Adaptive Optics and
Optical Interferometryor
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• Recent results
• 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
• 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
Atmospheric limit - wavefront
• Think of phase changes in wavefront - advancing and retarding wavefronts
Phase map+0-
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
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
Atmospheric limit - motivation
Science goals
Science goals
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
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 m) light
– r0 6/5; r0 ~ 60 cm for =2.2 m (IR)
– for =20 m (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 = ~ 10 ms
• So we need ~ (D/r0)2 actuators, making corrections every seconds– for =0.5 m, D =10 m, (D/r0)2 =104, =10 ms
– for =2.2 m, D =10 m, (D/r0)2 =250, =60 ms
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 r0 sub-apertures
• Position of single sub-aperture image tells you slope of wavefront– Connect slopes to determine wavefront shape
• 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/r0
– For h=10 km, =0.5 m, iso=2 arcsec =2.2 m, iso=12 arcsec
Adaptive Optics - isoplanatism
h
r0
iso
Adaptive Optics - natural guide stars
• Corrections need to be measured for each r0-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
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)
Adaptive Optics - results
Adaptive Optics - results
Adaptive Optics - results
NGC 7469
Interferometry - Young’s double-slit
• Young’s double-slit experiment
Path lengths equalphase difference 0º
constructive interference
Path lengths differ by /2phase difference 180ºdestructive interference
0
Inte
nsit
y
/d
d
Interferometry - Two objects
• Two objects give same interference pattern, shifted by position of object
+ =
/d)/2
Interferometry - Michelson
• Michelson put double-slit on top of Mount Wilson 100”– vary “baseline” d to find x=(/d)/2, where fringes disappear
d
Interferometry - atmosphere
• Atmosphere adds random phase errors to two slits
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
• 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 • Stars must be within iso of each other
Interferometry - detection
t
Imax
Imin
I
• 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
• 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
• 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
• 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
• 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
Interferometry - large apertures
• No atmospheric distortions in space
• Spacecraft control (vibrations, positions) must be controlled to ~ picometer precision
Interferometry - space
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
Interferometry - facilities
Interferometry - results Capella
Sep 13 1995 Sep 28 1995
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