From direct interferometry imaging to intensity interferometry - PowerPoint PPT Presentation

From direct interferometry imaging to intensity interferometry imaging F. Malbet CNRS/Caltech Workshop on Stellar Intensity Interferometry 29-30 January 2009 - Salt Lake City

Principle of direct interferometry A B I AB I AB = < ( E A +E B ) ( E A +E B ) *> = I A + I B +2 √ I A I B V AB cos φ AB 2 I AB = I 0 (1 + V AB cos φ AB ) if I A = I B = I 0 /2

Principle of direct interferometry Visibility A B amplitude V(u,v) Visibility phase Φ (u,v) I AB I AB = < ( E A +E B ) ( E A +E B ) *> = I A + I B +2 √ I A I B V AB cos φ AB 2 I AB = I 0 (1 + V AB cos φ AB ) if I A = I B = I 0 /2

Spatial coherence • Each unresolved element of the image produces its own fringe pattern. • These elements have unit visibility and a phase corresponding to the location of the element in the sky. • The observed fringe pattern from a distributed source is the intensity superposition of these individual fringe pattern. • This relies upon the individual elements of the source being “spatially incoherent”. • The resulting fringe pattern has a modulation depth that is reduced with respect to that from each source individually, called object visibility • The positions of the sources are encoded in the resulting fringe phase. Visibility = Fourier transform of the brightness spatial distribution Haniff (Goutelas, 2006) Zernicke-van Cittert theorem 3

Visibilities Visibility Projected baseline (m) Projected baseline (m) Projected baseline (m) Binary with resolved Binary with unresolved Uniform disk component components For a resolved source, given a simple model (uniform disk, Gaussian, ring,...), there is a univoque relationship between a visibility amplitude and a size. However this size is very dependent on the input model 4

Imaging process We start with the fundamental relationship between the visibility function and the normalized sky brightness: I norm ( α , β ) = ∫ V ( u, v ) e +i2 π ( u α + v β ) d u d v In practice what we measure is a sampled version of V ( u, v ), so the image we have access to is to the so-called “dirty map”: I ( α , β ) = ∫ S ( u, v ) V ( u, v ) e +i2 π ( u α + v β ) d u d v = B dirty ( α , β ) * I norm ( α , β ) , where B dirty ( α , β ) is the Fourier transform of the sampling distribution, or dirty-beam. The dirty-beam is the interferometer PSF. While it is generally far less attractive than an Airy pattern, it’s shape is completely determined by the samples of the visibility function that are measured. 5

Actual image reconstruction A B Altair Image Reconstruction High-Fidelity Image S2-W1 CHARA UV Coverage 300 S2-W2 S2-E2 W1-W2 E2-W1 200 2 2 E2-W2 North (milliarcseconds) North (milliarcseconds) 7500K 100 North (m) 1 1 8000K 0 0 0 7500K -100 -1 -1 7000K 7 0 0 -200 0 K -2 -2 Convolving -300 Beam (0.64 mas) 300 200 100 0 -100 -200 -300 2 1 0 -1 -2 2 1 0 -1 -2 East (m) East (milliarcseconds) East (milliarcseconds) Image of the surface of Altair with CHARA/MIRC Monnier et al. (2007) 6

Imaging issues independent of interferometric process • UV sampling, i.e. the number of visibility data ≥ number of filled pixels in the recovered image: N(N-1)/2 × number of reconfigurations ≥ number of filled pixels. • UV coverage , i.e. the distribution of samples, should be as uniform as possible: • The range of interferometer baselines : • B max /B min , will govern the range of spatial scales in the map. • No need to sample the visibility function too finely: for a source of maximum extent θ max , sampling very much finer than Δ u ∼ 1/ θ max is unnecessary. • Field of view is limited by: - FOV of individual telescopes - Vignetting of optics - Coherence length. The interference condition OPD < λ 2/ Δλ must be satisfied for all field angles. Generally ⇒ FOV ≤ [ λ /B][ λ / Δλ ]. • Dynamic range : the ratio of maximum intensity to the weakest believable intensity in the image. Several × 100:1 is usual. DR ∼ [ S/N ] per-datum × [ N data ] 1/2 • Fidelity : Difficult to quantify, but clearly dependent on the completeness of the Fourier plane sampling 7

