1Seeing Profile from Racine (1996)

Movie of short exposure images (B. Tubbs, wikipedia.org)

Adaptive Optics OverviewWhat (Good) is Adaptive Optics? System Overview Atmospheric Turbulence

Image Structure Useful Relations

Nuts and Bolts of AO Wavefront Sensors and Correctors Natural and Artificial Guide Stars

AO Modes

AO refinements Wide Field AO High Contrast Imaging

Adaptive Optics for Astronomical Telescopes

John Hardy

SPIE field guide for Adaptive Optics

References:

Backgroundl It has been long known that

the atmosphere limits the resolution achievable by optical telescopes. For example, Newton wrote that

“ . . . the Air through which we look upon the Stars, is in a perpetual Tremor . . . all these illuminated Points [from different portions of the telescope] constitute one broad lucid Point, composed of these 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, and without any trembling of the whole. Long telescopes may cause Objects to appear brighter and larger than short ones can do, but they cannot be so formed to take away the confusion of Rays which arises from the Tremors of the Atmosphere. 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.

Images with Increasing Aperture

What is Adaptive Optics?l Real time (<100 ms update rate) correction of

wavefront aberrations induced by atmospheric refraction.

l Useful for diffraction-limited imaging mainly in the 1-10 micron wavelength range but effort is ongoing to use at shorter wavelengths as well.

l Requires a relatively bright (V<15) reference star although artificial beacons are in use.

l Field of view for observations is governed by the height of the turbulence.

Usefulness of Adaptive Optics

The use of adaptive optics is expanding as the capabilities increase, but typical observations include:

• faint companion detection • studies of protoplanetary disks around young stars • high resolution imaging of planets and moons • close binaries • quasar host characterization • spectroscopy at high spectral resolution • photometry and spectroscopy in crowded regions

from Brown, Bouchez and Griffith, 2002

7

Some local telescopes using AO

8

The 6.5 m MMT on Mt. Hopkins The 2x8.4 m Large Binocular Telescope on Mt. Graham

The MMT AO System

[7736-12]

AstronomicalTelescopesandInstrumenta3on2010,June27-July2,SanDiego,2010

Paper7736-12

Intensi3esbetweenopenandclosedlooprescaledfordisplayingpurposes.

LBTInfraRedTestCameraimages:Hband,10mas/pixelscale

Theobject:HD124085,K0,R=7.5,I=6.9,H=5.8,TripleStarTheatmosphere:seeing0.6arcsecVbandEleva3on58..64FLAOparameters:1KHz,30x30subaps,400correctedmodesResults:SRH65%..73%

3.2arcsec

Imaging with one telescope of the 2x8.4 m LBT

12

Star subtracted from right image is 10,000brighter than the four planets.

no correction

AO correction

13

courtesyA.Skemer

Exoplanet Observations

PSF-subtracted

HR87994planetsystemobservedat3.8µm

14

HL Tau

15

Testi, Skemer, et al. 2015

ALMA Image

LBTI enables: • guiding on the obscured star • observations at long

wavelengths to pierce the extinction and scattered light.

EPSC2015Conrad

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Looking at Jupiter’s moon, Io

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WeobservedIowithLBTIforonehouronChristmasEve2013

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Loki Resolved – Comparison

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Theresultingimageprovidesbetterthantwicetheresolutionachievableonatelescopewithasingle8.4meteraperture.

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Loki Resolved – Bilobal Structure

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AllvolcanoesbutLokiwereunresolved

TheM-bandemissionfeatureatLokihoweverwaslargeenoughtoberesolvedandrevealedabilobalstructure.

OccultationbyEuropa:

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Loki Resolved – Voyager Overlay

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havefromtheVoyagermission

ThisisourM-bandmeasurementoverlaidonthatimageandsmoothedtobetterindicatetheachievedresolution.

Credit:NASAPIA00320March1979

100km

Atmospheric Turbulence

Temperature variations in the atmosphere result in index of refraction variations. This, in turn causes corrugations in wavefronts propagating through the atmosphere.

Large scale temperature variations create flow of air which will interact at boundary layers to create turbulence. Large scale eddies cascade into smaller scale turbulence. The resulting index variations have typical power spectra (strength versus spatial scale) which are characteristic of the turbulent process.

Turbulence from a boundary layer

Bigger whirls have little whirls, Which feed on their velocity; Little whirls have smaller whirls, and so on to viscosity.

