Most observational techniques in astronomy can be understood as exploiting the various forms of the first-order correlation function g^(1). As however demonstrated by the Narrabri Stellar Intensity Interferometer back in the 1960's by Hanbury Brown & Twiss, and which is the first experiment to measure the second-order correlation function g^(2), light can carry more information than simply its intensity, spectrum and polarization. Since this experiment, theoretical and laboratory studies of non-classical properties of light have become a very active field of research, namely quantum optics. Despite the variety of results in this field, astrophysics remained focused essentially on first-order coherence. In this paper, we study the possibility that quantum properties of light could be observed in cosmic sources. We provide the basic mathematical ingredients about the first and the second order correlation functions, applied to the modern context of astronomical observations. The exploitation of g^(2) is certainly richer than what a modern intensity interferometer could bring and is particularly interesting for sources of non-thermal light. We conclude by briefly presenting why microquasars in our galaxy and their extragalactic parents can represent an excellent first target in the optical/near-infrared where to observe non-thermal light, and test the use of g^(2) in astrophysical sources.
More than sixty years after the first intensity correlation experiments by Hanbury Brown and Twiss, there is renewed interest for intensity interferometry techniques for high angular resolution studies of celestial sources. We report on a successful attempt to measure the bunching peak in the intensity correlation function for bright stellar sources with 1 meter telescopes (I2C project). We propose further improvements of our preliminary experiments of spatial interferometry between two 1 m telescopes, and discuss the possibility to export our method to existing large arrays of 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 emissio…
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 v…
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 1970's. 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 $g^{(2)}(τ= 0, r)$ between the light collected by two 1-m optical telescopes separated by 15 m. Using two marginally resolved stars ($α$ Lyr and $β$ Ori) with R magnitudes of 0.01 and 0.13 respectively, we demonstrate that 4-hour correlation exposures…
Recent advances in photonics have revived the interest in intensity interferometry for astronomical applications. The success of amplitude interferometry in the early 1970s, which is now mature and producing spectacular astrophysical results (e.g. GRAVITY, MATISSE, CHARA, etc.), coupled with the limited sensitivity of intensity interferometry stalled any progress on this technique for the past 50 years. However, the precise control of the optical path difference in amplitude interferometry is constraining for very long baselines and at shorter wavelengths. Polarization measurements are also ch…
A novel interferometric technique that uses the spectrum of the current fluctuations of a quadratic detector, a type of detector commonly used in Astronomy, has recently been introduced. It has major advantages with respect to classical interferometry. It can be used to observe gravitational lenses that cannot be detected with standard techniques. It can be used to carry out very long baseline interferometry. Although the original theoretical analysis, that uses wave interaction effects, is rigorous, it is not easy to understand. The present article therefore carries out a simpler analysis, us…
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 di…
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…
Recent dynamical studies indicate that the possibility of an Earth-like planet around $α\;$Cen A or B should be taken seriously. Such a planet, if it exists, would perturb the orbital astrometry by $<10 \ μ\rm as$, which is $10^{-6}$ of the separation between the two stars. We assess the feasibility of detecting such perturbations using ground-based intensity interferometry. We simulate a dedicated setup consisting of four 40-cm telescopes equipped with photon counters and correlators with time resolution $0.1\,\rm ns$, and a sort of matched filter implemented through an aperture mask. The ast…
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 $1/Δν$ (where $Δν$ 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 obser…
