Adaptive Optics Nicholas Devaney GTC project, Instituto de Astrofisica de Canarias 1. Principles 2. Multi-conjugate 3. Performance & challenges

Guide star Anisoplanatic Error Science object Telescope pupil Turbulent layer |

Anisoplanatic Error Anisoplanatism limits the AO field of view – =0.5  m,  0 ~ 2 arcseconds –  0  r 0  6/5 – =2.2  m,  0 ~ 12 arcseconds Inside the Field of View the PSF is not constant If turbulence were concentrated in a single layer then a deformable mirror conjugate to that layer would give isoplanatic correction. –The DM should be over-sized –A single reference source requires wavefront extrapolation

DM Guide star footprint on wavefront sensor Single-conjugate correction Telescope pupil Deformable mirror Ref: Véran, JOSA A, 17, p1325 (2000)

Optimized Single Conjugate Correction Real turbulence is distributed in altitude; average profile of Cn 2 is smooth, but during a given observation has layerd structure. Can find an optimal conjugate altitude for the deformable mirror This approach is employed in the Altair system on Gemini North

Multi-Conjugate AO MCAO is an extension of the idea of conjugating to turbulence to N deformable mirrors. In proposed systems N=2-3. Controller WFS DM1 DM2 Layer 1 Layer 2 Telescope

Multi-Conjugate AO –To what altitudes should the deformable mirrors be made conjugate ? –What wavefront sensing approach can be used to control the deformable mirrors ? –What are the limitations ?

Optimal altitudes for deformable mirrors Tokovinin (JOSA A17,1819) has shown that for very large apertures where  M is a generalisation of the isoplanatic angle when M deformable mirrors are employed.  M depends on the altitudes of the M mirrors and the turbulence distribution in altitude This assumes perfect measurement of all the turbulence in the volume defined by the field of view

 M for 2 deformable mirrors La Palma turbulence profiles Optimal altitude DM1~0, DM2 ~13km Optimal altitudes similar for all profiles Smooth decrease in isoplanatic angle as move away from optimal

Wavefront sensing for MCAO We would like to perform ‘tomography’ of the turbulent volume defined by the telescope pupil and the field of view. It is not necessary to reconstruct the turbulent layers; ‘only’ need to determine the commands for the deformable mirrors. Tomography involves taking images with source and detector placed in different orientations. MCAO will employ multiple guide stars for simultaneous wavefront sensing. There are two approaches: –Star-oriented, sometimes referred to as ‘classical’ (!) –Layer-oriented

WFSs Reference Stars DM2 Telescope High Altitude Layer Ground Layer DM1 WFC Star Oriented MCAO Single Star WFS architecture Global Reconstruction n GS, n WFS, m DM, 1 RTC The correction applied at each DM is computed using all the input data. The correction across the FoV can be optimised for specified directions.

WFC2 DM2 WFS2 WFC1 DM1 WFS1 Telescope High Altitude Layer Ground Layer Reference Stars Layer Oriented MCAO Layer Oriented WFS architecture Local Reconstruction x GS, n WFS, n DM, n RTC The wavefront is reconstructed at each altitude independently. Each WFS is optically coupled to all the others. GS light is co-added for a better SNR.

MCAO wavefront sensing Star-oriented systems plan to use multiple Shack- Hartmann sensors Layer-oriented systems can use any pupil-plane wavefront sensor; proposed to use pyramid sensor Layer oriented can adapt spatial and temporal sampling at each layer independently As in single-conjugate AO the wavefront reconstruction can be zonal or modal. Most theoretical work based on modal approach.

Modal Tomography Describe turbulence on each layer as a Zernike expansion, a (l) (Unit circle = metapupil) looking towards GS in direction  at each layer intercept a circle of diameter D. Determine phase as Zernike expansion b (l) P is a projection matrix (This is similar to sub-aperture testing of aspheres)

Modal Tomography The phase at r on the pupil for wavefronts coming from direction  = sum of phase from L layers along that direction (near-field approximation) ; where for G guide stars (g=1...G)

Modal Tomography So there is a linear relation between the phase measured at the pupil for G guide stars and the phase on L metapupils This is inverted to give a In practice measure slopes (or curvatures), but these are also linearly related to the pupil phase.

Wavefront sensing for MCAO Whichever approach is employed, there are (of course) some limitations. Aliasing: GS1 GS2 This looks the same to both GS This also looks the same to both GS H 

Wavefront sensing for MCAO Aliasing occurs between layers separated by H for frequencies higher than f c trade-off between field of view and degree of correction (unless increase the number of guide stars)

Gaps in the ‘meta-pupil’ Telescope Pupil for field position   ‘Meta-pupil’ Guide star beam footprints at altitude H

MCAO Numerical Simulations Use numerical simulations to determine the performance of a dual-conjugate system suitable for use on a 10m telescope on La Palma (e.g. the GTC). Want to determine performance as a function of guide star configuration and DM2 conjugate altitude (DM1 will be conjugate to the pupil). Use a 7-layer approximation to balloon measurements of vertical distribution of turbulence; simulate 7 Kolmogorov screens for each ‘frame’. Geometric propagation Shack-Hartmann wavefront sensing (16x16 subaps) Zernike deformable mirrors No noise

MCAO Simulations 3 NGS FoV=1.5 arcmin Average SR drops and variation over FoV increases as FoV is increased SR at 2.2  m 3 NGS FoV=1 arcmin Ref: Femenía & Devaney, in preparation

Optimal altitude of DM2 ?

