Introduction to Adaptive Optics

Tim Morris

Contents

• Definitions and introduction

• Atmospheric turbulence

• Components of an AO system

• Wavefront Sensing

• Wavefront Correction

• Turbulence Conjugation

• Laser Beacons

• AO Modelling

Adaptive Optics (AO)Real-time correction of wavefront distortion

• The diffraction limit of an 10m telescope in in the visible is approximately 0.01” FWHM

• At the very best astronomical sites in the world, you’ll very rarely see images much better than 0.4” FWHM.

Why?!?

• Atmospheric turbulence distorts stellar wavefronts– Turbulence results in blurred images

• Two solutions:– Put your telescope in space

• Limited to a small mirror

• Expensive

– Correct for the atmospheric distortion• ADAPTIVE OPTICS!

Know Your Enemy

AO Conference

(me)

Enemies

The Atmosphere

What does turbulence look like?

• Kinetic energy in large scale turbulence cascades to smaller scales

• Inertial interval – Inner scale l0 ­ 2mm. Outer scale L0­10 to 100 m

• Turbulence distributed within discrete layers

• The strength of these layers is described by a refractive index structure function:

The AtmosphereKolmogorov model of turbulence

J. Vernin, Universite de Nice.

Cerro Pachon for Gemini IGPO

2

2 2 / 3

( ( ) ( )

( )

n

n n

D r n r n

D r C r

• Strength of turbulence can be described by a single parameter, r0 , Fried’s parameter

• Fried’s parameter is the diameter of a circular aperture over which the wavefront phase variance equals 1 rad2

Isoplanatic angle, temporal variation

• Angle over which wavefront distortions are essentially

the same:83

32 5

2 5 / 3

0

22.91 sec ( )nC h h dh

• It is possible to perform a similar turbulence weighted

integral of transverse wind speed in order to derive an

effective wind speed and approximate timescale of

seeing

• τ0 is the characteristic timescale of turbulence

• Note the importance of Cn2(h) in both cases

Atmospheric Seeing - Summary

Dependence on Wavelength

56

0 r 56

0 56

0

=0.55m =1.6m =2.2m

r0 10cm 36 53

0 10ms 36ms 53ms

0 5’’ 18’’ 27’’

Image quality

• Image quality is determined by the wavefront variance across the telescope pupil

• The above equation gives the phase variance over a telescope of diameter DT

• A phase variance of less than ~ 0.2 gives diffraction limited performance

• There are 3 regimes

– DT < r0 Diffraction dominates

– DT ~ r0 - 4r0 Wavefront tilt (image motion) dominates

– DT >> r0 Speckle (multiple tilts across the telescope aperture) dominates

4m telescope:

D/ r0(500nm)=20

D/ r0(2.2 m)=3.5

2

0

2

35

030.1 radiansr

DT

Strehl ratio

• There are two components of the PSF for 2 < 2 radians2

• So ‘width’ of the image is not a useful parameter, use height of PSF:

• Strehl ratio:

– For small 2 : R ~ exp (-2)

– Note that 2 should be expressed in radians2

R = Peak intensity in a (un)corrected image

Peak intensity in a diffraction limited image

MARTINI

WHT, K-band

Uncorrected

0.49” FWHM

Corrected

0.20” FWHM

AO Performance

• RMS error terms in AO add in quadrature

– Easiest to perform as nanometers RMS wavefront error

• Many sources of error

– Temporal

– DM sampling

– Anisoplanatism

– WFS noise

• Once added in quadrature, the RMS wavefront error can be converted to a Strehl Ratio

Wavefronts

• Zernike polynomials are normally used to

describe the actual shape of an incoming

wavefront

• Any wavefront can be described as a

superposition of zernike polynomials

Atmospheric Wavefront Variance after Removal of Zernike Polynomials

j n m Zernike Polynomial Name Resid. Var. (rad2)

1 0 0 1 Constant 1.030 (D/r0)5/3

2 1 1 Tilt 0.582 (D/r0)5/3

3 1 1 Tilt 0.134 (D/r0)5/3

4 2 0 Defocus 0.111 (D/r0)5/3

5 2 2 Astigmatism 0.0880 (D/r0)5/3

6 2 2 Astigmatism 0.0648 (D/r0)5/3

7 3 1 Coma 0.0587 (D/r0)5/3

8 3 1 Coma 0.0525 (D/r0)5/3

9 3 3 0.0463 (D/r0)5/3

10 3 3 0.0401 (D/r0)5/3

23 2 1

2 cos

2 sin

28 3 2 sin

26 sin 2

26 cos2

28 3 2 cos

38 sin3

38 cos3

Components of an AO System

High order AO architecture

• Wavefront controller

– Typically a deformable mirror (DM)

