Behind the Buzzwords The basic physics of adaptive optics
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Transcript of Behind the Buzzwords The basic physics of adaptive optics
Behind the Buzzwords
The basic physics of adaptive optics
Keck Observatory OA Meeting29 January 2004
James W. Beletic
Isoplanatic angle
Strehl
Kolmogorov
r0
0Shack-Hartmann
speckle
inner scaleouter scale
Curvature
Wave modelof image formation
Shui’s excellent animation
Interferometric modelof image formation
Phasors
Complex addition
Speckles
Images of Arcturus (bright star)
Lick Observatory, 1 m telescope
Long exposureimage
Short exposureimage
Image with adaptive optics
~ 1 arc sec ~ / D
Lick Observatory 1-meter telescope
Velocity of light
•Velocity V of light through any medium
V = c / n
c = speed of light in a vacuum (3.28108m/s)
n = index of refraction
• Index of refraction of air ~ 1.0003
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)
N (n 1) 106 77.6 1 7.5210 3 2 (P /T)
N 77.6 (P /T 2 )T
Index of refraction of dry air at sea level
Important things to remember
from 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. Doesn’t seem like much, eh?
1 wave distortion in 1 meter! (=1 m) • Thermal issues bite all who don’t pay
attention! Keck is almost certainly degrading the great natural Mauna Kea seeing!
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.
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 fastFactor of 5,000 reduction in horizontal dimension of the wavefront! But orthogonal dimension kept the same.
Kolmogorov turbulence cartoon
Outer scale L0
ground
Inner scale l0
hconvection
solar
h
Wind shear
Kolmogorov Turbulence Spectrum
Energy
Spatial Frequency
-5/3
= 2/
outerscale
innerscale
von Karmann spectrum(Kolmogorov + outer scale)
Kolmogorov turbulencein a nutshell
- L. F. Richardson (1881-1953)
Big whorls have little whorls,which feed on their velocity.
Little whorls have smaller whorls,and so on unto viscosity.
Computer simulation of the breakup of a Kelvin-Helmholtz vortex
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
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
Correlation time - 0
0 6/5
• 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.
Telescope primary
wind velocity = 30 mph = 13.4 m/sec
0 = 14 cm / v = 15 msec (visible) = 74 cm / v = 80 msec (K)
0 ≃ r0/v
Simplified AO system diagram
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).
Wavefront sensor family tree
Divide intosubapertures
OpticalProcessing
1st
Step
0
1
2
0
1
2
Shack-Hartmann Pyramid, Shearing
Curvature
Point source diffractionDerivativeof
measure
Shack-Hartmann wavefront sensing stands alone as to howit is implemented. Will it be the dominant wavefrontsensing method in 10 years time?
Shack-Hartmann wavefront 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, D=10m, r0 ~ 60 cm at = m. (D / r0)2 ~ 280. Actual # for Keck : ~250.
Shack-Hartmannwavefront sensing
Adaptive Optics Works!
Show GeminiAO animation
Measuring AO performance
Inte
nsity
x
Definition of “Strehl”:Ratio of peak intensity to that of “perfect” optical
system
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
Keck AO system performance on bright stars is very good,
but not perfect
Without AOFWHM 0.34 arc sec
Strehl = 0.6%
With AO FWHM 0.039 arc secStrehl = 34%
A 9th magnitude starImaged H band (1.6 m)
Dave Letterman’s Top 10 reasons why AO does not
work perfectly
10. Not enough light to measure distortion
Most important AO performance plot
Strehl
Guide star magnitude
Lower order system
Higher order system
Better WFS detectors
Keck system limit isabout 14th magnitude
Performance predictions
ESO SINFONI instrument
Performance predictions
Gemini comparison of Shack-Hartmann and curvature
Dave Letterman’s Top 10 reasons why AO does not
work perfectly
9. Sampling error of the wavefront (subapertures too large to see small distortions)
Dave Letterman’s Top 10 reasons why AO does not
work perfectly
8. Fitting error of the deformable mirror (not enough actuators)
Most deformable mirrors today have thin glass face-
sheets
Reflective coating
Glass face-sheet
PZT or PMN actuators: get longer and shorter as voltage is changed
Cables leading to mirror’s power supply (where
voltage is applied)
Light
Deformable mirrors - many sizes
• 13 to >900 actuators (degrees of freedom)
XineticsA couple of inches
About 12”
Dave Letterman’s Top 10 reasons why AO does not
work perfectly
7. There is software in the system
Dave Letterman’s Top 10 reasons why AO does not
work perfectly
6. Temporal error (a.k.a. phase lag, lack of sufficient bandwidth)
Dave Letterman’s Top 10 reasons why AO does not
work perfectly
5. Anisoplanatism
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.
Telescope primary
0 ≃ r0 / h
h
• Composite J, H, K band image, 30 second exposure in each band
• Field of view is 40”x40” (at 0.04 arc sec/pixel)• On-axis K-band Strehl ~ 40%, falling to 25% at field corner
Anisoplanatism (Palomar AO system)
credit: R. Dekany, Caltech
Vertical profile of turbulence
Measured from a balloon rising through various atmospheric layers
Dave Letterman’s Top 10 reasons why AO does not
work perfectly
4. Non-common path errors
Dave Letterman’s Top 10 reasons why AO does not
work perfectly
3. Wavefront sensor measurement error
(readout noise) and noise propagation
Dave Letterman’s Top 10 reasons why AO does not
work perfectly
2. Tip/tilt error(tip/tilt mirror not shown)
Dave Letterman’s Top 10 reasons why AO does not
work perfectly
1. There is software in the system
Thank you for
your attention