Download The basic physics of AO

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
r0
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
~ l/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108m/s)
n = index of refraction
• Index of refraction of air ~ 1.0003
Atmospheric distortions are due
to temperature fluctuations
• Refractivity of air
N  (n 1) 106  77.6 1 7.52103 l 2  (P /T)
where P = pressure in millibars, T = temp. in K,
n = index of refraction. VERY weak dependence on l
• Temperature fluctuations cause index fluctuations
N  77.6  (P / T )T
2
(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! (l=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 L0
Inner scale l0
h
Wind shear
convection
h
ground
Kolmogorov Turbulence Spectrum
von Karmann spectrum
Energy
(Kolmogorov + outer scale)
 = 2/l
-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 - 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 l)
• But a little tricky,
r0 l6/5
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.
l/r0 l-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 r0
 0 ≃ r0/v
wind velocity = 30 mph
= 13.4 m/sec
0 = 14 cm / v = 15 msec (visible)
= 74 cm / v = 80 msec (K)
 0 l6/5
• 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 1st or 2nd derivative of the
wavefront (defined by optical processing).
Wavefront sensor family tree
1st
Step
Divide into
subapertures
Derivative
of
measure
0
1
2
Shack-Hartmann
Optical
Processing
0
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 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 l = 2
m. (D / r0)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 ~ l/r0)
• Ratio between core and halo varies during night
Keck AO system performance on
bright stars is very good, but not
perfect
A 9th magnitude star
Imaged H band (1.6 m)
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 14th 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 ≃ r0 / 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”x40” (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