1. Adaptive Optics and Optical Interferometry or How I Learned to Stop Worrying and 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. Limit to spatial resolution set by diameter of optics –Fundamental limit; you can’t simply zoom in For 10-m telescope, in visible light ( = 0.5  m), /D = 0.010 arcsec /D = 0.045 arcsec for = 2.2  m Diffraction limit 1.2 /D

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

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

6. Atmospheric limit - seeing disk Atmosphere creates seeing disk, ~ 1 arcsec –Compare to 0.010 arcsec at =0.5  m, 0.045 arcsec at =2.2  m –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

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

14. Adaptive Optics - requirements Atmosphere sets spatial scale of correction –r 0 is coherence length (Fried’s parameter) –r 0 ~ 10 cm for 1 arcsec seeing in visible (0.5  m) light –r 0  6/5 ; r 0 ~ 60 cm for =2.2  m (IR) –for =20  m (mid-IR), r 0 > 8 m; no need for AO r 0 and wind speed v set time scale of correction –v ~ 10 m/s, so r 0 /v =  ~ 10 ms So we need ~ (D/r 0 ) 2 actuators, making corrections every  seconds –for =0.5  m, D =10 m, (D/r 0 ) 2 =10 4,  =10 ms –for =2.2  m, D =10 m, (D/r 0 ) 2 =250,  =60 ms

16. 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 r 0 sub-apertures Position of single sub-aperture image tells you slope of wavefront –Connect slopes to determine wavefront shape

17. 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  iso is angle where corrections stop being valid Angle  iso =h/r 0 –For h=10 km, =0.5  m,  iso =2 arcsec =2.2  m,  iso =12 arcsec Adaptive Optics - isoplanatism h r0r0  iso

18. Adaptive Optics - natural guide stars Corrections need to be measured for each r 0 -diameter patch in time  For accurate corrections, need ~ 100 photons per sub- aperture per  Magnitude limit is V ~ 9 K ~ 14 Need stars to be within  iso of science objects Sky coverage 3×10 -4 for =0.5  m 0.01 for =2.2  m

19. 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)

20. Adaptive Optics - results

22. NGC 7469

23. Interferometry - Young’s double-slit Young’s double-slit experiment Path lengths equal phase difference 0º constructive interference Path lengths differ by /2 phase difference 180º destructive interference 0 Intensity /d d

24. Interferometry - Two objects Two objects give same interference pattern, shifted by position of object +=  /d)/2

25. Interferometry - Michelson Michelson put double-slit on top of Mount Wilson 100” –vary “baseline” d to find  x=( /d)/2, where fringes disappear d

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

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

28. 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 ~ r 0, detector intensity changes every  Stars must be within  iso of each other Interferometry - detection t I max I min I

29. 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 Interferometry - visibility maps

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

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

34. 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 Interferometry - phase information

35. In order to use aperture much larger than r 0, its distortions have to be “flattened” Need AO on all large apertures before they can be interfered Interferometry - large apertures

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

37. NAME# telaperturebaseline CHARACenter for High-Angular Resolution Astronomy61.0350 COASTCambridge Optical Aperture Synthesis Tel.50.4020 GI2TGrand Intérferomètre à 2 Télescopes21.565 IOTAInfrared Optical Telescope Array20.4038 ISIInfrared Spatial Interferometer21.685 MIRA-IMitaka Infrared Array20.254 NPOINavy Prototype Optical Interferometer30.1235 PTIPalomar Testbed Interferometer30.40110 SUSISydney University Stellar Interferometer20.14640 KeckK1-K2210.060 KeckAuxiliary array upgrade41.8140 LBTLarge Binocular Telescope28.423 VIMAVLT Interferometer Main Array48.0130 VISAVLT Interferometer Sub-Array41.8202 Interferometry - facilities

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