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Adaptive Optics Nicholas Devaney GTC project, Instituto de Astrofisica de Canarias 1. Principles 2. Multi-conjugate 3. Performance & challenges Anisoplanatic Error Guide star Science object iso 0.3 r0 h Turbulent layer Telescope pupil | Anisoplanatic Error • Anisoplanatism limits the AO field of view – =0.5 m, 0 ~ 2 arcseconds – 0 r0 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 Single-conjugate correction Deformable mirror Telescope pupil DM Ref: Véran, JOSA A, 17, p1325 (2000) Guide star footprint on wavefront sensor Optimized Single Conjugate Correction • Real turbulence is distributed in altitude; average profile of Cn2 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. Layer 1 Layer 2 Telescope DM1 DM2 Controller WFS 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 M 2 5 3 • 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 Star Oriented MCAO Reference Stars • Single Star WFS architecture • Global Reconstruction • n GS, n WFS, m DM, 1 RTC High Altitude Layer Ground Layer Telescope DM2 The correction applied at each DM is computed using all the input data. The correction across the FoV can be optimised for specified directions. DM1 WFC WFSs Layer Oriented MCAO • Layer Oriented WFS architecture • Local Reconstruction • x GS, n WFS, n DM, n RTC Reference Stars High Altitude Layer Ground Layer Telescope 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. DM2 DM1 WFC1 WFS1 WFS2 WFC2 MCAO wavefront sensing • Star-oriented systems plan to use multiple ShackHartmann 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) l l b ( , hl ) P( ; hl )a 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) ; (r ) r xh L (l ) (l ) l l 1 2r bn ( ) Z n D n2 N where L bn ( ) b ( , hl ) l 1 (l ) n for G guide stars (g=1...G) L L (l ) (l ) bg ( g ) bg ( g , hl ) P( g , hl )a l 1 l 1 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 H GS2 This looks the same to both GS This also looks the same to both GS Wavefront sensing for MCAO • Aliasing occurs between layers separated by H for frequencies higher than fc 1 fc H • trade-off between field of view and degree of correction (unless increase the number of guide stars) Gaps in the ‘meta-pupil’ ‘Meta-pupil’ Guide star beam footprints at altitude H Telescope Pupil for field position 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 SR at 2.2 m 3 NGS FoV=1 arcmin 3 NGS FoV=1.5 arcmin Average SR drops and variation over FoV increases as FoV is increased 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 mR=17.5 =0.95 in FOV=2´ P ( n) p(n 3) 1 p(0) p(1) p(2) 1 exp( ) 1 2 p (n3) = 7% in 2´ = 2% in 1.5´ n exp( ) n! 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 = a1x2 h S1 = a0x2 ( x) a1 ( x h) a0 x 2 2 a1 x a1 h 2a1 xh a0 x 2 2 Anisoplanatic tilt 2 Measuring with LGS hi x H ( x ) S i 1 i ( x; ) Si hi 1 i H hi x H h x Measuring with LGS 2 h h ( x; ) a0 x a1 1 x 2 a1 h 2 2a1hx1 H H 2 a1 x2 piston if a0 -a1 (1-h/H)2 then don’t see anything !! a0x2 H tilt so can’t measure h Measuring with LGS 2 h h ( x; ) a0 x a1 1 x 2 a1 h 2 2a1hx1 H H 2 2 h ( x; ) a0 x a1 1 ' x 2 H 2 2 null if a0 -a1 (1-h/H´) a1x2 H´ H h a0x2 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/HFOV ,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 Multi-fov layer oriented wavefront sensing 2´ DM at altitude 6´ Telescope pupil Gemini South MCAO Science Path NGS WFS Path LGS Other WFS Stuff Path DM0 DM9 SCIBS ADC Source Simulators • f/33.4 output • Focal- and pupil plane WFSBS OAP1 locations preserved TTM • Standard optical bench DM4.5 design with space frame support • In-plane packaging with adequate room ADC for WFS electronics OAP2 Diagnostic WFS and Imaging Camera Zoom Focus OAP3 Lens LGS WFS Courtesy: Eric James & Brent Ellerbroek, Gemini Observatory ESO MAD Bench Optical design 14:45:32 To WFS 2’ 0.45-0.95m WFS Re-imaging objective MACAO-SINFONI DM 60 mm 0 Km conj. wavefront sensor objective 1st deformable mirror F/15 Nasmyth focus Nasmyth focus Telecentric F/20 focus MACAO-VLTI DM 100 mm 2nd deformable mirror 8.5 Km conj. To IR Camera 1-2.5m collimator dichroic derotator to IR imaging camera Dichroic IR/Vis Courtesy of E.Marchetti, N. Hubin ESO Scale: 250.00 MM derotator +/- 1’ FoV ESO 05-Mar-02 Collimator F=900 mm 0.10 Global Reconstruction SH WFS • Three movable SH WFS • Three Fast read-out CCD • XY tables fixed axes direction Lenslet Array Pick-Up Mirror • Acquisition camera Acquisition Camera FoV 2' Fast Read-Out CCD XY Table Courtesy of E.Marchetti, N. Hubin ESO Pupil Reimaging Lens 200mm Layer Oriented WFS • Multi Pyramid WFS, up to eight pyramids • Two CCD cameras for ground and high altitude conjugations Ground Conjugated CCD Pupil re-imaging objective Motions Higher altitude conjugated CCD Pyramid Star enlargers F/20 focal plane Courtesy of E.Marchetti, N. Hubin ESO