Transcript Diapositiva 1 - INAF-Osservatorio Astronomico di Roma

How does Optical-IR interferometry work?
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 get information on observed sources ?
• How to realize the Young experiment with telescopes ?
• What are the differences between LBT and VLTI ?
The /D resolution limit: the Point Spread function
• Pointlike source at infinity  Fraunhofer diffraction
• Circular aperture  Airy figure
Pupil Function:
P( x, y)
Circular aperture
1.22 /D
Focal plane
Point Spread Function:
~
PSF  P  Airy( x, y )
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
Airy
Binary
1.22 /D
Single star
Double
star
Image formation equation:
Fourier deconvolution:
I ( x, y)  O( x, y)  Airy( x, y)
~ ~
O  I Airy
 So, model fitting of the PSF or deconvolution should be able to resolve structures
smaller than /D !
The /D resolution limit: beyond /D ?
Theoretical limitations:
• The PSF of any finite aperture is upper limited in spatial frequency
Image decomposition in spatial frequencies:
Power Spectrum of the PSF:
OTF
+
=
low freq
+
mid freq
hi freq
D/
spatial frequency
Optical Transfer Function
OTF  PSF
 So, a single telescope acts as a low-pass spatial filter.
The /D resolution limit: beyond /D ?
Theoretical limitations:
• The PSF of any finite aperture is upper limited in spatial frequency
• Sources with power spectra differing only at high frequencies (i.e. > D/)
form identical images at the focal plane of a telescope!
OTF
D/
spatial frequency
OTF
D/
spatial frequency
OTF
Same image
D/
D/
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.
Interferometry: the Young experiment
• Pointlike source at infinity -> Fraunhofer diffraction
• Two circular apertures -> Fringes on Airy figure
Interferometric Pupil
Baseline B
Aperture
/B
Focal plane
Interferometric PSF, monochromatic
 Fringes intensity:
I  I1  I2  2 I1I2 μ12 cos
Interferometry: the Young experiment
• Pointlike source at infinity  Fraunhofer diffraction
• Two circular apertures  Fringes on Airy figure  one spatial frequency (B/) added
Interferometric Pupil
Baseline B
OTF
Aperture
B2 B1 B3
D/
B/ (B+D)/
spatial frequency
/B
Interferometric OTF
Focal plane
Interferometric PSF, monochromatic
 Interferometry gives access to higher frequencies: resolution limit is /(B+D) ~ /B
 More baselines  more frequencies
Interferometry: the u,v plane
• Observing with a baseline B  observing the B/ spatial frequency
u,v plane: spatial frequencies plane
v
OTF
Aperture
B
BY
D/
B
BX
B/
spatial frequency
Usually, spatial frequency in terms of baseline components:
u = BX/
v = BY/
u
Interferometry: double star closer than /D
• Wide band images of a pointlike double star
Double star along baseline direction projected on sky
Double star orthogonal to projected baseline
Baseline B
Baseline B
y
y
d < /D
x
D/
B/
u = BX/
spatial frequency
x
D/
B/
v = BY/
spatial frequency
 Interferometry increases resolution only along projected baseline
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
I  I1  I2  2 I1I2 μ12 cos
Resolved source (size > /B)
(incoherent light)
μ12
spatial coherence factor or visibility V
V  μ12
fringe contrast
Van Cittert – Zernike theorem:
μ12(u, v) 
ei  O(x,y)eik(ux  vy)dxdy
S
 O(x,y)dxdy
S
O(x,y): source brightness distribution on sky

