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Basics of Optical Interferometry. (Observationnal Astronomy II) Lecture by Stéphane Sacuto. Source with F s < l /D. PSF. The information on your object is lost. You NEED more spatial resolution from your instrument. . Power of Resolution and need for High Angular Resolution. D. - PowerPoint PPT Presentation
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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
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