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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 IAB IAB= < (EA+EB)(EA+EB)*> = IA+IB+2√IAIB VAB cos φAB IAB = I0 (1 + VAB cos φAB) if IA = IB = I0/2 2 Principle of direct interferometry A B Visibility amplitude V(u,v) Visibility phase Φ(u,v) IAB IAB= < (EA+EB)(EA+EB)*> = IA+IB+2√IAIB VAB cos φAB IAB = I0 (1 + VAB cos φAB) if IA = IB = I0/2 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 Visibility Visibilities Projected baseline (m) Uniform disk Projected baseline (m) Projected baseline (m) Binary with unresolved components Binary with resolved component 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: Inorm(α, β) = ∫ V(u, v) e +i2π(uα + vβ) du dv 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 +i2π(uα + vβ) du dv = Bdirty(α, β) * Inorm(α, β) , where Bdirty(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 100 0 -200 2 7500K 1 0 -1 70 00 K -2 -300 300 200 100 0 -100 -200 -300 East (m) B High-Fidelity Image 2 1 0 1 0 -1 -2 East (milliarcseconds) 700 0K -1 -2 2 0K 750 -100 Altair Image Reconstruction North (milliarcseconds) CHARA UV Coverage 8000K North (m) 200 S2-W1 S2-W2 S2-E2 W1-W2 E2-W1 E2-W2 North (milliarcseconds) 300 Convolving Beam (0.64 mas) 2 1 0 -1 -2 East (milliarcseconds) the Fourier UV coverage for the Altair observations, where each point represents the Figure A) shows intensity (λ = 1.65µm) created with the MACIM/MEM one pair of CHARA telescopes (S2-E2-W1-W2) (31). The 2: dashed ellipse the shows the image of the surface of Altair 2 method ptical aperture of 265×195 meters oriented alongimaging a Position Angle using of 135a◦ uniform East of brightness elliptical prior (χν = 0.98). Typical photometric errors in the imag Image of the surface of Altair with CHARA/MIRC correspond to ±4% in intensity. B) shows the reconstructed image convolved with a Gaussian beam of 0.64 ma corresponding to the diffraction-limit of CHARA for these observations. For both panels, the specific intensitie at 1.65µm were converted into the corresponding blackbody temperatures and contours for 7000K, 7500K, an Monnier et al. (2007) 8000K are shown. North is up and East is left. 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: • • Bmax/Bmin, 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 θmax, sampling very much finer than Δu ∼1/θmax is unnecessary. •Field of view is limited by: - FOV of individual telescopes - Vignetting of optics - Coherence length. The interference condition OPD < λ2/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 × [Ndata]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 • • • Photon detection: photon noise, read-out noise, dark current, cosmetics Individual elements of infrastructure: displacements (tip-tilts, optical path, piston), vibrations, drifts 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 • longitudinal dispersion loss of throughput 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. 2 Sensitivity is proportional to NV in photon rich regime or NV • 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 Capella 1996 Betelgeuse Mizar 2004 Capella 2000 2007 2007 Θ1 0ri C 13 Promising results in other domains 0.0479 data 1.0 0.0431 0.0383 0.0335 10 0.5 0.0287 0 0.0 0.0 0.024 0.5 1.0 10+7 1.5 spatial frequencies 50 0.0192 data −10 0.0144 0.00958 −20 0.00479 0 20 10 0 −10 mira closure phase (deg) relative δ (milliarcseconds) 20 squared visibilities mira 0 −50 −20 relative α (milliarcseconds) −0.5 0.0 0.5 Hour angle Renard, Malbet, Thiébaut & Berger (SPIE 2008) Work in progress... 14 Depends on dust grains size and distribution Promising results in other domains If inclined disk: asymmetries (skewness) depending on dust characteristics Closure phase is a powerful observable to probe such asymmetries [Monnier et al. 2006] 0.0479 data 1.0 0.0431 0.0383 0.0335 10 0.5 0.0287 0 0.0 0.0 0.024 0.5 1.0 10+7 1.5 spatial frequencies 50 0.0192 data −10 0.0144 0.00958 −20 0.00479 0 20 10 0 −10 mira closure phase (deg) relative δ (milliarcseconds) 20 squared visibilities mira 0 −50 −20 relative α (milliarcseconds) −0.5 0.0 0.5 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