Transcript Phénomènes de diffraction - IAG-Usp

Adaptive optics and
wavefront correctors
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Atmosphere from 0 to 20 km…
stratosphere
tropopause
10-12 km
wind flow over dome
Boundary layer
~ 1 km
Heat sources w/in dome
Measured from a balloon
rising through various
atmospheric layers
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And what about spatial telescopes ?
• It is definitively a solution for some applications
But extremely difficult and expensive to make large
telescopes…
Telescope under study for first light around 2015-2020:
USA : TMT diameter of 30 meter
Europe : E-ELT diameter 42 meter
42 meter in space ????????
No !!!!
• Ground based telescopes necessary to get more
photons & a better angular resolution with higher
diameter … large telescope WITH adaptive optics
• Space telescope will remain necessary anyway because
of atmosphere absorption at certain wavelengths
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How does adaptive optics help?
Measure details of
blurring from “guide
star” near the object
you want to observe
Calculate (on a
computer) the shape
to apply to
deformable mirror to
correct blurring
Light from both guide
star and astronomical
object is reflected from
deformable mirror;
distortions are removed
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Adaptive optics system
DM fitting
error
Feedback loop:
next cycle
corrects the
(small) errors
of the last cycle
Non-common
path errors
Phase lag,
noise
propagation
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Measurement error
Classical Adaptive optics
Deformable
miror
control
Wave front sensor
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astro.
imaging
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Close loop / open loop AO
wavefront
wavefront
WaveFront Sensor
Real Time Computer
WFS
RTC
Main advantage of close
loop :
the WFS is working around 0, measuring small perturbations
=> It is working in its linearity domain
DM
CAM
Deformable mirror
Imaging camera
CAM
DM
WFS
RTC
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Adaptive optics increases peak
intensity & width of a point source
Lick
Observatory
No AO
With AO
Intensity
How is the Point Spread Function
after adaptive Optics ?
No AO
With AO
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AO produces point spread functions
with a “core” and “halo”
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 ~ r0)
• Ratio between core and halo varies during night
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Correction quality ?
• Strehl ratio :
Post AO
Ideal case
I[0,0] is the intensity of the Point Spread Function
at the center of the image
(Strehl, K., 1902, Zeit. Instrumenkde, 22, 213)
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Correction quality ?
Other parameter might be more interesting,
depending upon the objective:
• Full width half maximum (FWHM) 
resolution
• Ensquared/encircled energy  spectroscopy
• Indirect criterium:
- detection/signal to noise ratio
- quality of image reconstruction
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Adaptive optics system elements
• Deformable mirror to correct the wavefront
• Wavefront sensor to measure the distortion that has to
be corrected
• Real time computer / control algorithm to calculate the
instructions to the DM from the WFS measurements
Each of them brings specific limitations / error terms
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Classical Adaptive optics
Residual phase variance
2 OA residu
=
2miror
+ 2wfs
2ph & ron
+ 2aliasing
+ 2scintill.
{
+ 2temp.
+ 2atm. res.
+ 2anisoplanatism
Now, we are going to study each of these elements…
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DM caracteristics
• Number of actuators and spatial arrangement
• Dynamic range: stroke (total up and down range)
– Typical “stroke” for astronomy  several microns. For vision science up to
10 microns
• Spectral range
• Temporal frequency response: faster than coherence time t0
• Influence function of actuators:
– Shape of mirror surface when you push just one actuator
• Surface quality: Small-scale bumps can’t be corrected by AO
• Hysteresis of actuators:
– Want actuators to go back to same position when you apply the same
voltage
• Power dissipation:
– Don’t want too much resistive loss in actuators, because heat is bad
(“seeing”, distorts mirror)
– Lower voltage is better (easier to use, less power dissipation)
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Influence function of deformable mirror
One actuator
Two actuators
correlation coeff
Between two actuators
Influence function and interactuator distance gives correlation coefficient
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Types of deformable mirrors: large
• Segmented
– Made of separate segments with small gaps
– Each segment has 1 - 3 actuators and can correct:
• Piston only (in and out), or
• Piston plus tip-tilt (three degrees of freedom)
• “Continuous face-sheet”
– Thin glass sheet with actuators glued to the back
– Zonal (square actuator pattern), or
– Modal (sections of annulae, as in curvature sensing)
• Bimorph
– 2 piezoelectric wafers bonded together with array of
electrodes between them. Front surface acts as mirror.
