Basics of Optical Interferometry

(Observationnal Astronomy II)Lecture by Stéphane Sacuto

Power of Resolution and need for High Angular Resolution

PSF IObj

D

Source with Fs< l/D

PSFThe information on your object is lost.

You NEED more spatial resolution from your instrument.

Objects Wavelength (µm) Angular size (mas) Telescope diameter (m)

Circumstellar envelope around

o Ceti (M star)

11 50 45

Volcanoes of Io (Jupiter satellite)

5 10 100

Nucleus of NGC 1068 (AGN) 2.2 < 1 > 400

Spots on the photosphere of

a Cen (Solar type)

0.5 0.07 1500

Typical monolithic telescope diameters

Those structures are not resolved with monolithic telescopes even with the ELT

We need something else

INTERFEROMETRY

PSF

D

Source with Fs< l/D

The signal of the source is found again but under the appearance of fringes

Interferometric signal

D DB

but Fs~ l/B < l/D

L3

L2

L1

Delay line and optical path compensation

B

Bp =B.sin(z)

z

=B.coszDL=L1

The interferometric signal

PSF of the telescope

Interferometric signal

l/Dl/B

Fringe contrast is given by :

Imax - Imin

Imax + IminV

An Interferometer is measuring the contrast of the total fringe pattern :

Fs +

The fringe contrast (part I)

High contrast Mid contrast Low contrast

V~1 V~0.6 V~0.2

Small source (Fs << l/B) Mid source (Fs ~ l/B) Large source (Fs ~ l/D)

For a given baseline length B and for different sizes of the source Fs

For a given dimension of the source Fs and for different baseline lengths B

High contrast Mid contrast Low contrast

V~1 V~0.6 V~0.2

Small base (B << l/Fs) Mid base (B ~ l/Fs) Large base (B >> l/Fs)

The fringe contrast (part II)

Object-Contrast RelationThe Van Cittert and Zernike theorem

?

V= |Ô (u,v) /Ô (0,0) |

The Van Cittert and Zernike theoremThe fringe contrast of a source of emissivity O is equal to the modulus of the Fourier Transform of O at a given spatial frequency normalized by the FT of O at the origin.

u

v

u

v

u

v

Fourier space/uv-plane/spatial frequencies plane

|Ô (u,v) /Ô (0,0)|

FDirect Space O(a,d)

a

d

a

d

a

d

O(a,d) . exp[-i.2p (ua +vd)]. da ddòòòòO(a,d) .da dd

Does someone recognize this denominator?

Some Fourier (Hankel) transformations

(*) r = (a² + d²)1/2 (*) q = (u ² + v ²)1/2 = Bp/l (**) J1c(X) = J1(X)/X

Plane of the star

Bx

By

B p=B=130 m

PA

T0

Plane of the star

B p=100 m

Bx

BY

PA

T1

After an Earth rotation

The uv-plane (part I)

spatial frequencies (u,v) : coordinates (Bx,By) of the projected baselines (Bp) seen from the star and divided by the observing wavelength )

u = Bx/l = Bp.cos(PA) / l

v = By/l = Bp.sin(PA) / l

PAEarth planeEarth plane

Bp/l = Öu² + v²

after 1 hour of observation

Wavelength dispersion (u=Bx/l ; v=By/l)

a

d

??

a

d

u

v=

v

ua

d

??

a

d

u

v=

v

u

after 6 hours

a

d

??

a

d

u=

v

u

after 42 hours with 7 pairs

v

The uv-plane (part II)Observation of R Scl (a=01:26:58 ; d=-32:32:35) at the date of 19 August 2011

This kind of coverage is very expensive in time !

FF-1

Observations

What is the appropriate uv coverage?

It depends on the complexity of the object

Is it really necessary to get a very large uv-coverage for such an object?

[hot star]

Is it necessary to get a very large uv-coverage for this one?

