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Mass and radius measurements of stars are important inputs for models of stellar structure. Binary stars are of particular interest in this regard, because astrometry and spectroscopy of a binary together provide the masses of both stars as well as the distance to the system, while interferometry can both improve the astrometry and measure the radii of the stars. In this work we simulate parameter recovery from intensity interferometry, especially the challenge of disentangling the radii of two stars from their combined interferometric signal. Two approaches are considered: separation of the visibility contributions of each star with the help of differing brightness ratios at different wavelengths, and direct fitting of the intensity correlation to a multi-parameter model. Full image reconstructions is not attempted. Measurement of angular radii, angular separation and first-order limb-darkening appears readily achievable for bright binary stars with current instrumentation.
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The present articlereports on the first spatial intensity interferometry measurements on stars since the observations at Narrabri Observatory by Hanbury Brown et al. in the 1970s. Taking advantage of the progresses in recent years on photon-counting detectors and fast electronics, we were able to measure the zero-time delay intensity correlation $g^{(2)}(tau = 0, r)$ between the light collected by two 1-m optical telescopes separated by 15 m. Using two marginally resolved stars ($alpha$ Lyr and $beta$ Ori) with R magnitudes of 0.01 and 0.13 respectively, we demonstrate that 4-hour correlation exposures provide reliable visibilities, whilst a significant loss of contrast is found on alpha Aur, in agreement with its binary-star nature.
We report the first intensity correlation measured with star light since Hanbury Brown and Twiss historical experiments. The photon bunching $g^{(2)}(tau, r=0)$, obtained in the photon counting regime, was measured for 3 bright stars, $alpha$ Boo, $alpha$ CMi, and $beta$ Gem. The light was collected at the focal plane of a 1~m optical telescope, was transported by a multi-mode optical fiber, split into two avalanche photodiodes and digitally correlated in real-time. For total exposure times of a few hours, we obtained contrast values around $2times10^{-3}$, in agreement with the expectation for chaotic sources, given the optical and electronic bandwidths of our setup. Comparing our results with the measurement of Hanbury Brown et al. on $alpha$ CMi, we argue for the timely opportunity to extend our experiments to measuring the spatial correlation function over existing and/or foreseen arrays of optical telescopes diluted over several kilometers. This would enable $mu$as long-baseline interferometry in the optical, especially in the visible wavelengths with a limiting magnitude of 10.
With the current revival of interest in astronomical intensity interferometry, it is interesting to revisit the associated theory, which was developed in the 1950s and 1960s. This paper argues that intensity interferometry can be understood as an extension of Fraunhofer diffraction to incoherent light. Interference patterns are still produced, but they are speckle-like and transient, changing on a time scale of $1/Delta u$ (where $Delta u$ is the frequency bandwidth) known as the coherence time. Bright fringes average less than one photon per coherence time, hence fringes change before they can be observed. But very occasionally, two or even more photons may be detected from an interference pattern within a coherence time. These rare coincident photons provide information about the underlying transient interference pattern, and hence about the source brightness distribution. Thinking in terms of transient sub-photon interference patterns makes it easy to see why intensity interferometry will have large optical-path tolerance, and be immune to atmospheric seeing. The unusual signal-to-noise properties also become evident. We illustrate the unobservable but conceptually useful transient interference patterns, and their observable correlation signal, with three simulated examples: (i) an elongated source like Achernar, (ii) a three-star system like Algol, and (iii) a crescent source that roughly mimics an exoplanet transit or perhaps the M87 black hole environment. Of these, (i) and (ii) are good targets for currently-planned setups, while (iii) is interesting to think about for the longer term.
We propose a new approach, based on the Hanbury Brown and Twiss intensity interferometry, to transform a Cherenkov telescope to its equivalent optical telescope. We show that, based on the use of photonics components borrowed from quantum-optical applications, we can recover spatial details of the observed source down to the diffraction limit of the Cherenkov telescope, set by its diameter at the mean wavelength of observation. For this, we propose to apply aperture synthesis techniques from pairwise and triple correlation of sub-pupil intensities, in order to reconstruct the image of a celestial source from its Fourier moduli and phase information, despite atmospheric turbulence. We examine the sensitivity of the method, i.e. limiting magnitude, and its implementation on existing or future high energy arrays of Cherenkov telescopes. We show that despite its poor optical quality compared to extremely large optical telescopes under construction, a Cherenkov telescope can provide diffraction limited imaging of celestial sources, in particular at the visible, down to violet wavelengths.
Stellar Intensity Interferometry is a technique based on the measurement of the second order spatial correlation of the light emitted from a star. The physical information provided by these measurements is the angular size and structure of the emitting source. A worldwide effort is presently under way to implement stellar intensity interferometry on telescopes separated by long baselines and on future arrays of Cherenkov telescopes. We describe an experiment of this type, realized at the Asiago Observatory (Italy), in which we performed for the first time measurements of the correlation counting photon coincidences in post-processing by means of a single photon software correlator and exploiting entirely the quantum properties of the light emitted from a star. We successfully detected the temporal correlation of Vega at zero baseline and performed a measurement of the correlation on a projected baseline of $sim$2 km. The average discrete degree of coherence at zero baseline for Vega is $< g^{(2)} > , = 1.0034 pm 0.0008$, providing a detection with a signal-to-noise ratio $S/N gtrsim 4$. No correlation is detected over the km baseline. The measurements are consistent with the expected degree of spatial coherence for a source with the 3.3 mas angular diameter of Vega. The experience gained with the Asiago experiment will serve for future implementations of stellar intensity interferometry on long-baseline arrays of Cherenkov telescopes.
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