Basic Principles of Interferometry Pierre L

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Basic Principles of InterferometryPierre Léna,
Université Paris VII Observatoire de
ParisInterferometry Week, Santiago-du-Chili,
January 14-16, 2002VERSION Jan.18, 2002

• 1. The Young Experiment its Telescope
  Equivalent
• 2. From Fizeau to the VLTI
• 3. Object, Instrument, Image Fourier spectra
• 4. Coherence of radiation
• 5. Measuring coherence with an ideal
  interferometer
• 6. From the visibility to an image
• 7. Types of interferometers
• 8. Effects of the Earths atmosphere
• 9. Methods of light recombination
• 10. Signal detection noise sources, sensitivity
• 11. Astrometry with an interferometer

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1. The Thomas Young Experiment

• A founding experiment
• Fringes spatial structure of the source
• The Telescope Equivalent

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Reference Glindeman, A., VLTI tutorial
http//www.eso.org/projects/vlti/general/tutorial_
introduction_to_stellar_interf.pdf
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The Golden Rules of Interferometry

• Relative modulation amplitude V (from 1 to 0) of
  the fringe pattern is related to the source
  angular size (a).
• For a given source angular size, modulation
  amplitude decreases when separation of holes (B)
  increases.
• For wavelength l, modulation becomes sensitive to
  size when a gt l /B

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Wavelength l
V.L.T.
Baseline B
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2. From Fizeau to the VLTI

• 1802 Fringes and nature of light Thomas Young,
  Londres
• 1868 Concept of interferometry with pupil
  mask Hippolyte Fizeau, Paris
• 1872 Upper limit (0.158) of stellar
  diameter Edouard Stephan, Marseille
• 1921 First stellar diameter measurement Albert
  Michelson, Pasadena
• 1950 First radio-interfometer Martin Ryle,
  Cambridge
• 1956 First intensity interferometer (visible) R.
  Hanbury-Brown R. Twiss
• 1970 Speckle interferometry (visible) Antoine
  Labeyrie, Paris
• 1972 First heterodyne fringes (10 ?m) Jean Gay
  Alain Journet, Grasse
• 1973 Deconvolution algorithm Leon Lucy
• 1975 Triple correlation (visible) Gerd Weigelt,
  Nuremberg
• 1976 Coupling two independent telescopes Antoine
  Labeyrie, Paris
• 1987 Decision of VLT Interferometer Observatoire
  Européen Austral
• 1989 First adaptive optics image (2.2 ?m) Gérard
  Rousset et al, Paris ESO
• 1996 First interferometric image (visible) James
  Baldwin, Cambridge
• 2001 VLTI Keck Interferometer first light C.
  Paranal, Chili Mauna Kea
• 2001 Adaptive optics on VLT (NAOS) Cerro
  Paranal, Chili

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Albert Michelsons Interferometric set-up, Mt.
Wilson, Calif. 1920
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Reference Glindeman, A., VLTI tutorial
http//www.eso.org/projects/vlti/general/ tutorial
_introduction_to_stellar_interf.pdf
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Antennas or telescopes ?
Cambridge (UK) 1957, l 1.7 m From Ryles Nobel
Prize lecture, 1974
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From Ryles Nobel Prize lecture, 1974
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The first Labeyrie interferometer (1975-1980)
Fringes on Vega at l 550 nm
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Three methods to achieve coherent combination of
light

• change the frequency of light at each telescope,
  
• carry to the common focus an Intermediate
  Frequency (IF) Signal, combine all these
  signals (fringes)
• heterodyne interferometer (l from10 mm to
  mm-cm)
• receive the light at each telescope on a quantum
  detector
• correlate the photo-currents
• intensity interferometer (visible l)
• Carry the light from each telescope to a common
  focus
• combine coherently, then detect interferometric
  signal (fringes),
• direct interferometer (optical l)

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The Narrabri (Australia) Intensity
Interferometer, constructed after the initial
success of Hanbury-Brown Twiss correlation on
Sirius at visible wavelengths Nature (1956),
177, 27-29
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2. From Fizeau to the VLTI

