Behind the Buzzwords The basic physics of adaptive optics

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Behind the BuzzwordsThe basic physics of
adaptive optics

• Keck Observatory OA Meeting
• 29 January 2004
• James W. Beletic

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speckle
Isoplanatic angle
inner scale outer scale
r0
Kolmogorov
?0
Shack-Hartmann
Curvature
Strehl
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Wave modelof image formation
Shuis excellent animation
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Interferometric modelof image formation
Phasors Complex addition Speckles
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Images of Arcturus (bright star)
Lick Observatory 1-meter telescope
Lick Observatory, 1 m telescope
? 1 arc sec
? l / D
Long exposure image
Short exposure image
Image with adaptive optics
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Velocity of light

• Velocity V of light through any medium
• V c / n
• c speed of light in a vacuum (3.28?108m/s)
• n index of refraction
• Index of refraction of air 1.0003

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Atmospheric distortions are due to temperature
fluctuations

• Refractivity of air
• where P pressure in millibars, T temp. in K,
• n index of refraction. VERY weak dependence on
  ?
• Temperature fluctuations cause index fluctuations
  
• (pressure is constant, because velocities are
  highly sub-sonic -- pressure differences are
  rapidly smoothed out by sound wave propagation)

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Index of refraction of dry air at sea level
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Important things to rememberfrom index of
refraction formula

• We can measure in visible (where we have better
  high speed, low noise detectors) and assume
  distortion is the same in the infrared (where it
  is easier to correct).
• 1.6 C temp difference at the summit causes
  change of 1 part in million in index of
  refraction. Doesnt seem like much, eh?
• 1 wave distortion in 1 meter! (?1 ?m)
• Thermal issues bite all who dont pay attention!
  Keck is almost certainly degrading the great
  natural Mauna Kea seeing!

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Misrepresentations Misinterpretations

• Almost all drawings are exaggerated, since need
  to exaggerate to show distortions angles.
• Maximum phase deviation across 10-m wavefront is
  about 10 ?m 1 part in 1 million. Like one dot
  offset on a straight line of 600 dpi printer in
  140 feet.
• From the point of view of the light, the
  atmosphere is totally frozen (30 ?sec through
  atmos). We draw one wavefront, but about 1012
  pass through telescope before atmospheric
  distortion changes.

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Goofy scales of AO

• 10 meter telescope aperture
• 20 cm deformable mirror set by actuator spacing
• 2 mm diameter set by max size detector that can
  read out fast
• Factor of 5,000 reduction in horizontal dimension
  of the wavefront! But orthogonal dimension kept
  the same.

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Kolmogorov turbulence cartoon
ground
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Kolmogorov Turbulence Spectrum
? 2?/?
Energy
?-5/3
Spatial Frequency
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Kolmogorov turbulencein a nutshell
Big whorls have little whorls, which feed on
their velocity. Little whorls have smaller
whorls, and so on unto viscosity.

• L. F. Richardson (1881-1953)

Computer simulation of the breakup of a
Kelvin-Helmholtz vortex
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Correlation length - r0

• Fractal structure (self-similar at all scales)
• Structure function (good for describing random
  functions)
• D(?x) phase(x) phase(x?x)2
• r0 Correlation length
• the distance ?x where D(?x) 1 rad2
• r0 max size telescope that is
  diffraction-limited
• r0 is wavelength dependent larger at longer
  wavelengths (since 1 radian is bigger for larger
  ?)
• But a little tricky,
• r0 ??6/5

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Correlation length - r0

• Rule of thumb 10 cm visible r0 is 1 arc sec
  seeing
• Visible r0 is usually quoted at 0.55 ?m.
• 0.7 arc sec - 14 cm r0 at 0.55 ?m
• 74 cm 2.2 ?m
  (K-band)
• Seeing is weakly dependent on wavelength, and
  gets a little better at longer wavelengths.
• ?/r0 ??-1/5

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Correlation time - ?0

• To first order, atmospheric turbulence is frozen
  (Taylor hypothesis) and it blows past the
  telescope.
• ?0 correlation time, the time it takes
  for the distortion to move one r0
• Determines how fast the AO system needs to run.

