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The Siegert relation relates field and intensity temporal correlations. After a historical review of the Siegert relation and the Hanbury Brown and Twiss effect, we discuss the validity of this relation in two different domains. We first show that this relation can be used in astrophysics to determine the fundamental parameters of stars, and that it is especially important for the observation with stellar emission lines. Second, we check the validity of this relation for moving quantum scatterers illuminated by a strong driving field.

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.

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.

Stellar intensity interferometry (SII) is used to measure the squared visibility, which corresponds to the Fourier transform of the distribution of brightness from a given source for the projected position angle of a pair of telescopes. SII measures the squared visibility through correlations of starlight intensity fluctuations between separated telescope pairs. SII has a significant advantage of being relatively insensitive to atmospheric effects and the minor imperfections of an optical system, allowing for observations over large baselines and low elevation angles, leading to the extension of uv-plane coverage.1 Such uv-plane extension subsequently allows high angular resolution measurements of stellar targets with submilliarcsecond (mas) resolution capabilities. Coincidentally, many telescope arrays constructed to perform gamma-ray observations also meet the requirements of SII. For example, the Very Energetic Radiation Imaging Telescope Array System (VERITAS)2 is an Imaging Air Cherenkov Telescope (IACT) array that is a prime candidate for SII observations.3 Recently, there has been great experimental progress using IACT arrays for SII, as evidenced by successful on-sky observations from VERITAS4,5 and MAGIC.6 Future arrays, such as the Cherenkov Telescope Array (CTA),7 would offer even greater SII capabilities than current observatories due to the increased number of telescopes and larger baselines.8

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 stellar intensity interferometry system developed for the four VERITAS imaging atmospheric-Cherenkov telescopes. The system was used to measure the angular diameter of the two sub-mas stars $\beta$ Canis Majoris and $\epsilon$ Orionis with a precision better than 5%. The system utilizes an off-line approach where starlight intensity fluctuations recorded at each telescope are correlated post-observation. The technique can be readily scaled onto tens to hundreds of telescopes, providing a capability that has proven technically challenging to current generation optical amplitude interferometry observatories. This work demonstrates the feasibility of performing astrophysical measurements with imaging atmospheric-Cherenkov telescope arrays as intensity interferometers and the promise for integrating an intensity interferometry system within future observatories such as the Cherenkov Telescope Array., Comment: Accepted for publication in Nature Astronomy (2020)

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., 6 pages, 4 figures. Proceedings of the 36th International Cosmic Ray Conference (ICRC2019) Madison, WI July 24-Aug 1, 2019

Nature astronomy 3(6), 511 - 516 (2019). doi:10.1038/s41550-019-0741-z, The angular size of a star is a critical factor in determining its basic properties$^1$. Direct measurement of stellar angular diameters is difficult: at interstellar distances stars are generally too small to resolve by any individual imaging telescope. This fundamental limitation can be overcome by studying the diffraction pattern in the shadow cast when an asteroid occults a star$^2$, but only when the photometric uncertainty is smaller than the noise added by atmospheric scintillation$^3$. Atmospheric Cherenkov telescopes used for particle astrophysics observations have not generally been exploited for optical astronomy due to the modest optical quality of the mirror surface. However, their large mirror area makes them well suited for such high-time-resolution precision photometry measurements$^4$. Here we report two occultations of stars observed by the Very Energetic Radiation Imaging Telescope Array System (VERITAS)$^5$ Cherenkov telescopes with millisecond sampling, from which we are able to provide a direct measurement of the occulted stars’ angular diameter at the ≤0.1 mas scale. This is a resolution never achieved before with optical measurements and represents an order of magnitude improvement over the equivalent lunar occultation method$^6$. We compare the resulting stellar radius with empirically derived estimates from temperature and brightness measurements, confirming the latter can be biased for stars with ambiguous stellar classifications., Published by Nature Publishing Group, London

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.

Sub-milliarcsecond imaging of nearby main sequence stars and binary systems can provide critical information on stellar phenomena such as rotational deformation, accretion effects, and the universality of starspot (sunspot) cycles. Achieving this level of resolution in optical wavelength bands (U/V) requires use of a sparse array of interferometric telescopes with kilometer scale baseline separations. Current ground based VHE gamma-ray observatories, such as VERITAS, HESS, and MAGIC, employ arrays of > 10 m diameter optical Imaging Atmospheric Cherenkov Telescopes (IACTs) with >80 m telescope separations, and are therefore well suited for sub-milliarcsecond astronomical imaging in the U/V bands using Hanbury Brown and Twiss (HBT) interferometry. We describe the development of instrumentation for the augmentation of IACT arrays to perform Stellar Intensity Interferometric (SII) imaging. Laboratory tests are performed using pseudo-random and thermal (blackbody) light to demonstrate the ability of high speed (250 MHz) digitizing electronics to continuously record photon intensity over long periods (minutes to hours) and validate the use of offline software correlation to calculate the squared degree of coherence . We then use the squared degree of coherence as the interferometric observable to populate the Fourier reciporical image plane, and apply standard inversion techniques to recover the original 2-D source image. The commercial availability of inexpensive fiber-optic based sub-nanosecond multi-crate (White Rabbit) synchronization timing enables the extension of SII to baselines greater than 10 km, theoretically allowing U/V band imaging with resolution

We present measurements of the second order spatial coherence function of thermal light sources using Hanbury-Brown and Twiss interferometry with a digital correlator. We demonstrate that intensity fluctuations between orthogonal polarizations, or at detector separations greater than the spatial coherence length of the source, are uncorrelated but can be used to reduce systematic noise. The work performed here can readily be applied to existing and future Imaging Air-Cherenkov Telescopes used as star light collectors for Stellar Intensity Interferometry (SII) to measure spatial properties of astronomical objects., Comment: 13 pages, 5 figures, Accepted into special issue of the Journal of Modern Optics