The Fantastical World of Adaptive Optics - EPN Campus · 2013-08-12 · ESI 2011 – Adaptive Optics 8 400 Years of the Telescope The era of the Extremely Large Telescopes (ELTs)

The Fantastical World of The Fantastical World of Adaptive OpticsAdaptive Optics

A multimedia presentation of the physics andtechnology of adaptive optics

James W. BeleticSenior Director, Astronomy & Civil Space

2ESI 2011 – Adaptive Optics

400 Years of the Telescope

Galileo Galilei (1564–1642)

1609 - First astronomical use of the telescope

~2 cm diameter aperture

PonteVecchioPonte

Vecchio

UffiziUffizi

MuseoGalileoMuseoGalileo

PalazzoVecchioPalazzoVecchio

Firenze, Italia


400 Years of the TelescopeWe have come a long way…….ESO 8-meter telescope



400 Years of the Telescope2009 - 17 telescopes with 6.5-meter aperture or larger


400 Years of the Telescope2009 - 17 telescopes with 6.5-meter aperture or larger

Keck – two 10-mKeck – two 10-m

Subaru 8.2-mSubaru 8.2-m Gemini 8-mGemini 8-m

LBT – twin 8.4-mLBT – twin 8.4-m

MMT 6.5-mMMT 6.5-m

Carnegie Magellan – two 6.5-mCarnegie Magellan – two 6.5-m

Gemini 8-mGemini 8-m

HET 9.2-m (effective)HET 9.2-m (effective) Grantecan 10.4-mGrantecan 10.4-m

SALT 10-m (eff.)SALT 10-m (eff.)

ESO VLT – four 8.2-mESO VLT – four 8.2-m


The Electromagnetic Spectrum


400 Years of the TelescopeThe era of the Extremely Large Telescopes (ELTs) is imminent

E-ELT42-m

1385 m2

TMT30-m

707 m2

Existing Large Telescopes

944 m2 ofcollecting area

3 6.5-m9 8-m5 10-m

GMT24.5-m359 m2


Why bigger telescopes ?

Light collection area = π r2See fainter objects

λ = wavelength of lightD = diameter of telescope aperturer = radius of telescope aperture = D / 2

Angular resolution = 1.22 λ / DResolve finer detail

13 milliarcsecis the apparent size ofa football in Moscowas seen from Madrid


Understanding the performance of optical telescopes


Introduction to Fourier Opticsby Joseph W. Goodman

(3rd edition 2005, first published in 1968)

Interferometric Imaging in Astronomyby Francois Roddier

(Physics Reports, 1988)(Vol. 170, No. 2, pp. 97-166)


Propagation of Light

Only need the electric field to

understand telescope optics


Wave modelof image formation

Shui Kwok’s animation


Phasor Representation of EM Wave

+▬ Electric Field

Direction ofPropagation

Increasing phaseIncreasing time

0° phase180°(π radians)

••

ω = 2πff = frequency


Huygens-Fresnel Principle of Wave Propagation

Christiaan Huygens(1629–1695)

Augustin-Jean Fresnel(1788–1827)


OpticalAxis

ImagePlane

Diffraction-Limited Resolution

•


•

Diffraction-Limit

Phasor Distribution E-field Amplitude

D

•λ / DIntensity

(Amplitude2)

•2 λ / D

ESI 2009 – Adaptive Optics – James Beletic

E-field Amplitude

Diffraction-Limited ResolutionSquare

Aperture

First zero at λ / D

CircularAperture

First zero at 1.22 λ / D

Airy Diffraction Pattern

Sir GeorgeBiddell Airy

(1801–1892)

Intensity&

EncircledEnergy

Intensity

Zeroes of function

First zero, diffraction limit

1.00

0.75

0.50

0.25

0.00


Strehl RatioMeasure of the quality of imaging system

The Strehl ratio is the ratio of the observed peak intensity at the detection plane of a telescope or other imaging system from a point sourcecompared to the theoretical maximum peak intensity of a perfect imaging system working at the diffraction limit.


