How does Optical-IR interferometry work?

1. How does Optical-IR interferometry work? Gianluca Li Causi, INAF – OAR Simone Antoniucci, Univ. Tor Vergata

2. Contents: • Can a single telescope observe sources smaller than /D ? • How does interferometry go beyond this limit ? • What do we really measure with an interferometer ? • How to get information on observed sources ? • How to realize the Young experiment with telescopes ? • What are the differences between LBT and VLTI ?

3. The /D resolution limit: the Point Spread function • Pointlike source at infinity  Fraunhofer diffraction • Circular aperture Airy figure Pupil Function: Circular aperture 1.22 /D Focal plane Point Spread Function:

4. Airy Binary The /D resolution limit: the Rayleigh criterion • Double pointlike star -> Rayleigh criterion: minimum resolvable feature ~ /D • Rayleigh criterion is empirical: it comes from visual observation 1.22 /D Single star Double star Image formation equation: Fourier deconvolution: • So, model fitting of the PSF or deconvolution should be able to resolve structures smaller than /D !

5. The /D resolution limit: beyond /D ? • Theoretical limitations: • The PSF of any finite aperture is upper limited in spatial frequency Image decomposition in spatial frequencies: Power Spectrum of the PSF: OTF + = + low freq mid freq hi freq D/ spatial frequency Optical Transfer Function • So, a single telescope acts as a low-pass spatial filter.

6. OTF OTF OTF D/ D/ D/ spatial frequency spatial frequency spatial frequency Same image The /D resolution limit: beyond /D ? • Theoretical limitations: • The PSF of any finite aperture is upper limited in spatial frequency • Sources with power spectra differing only at high frequencies (i.e. > D/) form identical images at the focal plane of a telescope! D/ • So, deconvolution and model fitting have no unique solutions • So /D is a limit in the sense that the information on smaller scales can beonly partially reconstructed.

7. Baseline B Interferometry: the Young experiment • Pointlike source at infinity -> Fraunhofer diffraction • Two circular apertures -> Fringes on Airy figure Interferometric Pupil Aperture /B Focal plane Interferometric PSF, monochromatic • Fringes intensity:

8. Baseline B Interferometry: the Young experiment • Pointlike source at infinity  Fraunhofer diffraction • Two circular apertures Fringes on Airy figure  one spatial frequency (B/l) added Interferometric Pupil OTF Aperture B1 B2 B3 D/ B/ (B+D)/ spatial frequency /B Interferometric OTF Focal plane Interferometric PSF, monochromatic • Interferometry gives access to higher frequencies: resolution limit is /(B+D) ~ /B • More baselines  more frequencies

9. v BY B BX u Interferometry: the u,v plane • Observing with a baseline B  observing the B/l spatial frequency u,v plane: spatial frequencies plane OTF Aperture B D/ B/ spatial frequency Usually, spatial frequency in terms of baseline components: u = BX/l v = BY/l

10. Baseline B Baseline B y y x x Interferometry: double star closer than /D • Wide band images of a pointlike double star Double star along baseline direction projected on sky Double star orthogonal to projected baseline d < /D u = BX/ v = BY/ D/ B/ D/ B/ spatial frequency spatial frequency • Interferometry increases resolution only along projected baseline

11. Interferometric observables: the visibility • Pointlike source -> high contrast fringes • Resolved source -> low contrast fringes Point-like source (size < /B) Resolved source (size > /B) • Unresolved -> high SNR, resolved -> low SNR • The best we resolve the source, the worst we see the fringes !

12. Interferometric observables: the visibility • Pointlike source high contrast fringes • Resolved source low contrast fringes Resolved source (size > /B) (incoherent light) spatialcoherence factor or visibility V fringe contrast Van Cittert – Zernike theorem: O(x,y): source brightness distribution on sky • The fringe contrast, i.e. visibility modulus, is dependent on the source shape • Hence, a measure of V(u,v) gives information on the source O(x,y)

13. Image reconstruction: the u,v coverage • So, the Visibility is a Complex Function defined on the (u,v) plane The relation: is invertible v -1 • The source is the inverse Fouriertransform of the complex visibility. The Real Part of V is the FT of the symmetric component of the object, the Imaginary Part is the antysymmetric component. u …BUT this is possible only if V is known on the WHOLE u,v plane • So, the highest the u,v coverage the better the O(x,y) reconstruction

14. Image reconstruction: how to fill the u,v plane? • Use many baselines: arrays of telescopes  VLTI, ALMA • Use large apertures D respect to baseline B  LBT • Use Earth rotation to scan the u,v plane  VLTI, LBT, all

15. 22.4 m Image reconstruction with LBT Projected Baseline 8.4 m 8.4 m u,v coverage of LBT Projected Baseline reconstruction real source single images with two baselines psf