Scintillation2mm/pixel, 1024x1024 pix (~2m x 2m)lambda=500nm, 30 deg zenith angle, 0.8” seeing at zenithSite: Mauna Loa observatory (3500 m altitude)

Cn2 profilesl The strength of the turbulence is measured as an

index of refraction variation (termed Cn2). l The turbulent layers are not limited to the ground, but

extend well up into the troposphere.

Cn2

Coherence Length

The integral of Cn2 over the height of the atmosphere

provide the characteristic scale for phase aberrations in the structure function.

Kolmogorov Turbulencel Resulting phase variations are characterized by a

structure function:

In radians2

The structure function is only valid for scales above the inner scale (where viscosity damps out the turbulence) and below the outer scale which is the characteristic input size of a cell of temperature variation.

Rule of thumb: RMS phase variations are 1 micron per m of separation.

The Fried (Coherence) Lengthl Defined as the size scale for which the rms

phase error is 1 radian. (~15 cm at visible wavelengths).

l Wavelength dependent:

l Can be estimated from the seeing:

Think of the Fried length as the largest coherent patch on a wavefront.

Coherence Timel A rough approximation (not accurate) is that the

turbulent wavefront is blown across the aperture at the average wind speed of the atmosphere.

l A typical wind speed is 10 m/s. So we expect coherence times of In the visible this is 5 ms.

Rule of Thumb: The correction speed should be ~10x the coherence time.

Isoplanatic Patchl The average height of the turbulence limits the

field of view over which the correction is valid The characteristic scale for this is the isoplanatic

patch, given by:

where h is the average height of the turbulence, typically 5 km.

Rule of thumb: the radius, in arcseconds, of a usable FOV is wavelength*10.

Image Structurel The point spread function of an adaptive optics system

is complicated by the fact that the light is only partially corrected.

l A portion of the total energy, S, is gathered into an Airy pattern.

l The remaining energy, 1-S, is spread into a halo with a characteristic size of the seeing disk.

Strehl Ratiol The Strehl Ratio is defined as the peak brightness of

an actual image relative to an unaberrated image. This can be related to the rms wavefront error by the

approximation:

where sigma is expressed in radians. This equation is appropriate for wavefront errors < 2 radians or a Strehl of > 0.1.

Strehl versus wavelengthl The wavefront error, in units of length, is essentially

wavelength independent. l If we express this in radians of phase error the quantity

is inversely proportional to wavelength. l We can scale the expected Strehl using the relation:

Contribution to Strehl

Potential sources of wavefront error include time delay, fitting error, isoplanatic error, photon noise error

If we assume the wavefront error terms are independent we can write:

Errors and System Designl Systems typically trade-off time delay errors and read

noise errors (due to low fluxes) l Flux can be increased by using large subapertures at

the expense of fitting errors. l For any system, the main two choices are:

− How many subapertures do you need? − How fast do the corrections need to happen?

l The answer depends on wavelength and the brightness of the guide star.

Error relations

Fitting Error

Photon error

Time Delay error

Isoplanatic error

d= subaperture size

t= integration time

Strehl versus seeing

Sigma (nm) 250 290 330 400

Predicted Strehl versus Guide Star

Esposito et al. 2010

Error Summary

How good a Strehl do you need?

Wavefront Sensorsl The phase of a wavefront of light is not directly

observable. l Laboratory optics measurements address this by

interfering the light with a reference source. − The source needs to be coherent to do this − You typically carry out this measurement by measuring the

interference at four different phase shifts between the beams.

l This is a problem for astronomy where the source is not necessarily coherent and the wavefront is changing quickly.

Astronomical Wavefront Sensorsl The solution is to measure image position variations

which correspond to the angle of arrival of a photon. l This gives you a delta phase over a delta distance.

l Various Designs: l Shack-Hartmann l Curvature l Pyramid

A Shack Hartmann Wavefront Sensor

Aspects of Shack Hartmann Designl Simple, most prevalent design l Not optimal design for wavefront measurement. l Number of subapertures is fixed by optics.

Shack-Hartmann based systems MMT AO

Keck AO

VLT NAOS

Gemini Altair

Quad cell signals

l If we want to maximize the signal to noise, we use the minimum number of pixels to sense the centroid.

l A quad cell gives us this ability where

but there is a loss of information in the scale of the offset.