Sky Coverage Stars per square degree using Guide Star Catalogue II There are 1326 stars deg -2 brighter than m R =17.5  =0.95 in FOV=2´ p (n  3) = 7% in 2´ = 2% in 1.5´ Does not take geometry into account

Sky coverage... The probability of finding ‘constellations’ of bright, nicely distributed natural guide stars is very small. The obvious solution is to use multiple laser guide stars. Besides the sky coverage, a major advantage is the stability of the system calibration –(roughly) constant guide star flux –constant configuration The cone effect is not a problem However.....

LGS in MCAO Recall cannot determine tip-tilt from LGS When using multiple LGS the result is tip-tilt anisoplanatism. Unless corrected, this will severely limit the MCAO performance How to correct ? –polychromatic LGS or other scheme to measure LGS tip-tilt –measure tip-tilt on several NGS in the field –make quadratic wavefront measurements on guide stars at different ranges..... huh ??

Quadratic errors and tip-tilt anisoplanatism S2 = a 1 x 2 S1 = a 0 x 2  h Anisoplanatic tilt

Measuring with LGS x h H

h H a0x2a0x2 a1x2a1x2 tilt so can’t measure piston if a 0  -a 1 (1-h/H) 2 then don’t see anything !! 

Measuring with LGS h H a0x2a0x2 a1x2a1x2  H´ null if a 0  -a 1 (1-h/H´) 2

Possible hybrid approaches... Na laser guide stars (H=90km) plus NGS (H=  ) Na laser guide stars plus Rayleigh guide star (H<30km) plus NGS (for global tip-tilt). Na laser guide stars plus Rayleigh guide stars at different ranges plus NGS

Results using 4 LGS + 1NGS SR at 2.2  m 3 LGS FoV=1 arcmin FOV =1.5 arcmin

Is there an alternative ? In principle, layer-oriented wavefront sensing can use multiple faint guide stars. Implementation with pyramid sensors can be complicated if need dynamic modulation. An extension to give better sky coverage is ‘multi-fov’ layer oriented.

Multi-fov layer oriented wavefront sensing Layers near the pupil can be corrected with large field of view High-layer field of view should be limited since correction of non-conjugate layers degrades as 1/H  FOV, where H is distance of layer from DM Example: –1 sensor with annular fov = 2-6´ conjugate to ground layer –1 sensor with fov=2´ conjugate to ground –1 sensor with fov=2´ conjugate to high altitude The ground layer will have a residual of high altitude turbulence

6´ Multi-fov layer oriented wavefront sensing Telescope pupil DM at altitude 2´

Science Path OAP1 OAP2 DM9 DM0 TTM DM4.5 SCIBS ADC NGS WFS Path OAP3 WFS WFSBS ADC LGS WFS Path Zoom Focus Lens LGS WFS Other Stuff Source Simulators Diagnostic WFS and Imaging Camera f/33.4 output Focal- and pupil plane locations preserved Standard optical bench design with space frame support In-plane packaging with adequate room for electronics Gemini South MCAO Courtesy: Eric James & Brent Ellerbroek, Gemini Observatory

ESO MAD Bench Optical design derotator +/- 1’ FoV derotator +/- 1’ FoV Collimator F=900 mm Collimator F=900 mm F/15 Nasmyth focus F/15 Nasmyth focus MACAO-VLTI DM 100 mm 8.5 Km conj. MACAO-VLTI DM 100 mm 8.5 Km conj. MACAO-SINFONI DM 60 mm 0 Km conj. MACAO-SINFONI DM 60 mm 0 Km conj. Dichroic IR/Vis Dichroic IR/Vis To IR Camera  m WFS Re-imaging objective WFS Re-imaging objective Telecentric F/20 focus Telecentric F/20 focus To WFS 2’  m Courtesy of E.Marchetti, N. Hubin ESO

FoV 2' 200mm Three movable SH WFS Global Reconstruction SH WFS Fast Read-Out CCD Pupil Re- imaging Lens Acquisition Camera XY Table Lenslet Array Pick-Up Mirror XY tables fixed axes direction Acquisition camera Three Fast read-out CCD Courtesy of E.Marchetti, N. Hubin ESO

Layer Oriented WFS Multi Pyramid WFS, up to eight pyramids Two CCD cameras for ground and high altitude conjugations Ground Conjugated CCD Higher altitude conjugated CCD Star enlargers Pupil re-imaging objective PyramidMotions F/20 focal plane Courtesy of E.Marchetti, N. Hubin ESO