[Post-AGB (triple system + envelope + disk)]

Spatial information

Spectral information

B=60m (mid dusty region)B=90m (inner dusty region)B=120m (molecular region)

1R 2R 3R 4R 5R 6R

B=30m (outer dusty region)

MgFeSiO4

TiO2

TiO2

Al2O3

Al2O3

Fe

Mg2SiO4

Mg2SiO4SiO2

SiO2

AmC

H2O

AmC

SiC

SiC

SiC

SiOTiO

C2H2 HCN

The Phase in Interferometry: V = V e-i

0

• Binary source at angle 0 => displacement of the fringes by OPD =

0.B OPD2

B0.B

information on the asymmetries of an object

12 = 12obj + d2 – d1

Van Cittert-Zernike theoremu,v) = arg[Ôu,v] = atan[Im(Ô)/Re(Ô)]

Atmospheric noise

The Closure Phase

Observed Object Atmosphere

12 = 12obj + d2 – d1

23 = 23obj + d3 – d2

31 = 31obj + d1 – d3

123 = 12 + 23 + 31 = 12

obj + 23obj + 31

obj

T1

T2

T3

Object Only!!

UD of 9 mas diameter with a spot of 2 mas diameter on its surface representing 25% of the total flux.

Fringe contrast Closure Phase

An Example

UDUD+spot

Real visibility data points (AMBER with 3 telescopes)

Closure Phase data

Model vs Data (part I)

Model vs Data (part II)

2.17 µmcontinuum

2.38 µmCO-line

10 mas

The calibration in Interferometry

The need for accurate determination of the calibrator diameters

Calibrated visibility

where

System response

Unresolved calibrator

Error on visibilitysolely due to uncertainty on the calibrator diameter

Resolved calibrator

Effects of diameter uncertainties on the visibility accuracy

cal/cal= 3% cal/cal= 1%

ASPRO

The Astronomical Software to PRepare Observations

http://www.jmmc.fr/aspro_page.htm

How to launch ASPRO in the web?

The interface

– WHEN: to define the date and time of the simulated observation

– WHERE: to select the interferometer (VLTI, IOTA, CHARA, …) and the number of telescopes– WHAT: to define the target properties (name, coordinates, brightness);– OBSERVABILITY/COVERAGE: to define the VLTI configuration to be used for the observations– MODEL/FIT: to calculate and plot interferometric observables and their associated uncertainties according to the chosen model (UD, LD, Binary, …) and the corresponding baseline configuration.

When

Where

What

Observability

delay line

Night

UT time

LST time

uv-coverage (part I)

uv-coverage (part II)

Model/Fit (part I)

Model/Fit (part II)

Model/Fit (part III)

Uniform disk Resolved binary Uniform disk + Uniform ring

Model/Fit (part IV)

[F1/F2]10µm=4

s = 40masq =45°

Æ = 10masÆ = 30mas [F1/F2]10µm=1

f ext=

40m

as

f in =

20m

as

Æ = 10mas

Bp

V

l=10µm

V

Bp

l=10µm

Bp

V

l=10µm

D IRECT

FOUR IER

SPACE

DEFINE THE BEST CALIBRATOR http://www.jmmc.fr/searchcal_page.htm

How to launch SearchCal in the web?

CALIBRATORS

Choose your observing wavelength (AMBER-H/K or MIDI-N)

The maximum baseline of your observation (limit of sensitivity)

The science target

The maximum location around the science target (close enough to avoid atmospheric biases)

And get your calibrators (from the various catalogs existing)

Table

Separation from the science target in degree

Evaluation of the corresponding equivalent UD visibility value

Selection criteria

location of the calibrator (as close as possible)

brightness (as bright as possible to get a high Signal to Noise ratio)

spectral type and luminosity (avoid complex object like cool stars)

visibility and accuracy (avoid too large objects -> V small -> poor S/N ratio)

variability (avoid to use variable objects that may lead to temporal biases in the calibrated measurements)

multiplicity (avoid multiple object that may lead to a wrong interpretation of the calibrated measurements)

DEFINE THE BEST CALIBRATOR

HD35497