Adaptive Optics and Optical Interferometry or How I Learned to Stop Worrying and Love the Atmosphere

1
Adaptive Optics andOptical 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 cant 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 l0.5 mm, 0.045 arcsec
  at l2.2 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, D2.4 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
(No Transcript)
13
(No Transcript)
14
Adaptive Optics - requirements

• Atmosphere sets spatial scale of correction
• r0 is coherence length (Frieds parameter)
• r0 10 cm for 1 arcsec seeing in visible (0.5
  mm) light
• r0 ? l6/5 r0 60 cm for l2.2 mm (IR)
• for l20 mm (mid-IR), r0 gt 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 l0.5 mm, D 10 m, (D/r0)2 104, t 10 ms
• for l2.2 mm, D 10 m, (D/r0)2 250, t 60 ms

15
(No Transcript)
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 r0
  sub-apertures
• Position of single sub-aperture image tells you
  slope of wavefront
• Connect slopes to determine wavefront shape

17
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 qisoh/r0
• For h10 km, l0.5 mm, qiso2 arcsec
  l2.2 mm, qiso12 arcsec

18
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 9
  K 14
• Need stars to be within qiso of science objects
• Sky coverage 310-4 for l0.5 mm
  0.01 for l2.2 mm

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 doesnt 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
21
Adaptive Optics - results
22
Adaptive Optics - results
NGC 7469
23
Interferometry - Youngs double-slit

• Youngs double-slit experiment

d
Path lengths equalphase difference
0ºconstructive interference
Path lengths differ by l/2phase difference
180ºdestructive interference
l/d
Intensity
0
24
Interferometry - Two objects

• Two objects give same interference pattern,
  shifted by position of object

(l/d)/2
25
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
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 (Imax - Imin) / (Imax
  Imin)
• V ranges from 0 to 1

V1
V0.5
V0
28
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
29
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

30
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
  l0.5 mm, d350 m

31
(No Transcript)
32
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
33
(No Transcript)
34
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

35
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

36
Interferometry - space

• No atmospheric distortions in space
• Spacecraft control (vibrations, positions) must
  be controlled to picometer precision

37
Interferometry - facilities
NAME tel aperture baseline CHARA Center
for High-Angular Resolution Astronomy 6 1.0 350CO
AST 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
38
Interferometry - results
Capella
Sep 28 1995
Sep 13 1995