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Brian Kern Observational Astronomy 10/25/00

Adaptive Optics and Optical Interferometry or How I Learned to Stop Worrying and Love the Atmosphere. Brian Kern Observational Astronomy 10/25/00. Brief summary. Diffraction limit vs. atmospheric limit Science goals vs. spatial scale Adaptive Optics principles Interferometry principles

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Brian Kern Observational Astronomy 10/25/00

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  1. Adaptive OpticsandOptical InterferometryorHow I Learned to Stop Worryingand Love the Atmosphere Brian Kern Observational Astronomy 10/25/00

  2. Brief summary • Diffraction limit vs. atmospheric limit • Science goals vs. spatial scale • Adaptive Optics principles • Interferometry principles • Recent results

  3. Diffraction limit • Limit to spatial resolution set by diameter of optics • Fundamental limit; you can’t simply zoom in • For 10-m telescope, in visible light (l = 0.5 mm), l/D = 0.010 arcsecl/D = 0.045 arcsec for l = 2.2 mm 1.2 l/D

  4. Atmospheric limit • Air has patches of different T, which gives different r, and therefore different indices of refration n. Tr n  diverging lens T r  n  converging lens

  5. Atmospheric limit - wavefront • Think of phase changes in wavefront - advancing and retarding wavefronts +0- Phase map

  6. Atmospheric limit - seeing disk • Atmosphere creates seeing disk, ~ 1 arcsec • Compare to 0.010 arcsec at l=0.5 mm, 0.045 arcsec at l=2.2 mm • Keck 10m telescope no better than 4” telescope • Features smaller than 1 arcsec lost in the blur • Seeing is site-dependent and time-dependent

  7. Atmospheric limit - motivation • Hubble Space Telescope unaffected by atmosphere • Diffraction-limited resolution, D=2.4 m • We can achieve 4x better resolution with a 10-m telescope

  8. Atmospheric limit - motivation

  9. Science goals

  10. Science goals

  11. Adaptive Optics - overview • Correct aberrated wavefront using deformable mirror • Mirror takes shape opposite to wavefront distortion • Must measure aberrations to know how to make correction • Can use natural guide star or laser guide star

  12. Adaptive Optics - requirements • Atmosphere sets spatial scale of correction • r0 is coherence length (Fried’s parameter) • r0 ~ 10 cm for 1 arcsec seeing in visible (0.5 mm) light • r0l6/5; r0 ~ 60 cm for l=2.2 mm (IR) • for l=20 mm (mid-IR), r0 > 8 m; no need for AO • r0 and wind speed v set time scale of correction • v ~ 10 m/s, so r0 /v = t ~ 10 ms • So we need ~ (D/r0)2 actuators, making corrections every t seconds • for l=0.5 mm, D =10 m, (D/r0)2 =104, t =10 ms • for l=2.2 mm, D =10 m, (D/r0)2 =250, t =60 ms

  13. Adaptive Optics - wavefront sensing • Guide star is necessary to determine corrections • Hartmann wavefront sensor is most common way to determine aberrations • Wavefront sensor looks at image of individual r0sub-apertures • Position of single sub-aperture image tells you slope of wavefront • Connect slopes to determine wavefront shape

  14. qiso h r0 Adaptive Optics - isoplanatism • To look at anything other than guide star, you look through a different line-of-sight • For a large off-axis angle, corrections are different for guide star and science object • Isoplanatic angle qiso is angle where corrections stop being valid • Angle qiso=h/r0 • For h=10 km, l=0.5 mm, qiso=2 arcsecl=2.2 mm, qiso=12 arcsec

  15. Adaptive Optics - natural guide stars • Corrections need to be measured for each r0-diameter patch in time t • For accurate corrections, need ~ 100 photons per sub-aperture per t • Magnitude limit is V ~ 9K ~ 14 • Need stars to be within qiso of science objects • Sky coverage 3×10-4 for l=0.5 mm0.01 for l=2.2 mm