Practical issues - What is in the black box ? telescopes, optical train, delay lines, optical switches, fibers, detectors... - Combining directly the photons is challenging in particular at optical wavelength - Instantaneous variables are integrated over time, over wavelength, over spatial frequencies - Main sources of perturbations: • Atmosphere: spatial and temporal fluctuations of wavefront • Individual elements of infrastructure: displacements (tip-tilts, optical path, piston), vibrations, drifts • Photon detection: photon noise, read-out noise, dark current, cosmetics • Polarization: light is naturally polarized • Human action 8

The telescopes

The delay lines

The instrument

Issues specific to direct interferometry • Atmosphere disturbance due to the fluctuations of the refractive index n ( P , T , λ ) • transverse atmospheric refraction ⇒ loss of throughput • longitudinal dispersion ⇒ loss of system visibility in broad band operation • wavefront corrugation ⇒ loss of throughput or visibility, need to operate fast enough to freeze the turbulence • piston ⇒ need to operate fast enough to freeze the fringes • All these effects reduce the performance and sensitivity of interferometers. • Sensitivity is proportional to NV in photon rich regime or NV 2 in photon starved regime. 10

How to overcome atmospheric perturbations? - Atmospheric dispersion compensator (ADC): - Made of pair of prisms to control the spectral dispersion - Beam stabilization (wavefront sensor + actuator): - Tip-tilt correction → angle tracker - Adaptive optics: requires a deformable mirror - Reducing the pupil size - Fringe tracking : - fringe sensor to act on delay line actuator - Spatial filtering : - pinhole or single mode fiber - photometric calibration - Detectors : - low read-out noise detectors, ideally photo counting ones. 11

But new subsystems can introduce new pertubations - When complexity increases, number of sources of perturbations too! - Reliability becomes also an issue when the number of subsystems increases (e.g. VLTI) - Collectors : guiding, active optics - Beam routing: 32 motors - Adaptive optics: wavefront sensors, deformable mirrors, real-time control, configuration - Delay lines : carriage trajectory, 3 translation stages, metrology, switches, - Beam stabilisation : variable curvature mirrors, image and pupil sensors (ARAL/IRIS), sources (LEONARDO) - Fringe tracking: fringe search, group delay, phase tracking, locks - Beam combination : spectral resolution, spatial filtering, atmospheric dispersion, polarization, detection - Control software : 60 computers, 750000 lines of code as for 2004 12

a few results 1996 1996 2000 Capella Betelgeuse Mizar 2004 2007 Θ 1 0ri C Capella 2007 13

Promising results in other domains 0.0479 data 1.0 mira squared visibilities 0.0431 20 relative δ (milliarcseconds) 0.0383 0.5 0.0335 10 0.0287 0.0 0.0 0.5 1.0 1.5 10 +7 0 0.024 spatial frequencies 50 0.0192 data − 10 0.0144 mira closure phase (deg) 0 0.00958 − 20 0.00479 − 50 0 20 10 0 − 10 − 20 − 0.5 0.0 0.5 relative α (milliarcseconds) Hour angle Renard, Malbet, Thiébaut & Berger (SPIE 2008) Work in progress... 14

Promising results in other domains 0.0479 data 1.0 mira squared visibilities 0.0431 20 relative δ (milliarcseconds) 0.0383 0.5 0.0335 10 0.0287 0.0 0.0 0.5 1.0 1.5 10 +7 0 0.024 spatial frequencies 50 0.0192 data − 10 0.0144 mira closure phase (deg) 0 0.00958 − 20 0.00479 − 50 0 20 10 0 − 10 − 20 − 0.5 0.0 0.5 relative α (milliarcseconds) Hour angle Renard, Malbet, Thiébaut & Berger (SPIE 2008) Work in progress... 14

Intensity interferometry prospects? • Phase : can it be measured? • UV coverage : number of telescopes and baselines? • operation : imnune to atmosphere effects? • astrophysical topics : different phenomena? • wavelength of operation: visible, UV, X-ray? • spectral resolution : for free? • sensitivity : gain compared to Hanbury Brown & Twiss interferometer ? Interest in Intensity Interferometry is driven by the imaging capabilities. 15