V(u, v)  O(x, y)
 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)
Image reconstruction: the u,v coverage
 So, the Visibility is a Complex Function defined on the (u,v) plane
The relation:
V(u, v)  O(x, y)
is invertible
-1
O(x, y)  V(u, v)
v
 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.
…BUT this is possible only if V is known
on the WHOLE u,v plane
So, the highest the u,v coverage the better the O(x,y) reconstruction
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
22.4 m
Image reconstruction with LBT
Projected Baseline
8.4 m
u,v coverage of LBT
8.4 m
Projected Baseline
reconstruction
real source
single images with two baselines
psf
Interferometry with sparse u,v sampling - VLTI
• Visibility modelling instead of image reconstruction
Baselines: 47 – 130m
VLTI @ Paranal
4 UTs (8m)
v
u
4 ATs (2m)
Baselines: 8 – 200m
u-v plane
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
Uniform disk
Let’s see some examples of visibility curves
Visibility curves
uniform disk
VLTI–VINCI on y Phe
1 mas
100 mas
Visibility amplitude V  info on source size
• Unresolved source (<< /B)  V ~ 1
• Resolved source
( ~ /B)  V ~ 0
Measurements  fit visibility curve  get model parameters
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
Binary
Binary
Limb
UD
(different
Gaussian
UD
Uniform
(equal
UD
darkened
++cold
hot
+ hole
brightness)
disk
spot
brightness)
disk
spot
disk
Let’s see some examples of visibility curves
Instrumentation @ VLTI
VINCI
• Combines the light from 2 telescopes in
the K band
•  ~ 4 mas (100m baseline)
• lim. magnitude (mK < 11)
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)
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
AMBER
VINCI
MIDI measurements
A scientific case – 1) modelling
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
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
Model
(Radiative Transfer software
“RaT” - Li Causi, Antoniucci)
 brightness distribution
 visibility
(visibility computation software
“IVC”– Li Causi)
 visibility curve
 prepare observations…
A scientific case – 2) planning observations
Accretion
AMBER: K band, R ~ 1500
Compare:
• visibility in the Brg line
(2.17 mm spectral channel)
• visibility in the continuum
(in an adjacent spectral channel)
Line
Continuum
UT1 + UT2 + UT4 VLT telescopes
Wind
Baseline (m)
UT1 + UT2 + UT4
A scientific case – 3) data
LAOG (Grenoble) software for AMBER data reduction
AMBER 3 telescopes images
Calibrator
dark
phot #1
phot #2
interfer
phot #3
Source
Data analysis in progress, but there seem to be
no fringes!
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
correlator


tape recorder

laser reference
atomic clock
VLA
2’ x 1’
VLA Cygnus A @ 21 cm
 Heterodyne:
- waves interfere with a local reference
- recorded and combined later
- no physical connection between telescopes
Young experiment realizations: radio vs. optical-IR
• Optical-IR -> light interferes in homodyne mode

beam
combiner
 Heterodyne is not sensible for
<10÷100mm because uncertainty
principle gives lower SNR respect to
homodyne.
 Homodyne:
- waves are physically combined
- telescopes are optically connected
Optical-IR interference with two telescopes
• Single mount telescopes, e.g. LBT
• Independent mount telescopes, e.g. VLTI
long baseline B
adaptive optics
beam combiner
fringe tracker
sideral motion delay line
 Zero OPD -> no delay lines
 Variable OPD -> variable delay lines
 Short (~20m) and fixed baseline
 Long and variable (30÷200m) proj. baseline
 Medium resolution ~20mas
 High resolution ~2mas
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
Michelson
(VLTI)
beam
splitter
b
MIDI@VLTI
d
pupils homoteticity
b/d = B/D
Fizeau
(LBT)
OPD scan
Intensity
detector
 Large interf. image
(up to 2 arcmin)
OPD
 Single point (~ 100 mas)
interferogram
VLTI optical delay lines
Fiber optic combiners for pupil-plane interferometers
• Monomodal fibers and spectral dispersion
prism
integrated
optics
monomodal
fibers
detector
Michelson
(VLTI)
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)
• 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)
meas
meas

B
sin(

)

C
OPD
meas
meas

B


C
OPD

reference star
Shao et al. 1990
Nulling interferometry: the Bracewell concept
• Co-axial beam combination with  phase shift in one arm (NIL@LBT, GENIE@VLTI)
beam
splitter
 phase
shifter
Star plus 10-6 flux planet
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
resolution (K band):
down to 2mas, Airy disk 56mas
FoV:
2 arcsec MIDI at 10mm, 56mas AMBER (H,K band)
• VLTI:
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 10mm, 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” @ 10mm
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 10marcsec 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 Brg 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
(D’Alessio, Di Paola, Lorenzetti, Li Causi, Pedichini, Speziali, Vitali)
“Patrol Camera”
adaptive
optics
Replied to ESO Call for second generation VLTI instrumentation:
 “VLTI Spectro-Imager”: imaging with 6 telescopes @ JHK
 “MATISSE”: dispersed fringes with 4 telescopes @ LMNQ