Astronom

ische Waarneem

technieken(Astronom

ical Observing T

echniques)10thLecture

: 23 November 2011

Co

nte

nt:

1.

Atm

osp

he

ric Tu

rbu

len

ce

2.

Wh

y A

O?

3.

Ba

sic Prin

ciple

Based

on:

“Adaptive O

ptics in Astronom

y” (Cambridge U

P) by F. Roddier (ed

.), Claire M

ax’s lecture course on A

O http://w

ww.ucolick.org/~

max/289C/

and ESO: http://w

ww.eso.org/projects/aot/D

SM/AO_modes.h

tml

4.

Ke

y C

om

po

ne

nts

5.

Erro

r Term

s

6.

Lase

r Gu

ide

Sta

rs

7.

Ty

pe

s of A

O C

on

cep

ts

Kolm

ogorov Turb

ulence

Ou

ter s

cale

L0

Inn

er s

cale

l0

so

lar

hννν ν

Win

d s

hear

gro

un

d

hννν ν

co

nve

ctio

nr0 , se

eing, τττ τ

0 , θθθ θ0

The Fried

parameter is th

e radius of th

e spatial coh

erence area.It is th

e average turbulent scale over w

hich the RMS optical ph

ase distortion is 1 rad

ian. Note that r

0increases as λ

6/5.

is called the seeing. A

t good sites r

0(0.5µm) ~10 -30 cm.

()

()

5/3

0

25/

6

01

85

.0

−∞

=∫

dz

zC

rn

λλ

5/1

0

~−

=∆

λλ

θr

The atm

ospheric coh

erence (or Greenw

ood delay)

timeis:

It is the m

aximum tim

e delay for th

e RMS wavefront

error to be less

than 1 rad

(where v

is the m

ean propagation velocity).

The isoplanatic

angleis th

e angle over which the RMS

wavefront

error is smaller th

an 1 rad.

0r

v r0

03

14

.0

=τ

h r0

0co

s3

14

.0

ζθ

=

Im

provem

ent in R

esolution a

nd S

ensitivity

1.Angular resolution:

2.Point source sensitivity:

00

gain

r D

Dr

=⇒

=→

=λ

θλ

θ

4in

t

21

~in

g

ain

D

~/

Dt

NS

⇒

PHARO LGS Ks im

ageWIRO H image

500s inte

g., 40" FOV, 15

0 masFWHM

Kobulnicky

et al. 2

005, AJ 129, 239-250

AO

Principle

1.Maximum scale

of tolerate

d wavefront d

eform

ation is r0

�sub

divid

e the telescope

aperture

into r0 ’s

2.Measure

the wavefront d

eform

ations.

3.Corre

ct the wavefront d

eform

ations by “b

ending b

ack” the patch

es of size

r0 .

The num

ber of sub

apertures is (D/r0 )2at th

e observing w

avelength �

can easily require hund

reds to th

ousands of actuators for very large

telescopes.

AO

Principle (2

)

Wave

front Description: Z

ernike

Polynom

ials

Expansion into a series of orth

ogonal terms:

Units

: Radia

ns o

f phase / (D

/ r0 )

5/6

Tip

-tilt is s

ing

le b

igg

est c

on

tribu

tor

Tip-

Tilt a

nd h

igher ord

er T

erm

s (1)

Refe

rence: N

oll

Fo

cu

s, a

stig

matis

m,

co

ma a

lso

big

Hig

h-o

rder te

rms g

o o

n

an

d o

n…

.

Wave

front Sensors –

Shack H

artm

ann

Most com

mon principle is th

e Shack H

artmann w

avefront sensor measuring sub

-aperture tilts:f

Pu

pil p

lan

eIm

ag

e p

lan

e

WFs: C

urvature

and

Pyra

mid

Sensors

Other com

mon principles are th

e

curvature sensor �

and the pyram

id sensor

�

Deform

able

Mirrors

Basic principle: piece-w

ise linear fit of the m

irror surface to the

wavefront. r

0sets th

e number of d

egrees of freedom.

Two general types: segm

ented mirrors

Two general types: segm

ented mirrors

and continuous face-sh

eet mirrors:

Note th

at the (piezo) actuator stroke is typically only a couple of

microm

eters �requires separate tip-tilt m

irror.

Adaptive

Second

ary

Mirrors

Concept: integrate D

M into th

e telescope �adaptive second

ary mirrors.

Advantages:

•no ad

ditional optical system

needed �

lower em

ission, higher th

roughput

•large surface �

higher actuator d

ensity

•larger stroke �

no tip-tilt mirror need

ed

...but also m

ore difficult to b

uild, control,

DM for M

MT Upgrad

e

...but also m

ore difficult to b

uild, control,

and hand

le.

Typica

l AO

Error T

erm

s•Fitting errors from

insufficient approximation of th

e wavefront (finite actuator spacing, influence function of actuators, etc.).

•Temporal errors from

the tim

e delay b

etween

measurem

ent and correction (com

puting, exposure

time).

3/5

0

23.

0

≈

r Dfit

σ

3/5

0

2

≈τ

σt

temp

•Measurem

ent errors from the W

FS (S/N!)

•Calib

ration errors from aberrations in th

e non-com

mon path

betw

een sensing channel and

imaging

channel.

•Angular anisoplanatism

from sam

pling different lines

of sight th

rough the atm

osphere.

3/5

0

2

≈θ θ

σa

niso

NS

mea

sure

/~

2σ

???