• 1802 Fringes and nature of light Thomas Young,
  Londres
• 1868 Concept of interferometry with pupil
  mask Hippolyte Fizeau, Paris
• 1872 Upper limit (0.158) of stellar
  diameter Edouard Stephan, Marseille
• 1921 First stellar diameter measurement Albert
  Michelson, Pasadena
• 1950 First radio-interfometer Martin Ryle,
  Cambridge
• 1956 First intensity interferometer (visible) R.
  Hanbury-Brown R. Twiss
• 1970 Speckle interferometry (visible) Antoine
  Labeyrie, Paris
• 1972 First heterodyne fringes (10 ?m) Jean Gay
  Alain Journet, Grasse
• 1973 Deconvolution algorithm Leon Lucy
• 1975 Triple correlation (visible) Gerd Weigelt,
  Nuremberg
• 1976 Coupling two independent telescopes Antoine
  Labeyrie, Paris
• 1987 Decision of VLT Interferometer Observatoire
  Européen Austral
• 1989 First adaptive optics image (2.2 ?m) Gérard
  Rousset et al, Paris ESO
• 1996 First interferometric image (visible) James
  Baldwin, Cambridge
• 2001 VLTI Keck Interferometer first light C.
  Paranal, Chili Mauna Kea
• 2001 Adaptive optics on VLT (NAOS) Cerro
  Paranal, Chili

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3. Object, Instrument, Image
Fourier spectra

• Object, instrument, image
• Intensity (irradiance) in object/image and its
  spatial spectrum
• Instrument as a spatial filter
• Modulation Transfer Function (MTF)
• Point Spread Function (PSF)
• Isoplanatism
• Degraded MTFs aberrations, atmosphere

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4. Coherence of radiation

• The field radiation ?(r,t) and the source
  characteristics
• Temporal coherence
• Spatial coherence
• Spatio-temporal coherence ?12(?)
• Quasi-monochromatic case
• Coherence over an illuminated surface the
  Zernike-van Cittert theorem
• Area of coherence Ac , étendue Ac ? l2, volume
  of coherence
• Beam transport coherence

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5. Measuring coherence with an ideal
interferometer

• Principles of coherence (correlation) measurement
• Fringes, complex visibility source spatial
  spectrum
• Some simple sources
• - point-like
• - uniform disk
• - binary star
• Wavefront structure
• - loss of coherence diffraction, scattering,
  atmospheric propagation
• - corrugation of amplitude and/or phase of
  visibility

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Measuring spatial coherence visibility
amplitudes in optical interferometry
Uniform disc star (Perrin,G. et al)
From A. Glindemans VLTI tutorial
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Chromatic dependence of spatial coherence
The star g Cass M16 Msun, R6Rsun, D100 pc
GI2T Interferometer, Calern, France - Mourard et
al., 1999
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6. From the visibility to an image

• Multiple baselines synthetized pupil
• The Single Telescope/Antenna MTF (Primary Beam)
• The Interferometer MTF (Dirty Beam)
• From Fourier space (visibilities) to image space
  (N -gt N)
• Filling holes of the MTF deconvolution
  techniques ( cleaning )
• Restoring a good PSF the densified pupil

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Aperture synthesis
1. Object is the Fourier transform of g(B/l) 2.
g(B/l) is measured on a limited support -gt
Frequency cut-off 3. g(B/l) is measured on a
sparse domain -gt irregular PSF (Dirty beam)
B
Image plane (q)
Fourier plane (u,v)
N x N requires N x N
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(VLTI)
From A. Glindeman, VLTI tutorial
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An example of Interferometer Point Spread
Function (or Dirty Beam) The PSF of the OHANA
array (7 télescopes, source at zenith)
0.25 mas _at_ l 1 mm
This would be the image of a point source.
Cleaning the image of an extended object can
be done with different techniques of
deconvolution.
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Etoile Wolf-Rayet WR 104 Peter Tuthill,
Telescope Keck, 2000
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OHANA interferometer on Mauna Kea
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7. Types of interferometers
LBT

• MTF of a real interferometer
• The Fizeau recombination (optical)
• The classical Michelson recombination (optical)
• The Heterodyne recombination (radio)
• Delay lines, coherencing, cophasing, fringe
  tracking optical radio
• Field-of-view of an interferometer optical
  radio
• Polarisation effects
• The densified pupil Michelson recombination

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A Fizeau interferometer The Large Binocular
Telescope (2 x 8.4 m), Mt Graham, Arizona
Interferometric field-of-view 1 arcmin (to
compare with VLTI 2 arcsec)
Orion proplyds, HST
23 m
6 arcsec
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coherencing
cophasing
wavetrain from telescope 1
wavetrain from telescope 2
zero OPD
temporal coherence length ctc

• Steps with metrology
• Coherencing find some fringes
• Cophasing adjust OPD0 from star to fringe
  center through 1 2
• Fringe tracking maintain OPD0 with delay line
  (compensating for
• Diurnal, atmospheric or instrument instant
  delays.

