Adaptive Optics OverviewPhil Hinz (phinz@as.arizona.edu)

What (Good) is Adaptive Optics?System Overview

MMT AO system

Atmospheric Turbulence

Image Structure

Useful Relations

Nuts and Bolts of AOWavefront Sensors and Correctors

Wavefront Reconstruction

Image quality

Natural and Artificial Guide Stars

AO Modes

Adaptive Optics for Astronomical Telescopes

John Hardy

SPIE field guide for Adaptive Optics

References:

Background● 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?● Real time (<100 ms update rate) correction of

wavefront aberrations induced by atmospheric refraction.

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

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

● Field size 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 detectionstudies of protoplanetary disks around young starsclose binariesquasar host characterizationspectroscopy at high spectral resolutionphotometry and spectroscopy in crowded regions

AO is available on all large ground-based telescopes.

AO system Overview

AO system components

The MMT AO System

1. Measure aberrationsdue to the atmospherewith WFS Camera

2. Calculate secondaryshape needed to correctmeasured aberration

3. Apply this shape to thedeformable secondary

This loop is performedat 550 Hz

WFSCamera

ReconstructorComputer

AdaptiveSecondary

Mirror

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.

Kolmogorov Turbulence● Resulting phase variations are characterized by a

structure function:

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.

2 x1, x2=⟨x1−x22⟩=D r =6.88r

r05/3

In radians2

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.

Cn2 profiles● The strength of the turbulence is measured as an

index of refraction variation (termed Cn2).● 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.

r 0 , z =0.196/5 cos z3/5∫C n2 dh

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

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

● Wavelength dependent: ● Can be estimated from the seeing:

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

r 0=r 0,5500

6 /5

r 0=FWHM seeing

Coherence Time● A rough approximation (not accurate) is that the

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

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

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

t 0=0.3r 0

v

Don't we also need to consider the Wavefront Amplitudes?

Amplitude variations occur if the angle the light is bent is sufficient to cause it to interfere with the next cell over.

We can write theta asso amplitude effects are small if

hr

0

r0

h

=r0

hr0

2

Isoplanatic Patch● The average height of the turbulence limits the

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

patch, given by:

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

0=0.31 r0/h

Image Structure● The point spread function of an adaptive optics system

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

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

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

Strehl Ratio● 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.

S=e−2

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

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

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

=00

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:

2=∑i2

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

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

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

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

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

Error relations

Fitting Error

Photon error

Time Delay error

Isoplanatic error

fit=a dr0 5/6

iso= 0 5/6

ph=4N ph

delay=5.5 tt0 5/6

Nph=

109

10−0.4Vd 2 t

d= subaperture size

t= integration time

Strehl versus seeing

Sigma (nm)250 290330400

Predicted Strehl versus Guide Star

1x1 2x2 3x3

K band

H band

J band

1x1 2x2 3x3

K band

H band

J band

How good a Strehl do you need?PSF, λ=2.2 µm, D/r0 = 8.5

1

0.1

0.01

0.001

0.0001

0 0.1 0.2 0.3 0.4 0.5Radius (arcsec)

Peak

inte

nsity

rela

tive

to d

iffra

ctio

n lim

it

uncorrected

218 DOF50 DOF24 DOF12 DOF2 DOF

Sky Coverage

Galactic Galactic latitude

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

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

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

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

Zernike Modes

Wavefront Sensors● The phase of a wavefront of light is not directly

observable.● 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.

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

Astronomical Wavefront Sensors● The solution is to measure image position variations

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

A Shack Hartmann Wavefront Sensor

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

Shack-Hartmann based systemsMMT AO

Keck AO

VLT NAOS

Gemini Altair

Curvature Systems● We can also derive phase information by looking at

the intensity to either side of the pupil plane.● 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 differenceimage

Actuator positions

Aspects of Curvature Sensors● 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.

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

Curvature Based SystemsCFHT Hokupa'a on GeminiSubaru Telescope

Wavefront Reconstruction● For wavefront sensors which measure slope we need

an intermediate step to calculate the wavefront

Wavefront Reconstruction● 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

● 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.

● In general we have the Relation: S= I N

Wavefront Correctors● Deformable Mirrors

– Voice Coil Actuators (adaptive secondaries)

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

● LCD optics

The MMT adaptive secondary640mm x 2mm Thin Glass Shell

Reference Body

Cooling Lines

Control Electronics

Voice Coil Actuator

Laser Beacons● Two flavors:

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

Laser Beacon issues

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

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

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

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

90 km

20 km

ErrorSummary

AO Modes● Single Conjugate AO: Diffraction-limited, field size determined

by isoplanatic patch.● Ground-Layer AO: Use of multiple guide stars to improve

seeing across a wide (5') FOV.● Multi-Conjugate AO (MCAO): Use of multiple DM's and multiple

guide stars to create wide-field diffraction-limited images.

Auxiliary Material

MMTAO Science CamerasARIES: 1-2.5 µm imager MIRAC-BLINC:

6-25 µm imager and nullerClio: 3-5 µm imager

Jupiter at 4.8 µm

Protoplanetary Nebula at 9.8 and 11.7µm

IC 2149 at 2.1 µm Don McCarthy Suresh Sivinandam Bill HoffmanCraig Kulesa Ari Heinze Phil Hinz

Phil Hinz

ARIES (1-2.5 um imager)IC 2149 at 2.1 microns. (courtesy Patrick A. Young, Donald W. McCarthy, and the ARIES-MMTAO team.)

● 1-2.5 um HAWAII imager commissioned

● 1-5 um spectrometer is currently being completed.

● Two magnifications provide for 20 and 40” FOV (0.019, and 0.038 “/pix).

Measured H band sensitivity: H=19.6, 10σ, for t = 10 s integration.

Mid-Infrared Array Camera (MIRAC) The Bracewell Infrared Nulling Cryostat (BLINC)

•256x256 5-25 um imager•Nulling channel using two subapertures

•Imaging scale is 0.055-0.11” /pixel.•N band sensitivity is ~0.1 Jy in 10 s•Chopping is carried out with an internal mirror.

Clio Design• Diffraction-limited imaging from H through M-bands

• 320256 large well-depth, high throughput InSb array optimized for 3-5 µm imaging (Indigo Systems Inc.)

• Cooled optics (77K), baffling, and cold stops to minimize instrument thermal background

• Coronographic option built in (have ability to add field and pupil stops and PSF shaping wave plates)

SPIE 2006 - Clio - Page 3

fake 10 Jupiter mass planet at 20 AU around nearby star

1 arcsec

Quad cell signals

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

● A quad cell gives us this ability where

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

x=I 2 I 1− I 3− I 4

I 1 I 2 I 3 I 4