Paul D. Nuñez

Optical Intensity Interferometry with the Cherenkov Telescope Array

With its unprecedented light-collecting area for night-sky observations, the Cherenkov Telescope Array (CTA) holds great potential for also optical stellar astronomy, in particular as a multi-element intensity interferometer for realizing imaging with sub-milliarcsecond angular resolution. Such an order-of-magnitude increase of the spatial resolution achieved in optical astronomy will reveal the surfaces of rotationally flattened stars with structures in their circumstellar disks and winds, or the gas flows between close binaries. Image reconstruction is feasible from the second-order coherence of light, measured as the temporal correlations of arrival times between photons recorded in different telescopes. This technique (once pioneered by Hanbury Brown and Twiss) connects telescopes only with electronic signals and is practically insensitive to atmospheric turbulence and to imperfections in telescope optics. Detector and telescope requirements are very similar to those for imaging air Cherenkov observatories, the main difference being the signal processing (calculating cross correlations between single camera pixels in pairs of telescopes). Observations of brighter stars are not limited by sky brightness, permitting efficient CTA use during also bright-Moon periods. While other concepts have been proposed to realize kilometer-scale optical interferometers of conventional amplitude (phase-) type, both in space and on the ground, their complexity places them much further into the future than CTA, which thus could become the first kilometer-scale optical imager in astronomy.

High angular resolution imaging with stellar intensity interferometry using air Cherenkov telescope arrays

Optical stellar intensity interferometry with air Cherenkov telescope arrays, composed of nearly 100 telescopes, will provide means to measure fundamental stellar parameters and also open the possibility of model-independent imaging. In addition to sensitivity issues, a main limitation of image recovery in intensity interferometry is the loss of phase of the complex degree of coherence during the measurement process. Nevertheless, several model-independent phase reconstruction techniques have been developed. Here we implement a Cauchy-Riemann based algorithm to recover images from simulated data. For bright stars (mv � 6) and exposure times of a few hours, we find that scale features such as diameters, oblateness and overall shapes are reconstructed with uncertainties of a few percent. More complex images are also well reconstructed with high degrees of correlation with the pristine image. Results are further improved by using a forward algorithm.

Stellar intensity interferometry: Experimental steps toward long-baseline observations

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.

Stellar Intensity Interferometry: Prospects for sub-milliarcsecond optical imaging

Using 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, enabling images of rapidly rotating hot stars with structures in their circumstellar disks and winds, or mapping out patterns of nonradial pulsations across stellar surfaces. Intensity interferometry (once pioneered by Hanbury Brown and Twiss) connects telescopes only electronically, and is practically insensitive to atmospheric turbulence and optical imperfections, permitting observations over long baselines and through large air-masses, also at short optical wavelengths. The required large telescopes (similar to 10 m) with very fast detectors (similar to ns) are becoming available as the arrays primarily erected to measure Cherenkov light emitted in air by particle cascades initiated by energetic gamma rays. Planned facilities (e.g., CTA, Cherenkov Telescope Array) envision many tens of telescopes distributed over a few square km. Digital signal handling enables very many baselines (from tens of meters to over a kilometer) to be simultaneously synthesized between many pairs of telescopes, while stars may be tracked across the sky with electronic time delays, in effect synthesizing an optical interferometer in software. Simulated observations indicate limiting magnitudes around m(v) = 8, reaching angular resolutions similar to 30 mu arcsec in the violet. The signal-to-noise ratio 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. Intensity interferometry directly provides the modulus (but not phase) of any spatial frequency component of the source image; for this reason a full image reconstruction requires phase retrieval techniques. This is feasible if sufficient coverage of the interferometric (u, v)-plane is available, as was verified through numerical simulations. Laboratory and field experiments are in progress; test telescopes have been erected, intensity interferometry has been achieved in the laboratory, and first full-scale tests of connecting large Cherenkov telescopes have been carried out. This paper reviews this interferometric method in view of the new possibilities offered by arrays of air Cherenkov telescopes, and outlines observational programs that should become realistic already in the rather near future

Monte Carlo simulation of stellar intensity interferometry

Stellar intensity interferometers will achieve stellar imaging with a tenth of a milli- arcsecond resolution in the optical band by taking advantage of the large light collect- ing area and broad range of inter-telescope distances offered by future gamma-ray Air Cherenkov Telescope (ACT) arrays. Up to now, studies characterizing the capabilities of intensity interferometers using ACTs have not accounted for realistic effects such as telescope mirror extension, detailed photodetector time response, excess noise, and night sky contamination. In this paper, we present the semi-classical quantum optics Monte-Carlo simulation we developed in order to investigate these experimental limi- tations. In order to validate the simulation algorithm, we compare our first results to models for sensitivity and signal degradation resulting from mirror extension, pulse shape, detector excess noise, and night sky contamination.

Optical aperture synthesis with electronically connected telescopes.

Highest resolution imaging in astronomy is achieved by interferometry, connecting telescopes over increasingly longer distances and at successively shorter wavelengths. Here, we present the first diffraction-limited images in visual light, produced by an array of independent optical telescopes, connected electronically only, with no optical links between them. With an array of small telescopes, second-order optical coherence of the sources is measured through intensity interferometry over 180 baselines between pairs of telescopes, and two-dimensional images reconstructed. The technique aims at diffraction-limited optical aperture synthesis over kilometre-long baselines to reach resolutions showing details on stellar surfaces and perhaps even the silhouettes of transiting exoplanets. Intensity interferometry circumvents problems of atmospheric turbulence that constrain ordinary interferometry. Since the electronic signal can be copied, many baselines can be built up between dispersed telescopes, and over long distances. Using arrays of air Cherenkov telescopes, this should enable the optical equivalent of interferometric arrays currently operating at radio wavelengths.

Stellar intensity interferometry: Optimizing air Cherenkov telescope array layouts

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.

Two-dimensional image recovery in intensity interferometry using the Cauchy-Riemann relations

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 SNRs as low as 7 at the origin in the Fourier plane (and thus even lower SNRs at higher angular frequencies).

Toward a revival of stellar intensity interferometry

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.

Long-baseline optical intensity interferometry - Laboratory demonstration of diffraction-limited imaging

A long-held vision has been to realize diffraction-limited optical aperture synthesis over kilometer baselines. This will enable imaging of stellar surfaces and their environments, and reveal interacting gas flows in binary systems. An opportunity is now opening up with the large telescope arrays primarily erected for measuring Cherenkov light in air induced by gamma rays. With suitable software, such telescopes could be electronically connected and also used for intensity interferometry. Second-order spatial coherence of light is obtained by cross correlating intensity fluctuations measured in different pairs of telescopes. With no optical links between them, the error budget is set by the electronic time resolution of a few nanoseconds. Corresponding light-travel distances are approximately one meter, making the method practically immune to atmospheric turbulence or optical imperfections, permitting both very long baselines and observing at short optical wavelengths. Previous theoretical modeling has shown that full images should be possible to retrieve from observations with such telescope arrays. This project aims at verifying diffraction-limited imaging experimentally with groups of detached and independent optical telescopes. In a large optics laboratory, artificial stars were observed by an array of small telescopes. Using high-speed photon-counting solid-state detectors, intensity fluctuations were cross-correlated over up to 180 baselines between pairs of telescopes, producing coherence maps across the interferometric Fourier-transform plane. These measurements were used to extract parameters about the simulated stars, and to reconstruct their two-dimensional images. As far as we are aware, these are the first diffraction-limited images obtained from an optical array only linked by electronic software, with no optical connections between the telescopes.