�x =I2 + I1 � I3 � I4

I1 + I2 + I3 + I4

Curvature Systemsl We can also derive phase information by looking at the

intensity to either side of the pupil plane. l The intensity difference is directly proportional to the

phase error in that zone.

Curvature System

Phase errorImage on

One-side of pupilImage on

other side of pupil

Intensity difference image

Actuator positions

Aspects of Curvature Sensorsl Curvature systems have historically used APDs to

optimize the signal to noise. This enhances the faint guide star limit compared to CCDs due to the low read noise.

l The zonal correction (no reconstructor) makes implementation easier.

Curvature Based Systems CFHT Hokupa'a on Gemini Subaru Telescope

A Pyramid WFS

Stellar image is placed on the tip of a four sided pyramid Creates four beams.

Intermediate optics form pupil images from the four beams.

47Credit: Sebastian Egner

Aspects of Pyramid Sensorsl More sensitive to low order modes.

l Ideal match to atmosphere.

l A change in sampling can easily be carried out via binning of CCD.

Pyramid Based Systems LBT Magellan Subaru SCexAO

Ways of describing the wavefrontl You can think of characterizing the wavefront in two

qualitatively different ways: − Zonal description of phase − Modal description of phase

l Zonal wavefront description are more straightforward but random errors are not smoothed out.

l Modal wavefronts describe the wavefront as an amplitude for functions of r, and theta: Zernike modes.

Zernike Modes

Wavefront Reconstructionl For wavefront sensors which measure slope we need

an intermediate step to calculate the wavefront

Wavefront Reconstructionl The process of a wavefront reconstruction is a matrix

operation where we have − a vector of slopes of length S=2*subapertures, − A vector of nodes on the corrector corresponding to N

actuators − An I=NxS matrix relating the influence of each actuator on

the slopes.

Reconstruction Example

l Assume we have a 2x2 Shack-Hartmann with a 3x3 actuator grid arranged as below

2 31

5 64

8 97

a b

dc

If we push up actuator n1 we expect to see a slope, ax, and ay. We have thus characterized A and C in the interaction matrix. The inverse matrix of I can be used to calculate actuators positions from slopes. This is called the reconstructor matrix.

l In general we have the Relation:

Wavefront Correctorsl Deformable Mirrors

− Voice Coil Actuators (adaptive secondaries)

− PZT actuators (Xinetics) − MEMs (Boston MicroMachine)

l LCD optics

Piezo actuated mirror (Cilas)

The MMT adaptive secondary

Piezo Stack Deformable Mirror (DM)Displacement is proportional to electric fieldLarge displacement = high electric field over long length of material

To avoid unreasonably high voltages, stack of piezo layers is usedVoltage is applied across each layer

Piezo actuated mirror (Cilas)

Bimorph DMs

Curvature DM made by IfA, University of Hawaii

An applied voltage across the structureinduces a constant stress per unit length,hence a change in curvature

Electrostrictive DM

The 4356-actuator deformable mirror for PALM-3000 (Xinetics Inc.)

Magnetic force

Adaptive secondarymirror

Thermal IR instruments need low thermal background => fewer warm optics

Adaptive secondary mirror (MMT, LBT x2, Magellan)

Magnetic force

Small magnetic DMsKey advantage is large stroke

241 actuator magnetic DM(Alpao)

> 20 micron stroke(high speed DM97, Alpao)

From: Adaptive Optics for Biological Imaging by Kubby (2013)

Small electrostatic MEMS mirror(Boston Micromachines, 1024 act)

Electrostatic DMsLarge number of actuators in a small space

Laser Beaconsl Two flavors:

− Rayleigh Backscatter (MMT) − Sodium Resonance (Keck)

Laser Beacon issues

l Laser Beacon Wavefront sensors are not sensitive to the tip-tilt variations of the image

l Consequently you need a tip-tilt natural guide star to derive this value.

l There is an additional error term due to focus anisoplanatism.

l Can be overcome with a constellation of beacons and multiple wavefront sensors.

90 km

20 km

Sky Coverage

Galactic Galactic latitude

AO Modesl Single Conjugate AO:

Diffraction-limited, field size determined by isoplanatic patch.

l Ground-Layer AO: Use of multiple guide stars to improve seeing across a wide (5') FOV.

l Multi-Conjugate AO (MCAO): Use of multiple DM's and multiple guide stars to create wide-field diffraction-limited images.

45” from axis