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 o…
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 th…
ESO White Paper on Intensity Interferometry: Cosmology, Fundamental Physics, Quantum Optics
Université Côte d’Azur（蔚蓝海岸大学）；CNRS（法国国家科学研究中心）；Institut de Physique de Nice（尼斯物理研究所）；Observatoire de la Côte d’Azur（蔚蓝海岸天文台）；Laboratoire Lagrange（拉格朗日实验室）；Université Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；IPAG（天体物理学与行星学研究所）；Czech Technical University in Prague（布拉格捷克理工大学）；Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所）；Lund Observatory（隆德天文台）；Lund University（隆德大学）；Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡大学）；University of Zurich（苏黎世大学）；University of Geneva（日内瓦大学）；Observatorió Nacional / MCTI（巴西国家天文台/科技部）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；New York University（纽约大学）；Flatiron Institute（平顿研究所）；University of Washington（华盛顿大学）；Stanford University（斯坦福大学）；Perimeter Institute for Theoretical Physics（理论物理珀米特研究所）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Most neighboring stars are still detected as point sources and are beyond the angular resolution reach of current observatories. Methods to improve our understanding of stars at high angular resolution are investigated. Air Cherenkov telescopes (ACTs), primarily used for Gamma-ray astronomy, enable us to increase our understanding of the circumstellar environment of a particular system. When used as optical intensity interferometers, future ACT arrays will allow us to detect stars as extended objects and image their surfaces at high angular resolution. Optical stellar intensity interferometry …
The original intensity interferometers were instruments built in the 1950s and 60s by Hanbury Brown and collaborators, achieving milli-arcsec resolutions in visible light without optical-quality mirrors. They exploited a then-novel physical effect, now known as HBT correlation after the experiments of Hanbury Brown and Twiss, and nowadays considered fundamental in quantum optics. Now a new generation of inten- sity interferometers is being designed, raising the possibility of measuring intensity correlations with three or more detectors. Quantum optics predicts some interesting features in hig…
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 celest…
Conventional ground-based astronomical observations suffer from image distortion due to atmospheric turbulence. This can be minimized by choosing suitable geographic locations or adaptive optical techniques, and avoided altogether by using orbital platforms outside the atmosphere. One of the promises of optical intensity interferometry is its independence from atmospherically induced phase fluctuations. By performing narrowband spectral filtering on sunlight and conducting temporal intensity interferometry using actively quenched avalanche photon detectors (APDs), the Solar $g^{(2)}(τ)$ signat…
Intensity interferometry, based on the Hanbury Brown-Twiss effect, is a simple and inexpensive method for optical interferometry at microarcsecond angular resolutions; its use in astronomy was abandoned in the 1970s because of low sensitivity. Motivated by recent technical developments, we argue that the sensitivity of large modern intensity interferometers can be improved by factors up to approximately 25,000, corresponding to 11 photometric magnitudes, compared to the pioneering Narrabri Stellar Interferometer. This is made possible by (i) using avalanche photodiodes (APD) as light detectors…
High resolution imaging is achieved using increasingly larger apertures and successively shorter wavelengths. Optical aperture synthesis is an important high-resolution imaging technology used in astronomy. Conventional long baseline amplitude interferometry is susceptible to uncontrollable phase fluctuations, and the technical difficulty increases rapidly as the wavelength decreases. The intensity interferometry inspired by HBT experiment is essentially insensitive to phase fluctuations, but suffers from a narrow spectral bandwidth which results in a lack of detection sensitivity. In this stu…
We provide a quantitative theory of discrimination between objects with the same color temperature but having different angular spectrum by intensity interferometry. The two-point correlation function of the black body image with extended angular spectrum has significant differences with a correlation function of a black body with a narrow angular spectrum.