– May not be optically conjugate to an image of the primary

• Wavefront sensor (WFS)

– Shack Hartmann (WFS) or Curvature Sensor (CS)

• Beamsplitter

– Dichroic, multi-dichroic, intensity, spatial or combination

• Controller

– Typically multi-processor or multi-DSP

• Interfaces

– Can be complex and include removal of non-common path errors to science instrumentation (hence an interface to science data path)

• Laser beacons

• Multi-conjugate AO: many beacons, DMs

4/12/2010 16

Astronomical Adaptive Optics

Telescope

Science

target

Laser

Natural

Guide

Star

Corrected

Science

focus

dichroic

beamsplitter

IR

light

Visible

light

Wave-

front

Sensor

Adaptive

Mirror

Control

System

wavefront

information

control

signals

atmospheric

turbulence

*

*

Uncorrected

image

Corrected

Image

Uncorrected

wavefront

Corrected

wavefront

Correcting the fluctuating

aberrations caused by

atmospheric turbulence

above ground-based

optical and near-infrared

telescopes.

Wavefront Sensing

Wavefront Sensing

• Types of Adaptive Optics Wavefront Sensor

(WFS)

– Shack-Hartmann WFS

– Curvature Sensor

– Interferometers

– Others

• Performance comparison of Shack-

Hartmann (SH) and Curvature Sensor (CS)

Shack-Hartmann

Wavefront Sensor (WFS)

Microlens Array

Wavefront

Detector

Each xy offsetmeasures the local wavefrontslope across thecorrespondinglenslet.

Curvature

Wavefront SensorFocal PlaneInput Wavefront

Sensing Planes

Wavefront Sensors and Detectors

• The curvature sensor minimises the number

of pixels required to remove a given

wavefront variance

– the use of noiseless fibre-coupled avalanche

photo-diodes is therefore feasible

• Shack-Hartmann requires more pixels so a

CCD is normally employed

– low read-noise multi-port specialised devices

Comparison of SH and CS

(~0.5” seeing)(Pete Doel, University of Durham)

Comparison of SH and CS

(~1” seeing)(Pete Doel, University of Durham)

Wavefront Control

Wavefront Control

• Deformable Mirror (DM) types:

– Continuous

– Bimorph

– Segmented

• Hysteresis

• System order

Types of Adaptive Mirror(J.C.Dainty, Imperial College)

Deformable Mirror

Flexible continuous phase sheet

reflectivesurface

Actuators:typically PZT or PMNthrow: 2-20 microns

Minimum physicalactuator separation ~ 1mm

Fitting error:2

f =k (rs/r0)5/3 rad2

rs= projected actuatorseparation on sky

k = fitting coefficientfor DM type.(continuous facesheet: 0.35-0.4)

One type of Deformable Mirror (DM):

Continuous Face-sheet

Deformable Mirror

Bimorph Mirror(J.C.Dainty, Imperial College)

Bimorph

Deformable Mirror

The ELECTRA Segmented Adaptive Mirror

(76 tip-tilt-piston segments)

built by ThermoTrex, San Diego

228 degreeof freedomadaptivemirror

Wavefront Fitting Error

Comparison

0.5 1 1.5 2 2.5 3 3.5 4

Wavelength microns

0.2

0.4

0.6

0.8

1

ev

it

al

eR

la

rt

ne

Cy

ti

sn

et

nI

Comparative AO Technology Limits for WHT r0 =0.155 ,t0 =1000 ,t=1,d0 =1000

Segmented 10, 0%

Segmented 0%

Segmented 0.2 % hysteresis

Continuous face sheet 8,0.4

Bimorph n=7

Bimorph n=5

tip - tilt

Actuator Hysteresis

PMN

(electrostrictive)

Low (<2%) hysteresis

at 20o C;

High (~40%) at 0o C

Low drive voltage

(<100V)

soft PZT ~15% but

temp. stable

low drive

voltage

hard PZT ~2%, stable high drive voltage

(1000V)

Hysteresis

• Effect of high hysteresis:

– Continuous mirror: 2-3 times more WFS samples

required

– Segmented mirror: makes piston control hard

• Solutions:

– low hysteresis actuators

– linearise with motion sensor (e.g., strain gauge)

– linearise with figure sensor

– Example: ELECTRA: has strain gauges (with

temperature compensation) which reduce hysteresis

from ~15% to <0.1%

Sky CoverageThe big problem with AO

You can’t observe off-axis!

