Diapositive 1

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Basics of Optical Interferometry
(Observationnal Astronomy II) Lecture by Stéphane
Sacuto
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Power of Resolution and need for High Angular
Resolution
D
PSF ? IObj
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Typical monolithic telescope diameters
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 lt 1 gt 400
Spots on the photosphere of a Cen (Solar type) 0.5 0.07 1500
Those structures are not resolved with monolithic
telescopes even with the ELT We need something
else
INTERFEROMETRY
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Interferometric signal
Source with Fslt l/D
D
The signal of the source is found again but under
the appearance of fringes
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Delay line and optical path compensation
BpB.sin(z)
B
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The interferometric signal
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The fringe contrast (part I)

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

Small source (Fs ltlt l/B)
Mid source (Fs l/B)
Large source (Fs l/D)
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The fringe contrast (part II)

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

Mid base (B l/Fs)
Large base (B gtgt l/Fs)
Small base (B ltlt l/Fs)
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Object-Contrast Relation The Van Cittert and
Zernike theorem
V Ô (u,v) /Ô (0,0)
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The Van Cittert and Zernike theorem
The 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.
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Some Fourier (Hankel) transformations
() r (a² d²)1/2
() q (u ² v ²)1/2 Bp/l

() J1c(X) J1(X)/X
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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 (l)
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The uv-plane (part II)
Observation of R Scl (a012658 d-323235)
at the date of 19 August 2011
This kind of coverage is very expensive in time !
Observations
F
F-1
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What is the appropriate uv coverage?
It depends on the complexity of the object
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• Spatial information

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• Spectral information

B30m (outer dusty region)
B60m (mid dusty region)
B90m (inner dusty region)
B120m (molecular region)
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The Phase in Interferometry V V e-i?
?12 ?12obj d2 d1
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The Closure Phase
T1
T2
T3
Object Only!!
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An Example
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
UD UDspot
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Real visibility data points (AMBER with 3
telescopes)
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Closure Phase data
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Model vs Data (part I)
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Model vs Data (part II)
2.17 µm continuum
10 mas
2.38 µm CO-line
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The calibration in Interferometry
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The need for accurate determination of the
calibrator diameters
Calibrated visibility
System response
where
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Effects of diameter uncertainties on the
visibility accuracy
Dfcal/fcal 3
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ASPRO
The Astronomical Software to PRepare Observations
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How to launch ASPRO in the web?
http//www.jmmc.fr/aspro_page.htm
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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.
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When
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Where
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What
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Observability
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uv-coverage (part I)
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uv-coverage (part II)
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Model/Fit (part I)
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Model/Fit (part II)
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Model/Fit (part III)
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Model/Fit (part IV)
Uniform disk Resolved binary Uniform disk Uniform ring



F1/F210µm4
D I R E C T
fext 40mas
fin 20mas
s 40mas q 45
Æ 30mas
F1/F210µm1
Æ 10mas
Æ 10mas
F O U R I E R S P A C E
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DEFINE THE BEST CALIBRATOR http//www.jmmc.fr/sear
chcal_page.htm
How to launch SearchCal in the web?
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CALIBRATORS
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Table
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Selection criteria
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DEFINE THE BEST CALIBRATOR
HD35497