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)
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