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8. Effects of the Earths atmosphere

• Overview on atmospheric coherence loss
• Parameters ro(??? ?o(?? , ?o (??, Lo, lo
• Adaptive optics, principle
• - Zernike polynomials description of wavefront
• - Strehl ratio S
• Effects on interferometric observables
• - speckled fringes and visibility degradation
• - piston noise
• Closure phase
• Going to space !

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./.
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/...
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IDEAL
REEL
Gerd Weigelt, Bonn
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Création F. Lacombe, Meudon
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Simulations, Daniel Rouan, Meudon
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Loss of coherence (wavefront aberrations) on a
single telescope effect on fringes
Telescope 1

Telescope 2
(A. Glindeman, VLTI Tutorial)
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Loss of coherence (differential piston) between
2 telescopes effect on fringes
Atmospheric Piston at 2.2 mm
VLTI-UT1 UT3 - Oct.2001 on Achernar
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Star 2 is the bright object for piston tracking
Star 1 is the faint object to be measured
Star 2
Star 1
Piston tracking with reference
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A. Glindeman, VLTI Tutorial
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Summary of atmospheric effects on interferometric
observations

• adaptive optics on individual telescopes is
  needed.
• But Strehl S lt1 leads to visibility amplitude
  loss and visibility noise,
• limiting accuracy.
• piston noise between telescopes can not be
  compensated.
• Limits exposure time, hence restricts observation
  to bright
• objects adds noise onto visibility amplitude
  measurement.
• if differential piston is tracked on a
  bright source, long time
• integration can be achieved to determine V of a
  faint source,
• but atmosphere imposes a proximity (lt 1 arcmin).
• differential piston makes absolute phase
  measurement of the
• complex visibility impossible. Closure phase
  partially solves this.
• absolute phase of source can yet be measured, if
  a known
• (e.g. pointlike star, quasar) phase calibrator
  lies close enough.

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9. Methods
of light recombination
The VLTI Central Laboratory

• Internal metrology in an interferometer
• Image plane recombination
• - dispersed fringes spectral analysis
• - pupil reconfiguration (Ntélescopes gt 2)
• Pupil plane recombination
• - Double Fourier spectral analysis
• Integrated optics recombiners
• Dual-beam (dual-feed) operation

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10. Signal detection noise sources,
sensitivity

• From measured to real visibility calibration
• Expression of the interferometric signal
  amplitude phase
• Noise sources
• - signal photon noise (0.3 - 1 mm)
• - detector read-out noise (1 to 2.5 mm)
• - background (thermal) noise (2.5 mm -gt radio)
• - atmospheric noises (piston, scintillation)
  all l
• Sensitivity accuracy

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The interferometric signal (optical)

• Complex visibility V exp(if)

V
Measuring (unwrapped) f needs a reference
Telescope reference
Another nearby object (star)
Same object at different l
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The interferometric signal (optical)

• The signal amplitude

• SIGNAL 1/2 . Intensity . Area . Spectral
  bandwidth .
• (polarisation) (source)(telescopes)
  (detection)
• Exposure time . Instrument transmission .
• (piston) (coatings,
  detector)
• . Instrument visibility . Source visibility.
  Strehl ratio
• (coherence losses) (source size)
  (adaptive optics)
• The noise
• NOISE Signal Photon noise / Detector noise/
  Thermal noise / Atmospheric noise/.

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The FLUOR/VINCI principle to control intensity
fluctuations
(I1I2)1/2 V
Interferometric signal Photometric signals

V
(I1) 1/2(I2)1/2
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11. Astrometry with an interferometer

• Astrometric observables

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Interferomeric astrometry
Measure B, dinternal, f, deduce direction s (two
measurements required)
Phase f
Phase reference ?