• Angle over which wavefront distortions are essentially

the same:83

32 5

2 5 / 3

0

22.91 sec ( )nC h h dh

– This is a very small angle

~5” in the visible

– It means that if you look at

an object that’s a large

angular distance away from

your guide star, you get

poor correction!

Guide Star Availability.

All sky.Model: D. Simons, Gemini

10

12

14

16

18

20

R mag

0

20

40

60

radius (arcsec)

0

0.25

0.5

0.75

1

prob >=1 stars

10

12

14

16

18

20

R mag

Guide Star Availability.

(Galactic Latitude > 30 degrees)Model: D. Simons, Gemini

10

12

14

16

18

20

R mag

0

20

40

60

radius (arcsec)

0

0.2

0.4

0.6

0.8

prob >=1 stars

10

12

14

16

18

20

R mag

NGS sky coveragemodel for ING by Remko Stuik, Leiden Observatory

Remember the Enemy?

The Atmosphere

Physicist+Enemy

leads to…

Complicated plan to defeat enemy

Part of plan that requires

a really big laser

Adaptive Optics is no different…

Laser Guide StarsCreating an artificial wavefront reference

Really Big

LaserPhysicist

GLAS LGS AO system commissioning 2007

Laser Guide Star• Purpose of a laser guide star (LGS) is to increase the sky

coverage by creating a bright wavefront reference

anywhere in the sky to replace the natural guide star

• Two types of LGS:

– Rayleigh (Green or UV)

• uses Rayleigh backscatter

• beacon height up to ~20km

• requires time-gating to set beacon height

– Sodium D (Orange)

• uses excitation of mesospheric sodium atoms

• beacon height 80-90km

• no time-gating required

• tuned to sodium D line at 589nm

Comparison of Rayleigh backscatter

and sodium-resonance backscatter.

(Courtesy of MIT Lincoln Lab.)

Rayleigh and Sodium Guide Stars at La Palma(IC Applied Optics Group + Tom Gregory, ING)

Durham’s Rayleigh Laser Guide Star

Other LGS Systems

KeckSubaru (Keck)

Other LGS Systems

VLT

WHT

US Military

LGS sky coveragemodel for ING by Remko Stuik, Leiden Observatory

LGS sky coveragemodel for ING by Remko Stuik, Leiden Observatory

Laser Beacon Limitations

• Tilt reciprocity

– no tip-tilt signal from laser beacons

• must use a natural guide star

– focus is complicated for sodium beacons

• low frequency atmospheric focus may be masked by

changes in effective beacon height

• Focus Anisoplanatism (cone effect)

• Sodium layer saturation

• Safety/site issues

Tilt Reciprocity(J.C.Dainty, Imperial College)

Multiple Tip/Tilt NGS’s?

– Consider a turbulence profile with focus aberrations at two ranges (blue)

– LGS measurements (yellow)cannot determine range of the aberration

• Tip/tilt information lost

• Equal focus measurement from each LGS, regardless of aberration range

– Tip/tilt NGS measurements can determine range from the differential tilt between stars

– Three tip/tilt NGS’s needed for all three quadratic modes

– Alternate approaches: Rayleigh LGS’s, or a solution to the LGS tilt indeterminacy problem

fr)=ar2

fr)=a(cr+d)2

=ac2r2+2acdr+ad2

~ ac2r2

After tilt removal

Angular and Focal

Anisoplanatism

Focal Anisoplanatism

0 0.5 1 1.5 2 2.5

Wavelength (microns)

0

0.2

0.4

0.6

0.8

Strehl Ratio

Effect of Na beacon Focal Anisoplanatism (Cone Effect)

d0=3m

d0=5m

d0=8m

Schemes for the use of multiple

laser beacons(J.C.Dainty, Imperial College)

Turbulence Conjugation(if normal AO is just a bit too easy)

Multiple Conjugate AO

• Putting a second

DM in a plane

conjugated to a

higher layer of

turbulence allows

off-axis correction

• Requires multiple

guide stars

Multi-Conjugate AO

(MCAO)Multiple LGS, Multiple DM: Wide

corrected FOV

Conventional AO MCAONo AO

Courtesy of GEMINI

Strehl Uniformity vs. FOV

• 0 degree zenith angle, 50% Cerro Pachon Turbulence Profile• 5 LGS, 16 by 16 subapertures, 3 DM’s• No WFS noise or servo lag

Courtesy of GEMINI

Tip/Tilt

Focus+Astig.

