How does Optical-IR interferometry work?How does Optical-IR interferometry work?

Gianluca Li Causi, INAF – OAR

Simone Antoniucci, Univ. Tor Vergata

Gianluca Li Causi, INAF – OAR

Simone Antoniucci, Univ. Tor Vergata

Contents:

• Can a single telescope observe sources smaller than /D ?

• How does interferometry go beyond this limit ?

• What do we really measure with an interferometer ?

• How to realize the Young experiment with telescopes ?

• What are the differences between LBT and VLTI ?

• How to get information on observed sources ?

The /D resolution limit: the Point Spread function

Point Spread Function:

Pupil Function:

• Pointlike source at infinity Fraunhofer diffraction

• Circular aperture Airy figure

Focal plane

Circular aperture

1.22 /D

),(~

yxAiryPPSF

),( yxP

Single star

The /D resolution limit: the Rayleigh criterion

• Double pointlike star -> Rayleigh criterion: minimum resolvable feature ~ /D

• Rayleigh criterion is empirical: it comes from visual observation

1.22 /D

So, model fitting of the PSF or deconvolution should be able to resolve structures smaller than /D !

Airy Binary

Double star

),(),(),( yxAiryyxOyxI Image formation equation:

AiryIO~~

Fourier deconvolution:

The /D resolution limit: beyond /D ?

Theoretical limitations:• The PSF of any finite aperture is upper limited in spatial frequency

Power Spectrum of the PSF:Image decomposition in spatial frequencies:

Optical Transfer Function

So, a single telescope acts as a low-pass spatial filter.

D/ spatial frequency

OTF

PSFOTF

= + +

low freq mid freq hi freq

The /D resolution limit: beyond /D ?

Theoretical limitations:• The PSF of any finite aperture is upper limited in spatial frequency

So, deconvolution and model fitting have no unique solutions

So /D is a limit in the sense that the information on smaller scales can be only partially reconstructed.

Same image

• Sources with power spectra differing only at high frequencies (i.e. > D/) form identical images at the focal plane of a telescope!

D/spatial frequency

OTF

D/spatial frequency

OTF

D/spatial frequency

OTF

D/

Interferometry: the Young experiment

Interferometric PSF, monochromatic

Interferometric Pupil

• Pointlike source at infinity -> Fraunhofer diffraction

• Two circular apertures -> Fringes on Airy figure

/B

Baseline B

Aperture

Focal plane

cosμII2III 122121 Fringes intensity:

Interferometry: the Young experiment

Interferometric PSF, monochromatic

• Pointlike source at infinity Fraunhofer diffraction

• Two circular apertures Fringes on Airy figure one spatial frequency (B/) added

Focal plane

/BInterferometric OTF

B1B2 B3

Interferometry gives access to higher frequencies: resolution limit is /(B+D) ~ /B More baselines more frequencies

Interferometric PupilBaseline B

Aperture

D/ B/ (B+D)/spatial frequency

OTF

Interferometry: the u,v plane

• Observing with a baseline B observing the B/ spatial frequency

Aperture

B

BX

BY

v

u

u,v plane: spatial frequencies plane

Usually, spatial frequency in terms of baseline components:

u = BX/

v = BY/

B

D/ B/spatial frequency

OTF

Double star along baseline direction projected on sky

Interferometry: double star closer than /D

• Wide band images of a pointlike double star

Double star orthogonal to projected baseline

d < /D

u = BX/

v = BY/

Interferometry increases resolution only along projected baseline

x

y

x

y

D/ B/spatial frequency

D/ B/spatial frequency

Baseline BBaseline B

Interferometric observables: the visibility

• Pointlike source -> high contrast fringes

• Resolved source -> low contrast fringes

Point-like source (size < /B) Resolved source (size > /B)

Unresolved -> high SNR, resolved -> low SNR The best we resolve the source, the worst we see the fringes !

Interferometric observables: the visibility

• Pointlike source high contrast fringes

• Resolved source low contrast fringes

Resolved source (size > /B)cosμII2III 122121

)dxdyyO(x,

dxdyy)eO(x,e

v)(u,μ

S

S

vy)ik(uxi

12

Van Cittert – Zernike theorem:

y)O(x,v)V(u,

fringe contrast

12μ spatial coherence factor or visibility V

The fringe contrast, i.e. visibility modulus, is dependent on the source shape Hence, a measure of V(u,v) gives information on the source O(x,y)

O(x,y): source brightness distribution on sky

12μV

(incoherent light)

Image reconstruction: the u,v coverage

So, the highest the u,v coverage the better the O(x,y) reconstruction

…BUT this is possible only if V is known on the WHOLE u,v plane

y)O(x,v)V(u, The relation:

is invertible

v)V(u,y)O(x,

The source is the inverse Fourier transform of the complex visibility.

The Real Part of V is the FT of the symmetric component of the object, the Imaginary Part is the antysymmetric component.

-1

So, the Visibility is a Complex Function defined on the (u,v) plane

v

u

Image reconstruction: how to fill the u,v plane?

