Stellar intensity interferometry in the photon-counting regime

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 underway 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 ∼2 km. The average discrete degree of coherence at zero baseline for Vega is $\lt g^{(2)} \gt \, = 1.0034 \pm 0.0008$, providing a detection with a signal-to-noise ratio S/N ≳ 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.

A modern implementation of a stellar intensity interferometry (SII) system on an array of large optical telescopes would be a highly valuable complement to the current generation of optical amplitude interferometers. The SII technique allows for observations at short optical wavelengths (U/B/V bands) with potentially dense (u,v) plane coverage. We describe a complete SII system that is used to measure the spatial coherence of a laboratory source which exhibits signal to noise ratios comparable to actual stellar sources. A novel analysis method, based on the correlation measurements between orthogonal polarization states, was developed to remove unwanted effects of spurious correlations. Our system is currently being tested in night sky observations at the StarBase Observatory (Grantsville, Utah) and will soon be ported to the VERITAS (Amado, AZ) telescopes. The system can readily be integrated with current optical telescopes at minimal cost. The work here serves as a technological pathfinder for implementing SII on the future Cherenkov Telescope Array.

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.

Intensity interferometry permits very long optical baselines and the\nobservation of sub-milliarcsecond structures. Using planned kilometric arrays\nof air Cherenkov telescopes at short wavelengths, intensity interferometry may\nincrease the spatial resolution achieved in optical astronomy by an order of\nmagnitude, inviting detailed studies of the shapes of rapidly rotating hot\nstars with structures in their circumstellar disks and winds, or mapping out\npatterns of nonradial pulsations across stellar surfaces. Signal-to-noise in\nintensity interferometry favors high-temperature sources and emission-line\nstructures, and is independent of the optical passband, be it a single spectral\nline or the broad spectral continuum. Prime candidate sources have been\nidentified among classes of bright and hot stars. Observations are simulated\nfor telescope configurations envisioned for large Cherenkov facilities,\nsynthesizing numerous optical baselines in software, confirming that\nresolutions of tens of microarcseconds are feasible for numerous astrophysical\ntargets.\n

A long-held astronomical vision is to realize diffraction-limited optical aperture synthesis over kilometer baselines. This will enable imaging of stellar surfaces and their environments, show their evolution over time, and reveal interactions of stellar winds and gas flows in binary star 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 used also for intensity interferometry. With no optical connection between the telescopes, the error budget is set by the electronic time resolution of a few nanoseconds. Corresponding light-travel distances are on the order of one meter, making the method practically insensitive to atmospheric turbulence or optical imperfections, permitting both very long baselines and observing at short optical wavelengths. Theoretical modeling has shown how stellar surface images can be retrieved from such observations and here we report on experimental simulations. In an optical laboratory, artificial stars (single and double, round and elliptic) are observed by an array of telescopes. Using high-speed photon-counting solid-state detectors and real-time electronics, intensity fluctuations are cross correlated between up to a hundred baselines between pairs of telescopes, producing maps of the second-order spatial coherence across the interferometric Fourier-transform plane. These experiments serve to verify the concepts and to optimize the instrumentation and observing procedures for future observations with (in particular) CTA, the Cherenkov Telescope Array, aiming at order-of-magnitude improvements of the angular resolution in optical astronomy.

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 (m_v~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.

Imaging air Cherenkov telescope (IACT) arrays have long been viewed as potential observatories for performing stellar intensity interferometry (SII). We present results and the current status of an ongoing SII campaign using the four 12 m diameter VERITAS telescopes located at the Fred Lawrence Whipple Observatory. Each of the telescopes have been equipped with SII instrumentation, consisting of a removable SII camera and a continuous high speed data acquisition system. The correlation of digitized starlight intensities is performed off-line using FPGA hardware to calculate the squared visibilities. The system enables high angular resolution measurements with baselines ranging from approximately 81.5 to 173 m in the B photometric band. Stellar angular diameter measurements were successfully performed using all four VERITAS telescopes. These results show that IACTs can operate as SII observatories, demonstrating a technological pathway for a similar system with future IACT observatories with a hundred fold increase in the number of simultaneous baselines.

The ASTRI Mini-Array is an International collaboration, led by the Italian National Institute for Astrophysics, that is constructing and operating an array of nine Imaging Atmospheric Cherenkov Telescopes to study gamma-ray sources at very high energy and perform optical stellar intensity interferometry (SII) observations. Angular resolutions below 100 microarcsec are achievable with stellar intensity interferometry, using telescopes separated by hundreds to thousands of meters baselines. At this level of resolution it turns out to be possible to reveal details on the surface and of the environment surrounding bright stars on the sky. The ASTRI Mini-Array will provide a suitable infrastructure for performing these measurements thanks to the capabilities offered by its 9 telescopes, which provide 36 simultaneous baselines over distances between 100 m and 700 m. After providing an overview of the scientific context and motivations for performing SII science with the ASTRI Mini-Array telescopes, we present the baseline design for the ASTRI Stellar Intensity Interferometry Instrument, a fast single photon counting instrument that will be mounted on the ASTRI telescopes and dedicated to performing SII observations of bright stars.

