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