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Optics in Astronomy
- Interferometry -
Oskar von der Lühe
Kiepenheuer-Institut für Sonnenphysik
Freiburg, Germany
Contents
• Concepts of interferometry
• –Fundamentals
of interferometry
Elements of an interferometer
– Baselines
• Concepts of interferometry
– Projected baselines
– Array
configurationinterferometry
and Earth-rotational synthesis
• Practical
– Methods of beam combination
– Fizeau and Michelson stellar interferometers
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What do you need for an interferometer?
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Which baseline is needed for which resolution?
Source of radiation
Stars
(Teff = 5 103 K)
Wavelength
Gas, dust
(T = 100 K)
Interstellar
hydrogen
Telescope type
Diameter /
Baseline [m]
 = 0.5 µm
 = 10 µm
 = 21 cm
Optical standard
telescope
1
10
Optical
Interferometer
100
RadioInterferometer
104
10-5 rad
2 arcsec
10-5 rad
2 arcsec
10-5 rad
2 arcsec
-
-
Optical large
telescope
5 10-7 rad
0.1 arcsec
5 10-8 rad
0.01 arcsec
5 10-9 rad
0.001 arcsec
-
Radio VLBI
107
-
-
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0.021 rad
72 arcmin
2.1 10-3 rad
7.2 arcmin
2.1 10-5 rad
4.3 arcsec
2.1 10-8 rad
4.3 mas
4
Beam entrance and array configuration
source

S

B13

B12
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
B24
• telescopes i = 1 ... N

• unit vector
 S pointing at coordinate
origin   0 at source

• baseline vectors Bik connecting
centers of telescope entrance
apertures i and k


• Bki   Bik
• observing wavelength  determines

the angular frequencies uik  1 Bik
at which samples of the visibility
function are taken
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Projected baselines I
to source
geometric
delay wik
telescope i
projected baseline Bik‘
baseline Bik
telescope k
delay line k
delay line i
1/2 ik
beamsplitter and detectors
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Projected baselines II

• The layout detemines the baseline vectors Bik which are present the array.
• The source declination  and hour angle h determine the projected
 (baseline as seen from the direction of the source).
baseline Bik
• The observing wavelength  determines the set of two-dimensional

angular frequencies u ik which is measured by the interferometer.
Geometric delay:
 


  S  Bik  S 
Bik
 
wik  Bik  S 
frequency projected on
celestial sphere:
 uik 

u ik   
 vik 
Projected baseline:
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Projected baselines III
Describe array geometry by
3D element positions:
 X  northwards
 
 Y  eastwards
 Z  zenithwards
 
Compute fringe frequency and geometric delay:
 uik 
  cos sin h  sin  cos  cos h sin  cos  sin h  cos cos h  sin  sin    X k  X i 

 1


 sin  cos h
sin  sin h
cos 
 vik   
  Yk  Yi 
 w    sin  sin h  cos cos  cos h sin  cos h  cos cos  cos h  cos sin    Z  Z 
 ik 

 k
i 
site latitude 
source declination 
hour angle h
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Array configuration and Earth-rotational synthesis I
Large Binocular Telescope (LBT), Arizona
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Array configuration and Earth-rotational synthesis I
Large Binocular
Telescope (LBT),
Arizona
UV coverage - range
of frequencies that can
be reached by ERS
UV coverage is
independent of source
position with the LBT
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Array configuration and Earth-rotational synthesis II
ESO VLT Interferometer Cerro Paranal, Chile
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Array configuration and Earth-rotational synthesis II
VLTI - 4 Unit telescopes,
source at  = -30°
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VLTI - 4 Unit telescopes
plus 4 Auxiliary telescopes
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Array configuration and Earth-rotational synthesis II
Dependence of VLTI
„sausage pattern“ on
source declination
(+10°, -10°, -30°, -50°,
-70°)
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Array configuration and Earth-rotational synthesis III
Keck Imaging Interferoemtric
Array - Mauna Kea, Hawaii
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Array configuration and Earth-rotational synthesis III
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Principle of a Multiple Telescope Interferometer
 Telescopes i, ..., k track sources during observation
• Baselines between telescopes rotate with Earth
• "Projected" baselines change with source declination and hour
angle  extended coverage of Fourier ("UV") plane
 Electromagnetic fields are superimposed at point of beam
combination
• Geometric delays changes with source declination and hour angle
 optical delay tracking required
 Off-set sources suffer a differential geometric delay  differential
optical delay tracking required
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Methods of beam combination
Beam combination
single mode
multi-mode
pupil plane
The detected field of
view is equivalent to
the Airy disk of an
array element
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image plane
The detected field of view exceeds the
Airy disk of an array element.
Beam combination takes place in the
plane of a transferred pupil or an image.
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Methods of beam combination
pupil plane
image plane
Focused and collimated
beams of a single array
element accepting an
extended field of view.
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The red (on-axis) beam only is used for
single mode beamcombination.
Both red and green beams are used for
multimode beamcombination.
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Single mode beam combination
Popular implementation with
optical fibers
Field stops with size of Airy
disk and beamsplitteralso
possible.
from array
elements
single pixel
detectors
Fibers make good mixers
once the light has entered.
Two-way combiner (top)
and three-way combiner
(below).
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Single mode beam combination
Intensities from Telescopes A and B:
Measured intensities at Detectors 1 and 2:
I1, I2
C1, C2
Measured intenstites as function of delay :




C1  I1  I 2  2 I1I 2 V sin 2   
C2  I1  I 2  2 I1I 2 V sin 2   
Calibrated visibility:

C1  C2
 V sin 2   
4 I1I 2

Visibility V due to all sources in the Airy disk of the elements
Fringe detection by scanning of coherence envelope :
IOTA/FLUOR, VLTI/VINCI
Beam combination with fibers of more than two elements prone to baseline
dependent errors!
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VLTI/VINCI GUI
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The visibility of which source is detected with
pupil plane beam combination?
The common visibility of all
sources which are allowed to
interfere!
Field stops need to be used for
sources which are not desired.
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Multimode pupil plane beamcombination
Detection thesame as with single mode beamcombination
Visibility V due to all sources in the Airy disk of the elements
Fringe detection by:
- modulation of optical path length:
NPOI, PTI, KIIA, VLTI/MIDI
- scanning of coherence envelope:
COAST
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Multimode pupil plane beamcombination
Example: beamcombiner of COAST
Up to four elements
can be combined
simultaneously
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Multimode image plane beamcombination
Focus collimated beams from
elements with the same optical
element onto a common detector
Easy simultaneous combination of
more than two elements
Easy detection of fringes in an
extended field
Needs detectors with many pixels
Image plane fringe detection by
fringe dispersion:
GI2T
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Imaging beamcombination example:
Pupil masking at ESO/NTT
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Imaging beamcombination example:
Pupil masking at ESO/NTT
program star
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reference star
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Fizeau vs. Michelson interferometers:
a continuing confusion
Def.: A Fizeau stellar interferometer is an interferometer where the
Helmholtz-Lagrange (optical) invariant is preserved throughout
the optical train.
A Michelson stellar interferometer is an interferometer where
this is not the case.
Helmholtz-Lagrange invariant: the product of (object sided)
field angle and radius of entrance pupil. This quantity characterizes
a given optical system.
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Fizeau vs. Michelson interferometers:
a continuing confusion
Fizeau interferometer
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Michelson interferometer
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Field effect in a Michelson interferometer





 g  

  

     g     g       



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