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Register a new userA quantitative comparison of amplitude versus intensity interferometry for astronomy
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Astronomical imaging can be broadly classified into two types. The first type is amplitude interferometry, which includes conventional optical telescopes and Very Large Baseline Interferometry (VLBI). The second type is intensity interferometry, which relies on Hanbury Brown and Twiss-type measurements. At optical frequencies, where direct phase measurements are impossible, amplitude interferometry has an effective numerical aperture that is limited by the distance from which photons can coherently interfere. Intensity interferometry, on the other hand, correlates only photon fluxes and can thus support much larger numerical apertures, but suffers from a reduced signal due to the low average photon number per mode in thermal light. It has hitherto not been clear which method is superior under realistic conditions. Here, we give a comparative analysis of the performance of amplitude and intensity interferometry, and we relate this to the fundamental resolution limit that can be achieved in any physical measurement. Using the benchmark problem of determining the separation between two distant thermal point sources, e.g., two adjacent stars, we give a short tutorial on optimal estimation theory and apply it to stellar interferometry. We find that for very small angular separations the large baseline achievable in intensity interferometry can more than compensate for the reduced signal strength. We also explore options for practical implementations of Very Large Baseline Intensity Interferometry (VLBII).
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Compact Galactic binary systems with orbital periods of a few hours are expected to be detected in gravitational waves (GW) by LISA or a similar mission. At present, these so-called verification binaries provide predictions for GW frequency and amplitude. A full polarisation prediction would provide a new method to calibrate LISA and other GW observatories, but requires resolving the orientation of the binary on the sky, which is not currently possible. We suggest a method to determine the elusive binary orientation and hence predict the GW polarisation, using km-scale optical intensity interferometry. The most promising candidate is CD-30$^{circ}$ 11223, consisting of a hot helium subdwarf with $m_B = 12$ and a much fainter white dwarf companion, in a nearly edge-on orbit with period 70.5 min. We estimate that the brighter star is tidally stretched by 6%. Resolving the tidal stretching would provide the binary orientation. The resolution needed is far beyond any current instrument, but not beyond current technology. We consider scenarios where an array of telescopes with km-scale baselines and/or the Very Large Telescope (VLT) and Extremely Large Telescope (ELT) are equipped with recently-developed kilo-pixel sub-ns single-photon counters and used for intensity interferometry. We estimate that a team-up of the VLT and ELT could measure the orientation to $pm 1^{circ}$ at 2$sigma$ confidence in 24 hours of observation.
Improved quantum sensing of photon wave-functions could provide high resolution observations in the optical benefiting numerous fields, including general relativity, dark matter studies, and cosmology. It has been recently proposed that stations in optical interferometers would not require a phase-stable optical link if instead sources of quantum-mechanically entangled pairs could be provided to them, potentially enabling hitherto prohibitively long baselines. A new refinement of this idea is developed, in which two photons from different sources are interfered at two separate and decoupled stations, requiring only a slow classical information link between them. We rigorously calculate the observables and contrast this new interferometric technique with the Hanbury Brown & Twiss intensity interferometry. We argue this technique could allow robust high-precision measurements of the relative astrometry of the two sources. A basic calculation suggests that angular precision on the order of 10 microarcsecond could be achieved in a single nights observation of two bright stars.
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.
In the last years we have operated two very similar ultrafast photon counting photometers (Iqueye and Aqueye+) on different telescopes. The absolute time accuracy in time tagging the detected photon with these instruments is of the order of 500 ps for hours of observation, allowing us to obtain, for example, the most accurate ever light curve in visible light of the optical pulsars. Recently we adapted the two photometers for working together on two telescopes at Asiago (Italy), for realizing an Hanbury-Brown and Twiss Intensity Interferometry like experiment with two 3.9 km distant telescopes. In this paper we report about the status of the activity and on the very preliminary results of our first attempt to measure the photon intensity correlation.
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