Adaptive optics and wavefront correctors

1
Adaptive optics and wavefront correctors
2
Atmosphere from 0 to 20 km
Measured from a balloon rising through various
atmospheric layers
3
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

4
How does adaptive optics help?
Light from both guide star and astronomical
object is reflected from deformable mirror
distortions are removed
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
5
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
Measurement error
6
Classical Adaptive optics
Deformable miror
control
astro. imaging
Wave front sensor
7
Close loop / open loop AO
WaveFront Sensor
Real Time Computer
RTC
WFS
Main advantage of close loop the WFS is working
around 0, measuring small perturbations gt It is
working in its linearity domain
wavefront
DM
CAM
Open loop
Deformable mirror
Imaging camera
CAM
DM
wavefront
WFS
Close loop
RTC
8
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 ?
With AO
No AO
9
AO produces point spread functions with a core
and halo

• 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

10
Correction quality ?

• Strehl ratio
• I0,0 is the intensity of the Point Spread
  Function
• at the center of the image
• (Strehl, K., 1902, Zeit. Instrumenkde, 22, 213)

Post AO
Ideal case
11
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

12
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
13
Classical Adaptive optics
Now, we are going to study each of these elements
14
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 cant be
  corrected by AO
• Hysteresis of actuators
• Want actuators to go back to same position when
  you apply the same voltage
• Power dissipation
• Dont want too much resistive loss in actuators,
  because heat is bad (seeing, distorts mirror)
• Lower voltage is better (easier to use, less
  power dissipation)

15
Influence function of deformable mirror
One actuator
Two actuators
correlation coeff Between two actuators
Influence function and interactuator distance
gives correlation coefficient
16
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.

17
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
• Potential to be very inexpensive
• Very large number of actuators possible
• No problem of response time

18
Continuous face-sheet deformable mirrors
Glass face-sheet

• DMs generates a wavefront fitting error due to
  its limited degree of freedom
• sfitting2 aF ( d / r0 )5/3 rad2
• Characteristics actuator separation, temporal
  response, influence function, surface quality,
  hysteresis

Light
Cables leading to mirrors power supply (where
voltage is applied)
PZT or PMN actuators get longer and shorter as
voltage is changed
Anti-reflection coating
19
Continuous face-sheet DMs Xinetics
product line

• Range from 13 to gt 900 actuators (degrees of
  freedom)

About 12
Xinetics
20
Influence functions for Xinetics DM

• Push on four actuators, measure deflection with
  an optical interferometer

21
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

22
MOEMS
Micro deformable mirror in poly-Silicium
(continuous membrane)
Influence function of the deformable mirror
23
Fitting error

• sfitting2 aF ( d / r0 )5/3 rad2
• Physical interpretation If we assume the DM does
  a perfect correction of all modes with spatial
  frequencies lt 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

24
Fitting error and number of actuators

• sfitting2 aF ( d / r0 )5/3 rad2
• DM Design aF
  Actuators / segment
• Piston only, 1.26 1
• square segments
• Pistontilt, 0.18 3
• Square segments
• Continuous DM 0.28 1

25
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
• 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

26
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 mirrors edges (no outer
  ring of actuators outside the pupil)

27
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.

28
Adaptive secondary for the MMT

• U. Arizona
• Arcetri Observatory
• gt 300 actuators