16. 4 UTs (8m) v u u-v plane 4 ATs (2m) Interferometry with sparse u,v sampling - VLTI • Visibility modelling instead of image reconstruction Baselines: 47 – 130m VLTI @ Paranal Baselines: 8 – 200m

17. Uniform disk Visibility curves • Visibility for a limited number of spatial frequencies  need of amodel for the source brightness distribution • Visibility curve = visibility amplitude vs spatial frequencies (baseline) • Model  Fourier Transform  expected visibility curve Let’s see some examples of visibility curves

18. 1 mas uniform disk VLTI–VINCI on y Phe • Visibility amplitude V info on source size • Unresolved source (<< /B) V ~ 1 • Resolved source ( ~ /B) V ~ 0 100 mas Measurements fit visibility curve  get model parameters Visibility curves

19. Uniform disk Limb darkened disk Gaussian disk UD + hot spot UD + hole UD + cold spot Binary (equal brightness) Binary (different brightness) Visibility curves • Visibility for a limited number of spatial frequencies  need amodel for the source brightness distribution • Visibility curve = visibility amplitude vs spatial frequencies (baseline) • Model  FT  expected visibility curve Let’s see some examples of visibility curves

20. Instrumentation @ VLTI • VINCI • Combines the light from 2 telescopes in the K band •  ~ 4 mas (100m baseline) • lim. magnitude (mK < 11) • MIDI • Combines the light from 2 telescopes in the N band •  ~ 20 mas in N (100m baseline) • Light interferes, then is dispersed •  Visibility at different wavelengths • (“visibility spectrum”, up to R ~ 200) • lim. magnitude (mN < 4, UTs) • AMBER • Combines the light from 2 or 3 telescopes in the H, K bands •  ~ 4 mas in K (100m baseline) • Visibility spectrum (up to R ~ 1500) • lim. magnitude (mK < 4 – 7, UTs) Analyse “differential” visibilities: Vlinevs Vcontinuum get info on geometry of different emission zones VINCI measurements MIDI measurements AMBER measurements

21. A scientific case – 1) modelling Observation of the young stellar source Z CMa with AMBER (ESO P76 - Nisini, Antoniucci, Li Causi, Lorenzetti, Paresce, Giannini) HI emission: discriminate between origin in accretion flows or wind • Investigate source central regions  tens of mas  use AMBER • Model for the source: • HI emission from an infalling/outflowing spherical ionized envelope • Optically thick face-on disk, T  R-1/2 • Central star, black body spectrum Model (Radiative Transfer software “RaT” - Li Causi, Antoniucci) brightness distribution • visibility (visibility computation software “IVC”– Li Causi) visibility curve  prepare observations…

22. A scientific case – 2) planning observations Accretion Line Continuum Visibility Wind Baseline (m) UT1 + UT2 + UT4 AMBER: K band, R ~ 1500 • Compare: • visibility in the Brg line • (2.17 mm spectral channel) • visibility in the continuum • (in an adjacent spectral channel) UT1 + UT2 + UT4 VLT telescopes

23. A scientific case – 3) data dark phot #1 interfer phot #2 phot #3 LAOG (Grenoble) software for AMBER data reduction AMBER 3 telescopes images Source Calibrator Data analysis in progress, but there seem to be no fringes! • Problems: • Light injection: poor adaptive optics performance • Source fainter than expected • Very low visibility?

24. VLA 2’ x 1’ VLA Cygnus A @ 21 cm Young experiment realizations: radio vs. optical-IR • Radio -> light interferes in heterodyne mode correlator  tape recorder   laser reference atomic clock • Heterodyne: - waves interfere with a local reference - recorded and combined later - no physical connection between telescopes

25. Young experiment realizations: radio vs. optical-IR • Optical-IR -> light interferes in homodyne mode  beam combiner • Heterodyne is not sensible for <10÷100m because uncertainty principle gives lower SNR respect to homodyne. • Homodyne: - waves are physically combined - telescopes are optically connected

26. Optical-IR interference with two telescopes • Independent mount telescopes, e.g. VLTI • Single mount telescopes, e.g. LBT optical path difference OPD projected baseline short baseline B long baseline B adaptive optics beam combiner sideral motion delay line fringe tracker • Zero OPD -> no delay lines • Short (~20m) and fixed baseline • Medium resolution ~20mas • Variable OPD -> variable delay lines • Long and variable (30÷200m) proj. baseline • High resolution ~2mas

27. Michelson and Fizeau beam combining • Light interferes on the focal plane -> Fizeau or “image plane” interferometry • Light interferes in collimated beams -> Michelson or “pupil plane” interferometry B D Michelson (VLTI) beam splitter b MIDI@VLTI d pupils homoteticity b/d = B/D Fizeau (LBT) OPD scan detector Intensity • Single point (~ 100 mas) interferogram OPD • Large interf. image (up to 2 arcmin)