Power Spectrumof Wavefront Surface

Spatial frequency (cycles/m)

OPD Histogram with phase wrapping-λ 0 +λ

OPD Histogram-3λ 0 +3λ

+2λ

-2λ

OPD

Power

Square Aperture - no distortionsWavefront (rms = 0 wave) Point Spread

Function

Strehl = 1.27relative to circular aperture

Only DC power






+2λ

-2λ

OPD

Power

Circular Aperture - no distortionsWavefront (rms = 0 wave) Point Spread

Function

Strehl = 1.00

Only DC power

SPECSPEC Mirror 1Mirror 1 Mirror 2Mirror 2 Mirror 3Mirror 3 Mirror 4Mirror 4

R. curvature (mm)R. curvature (mm) 28800+28800+--100100 28762.928762.9 28760.028760.0 28762.628762.6 28759.228759.2WFE RMS (nm)WFE RMS (nm) N/AN/A 4242 3939 3535 1717θθ RMS (arc secs)RMS (arc secs) N/AN/A 0.0800.080 0.0740.074 0.0870.087 0.0620.062CIR @ rCIR @ r00=500mm=500mm >0.82(*)>0.82(*) 0.8750.875 0.8980.898 0.8930.893 0.9750.975CIR @ rCIR @ r00=250mm=250mm N/AN/A 0.9350.935 0.9510.951 0.9350.935 0.9810.981StrehlStrehl >0.25(*)>0.25(*) 0.7620.762 0.7910.791 0.8240.824 0.9530.953(*) (*) λλ=500 nm=500 nm

-- Very high spatial frequency errors ~3Very high spatial frequency errors ~3--7 nm RMS (wavefront)7 nm RMS (wavefront)-- Microroughness < 20 Microroughness < 20 Å- Correction forces typically ~80 N (spec <120 N)- Matching error measured by direct Hartmann test, negligible

(below measurement accuracy)- All radii of curvature within 3.7 mm

ESO VLT 8.2-m telescope






+2λ

-2λ

OPD

Power

Circular Aperture - white noiseWavefront (PV= 0.4 wave, rms = 0.05 wave) Point Spread

Function

Strehl = 0.91

Equal power atall spatial frequencies






+2λ

-2λ

OPD

Power

Circular Aperture - white noiseWavefront (PV = 0.81 wave, rms = 0.10 wave) Point Spread

Function

Strehl = 0.67







+2λ

-2λ

OPD

Power

Circular Aperture - white noiseWavefront (PV = 1.21 waves, rms = 0.15 wave) Point Spread

Function

Strehl = 0.41







+2λ

-2λ

OPD

Power


Function

Strehl = 0.21







+2λ

-2λ

OPD

Power


Function

Strehl = 0.09







+2λ

-2λ

OPD

Power


Function

Strehl = 0.03







+2λ

-2λ

OPD

Power


Function

Strehl = 0.01







+2λ

-2λ

OPD

Power


Function

Strehl = 0.00







+2λ

-2λ

OPD

Power


Function

Strehl = 0.00



Mirror 4Mirror 4

WFE RMS (nm)WFE RMS (nm) 1717StrehlStrehl 0.9530.953(*) (*) λλ=500 nm=500 nm

ESO VLT 8.2-m telescope

Point SpreadFunction

Strehl = 0.91


Atmospheric BlurringThe bane of ground-based astronomy

Long exposure imageis called the “seeing disk”

Long exposure imageBinary star pair 100 Her, 14 arc sec separation (Vmag = 6.0)

10 msec frame time


Resolution of Ground-based telescopes

Isaac Newton (1643–1727)

If the Theory of making Telescopes could at length be fully brought in Practice, yet there would be certain Bounds beyond which Telescopes could not perform. For the Air through which we look upon the Stars, is in a perpetual Tremor; as may be seen by the tremulous Motion of Shadows cast from high Towers, and by the twinkling of the fix’d Stars…

And all these illuminated Points constitute one broad lucid Point, composed of those many trembling Points confusedly and insensibly mixed with one another by very short and swift Tremors, and thereby cause the Star to appear broader than it is…

The only Remedy is a most serene and quiet Air, such as may perhaps be found on the tops of the highest Mountains above the grosser Clouds.

Isaac Newton, Opticks, 1704


Long exposureimage

the “seeing disk”

Short exposureimage

(1/100 sec)

ESO Paranal ObservatorySeeing statistics for 1999-2004

Atmospheric Seeing

Full Width Half Maximum (arc sec) 0.5 µm, zenith


The Devilbehind

atmosphericdistortions

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

where P = pressure in millibars, T = temp. in K, n = index of refraction. VERY weak dependence on λ

• 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 λ −2( )× (P /T)

δN = −77.6 × (P / T 2 )δT

Important things to rememberabout the index of refraction (n) formula

• Wavefront shape (x,y,z) is the same in visible and IRCan measure in visible (lower noise detectors) and compensate for the infrared (easier to correct)

• 1 °C temp change = 1 part in a million change in nDoesn’t seem like much, eh?