• Use many baselines: arrays of telescopes VLTI, ALMA

• Use large apertures D respect to baseline B LBT

• Use Earth rotation to scan the u,v plane VLTI, LBT, all

Image reconstruction with LBT

u,v coverage of LBT

22.4 m

8.4 m 8.4 m

reconstructionreal source

single images with two baselines psf

Projected Baseline

Projected Baseline

Interferometry with sparse u,v sampling - VLTI

• Visibility modelling instead of image reconstruction

VLTI @ Paranal

u

v

u-v plane

4 UTs (8m)

4 ATs (2m)

Baselines: 8 – 200m

Baselines: 47 – 130m

Let’s see some examples of visibility curves

• Visibility for a limited number of spatial frequencies need of a model for the source brightness distribution

• Visibility curve = visibility amplitude vs spatial frequencies (baseline)

• Model Fourier Transform expected visibility curve

Visibility curves

Uniform disk

1 mas

100 mas

Visibility amplitude V info on source size

• Unresolved source (<< /B) V ~ 1

• Resolved source ( ~ /B) V ~ 0

uniform disk

Measurements fit visibility curve get model parameters

VLTI–VINCI on Phe

Visibility curves

Let’s see some examples of visibility curves

• Visibility for a limited number of spatial frequencies need a model for the source brightness distribution

• Visibility curve = visibility amplitude vs spatial frequencies (baseline)

• Model FT expected visibility curve

Visibility curves

Uniform diskLimb darkened diskGaussian diskUD + hot spotUD + holeUD + cold spotBinary (equal brightness)Binary (different brightness)

Instrumentation @ VLTI

AMBER• Combines the light from 2 or 3 telescopes in the H, K bands• ~ 4 mas in K (100m baseline)• Visibility spectrum (up to R ~ 1500)• lim. magnitude (mK < 4 – 7, UTs)

Analyse “differential” visibilities: Vline vs Vcontinuum

get info on geometry of different emission zones

MIDI• Combines the light from 2 telescopes in the N band• ~ 20 mas in N (100m baseline)• Light interferes, then is dispersed Visibility at different wavelengths (“visibility spectrum”, up to R ~ 200)• lim. magnitude (mN < 4, UTs)

VINCI • Combines the light from 2 telescopes in the K band• ~ 4 mas (100m baseline)• lim. magnitude (mK < 11)

VINCI measurementsMIDI measurementsAMBER measurements

brightness distribution

visibility (visibility computation software “IVC”– Li Causi)

Model (Radiative Transfer software “RaT” - Li Causi, Antoniucci)

Investigate source central regions tens of mas use AMBER

Model for the source:• HI emission from an infalling/outflowing spherical ionized envelope• Optically thick face-on disk, T R-1/2

• Central star, black body spectrum

prepare observations…

Observation of the young stellar source Z CMa with AMBER(ESO P76 - Nisini, Antoniucci, Li Causi, Lorenzetti, Paresce, Giannini)

HI emission: discriminate between origin in accretion flows or wind

visibility curve

A scientific case – 1) modelling

Baseline (m)

Vis

ibili

ty

Continuum

Line

Accretion

Wind

Compare:

• visibility in the Br line (2.17 m spectral channel)• visibility in the continuum (in an adjacent spectral channel)

AMBER: K band, R ~ 1500

UT1 + UT2 + UT4 VLT telescopes

A scientific case – 2) planning observations

UT1 + UT2 + UT4

A scientific case – 3) data

dark

phot #1 interfer

phot #2 phot #3

AMBER 3 telescopes images

LAOG (Grenoble) software for AMBER data reduction

Data analysis in progress, but there seem to be no fringes!

Calibrator Source

Problems:• Light injection: poor adaptive optics performance• Source fainter than expected• Very low visibility?

Young experiment realizations: radio vs. optical-IR

• Radio -> light interferes in heterodyne mode

Heterodyne: - waves interfere with a local reference - recorded and combined later - no physical connection between telescopes

laser referenceatomic clock

tape recorder

correlator

VLA

VLA Cygnus A @ 21 cm

2’ x 1’

Young experiment realizations: radio vs. optical-IR

• Optical-IR -> light interferes in homodyne mode

Homodyne: - waves are physically combined - telescopes are optically connected

Heterodyne is not sensible for <10÷100m because uncertainty principle gives lower SNR respect to homodyne.

beam

combiner

Optical-IR interference with two telescopes

• Single mount telescopes, e.g. LBT

optic

al p

ath

diff

eren

ce O

PD

sideral motion delay line

Zero OPD -> no delay lines Short (~20m) and fixed baseline Medium resolution ~20mas

short baseline B

long baseline B

projected baseline

Variable OPD -> variable delay lines Long and variable (30÷200m) proj. baseline High resolution ~2mas

• Independent mount telescopes, e.g. VLTI

beam combinerfringe tracker

adaptive optics

Michelson and Fizeau beam combining

• Light interferes on the focal plane -> Fizeau or “image plane” interferometry

• Light interferes in collimated beams -> Michelson or “pupil plane” interferometry

B

D

b

d

beamsplitter

detector

Fizeau

(LBT)

Michelson

(VLTI)