28. VLTI optical delay lines

29. Fiber optic combiners for pupil-plane interferometers • Monomodal fibers and spectral dispersion integrated optics prism monomodal fibers detector Michelson (VLTI) 50mas

30. Types of observations with Optical-IR interferometry • Modellable sources: visibility from two or more telescopes (stellar diameters, binary orbits, circumstellar envelopes and disks – MIDI_&_AMBER@VLTI) • Image reconstruction: aperture synthesis from high (u,v) coverage (sources morphology – LINC_NIRVANA@LBT) • Wide-angle astrometry: /B precision over degrees (VLTI) • Narrow-angle astrometry: ~ 10-2/B precision over isoplanatic angle (reflex motion of stars due to exoplanets – PRIMA@VLTI) • Nulling interferometry: ~ 10-4-10-9 attenuation of on-axis source (extrasolar planets direct observation – NIL@LBT) reference star Shao et al. 1990

31. Nulling interferometry: the Bracewell concept • Co-axial beam combination with  phase shift in one arm (NIL@LBT, GENIE@VLTI) beam splitter  phase shifter Star plus 10-6 flux planet

32. LBT versus VLTI ? Different instruments: complementarity, not competitiveness: • LBT: • resolution (K band): 25mas, Airy disk 100mas • FoV: 20 arcsec • limiting K magnitude (LINC): 25mag in 1h for K band filter • spectral channels: 1 channel at a time (broad or narrow filter) • mirrors before combining: 3 (primary, secondary, Nasmyth) • u-v coverage: quite uniform from zero to max freq. • imaging time: one night • adaptive optics (NIRVANA): Multi-FoV Layer-Oriented • VLTI: • resolution (K band): down to 2mas, Airy disk 56mas • FoV: 2 arcsec MIDI at 10m, 56mas AMBER (H,K band) • limiting K magnitude (AMBER): 17mag* in 15min for hi-res mode R=1000 • spectral channels (AMBER): 27 channels at hi-res mode R=1000 • mirrors before combining: ~20 (telescope plus delay line) • u-v coverage: narrow around baseline freq. (low freq. filtered out) • imaging time: many nights • adaptive optics: MACAO • * So far fringe tracking FINITO is not yet working, so current AMBER limit is 4.5mag

33. LBT versus VLTI ? Different instruments: complementarity, not competitiveness. • Limiting magnitude of VLTI and LBT with fringe tracking is roughly comparable • LBT samples the shorter baselines which are inaccessible to VLTI • VLTI is best suited for high resolution on morphologically simple sources • LBT is best suited for complex objects sampled at lower but uniform resolution

34. LBT and VLTI: example #1 Extrasolar planets direct observation via nulling interferometry • requires very low background at 10m, i.e. thermal infrared:NIL@LBT: all cryogenic, only 3 warm mirrors (primary, secondary, Nasmyth) • VLTI: at least 20 warm mirrors (telescope, delay lines, etc.) • requires high nulling, i.e. minimize nulling leakage from not-pointlike stars: • LBT: short baseline (22.4m) -> 10pc stars less resolved -> low leakage • VLTI: long baselines (30-200m) -> 10pc stars resolved -> high leakage • requires simultaneous imaging of exo zodiacal light: • LBT: true imaging for scales greater than 0.25” @ 10m • VLTI: no imaging • does not require high resolution: • LBT: good compromise between leackage and resolution • VLTI: greater resolution but also greater leackage • LBT is best tailored for such kind of observations, but: Extrasolar planets indirect observation via reflex motion of star • requires very high resolution: • PRIMA@VLTI: down to 10arcsec narrow angle astrometry with differential phase • VLTI is best tailored for such kind of observations

35. LBT and VLTI: example #2 Investigating the inner regions of star forming disks • requires high resolution spectroscopy to get Br line and nearby continuum: • LBT: would need two observations in different narrow filters • AMBER@VLTI: spectral resolution Ry10000 with 27 channels simultaneously • requires high spatial resolution ~2-10mas: • LBT: structure not resolved by short baseline (22.4m) • VLTI: structure resolved by long baselines (30-200m) • VLTI is best tailored for such kind of observations, but: Investigating the transversal structure of the base of star forming jets • requires imaging in narrow band filters of H2 and [FeII] lines • requires arcsec resolution along the jetdirection • requires sub-arcsec resolution orthogonal to the jet: • LBT: satisfies the requirements for a field of 20 arcsec • LBT is best tailored for such kind of observations

36. OAR technological contribution: LINC-NIRVANA@LBT (D’Alessio, Di Paola, Lorenzetti, Li Causi, Pedichini, Speziali, Vitali) “Patrol Camera” adaptive optics • Replied to ESO Call for second generation VLTI instrumentation: • “VLTI Spectro-Imager”: imaging with 6 telescopes @ JHK • “MATISSE”: dispersed fringes with 4 telescopes @ LMNQ