Intensity Interferometry workshop – Salt Lake City, January 2009 Dainis Dravins Lund Observatory, Sweden DIGITAL CORRELATORS FOR INTENSITY INTERFEROMETRY AND HIGH-SPEED ASTROPHYSICS

Photon Correlators ! But first a little history…

Laurie M. Brown, Abraham Pais, A. B. Pippard Twentieth Century Physics CRC Press, 1995 EARLY PHOTON-CORRELATION SPECTROSCOPY The birth of digital photon correlation spectroscopy dates back to a conference paper by Foord et al. (Malvern, U.K.), at about the same time as Benedek described experiments in ’light-beating’ spectroscopy by analogue means. Photon counting statistics of the new light sources had been widely explored from 1963, but the Malvern group recognized that much was to be gained from direct electronic computation of Glauber’s G (2), the second-order temporal correlations in photon counts, in place of simple photon counting. --- The first photon correlator to perform such computations was used in 1970 to measure the size of the molecule haemocyanin. The autocorrelation function from a monodisperse suspension is a single exponential whose decay rate is proportional to the hydrodynamic size of the molecule. --- The photon correlator provided a seven-decade leap in optical resolution, down to a few Hertz … Commercial construction of digital photon correlators and their worldwide use followed quickly, with application to the analysis of macromolecular suspensions (proteins, enzymes, viruses, polymers, etc.), viscosity, thermal diffusion, mutual diffusion, air and fluid velocity flows and turbulence and many other problems with moving atoms, molecules or macroscopic objects. --- Some 15 years later the speed of digital electronics had advanced sufficiently … and recently the whole operation has been performed with software using a single high-speed CPU chip in the expansion slot of a portable computer. Such a single-board correlator was used, for example, in the recent space- shuttle experiments on critical xenon.

E.R.Pike The Malvern Correlator: Case study in development Phys.Technol. 10, 104 (1979)

FIRST APPLICATION USING PHOTON CORRELATORS 1980’S STATE-OF-THE-ART: MALVERN PHOTON CORRELATOR

5 Application of Modern TCSPC Techniques 5.1 Classic Fluorescence Lifetime Experiments 5.2 Multispectral Fluorescence Lifetime Experiments 5.3 Excitation-Wavelength Multiplexing 5.4 Transient Fluorescence Lifetime Phenomena 5.5 Diffuse Optical Tomography and Photon Migration 5.6 Autofluorescence of Biological Tissue 5.7 TCSPC Laser Scanning Microscopy 5.8 Other TCSPC Microscopy Techniques 5.9 Picosecond Photon Correlation 5.10 Fluorescence Correlation Spectroscopy 5.11 Combinations of Correlation Techniques 5.12 The Photon Counting Histogram 5.13 Time-Resolved Single Molecule Spectroscopy 5.14 Miscellaneous TCSPC Applications (Springer 2005)

PRINCIPLE OF A DIGITAL PHOTON CORRELATOR

Example of correlator features Flex02-01D from Correlator.com with inputs A & B Calculates correlation function(s) in real time for delays from 1.6 ns to about 30 minutes Minimum sample time T = 1.6 ns First 64 channels: T = 1.6 ns, delay times T to 64*T Second 32 channels: T = 2*1.6 ns, delay times 66*T to 128*T Third 32 channels: T = 4*1.6 ns, delay times 66*T to 128*T Fourth 32 channels: T = 8*1.6 ns, delay times 66*T to 128*T, etc. Sample time doubles every 32 channels and data width increases by 1 bit to prevent overflow Single real-time multiple-tau digital correlator (AxA or AxB) Dual multiple tau digital correlator ({AxA, BxB}, or {AxB, BxA}) Quad multiple tau digital correlator {AxA, BxB, AxB, BxA} One or two-channel photon-history recorder for sample times 0.1  s or greater. In photon history mode, it records the time between successive photon events by counting the number of ticks of the system clock between the photon events. The time series is recorded without gaps for average count rates up to many MHz. List price US $ 10,500

Custom-made 32-channel correlator Correlator.com (2008)

DIGITAL PHOTON Lund Observatory 2008/09: 700 MHz clock rate (1.4 ns time resolution) 200 MHz maximum photon count rates per channel (pulse-pair resolution 5 ns) 8 input channels for photon pulses at TTL voltages Custom-made by Correlator.com for applications in intensity interferometry

Real-time correlation Pro: Search all timescales in real time, store only reduced data Con: Lose information on transients, no alternative analyses

QVANTOS: Rapid variability in laboratory sources (Dravins, Hagerbo, Lindegren, Mezey & Nilsson; Lund Observatory)

Skinakas Observatory, Crete The OPTIMA instrument (Optical Pulsar TIMing Analyzer) of the Max-Planck-Institute for Extraterrestrial Physics (Garching), mounted at the Cassegrain focus of a 1.3 m telescope

Real-time correlation: Identifying telescope vibrations in real time Ricky Nilsson, MSc thesis, Lund Observatory 2005

Autocorrelation functions of the Crab pulsar, measured by photon-counting avalanche photodiodes in the OPTIMA instrument, computed by a real-time digital signal correlator of QVANTOS Mark II (Lund Observatory). The rise below 1 µs is due to detector afterpulsing.