OPD scan

OPD

Inte

nsi

ty

pupils homoteticity

b/d = B/D

Large interf. image (up to 2 arcmin)

Single point (~ 100 mas) interferogram

MIDI@VLTI

VLTI optical delay lines

Fiber optic combiners for pupil-plane interferometers

• Monomodal fibers and spectral dispersion

detector

Michelson

(VLTI)

monomodal fibers

prism

integrated optics

50mas

Types of observations with Optical-IR interferometry

• Modellable sources: visibility from two or more telescopes (stellar diameters, binary orbits, circumstellar envelopes and disks – MIDI_&_AMBER@VLTI)

Shao et al. 1990

• Image reconstruction: aperture synthesis from high (u,v) coverage (sources morphology – LINC_NIRVANA@LBT)• Wide-angle astrometry: /B precision over degrees (VLTI)• Narrow-angle astrometry: ~ 10-2 /B precision over isoplanatic angle (reflex motion of stars due to exoplanets – PRIMA@VLTI)• Nulling interferometry: ~ 10-4- 10-9 attenuation of on-axis source (extrasolar planets direct observation – NIL@LBT)

measmeasOPD CB )sin(measmeas

OPD CB

reference star

beamsplitter

phase shifter

Nulling interferometry: the Bracewell concept

Star plus 10-6 flux planet

• Co-axial beam combination with phase shift in one arm (NIL@LBT, GENIE@VLTI)

LBT versus VLTI ?

Different instruments: complementarity, not competitiveness:

• LBT:resolution (K band): 25mas, Airy disk 100mas

FoV: 20 arcsec

limiting K magnitude (LINC): 25mag in 1h for K band filter

spectral channels: 1 channel at a time (broad or narrow filter)

mirrors before combining: 3 (primary, secondary, Nasmyth)

u-v coverage: quite uniform from zero to max freq.

imaging time: one night

adaptive optics (NIRVANA): Multi-FoV Layer-Oriented

• VLTI:resolution (K band): down to 2mas, Airy disk 56mas

FoV: 2 arcsec MIDI at 10m, 56mas AMBER (H,K band)

limiting K magnitude (AMBER): 17mag* in 15min for hi-res mode R=1000

spectral channels (AMBER): 27 channels at hi-res mode R=1000

mirrors before combining: ~20 (telescope plus delay line)

u-v coverage: narrow around baseline freq. (low freq. filtered out)

imaging time: many nights

adaptive optics: MACAO

* So far fringe tracking FINITO is not yet working, so current AMBER limit is 4.5mag

LBT versus VLTI ?

Different instruments: complementarity, not competitiveness.

Limiting magnitude of VLTI and LBT with fringe tracking is roughly comparable

LBT samples the shorter baselines which are inaccessible to VLTI

VLTI is best suited for high resolution on morphologically simple sources

LBT is best suited for complex objects sampled at lower but uniform resolution

LBT and VLTI: example #1

Extrasolar planets direct observation via nulling interferometry

• requires very low background at 10m, i.e. thermal infrared: NIL@LBT: all cryogenic, only 3 warm mirrors (primary, secondary, Nasmyth)

VLTI: at least 20 warm mirrors (telescope, delay lines, etc.)

• requires high nulling, i.e. minimize nulling leakage from not-pointlike stars: LBT: short baseline (22.4m) -> 10pc stars less resolved -> low leakage

VLTI: long baselines (30-200m) -> 10pc stars resolved -> high leakage

• requires simultaneous imaging of exo zodiacal light: LBT: true imaging for scales greater than 0.25” @ 10m

VLTI: no imaging

• does not require high resolution: LBT: good compromise between leackage and resolution

VLTI: greater resolution but also greater leackage

LBT is best tailored for such kind of observations, but:

Extrasolar planets indirect observation via reflex motion of star

• requires very high resolution: PRIMA@VLTI: down to 10arcsec narrow angle astrometry with differential phase

VLTI is best tailored for such kind of observations

LBT and VLTI: example #2

Investigating the inner regions of star forming disks

• requires high resolution spectroscopy to get Br line and nearby continuum: LBT: would need two observations in different narrow filters

AMBER@VLTI: spectral resolution Ry10000 with 27 channels simultaneously

• requires high spatial resolution ~2-10mas: LBT: structure not resolved by short baseline (22.4m)

VLTI: structure resolved by long baselines (30-200m)

VLTI is best tailored for such kind of observations, but:

Investigating the transversal structure of the base of star forming jets

• requires imaging in narrow band filters of H2 and [FeII] lines

• requires arcsec resolution along the jet direction

• requires sub-arcsec resolution orthogonal to the jet: LBT: satisfies the requirements for a field of 20 arcsec

LBT is best tailored for such kind of observations

OAR technological contribution: LINC-NIRVANA@LBT

adaptive optics

“Patrol Camera”

Replied to ESO Call for second generation VLTI instrumentation:

“VLTI Spectro-Imager”: imaging with 6 telescopes @ JHK

“MATISSE”: dispersed fringes with 4 telescopes @ LMNQ

(D’Alessio, Di Paola, Lorenzetti, Li Causi, Pedichini, Speziali, Vitali)