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Behind the Buzzwords The basic physics of adaptive optics

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.

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Behind the Buzzwords The basic physics of adaptive optics

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  1. Behind the BuzzwordsThe basic physics of adaptive optics Keck Observatory OA Meeting 29 January 2004 James W. Beletic

  2. speckle Isoplanatic angle inner scale outer scale r0 Kolmogorov 0 Shack-Hartmann Curvature Strehl

  3. Wave modelof image formation Shui’s excellent animation

  4. Interferometric modelof image formation Phasors Complex addition Speckles

  5. 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

  6. 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

  7. 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)

  8. Index of refraction of dry air at sea level

  9. 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. 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!

  10. 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.

  11. 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.

  12. solar Outer scale L0 Inner scalel0 h Wind shear convection h Kolmogorov turbulence cartoon ground

  13. von Karmann spectrum (Kolmogorov + outer scale) outer scale inner scale Kolmogorov Turbulence Spectrum  = 2/ Energy -5/3 Spatial Frequency

  14. 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

  15. 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

  16. 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

  17. 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≃ r0/v 06/5 Telescope primary

  18. Simplified AO system diagram

  19. 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).

  20. 0 0 1 1 2 2 Wavefront sensor family tree 1st Step Optical Processing 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?

  21. Shack-Hartmann wavefront sensing

  22. Shack-Hartmannwavefront sensing • Divide primary mirror into “subapertures” of diameter r0 • Number of subapertures ~ (D / r0)2where r0 is evaluated at the desired observing wavelength • Example: Keck telescope, D=10m, r0 ~ 60 cm at l = 2mm. (D / r0)2 ~ 280. Actual # for Keck : ~250.

  23. Adaptive Optics Works! Show Gemini AO animation

  24. Definition of “Strehl”: Ratio of peak intensity to that of “perfect” optical system Intensity x 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

  25. 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%

  26. Not enough light to measure distortion Dave Letterman’s Top 10 reasons why AO does not work perfectly

  27. Higher order system Better WFS detectors Lower order system Most important AO performance plot Strehl Keck system limit is about 14th magnitude Guide star magnitude

  28. Performance predictions ESO SINFONI instrument

  29. Performance predictions Gemini comparison of Shack-Hartmann and curvature

  30. Sampling error of the wavefront • (subapertures too large to see small distortions) Dave Letterman’s Top 10 reasons why AO does not work perfectly

  31. Fitting error of the deformable mirror • (not enough actuators) Dave Letterman’s Top 10 reasons why AO does not work perfectly

  32. 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

  33. Deformable mirrors - many sizes • 13 to >900 actuators (degrees of freedom) About 12” A couple of inches Xinetics

  34. There is software in the system Dave Letterman’s Top 10 reasons why AO does not work perfectly

  35. Temporal error • (a.k.a. phase lag, lack of sufficient bandwidth) Dave Letterman’s Top 10 reasons why AO does not work perfectly

  36. Anisoplanatism Dave Letterman’s Top 10 reasons why AO does not work perfectly

  37. 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% • 0depends on distribution of turbulence and conjugate of the deformable mirror. h 0≃ r0 / h Telescope primary

  38. Anisoplanatism (Palomar AO system) • 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 credit: R. Dekany, Caltech

  39. Vertical profile of turbulence Measured from a balloon rising through various atmospheric layers

  40. Non-common path errors Dave Letterman’s Top 10 reasons why AO does not work perfectly

  41. Wavefront sensor measurement error • (readout noise) and noise propagation Dave Letterman’s Top 10 reasons why AO does not work perfectly

  42. Dave Letterman’s Top 10 reasons why AO does not work perfectly • Tip/tilt error • (tip/tilt mirror not shown)

  43. There is software in the system Dave Letterman’s Top 10 reasons why AO does not work perfectly

  44. Thank you for your attention

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