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Types of deformable mirrors: small
• Liquid crystal spatial light modulators
– Technology similar to LCDs for computer screens
– Applied voltage orients long thin molecules, changes index of
refraction
– Allows large number of pixels DM (typically LCD : 512x512 pixels)
– Only problem… response time slow…
• MOEMS (micro-Opto-electro-mechanical systems)
– Fabricated using microfabrication methods of the integrated circuit
industry
– Many mirror configurations possible
E l e c t r o s t a t i c a l
a c t u a t e dA t t a c h M
m
m
– Potential to be very inexpensive
d i a p h r a gp m
o s t
– Very large number of actuators possible
– No problem of response time
l
e
ie
y
m b
rn rt o
C o n t i n u o u s 17m
i r
Continuous face-sheet deformable
mirrors
Glass face-sheet
• DMs generates a wavefront fitting
error due to its limited degree of
freedom
fitting2 = aF ( d / r0 )5/3 rad2
•Characteristics: actuator separation,
temporal response, influence
function, surface quality, hysteresis
Light
Cables leading to mirror’s power
supply (where voltage is applied)
Anti-reflection coating
PZT or PMN actuators: get
longer and shorter as
voltage is changed
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Continuous face-sheet DM’s:
Xinetics product line
• Range from 13 to > 900 actuators (degrees of freedom)
About 12”
Xinetics
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Influence functions for Xinetics DM
• Push on four actuators, measure deflection with
an optical interferometer
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Bimorph mirrors
Bimorph mirror made from 2
piezoelectric wafers with an
electrode pattern between
the two wafers to control
deformation
Front and back surfaces are
electrically grounded.
When V is applied, one wafer
contracts as the other
expands, inducing curvature
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MOEMS
Micro deformable mirror in poly-Silicium (continuous membrane)
600µm
Influence function of the deformable
mirror
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Fitting error
fitting2 = aF ( d / r0 )5/3 rad2
• Physical interpretation: If we assume the DM does
a perfect correction of all modes with spatial
frequencies < 1 / r0 and does NO correction of any
other modes, then aF = 0.26
• Equivalent to assuming that a DM is a “high-pass
filter”:
– Removes all disturbances with low spatial frequencies,
does nothing to correct modes with spatial frequencies
higher than 1/r0
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Fitting error and number of
actuators
fitting2 = aF ( d / r0 )5/3 rad2
DM Design
aF
Actuators / segment
Piston only,
square segments
1.26
1
Piston+tilt,
Square segments
0.18
3
Continuous DM
0.28
1
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Consequences: different types of DMs need
different actuator counts, for same conditions
• To equalize fitting error for different types of DM, number of
actuators must be in ratio
6/ 5
 N1  d2  aF1 
       
 N2   d1  aF2 
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• So a piston-only segmented DM needs
( 1.26 / 0.28 )6/5 = 6.2 times more actuators than a
continuous face-sheet DM
• Segmented mirror with piston and tilt requires 1.8 times
more actuators than continuous face-sheet mirror to
achieve same fitting error:
N1 = 3N2 ( 0.18 / 0.28 )6/5 = 1.8 N2
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Adaptive secondary mirrors
• Make the secondary mirror into the “deformable mirror”
• Curved surface ( ~ hyperboloid)  tricky
• Advantages:
– No additional mirror surfaces
• Lower emissivity. Ideal for thermal infrared.
• Higher reflectivity. More photons hit science camera.
– Common to all imaging paths except prime focus
• Disadvantages:
– Harder to build: heavier, larger actuators, convex.
– Difficult to control mirror’s edges (no outer “ring” of actuators outside
the pupil)
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MMT-Upgrade:
adaptive secondary
• Magnets glued to back of
thin mirror, under each
actuator.
• On end of each actuator is
coil through which current
is driven to provide
bending force.
• Within each copper finger
is small bias magnet, which
couples to the
corresponding magnet on
the mirror.
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Adaptive secondary for
the MMT
U. Arizona +
Arcetri Observatory
> 300 actuators
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