wind velocity 30 mph
13.4 m/sec
?0 14 cm / v 15 msec (visible) 74
cm / v 80 msec (K)
? 0 ??6/5
? 0 ? r0/v
Telescope primary
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Simplified AO system diagram
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Wavefront sensing

• MANY ways to sense the wavefront !
• Three basic things must be done
• Divide the wavefront into subapertures
• Optically process the wavefront
• Detect photons
• Detecting photons must be done last, but order of
  the first two steps can be interchanged.
• Can measure the phase or 1st or 2nd derivative of
  the wavefront (defined by optical processing).

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Wavefront sensor family tree
Optical Processing
1st Step
Divide into subapertures
Point source diffraction
Derivative of measure
Shack-Hartmann
Pyramid, Shearing
Curvature
Shack-Hartmann wavefront sensing stands alone as
to how it is implemented. Will it be the
dominant wavefront sensing method in 10 years
time?
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Shack-Hartmann wavefront sensing
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Shack-Hartmannwavefront sensing

• Divide primary mirror into subapertures of
  diameter r0
• Number of subapertures (D / r0)2 where r0 is
  evaluated at the desired observing wavelength
• Example Keck telescope, D10m, r0 60 cm at l
  2 mm. (D / r0)2 280. Actual for Keck 250.

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Adaptive Optics Works!
Show Gemini AO animation
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Measuring AO performance
Strehl ratio

• When AO system performs well, more energy in core
• When AO system is stressed (poor seeing), halo
  contains larger fraction of energy (diameter
  ?/r0)
• Ratio between core and halo varies during night

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Keck AO system performance on bright stars is
very good, but not perfect
A 9th magnitude star Imaged H band (1.6 mm)
Without AO FWHM 0.34 arc sec Strehl 0.6
With AO
FWHM 0.039 arc sec Strehl 34
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Dave Lettermans Top 10 reasons why AO does not
work perfectly
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Most important AO performance plot
Strehl
Keck system limit is about 14th magnitude
Guide star magnitude
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Performance predictions
ESO SINFONI instrument
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Performance predictions
Gemini comparison of Shack-Hartmann and curvature
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Dave Lettermans Top 10 reasons why AO does not
work perfectly
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Dave Lettermans Top 10 reasons why AO does not
work perfectly
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Most deformable mirrors today have thin glass
face-sheets
Glass face-sheet
Light
Cables leading to mirrors power supply (where
voltage is applied)
PZT or PMN actuators get longer and shorter as
voltage is changed
Reflective coating
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Deformable mirrors - many sizes

• 13 to gt900 actuators (degrees of freedom)

About 12
A couple of inches
Xinetics
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Dave Lettermans Top 10 reasons why AO does not
work perfectly
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Dave Lettermans Top 10 reasons why AO does not
work perfectly
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Dave Lettermans Top 10 reasons why AO does not
work perfectly
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Anisoplanatism - ?0

• An object that is not in same direction as the
  guide star (used for AO system) has a different
  distortion.
• ?0 isoplanatic angle, the angle over
  which the max. Strehl drops by 50
• ?0 depends on distribution of turbulence and
  conjugate of the deformable mirror.

h
?0 ? r0 / h
Telescope primary
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Anisoplanatism (Palomar AO system)
credit R. Dekany, Caltech

• Composite J, H, K band image, 30 second exposure
  in each band
• Field of view is 40x40 (at 0.04 arc sec/pixel)
• On-axis K-band Strehl 40, falling to 25 at
  field corner

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Vertical profile of turbulence
Measured from a balloon rising through various
atmospheric layers
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Dave Lettermans Top 10 reasons why AO does not
work perfectly
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Dave Lettermans Top 10 reasons why AO does not
work perfectly
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Dave Lettermans Top 10 reasons why AO does not
work perfectly

• Tip/tilt error
• (tip/tilt mirror not shown)

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Dave Lettermans Top 10 reasons why AO does not
work perfectly
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Thank you for your attention