We report on observations of the extended environment of the bright Be star $γ$-Cas performed using intensity interferometry measurements within its H$α$ emission line. These observations were performed using a modified version of the I2C intensity interferometry instrument installed onto the 1.54 meter MéO optical metrology telescope and a portable 1-meter telescope (T1M). In order to better constrain the extent of the H$α$ envelope, observations were performed for two different positions of the T1M telescope, corresponding to an intermediate and long baselines in which the extended region wa…
Imaging Atmospheric Cherenkov Telescopes (IACTs) currently in operation feature large mirrors and order of 1 ns time response to signals of a few photo-electrons produced by optical photons. This means that they are ideally suited for optical interferometry observations. Thanks to their sensitivity to visible wavelengths and long baselines optical intensity interferometry with IACTs allows reaching angular resolutions of tens to microarcsec. We have installed a simple optical setup on top of the cameras of the two 17 m diameter MAGIC IACTs and observed coherent fluctuations in the photon inten…
We analyze an intensity interferometry measurement carried out with two point-like detectors facing a distant source (e.g., a star) that may be partially occluded by an absorptive object (e.g., a planet). Such a measurement, based on the perturbation of the observed covariance function due to the object's presence, can provide information of the object complementary to a direct optical intensity measurement. In particular, one can infer the orientation of the object's transient trajectory. We identify the key parameters that impact this perturbation and show that its magnitude is equal to the …
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 da…
Radial Pulsations in Polaris: A Secondary Science Application of Cherenkov Telescopes via Intensity Interferometry
Indian Institute of Science Education and Research Thiruvananthapuram（印度科学教育研究所特里凡得琅分校）；Aryabhatta Research Institute of Observational Sciences（阿亚帕塔观测科学研究机构）；University of Zurich（苏黎世大学）；Centurion University of Technology and Management（世纪科技与管理大学）；Inter-University Centre for Astronomy and Astrophysics（大学间天文学与天体物理学中心）
Astrometry is a powerful technique in astrophysics to measure three-dimensional positions of stars and other astrophysical objects, including exoplanets and the gravitational influence they have on each other. Interferometric astrometry is presented here as just one in a suite of powerful astrometric techniques, which include space-based, seeing-limited and wide-angle adaptive optics techniques. Fundamental limits are discussed, demonstrating that even ground-based techniques have the capability for astrometry at the single micro-arcsecond level, should sufficiently sophisticated instrumentati…
The VERITAS Imaging Air Cherenkov Telescope (IACT) array was augmented in 2019 with high-speed focal plane electronics to allow its use for Stellar Intensity Interferometry (SII) observations. Since January 2019, the VERITAS Stellar Interferometer (VSII) recorded more than 250 hours of moonlit observations on 39 different bright stars and binary systems ($m_V < 3.74$) at an effective optical wavelength of 416 nm. These observations resulted in the measurement of the diameters of several stars with better than 5% resolution. This talk will describe the status of the VSII survey and analysis.
We present the current status of the I2C stellar intensity interferometer used towards high angular resolution observations of stars in visible wavelengths. In these proceedings, we present recent technical improvements to the instrument, and share results from ongoing campaigns using arrays of small diameter optical telescopes. A tip-tilt adaptive optics unit was integrated into the optical system to stabilize light injection into an optical fiber. The setup was successfully tested with several facilities on the Calern Plateau site of the Observatoire de la Côte d'Azur. These include one of t…
The VERITAS Imaging Air Cherenkov Telescope array (IACT) was augmented in 2019 with high-speed focal plane electronics to allow the use of VERITAS for Stellar Intensity Interferometry (SII) observations. Since that time, several improvements have been implemented to increase the sensitivity of the VERITAS Stellar Intensity Interferometer (VSII) and increase the speed of nightly data processing. This poster will describe the use of IACT arrays for performing ultra-high resolution (sub-milliarcsecond) astronomical observations at short visible wavelengths. The poster presentation will include a …
Stellar intensity interferometers correlate photons within their coherence time and could overcome the baseline limitations of existing amplitude interferometers. Intensity interferometers do not rely on phase coherence of the optical elements and thus function without high grade optics and light combining delay lines. However, the coherence time of starlight observed with realistic optical filter bandwidths (> 0.1 nm) is usually much smaller than the time resolution of the detection system (> 10 ps), resulting in a greatly reduced correlation signal. Reaching high signal to noise in a reasona…
Recent proposals have been advanced to apply imaging air Cherenkov telescope arrays to stellar intensity interferometry (SII). Of particular interest is the possibility of model-independent image recovery afforded by the good (u, v)-plane coverage of these arrays, as well as recent developments in phase retrieval techniques. The capabilities of these instruments used as SII receivers have already been explored for simple stellar objects, and here the focus is on reconstructing stellar images with non-uniform radiance distributions. We find that hot stars (T > 6000 K) containing hot and/or cool…