1 wave distortion in 1 meter! (λ=1 μm)

• Thermal issues bite all major telescopes who don’t pay attention to thermal issues!


Adaptive Optics“Takes the twinkle out of the stars”

θ = λ / D

Long exposureimage

Short exposureimage

Image with adaptive optics

θ = 1 arc sec


Neptune in infra-red light (1.65 microns)

Without adaptive optics With Keck AO

June 27, 1999May 24, 1999

Adaptive Optics (AO)The technology of sensing and removing atmospheric distortions

2.3

arc

sec


Galactic Center


Adaptive Optics in AstronomyEdited by Francois Roddier

(1999)

Adaptive Optics for Astronomical Telescopesby John W. Hardy

(1998)


Simplified AO system diagram



An example of correcting optics


Not to scale



Faint Object CameraImages before and after COSTAR repair


Demonstration ofatmospheric turbulence


Quantifying Atmospheric Distortions

- Power Spectrum- Correlation Length- Correlation time


Kolmogorov turbulence cartoon

Outer scale L0

ground

Inner scale l0

hνconvection

solar

hν

Wind shear

Andrei Kolmogorov (1903-1987)


Kolmogorov turbulence in 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

Kolmogorov Turbulence Spectrum

Energy(log)

Spatial Frequency (log)

κ-11/3

κ = 2π/λ

outerscale

innerscale

von Karmann spectrum(Kolmogorov + outer scale)


Circular Aperture – Fractal Noise






+2λ

-2λ

OPD

Power

Circular Aperture - no distortionsWavefront (rms = 0.0 wave) Point Spread

Function

Strehl = 1.00

Only DC power






+2λ

-2λ

OPD

Power

Circular Aperture - fractal noiseWavefront (PV = 0.23 wave, rms = 0.05 wave) Point Spread

Function

Strehl = 0.92

Power f – 11/3






+2λ

-2λ

OPD

Power

Circular Aperture - fractal noiseWavefront (PV = 0.69 wave, rms = 0.15 wave) Point Spread

Function

Strehl = 0.45

Power f – 11/3






+2λ

-2λ

OPD

Power

Circular Aperture - fractal noiseWavefront (PV = 1.60 waves, rms = 0.35 wave) Point Spread

Function

Strehl = 0.11

Power f – 11/3






+2λ

-2λ

OPD

Power

Circular Aperture - fractal noiseWavefront (PV = 2.29 waves, rms = 0.50 wave) Point Spread

Function

Strehl = 0.07

Power f – 11/3






+2λ

-2λ

OPD

Power

Circular Aperture - atmospheric distortionWavefront (PV = 4.57 waves, rms = 1.01 waves) Point Spread

Function

Strehl = 0.01

Power f – 11/3






+2λ

-2λ

OPD

Power


Function

Strehl = 0.02

Power f – 11/3






+2λ

-2λ

OPD

Power


Function

Strehl = 0.02

Power f – 11/3






+2λ

-2λ

OPD

Power


Function

Strehl = 0.02

Power f – 11/3






+2λ

-2λ

OPD

Power


Function

Strehl = 0.02

Power f – 11/3


Quantifying Atmospheric Distortions

- Power Spectrum- Correlation Length- Correlation time


Correlation length - r0

• Fractal structure (self-similar at all scales)• Structure function (good for describing random functions)

D(Δx) = [phase(x) – phase(x+Δx)]2

• r0 = Correlation lengththe distance Δx where D(Δx) = 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 λ)• But a little tricky,

r0 ∝ λ6/5

Δx

D(Δx)

r0

1 rad


Correlation length - r0

• Rule of thumb: 10 cm visible r0 is 1 arc sec seeing• Visible r0 is usually quoted at 0.55 μm.

0.7 arc sec seeing is 14 cm r0 at 0.55 μmwhich provides 74 cm r0 at 2.2 μm (K-band)

• Seeing is weakly dependent on wavelength, and gets a little better at longer wavelengths.

λ/r0 ∝ λ-1/5


Correlation time - τ0

τ 0 ∝ λ6/5

• To first order, atmospheric turbulence is frozen (Taylor hypothesis) and it “blows”past the telescope.

• τ0 = 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

τ0 = 14 cm / v = 15 msec (visible)= 74 cm / v = 80 msec (K)

τ 0 ≃ r0/v


Wavefront Sensing

Misrepresentations & Misinterpretations

• All drawings are exaggerated, since need to exaggerate to show distortions & angles.

Maximum phase deviation across 10-meter wavefront is about 10 μm – 1 part in 1 million. Like one dot offset on a straight line of 600 dpi printer in 165 feet (50 meters).

