Intensity interferometry utilizes measurements of the squared-magnitude of the Fourier transform of an object using
relatively simple, phase-insensitive hardware, and therefore holds the promise of extremely high spatial resolution in
astronomy and various branches of physics. However, this promise has not been realized due to signal-noise-ratio
(SNR) issues and due to the maturity of image recovery algorithms. To recover an image, the phase of the Fourier
transform must be determined in addition to its magnitude. In a recent paper, relatively good one-dimensional (1-D)
image recoveries were obtained with a fast non-iterative algorithm utilizing the Cauchy-Riemann relations and a mild
constraint on the symmetry of the object. In this paper, the approach is extended to two spatial dimensions by
combining multiple 1-D reconstructions, and ensuring mutual consistency between 1-D slices. Mutual consistency is
enforced using several different approaches, including phase retrieval. This use of the Cauchy-Riemann approach
combined with imposition of mutual consistency is found to reduce noise sensitivity significantly. Three approaches are
evaluated for image quality for different objects using sparse Fourier-plane sampling, showing good reconstruction of
images at SNR's as low as 7 at the origin in the Fourier plane (and thus even lower SNR's at higher angular
Sub milli-arcsecond imaging in the visible band will provide a new perspective in stellar astrophysics. Even
though stellar intensity interferometry was abandoned more than 40 years ago, it is capable of imaging and
thus accomplishing more than the measurement of stellar diameters as was previously thought. Various phase
retrieval techniques can be used to reconstruct actual images provided a sufficient coverage of the interferometric
plane is available. Planned large arrays of Air Cherenkov telescopes will provide thousands of simultaneously
available baselines ranging from a few tens of meters to over a kilometer, thus making imaging possible with
unprecedented angular resolution. Here we investigate the imaging capabilities of arrays such as CTA or AGIS
used as Stellar Intensity Interferometry receivers. The study makes use of simulated data as could realistically
be obtained from these arrays. A Cauchy-Riemann based phase recovery allows the reconstruction of images
which can be compared to the pristine image for which the data were simulated. This is first done for uniform
disk stars with different radii and corresponding to various exposure times, and we find that the uncertainty
in reconstructing radii is a few percent after a few hours of exposure time. Finally, more complex images are
considered, showing that imaging at the sub-milli-arc-second scale is possible.
Kilometric-scale optical imagers seem feasible to realize by intensity interferometry, using telescopes primarily
erected for measuring Cherenkov light induced by gamma rays. Planned arrays envision 50-100 telescopes, distributed
over some 1-4 km2. Although array layouts and telescope sizes will primarily be chosen for gamma-ray
observations, also their interferometric performance may be optimized. Observations of stellar objects were numerically
simulated for different array geometries, yielding signal-to-noise ratios for different Fourier components
of the source images in the interferometric (u, v)-plane. Simulations were made for layouts actually proposed for
future Cherenkov telescope arrays, and for subsets with only a fraction of the telescopes. All large arrays provide
dense sampling of the (u, v)-plane due to the sheer number of telescopes, irrespective of their geographic orientation
or stellar coordinates. However, for improved coverage of the (u, v)-plane and a wider variety of baselines (enabling better image reconstruction), an exact east-west grid should be avoided for the numerous smaller telescopes, and repetitive geometric patterns avoided for the few large ones. Sparse arrays become severely limited by a lack of short baselines, and to cover astrophysically relevant dimensions between 0.1-3 milliarcseconds in visible wavelengths, baselines between pairs of telescopes should cover the whole interval 30-2000 m.
Experiments are in progress to prepare for intensity interferometry with arrays of air Cherenkov
telescopes. At the Bonneville Seabase site, near Salt Lake City, a testbed observatory has been set
up with two 3-m air Cherenkov telescopes on a 23-m baseline. Cameras are being constructed, with
control electronics for either off- or online analysis of the data. At the Lund Observatory (Sweden),
in Technion (Israel) and at the University of Utah (USA), laboratory intensity interferometers simulating stellar observations have been set up and experiments are in progress, using various analog and digital correlators, reaching 1.4 ns time resolution, to analyze signals from pairs of laboratory telescopes.
Intensity interferometry permits very long optical baselines and the observation of sub-milliarcsecond structures. Using
planned kilometric arrays of air Cherenkov telescopes at short wavelengths, intensity interferometry may increase the
spatial resolution achieved in optical astronomy by an order of magnitude, inviting detailed studies of the shapes of
rapidly rotating hot stars with structures in their circumstellar disks and winds, or mapping out patterns of nonradial
pulsations across stellar surfaces. Signal-to-noise in intensity interferometry favors high-temperature sources and
emission-line structures, and is independent of the optical passband, be it a single spectral line or the broad spectral
continuum. Prime candidate sources have been identified among classes of bright and hot stars. Observations are
simulated for telescope configurations envisioned for large Cherenkov facilities, synthesizing numerous optical baselines
in software, confirming that resolutions of tens of microarcseconds are feasible for numerous astrophysical targets.
Building on technological developments over the last 35 years, intensity interferometry now appears a feasible option by which to achieve diffraction-limited imaging over a square-kilometer synthetic aperture. Upcoming Atmospheric Cherenkov Telescope projects will consist of up to 100 telescopes, each with ~100m2 of light gathering area, and distributed over ~1km2. These large facilities will offer thousands of baselines from 50m to more than 1km and an unprecedented (u,v) plane coverage. The revival of interest in Intensity Interferometry has recently led to the formation of a IAU working group. Here we report on various ongoing efforts towards implementing modern Stellar Intensity Interferometry.
Much of the progress in astronomy follows imaging with improved resolution. In observing stars, current capabilities
are only marginal in beginning to image the disks of a few, although many stars will appear as surface objects for
baselines of hundreds of meters. Since atmospheric turbulence makes ground-based phase interferometry challenging
for such long baselines, kilometric space telescope clusters have been proposed for imaging stellar surface details. The
realization of such projects remains uncertain, but comparable imaging could be realized by ground-based intensity
interferometry. While insensitive to atmospheric turbulence and imperfections in telescope optics, the method requires
large flux collectors, such as being set up as arrays of atmospheric Cherenkov telescopes for studying energetic gamma
rays. High-speed detectors and digital signal handling enable very many baselines to be synthesized between pairs of
telescopes, while stars may be tracked across the sky by electronic time delays. First observations with digitally
combined optical instruments have now been made with pairs of 12-meter telescopes of the VERITAS array in Arizona.
Observing at short wavelengths adds no problems, and similar techniques on an extremely large telescope could achieve
diffraction-limited imaging down to the atmospheric cutoff, achieving a spatial resolution significantly superior by that
feasible by adaptive optics operating in the red or near-infrared.
The Very Energetic Radiation Imaging Telescope Array System (VERITAS) is an array of seven 10m aperture telescopes used for gamma-ray astronomy in the 50 GeV to 50 TeV (1 TeV= 1012 electron Volt) energy range. The gamma rays are detected by measuring the optical Cherenkov light emitted by the cascade of electromagnetic particles that is generated by interactions of the high energy gamma-ray with the Earth's Atmosphere. This paper describes the science goals of the VERITAS array, a description of the array, and expected performance of the instrument.