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 km$^2$. 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 interfero…
Context: Some stellar objects exhibit very narrow spectral lines in the visible range additional to their blackbody radiation. Natural lasing has been suggested as a mechanism to explain narrow lines in Wolf-Rayet stars. However, the spectral resolution of conventional astronomical spectrographs is still about two orders of magnitude too low to test this hypothesis. Aims: We want to resolve the linewidth of narrow spectral emissions in starlight. Methods: A combination of spectral filtering with single-photon-level temporal correlation measurements breaks the resolution limit of wavelength-dis…
This article presents a novel type of very long baseline astronomical interferometer that uses the fluctuations, as a function of time, of the intensity measured by a quadratic detector, which is a common type of astronomical detector. The theory on which the technique is based is validated by laboratory experiments. Its outstanding principal advantages comes from the fact that the angular structure of an astronomical object is simply determined from the visibility of the minima of the spectrum of the intensity fluctuations measured by the detector, as a function of the frequency of the fluctu…
Optical imaging with microarcsecond resolution will reveal details across and outside stellar surfaces but requires kilometer-scale interferometers, challenging to realize either on the ground or in space. Intensity interferometry, electronically connecting independent telescopes, has a noise budget that relates to the electronic time resolution, circumventing issues of atmospheric turbulence. Extents up to a few km are becoming realistic with arrays of optical air Cherenkov telescopes (primarily erected for gamma-ray studies), enabling an optical equivalent of radio interferometer arrays. Pio…
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 counti…
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 nois…
The imminent availability of large arrays of large light collectors deployed to exploit atmospheric Cherenkov radiation for gamma-ray astronomy at more than 100GeV, motivates the growing interest in application of intensity interferometry in astronomy. Indeed, planned arrays numbering up to one hundred telescopes will offer close to 5,000 baselines, ranging from less than 50m to more than 1000m. Recent and continuing signal processing technology developments reinforce this interest. Revisiting Stellar Intensity Interferometry for imaging is well motivated scientifically. It will fill the short…
Since a number of years our group is engaged in the design, construction and operation of instruments with very high time resolution in the optical band for applications to Quantum Astronomy and more conventional Astrophysics. Two instruments were built to perform photon counting with sub-nanosecond temporal accuracy. The first of the two, Aqueye+, is regularly mounted at the 1.8 m Copernicus telescope in Asiago, while the second one, Iqueye, was mounted at the ESO New Technology Telescope in Chile, and at the William Herschel Telescope and Telescopio Nazionale Galileo on the Roque (La Palma, …
Imaging Atmospheric Cherenkov Telescopes have long been viewed as potential light collectors to be used for long baseline optical intensity interferometry observations. Intensity interferometry, as implemented with Cherenkov telescopes, is well suited for studying the spatial structure of stars of O/B/A stellar types at short optical wavelengths. Such observations complement those with the current generation of optical amplitude interferometers, which are typically restricted to longer wavelengths. Dedicated intensity interferometry instrumentation has been developed for the VERITAS observator…
We present intensity interferometry of the luminous blue variable P Cyg in the light of its H$α$ emission performed with 1\,m-class telescopes. We compare the measured visibility points to synthesized interferometric data based on the CMFGEN physical modeling of a high-resolution spectrum of P Cyg recorded almost simultaneously with our interferometry data. Tuning the stellar parameters of P Cyg and its H$α$ linear diameter we estimate the distance of P Cyg as $1.56\pm0.25$~kpc, which is compatible within $1σ$ with $1.36\pm0.24$~kpc reported by the Gaia DR2 catalogue of parallaxes recently pub…
Recent advances in telescope design, photodetector efficiency, and high-speed electronic data recording and synchronization have created the observational capability to achieve unprecedented angular resolution for several thousand bright (m< 6) and hot (O/B/A) stars by means of a modern implementation of Stellar Intensity Interferometry (SII). This technology, when deployed on future arrays of large diameter optical telescopes, has the ability to image astrophysical objects with an angular resolution better than 40 μ arc-sec. This paper describes validation tests of the SII technique in the la…
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 mete…
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 interf…
High angular resolution observations at optical wavelengths provide valuable insights in stellar astrophysics, directly measuring fundamental stellar parameters, and probing stellar atmospheres, circumstellar disks, elongation of rapidly rotating stars, and pulsations of Cepheid variable stars. The angular size of most stars are of order one milli-arcsecond or less, and to spatially resolve stellar disks and features at this scale requires an optical interferometer using an array of telescopes with baselines on the order of hundreds of meters. We report on the successful implementation of a st…
