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Basic Principles of Interferometry
Pierre Léna, Université Paris VII & Observatoire de Paris
Interferometry Week, Santiago-du-Chili, January 14-16, 2002
VERSION 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 Earth’s atmosphere
9. Methods of light recombination
10. Signal detection & noise sources, sensitivity
11 . Astrometry with an interferometer
1. The Thomas Young Experiment
• A founding experiment
• Fringes & spatial structure of the source
• The Telescope Equivalent
Reference : Glindeman, A., VLTI tutorial
http://www.eso.org/projects/vlti/general/tutorial_introduction_to_stellar_interf.pdf
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 >≈ l /B
V.L.T.
ALMA
1 mm
m
a
0 s
.2
m
a
s
2
a
rc
s
e
c
2
0
0
m
a2
s
0
m
a
2s
1 0 mm
1 0 0 m
1 0 m
VLTI
1 m
OHANA
0 .1 m
Baseline B
10 m
100 m
1 km
1 0 km
1 0 0 km
2. From Fizeau to the VLTI
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1802
1868
1872
1921
1950
1956
1970
1972
1973
1975
1976
1987
1989
1996
2001
2001
Fringes and nature of light
Concept of interferometry with pupil mask
Upper limit (0.158”) of stellar diameter
First stellar diameter measurement
First radio-interfometer
First intensity interferometer (visible)
Speckle interferometry (visible)
First heterodyne fringes (10 m)
Deconvolution algorithm
Triple correlation (visible)
Coupling two independent telescopes
Decision of VLT Interferometer
First adaptive optics image (2.2 m)
First interferometric image (visible)
VLTI & Keck Interferometer first light
Adaptive optics on VLT (NAOS)
Thomas Young, Londres
Hippolyte Fizeau, Paris
Edouard Stephan, Marseille
Albert Michelson, Pasadena
Martin Ryle, Cambridge
R. Hanbury-Brown & R. Twiss
Antoine Labeyrie, Paris
Jean Gay & Alain Journet, Grasse
Leon Lucy
Gerd Weigelt, Nuremberg
Antoine Labeyrie, Paris
Observatoire Européen Austral
Gérard Rousset et al, Paris & ESO
James Baldwin, Cambridge
C. Paranal, Chili & Mauna Kea
Cerro Paranal, Chili
Albert Michelson’s Interferometric set-up, Mt. Wilson, Calif. 1920
Reference : Glindeman, A., VLTI tutorial
http://www.eso.org/projects/vlti/general/
tutorial_introduction_to_stellar_interf.pdf
Antennas or telescopes ?
Cambridge (UK) 1957, l = 1.7 m
From Ryle’s Nobel Prize lecture, 1974
From Ryle’s Nobel Prize lecture, 1974
The first Labeyrie interferometer (1975-1980)
Fringes on Vega
at l = 550 nm
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 m 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)
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
2. From Fizeau to the VLTI
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•
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•
•
•
•
•
•
•
•
•
•
•
•
•
1802
1868
1872
1921
1950
1956
1970
1972
1973
1975
1976
1987
1989
1996
2001
2001
Fringes and nature of light
Concept of interferometry with pupil mask
Upper limit (0.158”) of stellar diameter
First stellar diameter measurement
First radio-interfometer
First intensity interferometer (visible)
Speckle interferometry (visible)
First heterodyne fringes (10 m)
Deconvolution algorithm
Triple correlation (visible)
Coupling two independent telescopes
Decision of VLT Interferometer
First adaptive optics image (2.2 m)
First interferometric image (visible)
VLTI & Keck Interferometer first light
Adaptive optics on VLT (NAOS)
Thomas Young, Londres
Hippolyte Fizeau, Paris
Edouard Stephan, Marseille
Albert Michelson, Pasadena
Martin Ryle, Cambridge
R. Hanbury-Brown & R. Twiss
Antoine Labeyrie, Paris
Jean Gay & Alain Journet, Grasse
Leon Lucy
Gerd Weigelt, Nuremberg
Antoine Labeyrie, Paris
Observatoire Européen Austral
Gérard Rousset et al, Paris & ESO
James Baldwin, Cambridge
C. Paranal, Chili & Mauna Kea
Cerro Paranal, Chili
3. Object, Instrument, Image & Fourier spectra
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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
4. Coherence of radiation
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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
5. Measuring coherence with an ideal interferometer
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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
