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1. The Young Experiment & its Telescope Equivalent 2. From Fizeau to the VLTI

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

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1. The Young Experiment & its Telescope Equivalent 2. From Fizeau to the VLTI

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  1. 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 Earth’s atmosphere 9. Methods of light recombination 10. Signal detection & noise sources, sensitivity 11. Astrometry with an interferometer

  2. 1. The Thomas Young Experiment • A founding experiment • Fringes & spatial structure of the source • The Telescope Equivalent

  3. Reference : Glindeman, A., VLTI tutorial http://www.eso.org/projects/vlti/general/tutorial_introduction_to_stellar_interf.pdf

  4. 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

  5. Wavelength l V.L.T. Baseline B

  6. 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

  7. Albert Michelson’s Interferometric set-up, Mt. Wilson, Calif. 1920

  8. Reference : Glindeman, A., VLTI tutorial http://www.eso.org/projects/vlti/general/ tutorial_introduction_to_stellar_interf.pdf

  9. Antennas or telescopes ? Cambridge (UK) 1957, l = 1.7 m From Ryle’s Nobel Prize lecture, 1974

  10. From Ryle’s Nobel Prize lecture, 1974

  11. The first Labeyrie interferometer (1975-1980) Fringes on Vega at l = 550 nm

  12. 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)

  13. 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

  14. 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

  15. 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

  16. 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 coherenceAc , étendueAc = l2, volume of coherence • Beam transport & coherence

  17. 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

  18. Measuring spatial coherence : visibility amplitudes in optical interferometry Uniform disc star (Perrin,G. et al) From A. Glindeman’s VLTI tutorial

  19. Chromatic dependence of spatial coherence The star g Cass M=16 Msun, R=6Rsun, D=100 pc GI2T Interferometer, Calern, France - Mourard et al., 1999

  20. 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 -> N) • Filling holes of the MTF : deconvolution techniques (« cleaning ») • Restoring a good PSF : the densified pupil

  21. Aperture synthesis 1. Object is the Fourier transform of g(B/l) 2. g(B/l) is measured on a limited support -> Frequency cut-off 3. g(B/l) is measured on a sparse domain -> irregular PSF (Dirty beam) B Image plane (q) Fourier plane (u,v) N x N requires N x N

  22. (VLTI) From A. Glindeman, VLTI tutorial

  23. 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 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.

  24. Etoile Wolf-Rayet WR 104 Peter Tuthill, Telescope Keck, 2000

  25. VLTI OHANA interferometer on Mauna Kea

  26. 7. Types of interferometers • 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 LBT

  27. 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

  28. 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 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.

  29. 8. Effects of the Earth’s atmosphere • Overview on atmospheric coherence loss • Parameters :ro(o(, o (, Lo, lo • Adaptive optics, principle - Zernike polynomials description of wavefront - Strehl ratioS • Effects on interferometric observables ` - speckled fringes and visibility degradation - piston noise • Closure phase • Going to space !

  30. …./….

  31. …/...

  32. IDEAL REEL Gerd Weigelt, Bonn

  33. Création F. Lacombe, Meudon

  34. Simulations, Daniel Rouan, Meudon

  35. Loss of coherence (wavefront aberrations) on a single telescope : effect on fringes Telescope 1 + Telescope 2 (A. Glindeman, VLTI Tutorial)

  36. Loss of coherence (differential piston) between 2 telescopes : effect on fringes Atmospheric Piston at 2.2 mm VLTI-UT1 & UT3 - Oct.2001 on Achernar

  37. OPD=0 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

  38. A. Glindeman, VLTI Tutorial

  39. 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.

  40. 9. Methods of light recombination • 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 The VLTI Central Laboratory

  41. 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 - 1mm) - detector read-out noise (1 to 2.5mm) - background (thermal) noise (2.5mm -> radio) - atmospheric noises (piston, scintillation) : alll • Sensitivity & accuracy

  42. 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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