Adaptive Optics Nicholas Devaney GTC project, Instituto de Astrofisica de Canarias

1. Adaptive OpticsNicholas DevaneyGTC project, Instituto de Astrofisica de Canarias 1. Principles 2. Multi-conjugate 3. Performance & challenges

2. Guide star Science object Turbulent layer Telescope pupil Anisoplanatic Error |

3. 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

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

5. 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

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

7. 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 ?

8. 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

9. M for 2 deformable mirrorsLa 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

10. 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

11. Reference Stars High Altitude Layer Ground Layer Telescope DM2 DM1 WFC WFSs 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.

12. Reference Stars High Altitude Layer Ground Layer Telescope DM2 DM1 WFC1 WFC2 WFS1 WFS2 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.

13. 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.

14. 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)

15. 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)

16. 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.

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

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

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

20. 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

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

22. Optimal altitude of DM2 ?

23. 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3) = 7% in 2´ = 2% in 1.5´ Does not take geometry into account

24. 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.....

25. 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 ??

26. Quadratic errors and tip-tilt anisoplanatism S2 = a1x2  h S1 = a0x2 Anisoplanatic tilt

27. Measuring with LGS H h x

28. tilt so can’t measure piston Measuring with LGS H a1x2  if a0 -a1 (1-h/H)2 then don’t see anything !! h a0x2

29. Measuring with LGS H´ null if a0 -a1 (1-h/H´)2 H a1x2  h a0x2

30. 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 • ........

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

32. 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.

33. 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

34. 6´ Multi-fov layer oriented wavefront sensing 2´ DM at altitude Telescope pupil

35. Science Path NGS WFS Path LGS WFS Path Other Stuff DM9 DM0 ADC SCIBS Source Simulators • 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 OAP2 OAP1 WFSBS Diagnostic WFS and Imaging Camera TTM DM4.5 LGS WFS Zoom Focus Lens OAP3 ADC WFS Gemini South MCAO Courtesy: Eric James & Brent Ellerbroek, Gemini Observatory

36. WFS Re-imaging objective MACAO-SINFONI DM 60 mm 0 Km conj. To WFS 2’ 0.45-0.95mm F/15 Nasmyth focus Telecentric F/20 focus MACAO-VLTI DM 100 mm 8.5 Km conj. derotator +/- 1’ FoV Dichroic IR/Vis To IR Camera 1-2.5mm Collimator F=900 mm ESO MAD Bench Optical design Courtesy of E.Marchetti, N. Hubin ESO

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

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