• From the point of view of light, the atmosphere is totally frozen (30 μsec through atmos). We draw one wavefront, but about 1012 wavefronts pass through telescope before atmospheric distortion changes.


Shack-Hartmann wavefront sensing

Flat wavefront

Subaperturefocal spots

uniformly spaced

Distorted wavefront

Subaperturefocal spots

unevenly spaced


• 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 λ = 2 μm. (D / r0)2 ~ 280. Actual # for Keck : ~250.

Shack-Hartmannwavefront sensing


Curvature wavefront sensing


Curvature wavefront sensing


Wavefront sensing

• Several ways to sense the wavefront.• Three basic things must be done:

Divide the wavefront into subaperturesOptically process the wavefrontDetect photons

Detecting photons must be done last, but order of the first two steps can be interchanged.Can measure the phase, or 1st derivative, or 2nd

derivative of the wavefrontDefined by optical processing


Wavefront sensor family tree

Divide intosubapertures

OpticalProcessing

1st

Step

012

012

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?


Deformable Mirrors


• Push-pull principle (piezoelectric effect)• Local influence functions• Pros:

• Fast (few kHz) resonance frequency• No theoretical limit for the number of

actuators• Cons:

• Few µm stroke• Print-through issues• ~$1k/actuator, bulky power supplies

(few hundred volts)• Generally used with Shack-Hartmann WFS• Rectangular or hexagonal geometry

Piezoelectric Transducer (PZT) Mirroror Stack-Array Mirror (SAM)


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)

Xinetics~5 cm

~30 cm


Bent / torsion principlePros:

• Global influence functions• Stroke of several microns• Cheaper than PZT• Less print-through than PZT

Cons:• Slower (few hundred Hz) resonance

frequency• Limited to a few hundred actuators

Generally used with curvature WFSRadial or hexagonal geometry

Bimorph (or curvature) Mirror


Adaptive Optics Works!



Neptune without Adaptive Optics


Neptune with Adaptive Optics


Imaging the galactic center



Mass of black hole atcenter of the Milky Way

4.1±0.6 million solar masses

Andrea Ghez (UCLA)


Reinhard Genzel Max-Planck-Institut für

extraterrestrische Physik

Flare at galactic center

Last cries of matter fallinginto the black hole?

Test ofGeneral Relativity?


U.S. Air Force 3.5-meter adaptive optics systems

3.5 meter telescopesCollapsible dome

30 subapertures across pupil690 controlled subapertures

>1 kHz update rate

3.5 meter telescopesCollapsible dome

30 subapertures across pupil690 controlled subapertures

>1 kHz update rate

AEOSMaui, Hawai’i

AEOSMaui, Hawai’i

Starfire Optical RangeAlbuquerque, New Mexico

Starfire Optical RangeAlbuquerque, New Mexico


SeaSat Imaged with Starfire AO System

• 3.5 meter telescope• 30 subapertures across pupil• 690 controlled subapertures• 740-840 nm wavelength

• 3.5 meter telescope• 30 subapertures across pupil• 690 controlled subapertures• 740-840 nm wavelength 3 arc sec


The Large Binocular Telescope (LBT)Two 8.4-meter mirrors, north of Tucson, Arizona


The LBT adaptive secondary mirror

LBT672a unit:• 911mm diameter• 1.6mm thick shell, (Mirror lab)• 672 actuators• Settling time < 1ms• 30nm WFE

Main advantages:•No extra surfaces•Position control of the mirror surface• 911mm diameter• 1.6mm thick shell• 672 actuators• Settling time < 1ms• 30nm WFE


0.16 arc sec separation

Triple Star

The LBT AO System installed in 2010Is now being commissioned


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 ~ λ/r0)• Ratio between core and halo varies during night

Strehl ≈ exp (-σ2)σ = mean-square

wavefront error






+2λ

-2λ

OPD

Power

Circular Aperture - no distortionsWavefront (rms = 0.0 wave) Point Spread

Function

Strehl = 1.00

Only DC power






+2λ

-2λ

OPD

Power

Circular Aperture - atmospheric distortionWavefront (PV = 4.57 waves, rms = 1.01 wave) Point Spread

