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