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

Isoplanatic angle Strehl Kolmogorov r0r0 00 Shack-Hartmann speckle inner scale outer scale Curvature

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 m telescope Long exposure image Short exposure image 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 (3.28  10 8 m/s) n = index of refraction Index of refraction of air ~

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)

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 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 Outer scale L 0 ground Inner scale l 0 h convection solar h Wind shear

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

Kolmogorov turbulence in a nutshell - L. F. Richardson ( ) 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 - 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 sec 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  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 r 0 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 ≃ r 0 /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 1 st or 2 nd derivative of the wavefront (defined by optical processing).

Wavefront sensor family tree Divide into subapertures Optical Processing 1 st Step Shack-HartmannPyramid, Shearing Curvature Point source diffraction Derivative of measure 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

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=10m, r 0 ~ 60 cm at =   m. (D / r 0 ) 2 ~ 280. Actual # for Keck : ~250. Shack-Hartmann wavefront sensing

Adaptive Optics Works! Show Gemini AO animation

Measuring AO performance Intensity 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 ~ /r 0 ) Ratio between core and halo varies during night

Keck AO system performance on bright stars is very good, but not perfect Without AO FWHM 0.34 arc sec Strehl = 0.6% With AO FWHM arc sec Strehl = 34% A 9th magnitude star Imaged 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 is about 14 th 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) Xinetics A 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 ≃ r 0 / 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