Measuring spatial coherence :
visibility amplitudes
in optical interferometry
Uniform disc star
(Perrin,G. et al)
From A. Glindeman’s VLTI tutorial
Chromatic dependence of spatial coherence
The star  Cass
M=16 Msun, R=6Rsun, D=100 pc
GI2T Interferometer, Calern, France - Mourard et al., 1999
6. From the visibility to an image
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Multiple baselines & synthetized pupil
The Single Telescope/Antenna MTF (Primary Beam)
The Interferometer MTF (Dirty Beam)
From Fourier space (visibilities) to image space : (N -> N)
Filling holes of the MTF : deconvolution techniques
(« cleaning »)
• Restoring a good PSF : the densified pupil
Aperture synthesis
1. Object is the Fourier transform of (B/l)
2. (B/l) is measured on a limited support -> Frequency cut-off
3. (B/l) is measured on a sparse domain -> irregular PSF (Dirty beam)
B
Image plane (q)
NxN
Fourier plane (u,v)
requires
NxN
(VLTI)
From A. Glindeman, VLTI tutorial
An example of Interferometer
Point Spread Function (or Dirty Beam)
The PSF of the ‘OHANA array
(7 télescopes, source at zenith)
0 .25 mas @ l =1 m
This would be the image of a point
source. Cleaning the image of an
extended object can be
done with different techniques
of deconvolution.
QuickT i me™ et un décompresseur
GIF sont requi s pour vi suali ser
cette i mage.
Etoile Wolf-Rayet WR 104
Peter Tuthill, Telescope Keck, 2000
VLTI
OHANA
interferometer
on Mauna Kea
7. Types of interferometers
LBT
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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
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
coherencing
cophasing
wavetrain from
telescope 1
wavetrain from
telescope 2
temporal coherence length cc
zero OPD
Steps with metrology :`
• Coherencing : find some fringes
• Cophasing : adjust OPD=0 from star to fringe center through 1 & 2
• Fringe tracking : maintain OPD=0 with delay line (compensating for
Diurnal, atmospheric or instrument instant delays.
8. Effects of the Earth’s atmosphere
• Overview on atmospheric coherence loss
• Parameters : ro(l), o(l) , qo (l), 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 !
…./….
…/...
IDEAL
REEL
Gerd Weigelt, Bonn
QuickTime™ et un décompresseur
Video sont requis pour visualiser
cette image.
Création F. Lacombe, Meudon
Qui ckTi me™ et un décompr esseur
Video sont req uis pour visualiser
cette i mag e.
Simulations, Daniel Rouan, Meudon
Telescope 1
Loss of coherence (wavefront aberrations)
on a single telescope : effect on fringes
+
Telescope 2
(A. Glindeman, VLTI Tutorial)
Loss of coherence (differential piston)
between 2 telescopes : effect on fringes
Atmospheric Piston at 2.2 m
VLTI-UT1 & UT3 - Oct.2001 on Achernar
Star 1 is the faint object
to be measured
Star 2 is the bright object
for piston tracking
Star 2
Star 1
OPD=0
Piston tracking
with reference
A. Glindeman, VLTI Tutorial
Summary of atmospheric effects on interferometric observations
• adaptive optics on individual telescopes is needed.
But Strehl S <1 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 (<≈ 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.
9. Methods of light recombination
The VLTI Central Laboratory
• Internal metrology in an interferometer
• Image plane recombination
- dispersed fringes & spectral analysis
- pupil reconfiguration (Ntélescopes > 2)
• Pupil plane recombination
- Double Fourier spectral analysis
• Integrated optics recombiners
• Dual-beam (dual-feed) operation
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 m)
- detector read-out noise (1 to 2.5 m)
- background (thermal) noise (2.5 m -> radio)
- atmospheric noises (piston, scintillation) : all l
• Sensitivity & accuracy
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
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/….
The FLUOR/VINCI principle to control intensity fluctuations :
(I1I2)1/2 V
Interferometric signal
=
Photometric signals
(I1) 1/2(I2)1/2
=V
11. Astrometry with an interferometer
• Astrometric observables
Interferomeric astrometry
Measure B, dinternal, f, deduce direction s
(two measurements required)
unit vect or t o t he source s
baseline B
Phase f
Delay
d = B.s
Measure
d = d(internal) +
l2 f
Phase reference ?