Cubic and Above

MCAO Control Loop Architecture

Focus

Adjustment

Integrator

SM

Tip/Tilt

Offload

Low-order

Offload to TCS

Integrator

Boresight

Adjustments

BTO Tip/

Tilt Loops

Average

Differential

LGS Tracking

(option)

(Option)

(Option)

Integrator

Boresight

Adjustment Primary

NGS WFS

LGS WFS’s

DM 1

DM 2

DM 3

Wave Front

Tomography

Auxiliary

NGS WFS’s

TTM

OIWFS

Blend

Blend

DMFS 2

DMFS 3

Blend

Blend

Piston and Waffle

Courtesy of GEMINI

AO Modelling(or AO on a budget)

AO Modelling

• Computer Modelling

– Required for performance prediction, instrumentation choices, instrumentation and AO systems engineering, detailed design.

– 8m Monte Carlo models using 10-12 processor Beowulf clusters are available, examples:

• ESO/RTN (LeLouarn et al)

• Durham (Wilson et al)

• Ellerbroek/Rigaut:

– Memory requirements scale as D4

– CPU requirements scale as D6

• D > L0 poses new challenges for optimisation of WFS sample rate and control law (both in performance model and implementation)

Durham 12-processor cluster simulations (Richard Wilson)

• DCAO I-band simulation (the full Monte Carlo):• D Tel diam (m) WFS order Tmx (s) Tloop (s)

4 8x8 18 0.14

8 16x16 140 0.52

12 24x24 847 1.4 (MOVIE)

16 32x32 4067 4.1– Tmx is the time taken to produce the poke/control matrix, which as expected goes as something like D4.

• Assuming that the wavefront reconstruction calculation does not take over as the slowest component (ie. we use sparse matrix techniques), then we can project the timings to higher orders assuming that Tloop goes as D2 and Tmx as D4: Projecting from the 24x24 case gives:

32 64x64 42831 (12 hours) 9.9

64 128x128 685296 (190 hours) 39.6

128 256x256 107 (3045 hours) 158.4 [ELT]

• 5000 loops required for 10 seconds of seeing

• Need a factor of ~100 speedup.– Assuming better parallelisation, this could be accomplished with order of magnitude larger

cluster of up-to-date CPUs, and hardware acceleration.

Durham 12-

processor cluster

simulations

(Richard Wilson)

• 24 x 24 WFS

• r0=20cm at V

• Science at 1μ.

• Cn2 is just 2 layers

(0km, 5km)

• 500Hz simulated sample rate

• Top left: 24x24 WFS

• Top right: phase map at science pupil

• Bottom left + right: science PSF at 2 field points: 30 arcsec apart.

Does it actually work on-sky?

AO Scientific Potential

0.1” slittip/tilt simulation of Galactic Center image(K) at CFHT

Actual AOimage

Doug Simons

Gemini

PUEO image: fov 10x10”, resolution~0.13”

NGC7469 - Starburst galaxy

Io imaged with Keck AO

INGRID J-band image of M15, 20s exposure, 20” diameter FOV, Open

loop FWHM ~0.45”, Closed loop ~0.2” (Moffat fit to PSF)

The GLAS LGS AO System

What does this mean to an

astronomer?

Observing with an AO System• Position of target in the sky?

– Nearer zenith is better (less atmosphere to correct)

• Is there a suitable guide star near your target?

• What wavelength do you want to observe in?– Longer is better for AO as turbulence is weaker

• What field of view do you require?

– Current facility-class AO systems are not multiconjugate

• What performance can you expect?

– Highly dependent on weather

• How long does it take to set-up the AO system?

• Will a variable PSF across the field affect your results?

• What is the throughput to the Science CCD with the AO system?

– Extra surfaces in the optical path lower efficiency

End