1brice.leroux@oamp.fr

Adaptive optics and wavefront correctors

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stratosphere

tropopause

Heat sources w/in dome

Boundary layer~ 1 km

10-12 km

wind flow over dome

Atmosphere from 0 to 20 km…

Measured from a balloon rising through various

atmospheric layers

brice.leroux@oamp.fr

And what about spatial telescopes ?

• It is definitively a solution for some applications

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But extremely difficult and expensive to make large telescopes…

Telescope under study for first light around 2015-2020:USA : TMT diameter of 30 meterEurope : 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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Phase lag, noise

propagation

DM fitting error

Measurement error

Non-common path errors

Feedback loop: next cycle

corrects the (small) errors

of the last cycle

Adaptive optics system

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Classical Adaptive optics

Wave front sensor

control

astro.imaging

Deformablemiror

brice.leroux@oamp.fr

Close loop / open loop AO

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RTCRTCWFSWFS

DMDM CAMCAM

WaveFront Sensor Real Time Computer

Deformable mirror Imaging camera

WFSWFS

CAMCAM

RTCRTC

DMDM

wav

efro

ntw

avef

ront

Open loop

Close loop

Main advantage of close loop :the WFS is working around 0, measuring small perturbations=> It is working in its linearity domain

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Adaptive optics increases peak intensity & width of a point source

Lick Observatory

No AO With AO

No AO With AO

Intensity

How is the Point Spread Functionafter adaptive Optics ?

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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

Inte

nsity

x

Definition of “Strehl”:Ratio of peak intensity to that of “perfect” optical

system

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Correction quality ?

• Strehl ratio :

I[0,0] is the intensity of the Point Spread Functionat the center of the image

(Strehl, K., 1902, Zeit. Instrumenkde, 22, 213)

Post AO

Ideal case

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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

Correction quality ?

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

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Each of them brings specific limitations / error terms

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2ph & ron

+ 2aliasing

+ 2scintill.

= 2

miror

+ 2wfs

+ 2temp.

+ 2atm. res.

+ 2anisoplanatism

{

Residual phase variance2

OA residu

Classical Adaptive optics

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 0

• 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)

Influence function of deformable mirror

15Influence function and interactuator distance gives correlation coefficient

correlation coeffBetween two actuators

One actuator Two actuators

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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

– Potential to be very inexpensive

– Very large number of actuators possible

– No problem of response time

Electrostaticallyactuateddiaphragm

Attachmentpost

Membranemirror

Continuous mirror

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Continuous face-sheet deformable mirrors

Anti-reflection 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

• DMs generates a wavefront fitting DMs generates a wavefront fitting error due to its limited degree of error due to its limited degree of freedom freedom

fittingfitting2 2 = a= aFF ( d / r ( d / r00 ) )5/3 5/3 radrad22

•Characteristics:Characteristics: actuator separation, actuator separation, temporal response, influence temporal response, influence function, surface quality, hysteresisfunction, surface quality, hysteresis

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

Xinetics

About 12”

Continuous face-sheet DM’s: Xinetics product line

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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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Micro deformable mirror in poly-Silicium (continuous membrane)

Influence function of the deformable mirror

600µm

MOEMS

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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, 1.26 1square segments

Piston+tilt, 0.18 3Square segments

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

• 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

N1

N2

d2

d1

2

aF1

aF2

6/ 5

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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