Behind the Buzzwords The basic physics of adaptive optics Keck Observatory OA Meeting 29 January 2004 James W. Beletic
speckle Isoplanatic angle inner scale outer scale r 0 Kolmogorov 0 Shack-Hartmann Curvature Strehl
Wave model of image formation Shui’s excellent animation
Interferometric model of image formation Phasors Complex addition Speckles
Images of Arcturus (bright star) Lick Observatory 1 -meter telescope Lick Observatory, 1 m telescope ~ 1 arc sec Long exposure image ~ /D Short exposure image Image with adaptive optics
Velocity of light • Velocity V of light through any medium V = c/n c = speed of light in a vacuum (3. 28 108 m/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 subsonic -- pressure differences are rapidly smoothed out by sound wave propagation)
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 fast Factor of 5, 000 reduction in horizontal dimension of the wavefront! But orthogonal dimension kept the same.
Kolmogorov turbulence cartoon solar Outer scale L 0 Inner scale l 0 h Wind shear convection h ground
Kolmogorov Turbulence Spectrum von Karmann spectrum Energy (Kolmogorov + outer scale) = 2 / -5/3 outer scale inner scale Spatial Frequency
Kolmogorov turbulence in 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
Correlation length - r 0 • Fractal structure (self-similar at all scales) • Structure function (good for describing random functions) D( x) = [phase(x) – phase(x+ x)]2 • r 0 = Correlation length the distance x where D( x) = 1 rad 2 • r 0 = max size telescope that is diffraction-limited • r 0 is wavelength dependent – larger at longer wavelengths (since 1 radian is bigger for larger ) • But a little tricky, r 0 6/5
Correlation length - r 0 • Rule of thumb: 10 cm visible r 0 is 1 arc seeing • Visible r 0 is usually quoted at 0. 55 m. 0. 7 arc sec - 14 cm r 0 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. /r 0 -1/5
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 r 0 0 ≃ r 0/v wind velocity = 30 mph = 13. 4 m/sec 0 = 14 cm / v = 15 msec (visible) = 74 cm / v = 80 msec (K) 0 6/5 • Determines how fast the AO system needs to run. Telescope primary
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 1 st or 2 nd derivative of the wavefront (defined by optical processing).
Wavefront sensor family tree 1 st Step Divide into subapertures Derivative of measure 0 0 1 2 Optical Processing Shack-Hartmann Point source diffraction 1 Pyramid, Shearing 2 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?
Shack-Hartmann wavefront sensing
Shack-Hartmann wavefront sensing • Divide primary mirror into “subapertures” of diameter r 0 • Number of subapertures ~ (D / r 0)2 where r 0 is evaluated at the desired observing wavelength • Example: Keck telescope, D=10 m, r 0 ~ 60 cm at l = 2 mm. (D / r 0)2 ~ 280. Actual # for Keck : ~250.
Adaptive Optics Works! Show Gemini AO animation
Measuring AO performance Strehl ratio Intensity Definition of “Strehl”: Ratio of peak intensity to that of “perfect” optical system x • When AO system performs well, more energy in core • When AO system is stressed (poor seeing), halo contains larger fraction of energy (diameter ~ /r 0) • Ratio between core and halo varies during night
Keck AO system performance on bright stars is very good, but not perfect A 9 th 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%
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 Higher order system Better WFS detectors Lower order system Keck system limit is about 14 th magnitude Guide star 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 Glass face-sheet Light Cables leading to mirror’s power supply (where voltage is applied) PZT or PMN actuators: get longer and shorter as voltage is changed Reflective coating
Deformable mirrors - many sizes • 13 to >900 actuators (degrees of freedom) About 12” A couple of inches Xinetics
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% h 0 ≃ r 0 / h • 0 depends on distribution of turbulence and conjugate of the deformable mirror. Telescope primary
Anisoplanatism (Palomar AO system) credit: R. Dekany, Caltech • Composite J, H, K band image, 30 second exposure in each band • Field of view is 40”x 40” (at 0. 04 arc sec/pixel) • On-axis K-band Strehl ~ 40%, falling to 25% at field corner
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
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