Intensity interferometry (II) offers a powerful means to observe stellar objects with a high resolution. In this work, we demonstrate that II can also probe internal stellar kinematics by revealing a time-asymmetric Hanbury Brown and Twiss (HBT) effect, causing a measurable shift in the temporal correlation peak away from zero delay. We develop numerical models to simulate this effect for two distinct astrophysical scenarios: an emission-line circumstellar disk and an absorption-line binary system. Our simulations reveal a clear sensitivity of this temporal asymmetry to the system’s inclination angle, velocity symmetry, and internal dynamics. This suggests that, with sufficiently high time resolution, II can be used to extract quantitative information about internal kinematics, offering a new observational window on stellar dynamics.

This year marks the 50th anniversary since the first scientific measurements were produced with the Narrabri Stellar Intensity Interferometer, which was constructed in the early 1960’s by Robert Hanbury Brown and Richard Twiss. A collaboration between the Universities of Sydney and Manchester, the interferometer was the culmination of a series of experiments which pioneered the technique of intensity interferometry. The immediate controversy surrounding the quantum implications of the technique enveloped some of the most eminent physicists of the day, sparking a debate about nonlocal effects and optical coherence. A full explanation of the workings of the intensity interferometer in a quantum context was finally put forward by Roy Glauber, ultimately earning him the 2005 Nobel Prize in Physics. The intensity interferometer rekindled the field of high resolution stellar imaging, which had been extinguished for a half century (following the failure of Pease’s 50-foot beam on Mt Wilson), while delivering the first ever measurements of the sizes of normal stars – establishing an effective temperature scaling relationship which has underpinned stellar astronomy for 50 years. This directly paved the way for the next generation of Michelson Stellar Interferometers. Intensity interferometry itself has found application in several fields (notably particle physics), and plans are in active development for modern reprises within stellar interferometry. However undoubtedly the greatest legacy lies in the Hanbury Brown Twiss (HBT) effect being the foundational experiment for what is now known as Quantum Optics – a field which underpins a huge sector of the technology which enables our modern world. This invited review discuses the development of the interferometer, including the controversy that its underlying principles generated within the contemporary physics community. The core scientific output generated by the instrument is presented, together with the impact of the device upon the subsequent course of stellar astrophysics and its role in resurrecting stellar optical interferometery.

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.

We use the stellar intensity interferometry system implemented with the Very Energetic Radiation Imaging Telescope Array System at Fred Lawrence Whipple Observatory as a light collector to obtain measurements of the rapid rotator star γ Cassiopeiae, at a wavelength of 416 nm. Using data from baselines sampling different position angles, we extract the size, oblateness, and projected orientation of the photosphere. Fitting the data with a uniform ellipse model yields a minor-axis angular diameter of 0.43 ± 0.02 mas, a major-to-minor-radius ratio of 1.28 ± 0.04, and a position angle of 116° ± 5° for the axis of rotation. A rapidly rotating stellar atmosphere model that includes limb and gravity darkening describes the data well with a fitted angular diameter of 0.60 4 − 0.034 + 0.041 mas corresponding to an equatorial radius of 10 . 9 − 0.6 + 0.8 R ⊙ , a rotational velocity with a 1 σ lower limit at 97.7% of breakup velocity, and a position angle of 114 . ° 7 − 5.7 + 6.4 . These parameters are consistent with H α line spectroscopy and infrared-wavelength Michelson interferometric measurements of the star’s decretion disk. This is the first measurement of an oblate photosphere using intensity interferometry.

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.

Recent proposals have been advanced to apply imaging air Cherenkov telescope\narrays to stellar intensity interferometry (SII). Of particular interest is the\npossibility of model-independent image recovery afforded by the good (u,\nv)-plane coverage of these arrays, as well as recent developments in phase\nretrieval techniques. The capabilities of these instruments used as SII\nreceivers have already been explored for simple stellar objects, and here the\nfocus is on reconstructing stellar images with non-uniform radiance\ndistributions. We find that hot stars (T > 6000 K) containing hot and/or cool\nlocalized regions (T \\sim 500 K) as small as \\sim 0.1 mas can be imaged at\nshort wavelengths ({\\lambda} = 400 nm).\n

Beginning in Fall 2018, the VERITAS high energy gamma-ray observatory (Amado, AZ) was upgraded to enable Stellar Intensity Interferometry (SII) observations during bright moon conditions. The system potentially allows VERITAS to spatially characterize stellar objects at visible wavelengths with sub milliarcsecond angular resolution. This research project was on the construction of a high voltage power supply for the photomultiplier tubes (PMTs) used in the SII camera. The high voltage supply was designed to be electrically isolated from all other electronics (except for the PMT) to reduce noise pickup. The HV supply operates on a Li-Ion battery, and the high voltage level is remotely programmed using a pulse width modulation (PWM) signal that is generated by an Arduino Yun microcontroller and distributed through a fiber optic cable. The electrical isolation of the fiber optic control system suppresses the pickup of radio frequency interference through ground loops. A separate fiber optic transceiver pair is used for the on-off control of the high voltage power supply. Tests were performed that show the high voltage level is reproducible to within one volt for a given duty cycle of the PWM signal. Furthermore, the high voltage output level was shown to be stable with respect to variations in the input battery voltage used to power the high voltage supply. The high voltage system is currently being used in regular SII observations at VERITAS. This poster will describe the detailed design and performance of the system.