Function

Strehl = 0.01

Power f – 11/3






+2λ

-2λ

OPD

Power

Wavefront (PV = 2.20 waves, rms = 0.32 wave) Point SpreadFunction

Strehl = 0.04

Circular Aperture - adaptive optics, 3x3 subapertures

Power = power (fc)freq < fc

Power f – 11/3

freq > fc

fc






+2λ

-2λ

OPD

Power


Strehl = 0.13



Power f – 11/3

freq > fc

fc






+2λ

-2λ

OPD

Power


Strehl = 0.29



Power f – 11/3

freq > fc

fc






+2λ

-2λ

OPD

Power

Wavefront (PV = 0.93 wave, rms = 0.13 wave) Point SpreadFunction

Strehl = 0.55



Power f – 11/3

freq > fc

fc






+2λ

-2λ

OPD

Power

Wavefront (PV = 0.43 wave, rms = 0.06 wave) Point SpreadFunction

Strehl = 0.90



Power f – 11/3

freq > fc

fc


AO Systems work well but not perfectly

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 μm)


Biggest limit to AO performance is noise of the wavefront measurement


Most important AOperformance plot

Stre

hl

Guide star magnitude

Lower order system

Higher order system

Better WFSdetectors

Factor of 2.51 per stellar magnitude2.515 = 100


• The core of the globular cluster M15.

• The brightest stars are about 13 mag, and the faintest visible in each frame are about 16 mag.

• Frame time is 80 msec, and the frame is 20 x 20 arc sec

Isoplanatism


Anisoplanatism - θ0

• An object that is not in same direction as the guide star (used for AO system) has a different distortion.

• θ0 = isoplanatic angle, the angle over which the max. Strehl drops by 50%

• θ0 depends on distribution of turbulence and conjugate of the deformable mirror.

Telescope primary

θ0 ≃ r0 / h

h


Turbulence arises in several placesstratosphere

Heat sources within dome

boundary layer

~ 1 km

tropopause10-12 km

wind flow around dome


Vertical profile of turbulence

Measured from a balloon rising through atmospheric layers


• 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

Simulation provided by Francois Rigaut


Combination of:- Brightness required for guide star- Isoplanatic angle- Distribution of “bright” stars on the sky

Only few % of the sky is accessible with natural guide star AO


Two choices for addressing limited sky coverage

(1) Find science “under the lamp post”(i.e. live within natural constraints)

(2) Make your own guide star !


Overcoming the limited sky coverage (few %)

provided by natural guide stars

Laser guide stars


The atmospheric sodium layer: altitude ~ 95 km , thickness ~ 10 km

• Layer of neutral sodium atoms in mesosphere (height ~ 95 km)• Thought to be deposited as smallest meteorites burn up• Total of about 200 kg around entire Earth

Credit: Clemesha, 1997

Credit: Milonni, LANL


ESO Laser Guide Star System


Multi-conjugate adaptive optics

(1) Provides wider field of view(2) Increases sky coverage with

natural guide stars

Overcoming limitations to the corrected field of view

118ESI 2011 – Adaptive OpticsCourtesy: F.Rigaut


Omega Centauri - Multi-Conjugate Adaptive Optics


Gemini South 8-meter Multiple Laser Guide Star System1st Light in January 2011


Highest resolution Earth based image of Jupiter (from ground or space)


Credits Many thanks to all who contributed materials and conversations to develop this talk:Many thanks to all who contributed materials and conversations to develop this talk:

• Thomas Craven-Bartle– Flatfrog Technologies, Sweden

• Francois Rigaut– Gemini Observatory, Chile

• Paola Amico– European Southern Observatory (ESO), Chile

• Philippe Dierickx– ESO, Germany

• Enrico Marchetti– ESO, Germany

• Claire Max– Center for Adaptive Optics, UC Santa Cruz, USA

• Craig Mackay– University of Cambridge, England

• Andrea Ghez– UCLA

• Reinhard Genzel– Max-Planck-Institut für extraterrestrische Physik

• Simone Esposito– Arcetri Observatory

• Robert Fugate– Starfire Optical Range (retired)

• Thomas Craven-Bartle– Flatfrog Technologies, Sweden

• Francois Rigaut– Gemini Observatory, Chile

• Paola Amico– European Southern Observatory (ESO), Chile

• Philippe Dierickx– ESO, Germany

• Enrico Marchetti– ESO, Germany

• Claire Max– Center for Adaptive Optics, UC Santa Cruz, USA

• Craig Mackay– University of Cambridge, England

• Andrea Ghez– UCLA

• Reinhard Genzel– Max-Planck-Institut für extraterrestrische Physik

• Simone Esposito– Arcetri Observatory

• Robert Fugate– Starfire Optical Range (retired)

Documents

The Fantastical World of Adaptive Optics - EPN Campus · 2013-08-12 · ESI 2011 – Adaptive Optics 8 400 Years of the Telescope The era of the Extremely Large Telescopes (ELTs)