Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
How does Optical-IR interferometry work? Gianluca Li Causi, INAF – OAR Simone Antoniucci, Univ. Tor Vergata 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 ? The /D resolution limit: the Point Spread function • Pointlike source at infinity Fraunhofer diffraction • Circular aperture Airy figure Pupil Function: P ( x, y ) Circular aperture 1.22 /D Focal plane Point Spread Function: ~ PSF P Airy ( x, y) 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 Airy Binary 1.22 /D Single star Double star Image formation equation: Fourier deconvolution: I ( x, y ) O( x, y ) Airy ( x, y ) ~ ~ O I Airy So, model fitting of the PSF or deconvolution should be able to resolve structures smaller than /D ! 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 OTF PSF So, a single telescope acts as a low-pass spatial filter. 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! OTF D/ spatial frequency OTF D/ spatial frequency OTF Same image D/ D/ spatial frequency So, deconvolution and model fitting have no unique solutions So /D is a limit in the sense that the information on smaller scales can be only partially reconstructed. Interferometry: the Young experiment • Pointlike source at infinity -> Fraunhofer diffraction • Two circular apertures -> Fringes on Airy figure Interferometric Pupil Baseline B Aperture /B Focal plane Interferometric PSF, monochromatic Fringes intensity: I I1 I2 2 I1I2 μ12 cos Interferometry: the Young experiment • Pointlike source at infinity Fraunhofer diffraction • Two circular apertures Fringes on Airy figure one spatial frequency (B/) added Interferometric Pupil Baseline B OTF Aperture B2 B1 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 Interferometry: the u,v plane • Observing with a baseline B observing the B/ spatial frequency u,v plane: spatial frequencies plane v OTF Aperture B BY D/ B BX B/ spatial frequency Usually, spatial frequency in terms of baseline components: u = BX/ v = BY/ u 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 Baseline B Baseline B y y d < /D x D/ B/ u = BX/ spatial frequency x D/ B/ v = BY/ spatial frequency Interferometry increases resolution only along projected baseline 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 ! Interferometric observables: the visibility • Pointlike source high contrast fringes • Resolved source low contrast fringes I I1 I2 2 I1I2 μ12 cos Resolved source (size > /B) (incoherent light) μ12 spatial coherence factor or visibility V V μ12 fringe contrast Van Cittert – Zernike theorem: μ12(u, v) e i O(x, y)e ik(ux vy)dxdy S O(x, y)dxdy S O(x,y): source brightness distribution on sky V(u, v) O(x, y) 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) Image reconstruction: the u,v coverage So, the Visibility is a Complex Function defined on the (u,v) plane The relation: V(u, v) O(x, y) is invertible -1 O(x, y) V(u, v) v The source is the inverse Fourier transform 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. …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 u 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 22.4 m Image reconstruction with LBT Projected Baseline 8.4 m u,v coverage of LBT 8.4 m Projected Baseline reconstruction real source single images with two baselines psf Interferometry with sparse u,v sampling - VLTI • Visibility modelling instead of image reconstruction Baselines: 47 – 130m VLTI @ Paranal 4 UTs (8m) v u 4 ATs (2m) Baselines: 8 – 200m u-v plane Visibility curves • Visibility for a limited number of spatial frequencies need of a model for the source brightness distribution • Visibility curve = visibility amplitude vs spatial frequencies (baseline) • Model Fourier Transform expected visibility curve Uniform disk Let’s see some examples of visibility curves Visibility curves uniform disk VLTI–VINCI on y Phe 1 mas 100 mas Visibility amplitude V info on source size • Unresolved source (<< /B) V ~ 1 • Resolved source ( ~ /B) V ~ 0 Measurements fit visibility curve get model parameters Visibility curves • Visibility for a limited number of spatial frequencies need a model for the source brightness distribution • Visibility curve = visibility amplitude vs spatial frequencies (baseline) • Model FT expected visibility curve Binary Binary Limb UD (different Gaussian UD Uniform (equal UD darkened ++cold hot + hole brightness) disk spot brightness) disk spot disk Let’s see some examples of visibility curves 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: Vline vs Vcontinuum get info on geometry of different emission zones AMBER VINCI MIDI measurements 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… A scientific case – 2) planning observations Accretion 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) Line Continuum UT1 + UT2 + UT4 VLT telescopes Wind Baseline (m) UT1 + UT2 + UT4 A scientific case – 3) data LAOG (Grenoble) software for AMBER data reduction AMBER 3 telescopes images Calibrator dark phot #1 phot #2 interfer phot #3 Source 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? Young experiment realizations: radio vs. optical-IR • Radio -> light interferes in heterodyne mode correlator tape recorder laser reference atomic clock VLA 2’ x 1’ VLA Cygnus A @ 21 cm Heterodyne: - waves interfere with a local reference - recorded and combined later - no physical connection between telescopes Young experiment realizations: radio vs. optical-IR • Optical-IR -> light interferes in homodyne mode beam combiner Heterodyne is not sensible for <10÷100mm because uncertainty principle gives lower SNR respect to homodyne. Homodyne: - waves are physically combined - telescopes are optically connected Optical-IR interference with two telescopes • Single mount telescopes, e.g. LBT • Independent mount telescopes, e.g. VLTI long baseline B adaptive optics beam combiner fringe tracker sideral motion delay line Zero OPD -> no delay lines Variable OPD -> variable delay lines Short (~20m) and fixed baseline Long and variable (30÷200m) proj. baseline Medium resolution ~20mas High resolution ~2mas 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 Intensity detector Large interf. image (up to 2 arcmin) OPD Single point (~ 100 mas) interferogram VLTI optical delay lines Fiber optic combiners for pupil-plane interferometers • Monomodal fibers and spectral dispersion prism integrated optics monomodal fibers detector Michelson (VLTI) 50mas 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) meas meas B sin( ) C OPD meas meas B C OPD reference star Shao et al. 1990 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 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 resolution (K band): down to 2mas, Airy disk 56mas FoV: 2 arcsec MIDI at 10mm, 56mas AMBER (H,K band) • VLTI: 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 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 LBT and VLTI: example #1 Extrasolar planets direct observation via nulling interferometry • requires very low background at 10mm, 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” @ 10mm 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 10marcsec narrow angle astrometry with differential phase VLTI is best tailored for such kind of observations LBT and VLTI: example #2 Investigating the inner regions of star forming disks • requires high resolution spectroscopy to get Brg 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 jet direction • 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 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