~2

nca

libra

tioσ

Angula

r Anisopla

natism

Angular anisoplanatism

is a severe limitation to:

•wide-field

imaging

•sky coverage (find

ing a guide star

within th

e isoplanatic angle)

“Typica

l” Corre

ction and

Resid

uals

http

://cfa

o.u

colic

k.o

rg/p

galle

ry/g

c.p

hp

Sky

Cove

rage

To sense th

e wavefront one need

s a brigh

t reference/guide star w

ithin

the isoplanatic angle.

0.0

1

0.1 1

Cummulative Sky Coverage

(mI < mag)G

ala

ctic Eq

ua

tor (|

l| <

5°)

Inte

rme

dia

te La

titud

es (-3

5°

< l <

-25

°)

Ga

lactic P

ole

(l < -8

0°)

All sk

y a

ve

rag

e (-9

0°

< l <

90

°)

0.0

00

1

0.0

01

0.0

1

91

21

51

8

Cummulative Sky Coverage

(mI < mag)

Gu

ide

Sta

r Ma

gn

itud

e (I)

Sk

yco

ve

rag

e g

ive

n b

y sta

r cou

nts in

teg

rate

d

ov

er g

ive

n b

an

ds in

ga

lactic la

titud

e fro

m

US

NO

-B1

.0 ca

talo

g. S

tar co

un

ts are

cum

mu

lativ

e,

i.e., g

uid

e sta

r sky

cov

era

ge

is for a

ll stars b

righ

ter

tha

n g

ive

n m

ag

nitu

de

Cu

mu

lativ

e s

ky c

overa

ge, i.e

., the c

han

ce o

f find

ing

sta

rs b

righ

ter th

an

giv

en

mag

nitu

de, fo

r a

ran

do

m ta

rget a

s a

fun

ctio

n o

f I-ban

d m

ag

nitu

de u

sin

g th

e U

SN

O-B

1.0

cata

log

ue.

Lase

r Guid

e S

tars

Solution to th

e sky coverage problem

: create your ow

n guide star.

Two principle concepts:

•Sodium LGS –excite atom

s in “sodium layer” at

altitude of ~

95 km

.8-1

2 k

m

~ 9

5 k

m

altitude of ~

95 km

.

•Rayleigh

beacon L

GS –scattering from

air molecules send

s light back into telescope, h

~ 10

kmTu

rbu

len

ce

Since th

e beam

travels twice (up and

down) th

rough the atm

osphere,

tip-tilt cannot be corrected

�LGS-AO still need

s a natural guide

star, but th

is one can be m

uch fainter (~

18mag)

as it is only needed for

tip-tilt sensing.

Sod

ium B

eacons

Layer of neutral sod

ium atom

s in mesosph

ere (heigh

t ~ 95 km

, thickness

~10km) th

ought to b

e deposited

as smallest m

eteorites burn up.

Resonant scattering occurs w

hen incid

ent laser is tuned to D

2 line of N

a at 5

89 nm

.

Rayle

igh B

eacons

Due to interactions

of the electrom

agnetic wave from

the laser b

eam

with molecules in th

e atmosph

ere.

Advantages:

•cheaper and

easier to build

•higher pow

er •independ

ent of Na layer

Disad

vantages:•larger focus anisoplanatism

•laser pulses �

timing

Focus A

nisoplana

tismThe LGS is at finite d

istance H above th

e telescope and does not

sample all turb

ulence and not th

e same colum

n of turbulent atm

osphere

(“cone effect”):

3/5

2

=d D

FA

σ

The contrib

ution to the wavefront

error contribution from

focus

anisoplanatismis:

0

d

FA

5/6

0~

λd

anisoplanatismis:

where d

epends only

on wavelength

and turb

ulence profile at th

e telescope site.

�very large telescopes need

multiple L

GSs due to th

is cone effect.

H

Ground

Layer A

O –

GLAO

•Useful if ground

layer (= ground

+ dome + m

irror seeing) is th

e dominant

component

•Uses several W

FS and

guide

stars within a large F

OV

(several arcmin).

•WFS signals are averaged

�•WFS signals are averaged

�control one D

M

•Reduction of F

WHM ~ factor

of two (only!)

•GLAO is th

us a "seeing enh

ancement" tech

nique .

•Advantage: w

ider field

s and

shorter w

avelengths

Lase

r Tom

ograph

y A

O –

LTAO

•Uses m

ultipelaser b

eacons

•each

laser has its W

FS

•com

bined

information is used

to optim

ize the correction b

y one D

Mon-ax

is.

•red

uces the cone effect

•red

uces the cone effect

•system

performance sim

ilar to natural guid

e star AO but

at much

higher sky coverage.

Multi-

Conjuga

te A

O –

MCAO

•to overcom

e anisoplanatism,

the basic lim

itation of single guid

e star AO.

•MCAO uses m

ultiple NGS or

LGS.

•MCAO controls several D

Ms

•each

DM is conjugated

to a different atm

ospheric layer

at a different altitud

e

•at least one D

M is

conjugated to th

e ground

layer

•best approach

to larger corrected

FOV.

Sid

e note

: MCAO

: Perform

ance

Multi-

Obje

ct AO

–M

OAO

•MOAO provid

es correctionnot over th

e entire FOV of several arcm

inbut only in local areas w

ithin several arcm

in�multi-ob

ject spectroscopy.•need

s (several) guide stars close to each

science target.•picks up th

e WFS ligh

t via small "arm

s“ inserted in th

e FOV.

•each

science target has its D

M•system

s work in open loop (!)

Extre

me A

O –

XAO

•XAO is configured

similarly th

an SCAO

•high Streh

lon-ax

is and small corrected

FOV

•however, S

trehlvalues in ex

cess of 90%

•requires m

any thousand

s of DM actuators

•requires to m

inimize optical and

alignment errors

•main application: search

for exoplanets, like

main application: search

for exoplanets, like

with SPHERE on th

e VLT �