  16. Adaptive Optics - laser guide stars • High atmosphere (90 km) has layer of sodium from meteors • Tune laser to sodium spectral line, laser makes artificial guide star 90 km up • Point it anywhere you want • Single wavelength doesn’t interfere with science observation • Still need tip/tilt from natural guide star, but can be farther away and much fainter (1 correction for whole telescope)

  17. Adaptive Optics - results

  18. Adaptive Optics - results

  19. Adaptive Optics - results NGC 7469

  20. Interferometry - Young’s double-slit • Young’s double-slit experiment d Path lengths equalphase difference 0ºconstructive interference Path lengths differ by l/2phase difference 180ºdestructive interference l/d Intensity 0

  21. Interferometry - Two objects • Two objects give same interference pattern, shifted by position of object + = (l/d)/2

  22. Interferometry - Michelson • Michelson put double-slit on top of Mount Wilson 100” • vary “baseline” d to find Dx=(l/d)/2, where fringes disappear d

  23. Interferometry - atmosphere • Atmosphere adds random phase errors to two slits

  24. Interferometry - visibility • Atmosphere affects two stars the same; combined interference pattern is shifted, but not changed • “modulation” is unaffected by atmosphere • Define visibility V = (Imax - Imin) / (Imax + Imin) • V ranges from 0 to 1 V=1 V=0.5 V=0

  25. Interferometry - detection • Atmospheric phase differences shift pattern around • Place detector at zero-point, let atmosphere shift pattern back and forth across detector • Time series of detected intensity gives visibility • Use “slit” sizes ~ r0, detector intensity changes every t • Stars must be within qiso of each other I Imax Imin t

  26. Interferometry - visibility maps • 2-dimensional map of baseline vectors is (u,v) plane • Map of visibilities in (u,v) plane is (u,v) map • Short baselines correspond to large angular separations, long baselines correspond to small angular separations

  27. Interferometry - bigger baselines • Apertures can be completely disconnected from each other • Extending baselines to hundreds of meters resolves features at l/d = 0.0003 arcsec for l=0.5 mm, d=350 m

  28. Interferometry - delay lines • When apertures are not carried by a single telescope, they need a path length compensation • The delay lines take up lots of space Path length difference Delay line

  29. Interferometry - phase information • Letting atmosphere shift modulation pattern around eliminates phase information • In order to get phase information, phase needs to be stabilized with respect to atmospheric distortions • Can use double-star feed, where phase is locked to a star, and a science target can be observed in full phase

  30. Interferometry - large apertures • In order to use aperture much larger than r0, its distortions have to be “flattened” • Need AO on all large apertures before they can be interfered

  31. Interferometry - space • No atmospheric distortions in space • Spacecraft control (vibrations, positions) must be controlled to ~ picometer precision

  32. Interferometry - facilities NAME # tel aperture baseline CHARA Center for High-Angular Resolution Astronomy 6 1.0 350COAST Cambridge Optical Aperture Synthesis Tel. 5 0.40 20GI2T Grand Intérferomètre à 2 Télescopes 2 1.5 65 IOTA Infrared Optical Telescope Array 2 0.40 38 ISI Infrared Spatial Interferometer 2 1.6 85 MIRA-I Mitaka Infrared Array 2 0.25 4 NPOI Navy Prototype Optical Interferometer 3 0.12 35 PTI Palomar Testbed Interferometer 3 0.40 110SUSI Sydney University Stellar Interferometer 2 0.14 640 Keck K1-K2 2 10.0 60 Keck Auxiliary array upgrade 4 1.8 140 LBT Large Binocular Telescope 2 8.4 23 VIMA VLT Interferometer Main Array 4 8.0 130 VISA VLT Interferometer Sub-Array 4 1.8 202

  33. Interferometry - results Capella Sep 28 1995 Sep 13 1995

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