eigenmodes, 7 stay at 0 (pistons + even tilts) Some eigenvalues are low: difficult to measure Le Louarn & Tallon 2000

Performance at 0.5 m on 8m: 

Performance at 0.5 m on 8m We consider here only fitting, aliasing + IM inversion errors Simulations made with 13x13 actuators on the ground, 13x13 (zero FOV) to 21x21 on the other DM. Atmosphere: 70% ground, 30% at 10km (median), 1 sub-aperture per r0 Scaled for 80x80 sub-apertures (visible/8m), 2 sub-apertures/r0 No anisoplanatism within the corrected FOV Result confimed by Rigaut et al. 2000. Le Louarn & Tallon 2000 *

Answers on MCAO: 

Answers on MCAO How to glue the pieces measured by the LGSs ? How to compute the commands ?  Generalized interaction matrix Effect of tilt indetermination  propagation on higher order modes What FOV can be reconstructed ?   100'' on 8m @ V, S=30% Effects of the turbulence profile ? anisoplanatism ?  no if 5 modes are measured  error is equally distributed anisoplanatic effects ? tilt residual  error is equally distributed

Laboratory experiment: 

Laboratory experiment Setup made in Lyon, in collaboration with IC-STM SLM: Phase modulator = “phase screen” (IC-STM) Shack-Hartmann 13x13 CCD, 11 pixels/sub-aperture (CRAL) To simulate spherical propagation+off axis stars: shift+magnification of the screens

Experimental results: 

Experimental results Comparison of the phase mesured with an NGS and a phase mesured with 4 LGS (from which the tilt can be measured) relative error  2% LGS NGS

Lab. experiment: conclusions: 

Lab. experiment: conclusions The phase can be reconstructed from 4 LGSs The error found is larger than predicted from theory (2 % >> 4 10-4). slopes additivity error is 2-3 % Influence of measurement noise on slope additivity (0.01%)  no Turbulence on the bench (not detected)  no Propagation effects  being modeled with Fresnel propagation code (IC-STM).

Questions on MCAO II: 

Questions on MCAO II There are many layers an few DMs ? Optimal conjugation heights ? Temporal variations of these heights ? What gain can be expected with M DMs ?

Analytic approach: 

Analytic approach assume: all the turbulence is perfectly known (x,y,h)  measurement process is not tackled We have M DMs How to make best use of these DMs ? assume: perfect correction at FOV center  generalized isoplanatic angle M : extension of 0 to the case of M DM. (Tokovinin, Le Louarn & Sarazin 2000)

Anisoplanatism and MCAO: 

Anisoplanatism and MCAO Use turbulence profiles measured in Paranal : 12 balloon measurements.  3 ~20’’ 0 ~2’’ (at 0.5 m) 3  6/5 M increases linearly with M (M2): the "continum" component dominates

Slide54: 

Resolution  100 m Tokovinin, Le Louarn & Sarazin 2000

Slide55: 

Resolution  100 m Tokovinin, Le Louarn & Sarazin 2000

Height optimization: 

Height optimization black: 2 DM red: 1 DM Tokovinin, Le Louarn & Sarazin 2000 Conjugation height depends only on z: good agreement with Fusco et al. (multi-NGS), Rigaut et al. 2000

Height optimization: 

Height optimization Blue: 3 DM Tokovinin, Le Louarn & Sarazin 2000 Conjugation height depends only on z: good agreement with Fusco et al. (multi-NGS), Rigaut et al. 2000

Field or better correction: 

Field or better correction - remove piston variance ( tel. diametre) - add L0 - DM finite correction level Parametrization - can choose the corrected FOV : spatial filtering to distribute the error over the whole FOV Error becomes constant over the corrected FOV ( 3D) 8m Tel., V, optimized for different FOVs, L0 = 26 m, 2 DMs Model is improved: Tokovinin, Le Louarn & Sarazin 2000

Answers on MCAO II: 

Answers on MCAO II Optimum conjugation heights ? There are many layers and few DMs  Generalized isoplanatic angle  ground, 8km, 15 km (tel.) Gain to be expected with M DMs ? Temporal variation of the heights ?  low  DM height varies only with z  ~ 10 with 3 DMs  linear (M  2)

Conclusions: 

Conclusions LGS: significant increase in sky coverage (IR) K, increases from 10 % to 100 % (avg. G., S=0.2) J, increases from 1% to 40 % (avg. G., S=0.2) J band: must have good atm. cond. (cone) cone effect solved + FOV is increased thanks to 3D mapping of turbulence  visible ! measure 5 modes (> 2) from the NGS, within corrected FOV (or several NGSs). no anisoplanatism within the corrected FOV: The error is equally distributed.

Conclusions II: 

Conclusions II M : quantification of the gain in corrected FOV as a fonction of the profile and number of DMs: Gain of a factor 7-10 with 3 DMs uniform image quality in the corrected FOV Low temporal variability of the conjugation height, at a given z Multiple LGSs and MCAO allow to: access the visible with large telescopes increase significantly the corrected FOV 2''  100'' @V No anisoplanatism within this FOV

Slide62: 

Effect of MCAO MCAO: 2 DM, 5 NGS (+),  = 2.1 m, seeing=0.7'' @ 550nm 165'' The stars are magnified by a factor of 15 320 stars, Rigaut et al. 99 165''

future: 

future Optical, ground based, Extremely large telescopes (D = 50-100m), which are being planned, will need MCAO + 3D mapping to: Achieve the diffraction limit (V)  1 mas Reduce background noise and increase sensitivity. Limiting magnitude (10h integration): mv  38 Technical challenges: DMs with large number of actuators Computing power Wavefront sensor detector Possibility to use only NGSs, because the geometrical limit is much larger. Sky coverages are high, with LGS (V) and NGS (J)