T.H. Hankins, J.S. Kern, J.C. Weatherall, J.A. Eilek Nanosecond radio bursts from strong plasma turbulence in the Crab pulsar Nature 422, 141 (2003)

Simulated MAGIC observations of the Crab pulsar integrated over 30 seconds Top: Period-folded light curve hints at the pulsar main peak around 5 ms for this 1  s time resolution. Bottom: The autocorrelation extracts all timescales of systematic variability Although the pulsar is orders of magnitude weaker than the background, already integrations over some tens of seconds reveal a sensible autocorrelation. A usable signal can probably be retrieved down to microsecond timescales with reasonable integration times of a few hours. (Ricky Nilsson, Lund Observatory)

Rapid astrophysical variability For resolutions below  1  s, light curves may become rather meaningless but statistical properties can be studied

Rapid oscillations in neutron stars Detection with RHESSI of High-Frequency X-Ray Oscillations in the Tail of the 2004 Hyperflare from SGR : Watts & Strohmayer, ApJ 637, L117 (2006) Power spectra after main flare (25–100 keV), at different rotational phases: QPO visible at 92.5 Hz. Possible identification: Toroidal vibration mode of neutron-star crust?

p-mode oscillating neutron star

Predicted non-radial oscillations in neutron stars McDermott, Van Horn & Hansen, ApJ 325, 725

Oscillation signature in simulated neutron-star light-curve with superposed sky background noise. (Ricky Nilsson, MSc thesis, Lund Observatory, 2005)

John M. Blondin (North Carolina State University) Hydrodynamics on supercomputers: Interacting Binary Stars

Kilohertz quasiperiodic oscillations in Sco X-1 (Miller, Strohmayer, Zhang & van der Klis, RXTE)

Model of Kilohertz QPOs M. C. Miller, F. K. Lamb, D. Psaltis Numerical computations in general relativity

Modeling Photon Bubble Oscillations in Accretion Klein, Arons, Jernigan & Hsu ApJ 457, L85

KUIPER-BELT OCCULTATIONS Diffraction & shadow of irregular 1-km Kuiper-belt object in front of a point star. Horizontal axes in km, vertical axis is stellar flux. Grey central spot indicates the geometrical shadow. (Roques & Moncuquet, 2000)

Atmospheric intensity scintillation Atmospheric scintillation of starlight affects all types of telescopes

Sunlight onto a pool of water projects patterns on the bottom. Refraction at the undulating water surface causes effects similar to flying shadows in air. Shadow bands (“flying shadows”) moving across a house in Sicily during a solar eclipse in Codona, Sky & Tel 81, 482, 1991

Pupil [= telescope main mirror, with secondary-mirror obscuration and its four holder vanes visible] image for the star Alpha Gem, recorded on the 1-meter Jakobus Kapteyn Telescope on La Palma [1ms exposure]. Brighter and darker patches are “flying shadows” caused by upper-atmospheric turbulence. Intensity scintillation results from incomplete intensity averaging of this pattern as it is both intrinsically evolving, and carried by winds. (Applied Optics group, Imperial College, London)

Pupil [= telescope main mirror, with secondary-mirror obscuration and its four holder vanes visible] image for the star Alpha Gem, recorded on the 1-meter Jakobus Kapteyn Telescope on La Palma [1ms exposure]. Brighter and darker patches are “flying shadows” caused by upper-atmospheric turbulence. Intensity scintillation results from incomplete intensity averaging of this pattern as it is both intrinsically evolving, and carried by winds. (Applied Optics group, Imperial College, London)

Pupil image movie [part of the telescope main mirror] for a bright star, recorded on the 4.2-meter William Herschel Telescope on La Palma. (Applied Optics group, Imperial College, London)

Simulated “flying-shadow” pattern on an extremely large telescope. Besides scintillation in intensity, diffraction by this pattern throws parasitic light into the far wings of any focused stellar image. Suppression of this effect is essential to enable direct imaging of faint extrasolar planets. Hubin et al.: “EPICS, Earth-like planets imaging camera spectrograph”, ESO OWL instrument concept study, OWL-CSR-ESO , 2005

60-cm telescope on La Palma, and the setup used for scintillation measurements

Typical photon-count distribution. A log-normal intensity distribution (combined with appropriate photon noise) is fitted to the data, with the difference to the fit seen in the bottom panel on a greatly expanded scale. The Poisson distribution corresponding to photon noise only, with zero atmospheric intensity fluctuation, is also shown. Atmospheric Intensity Scintillation of Stars. I. Statistical Distributions and Temporal Properties D.Dravins, L.Lindegren, E.Mezey & A.T.Young, PASP 109, 173 (1997)

Autocovariance of stellar intensity during a night, through a 60 cm telescope. The star was Polaris, assuring a constant position in the sky. Amplitude at the origin equals the intensity variance sigma 2. Each curve represents a 2-min integration. Scintillation changes on timescales of typically tens of minutes. Atmospheric Intensity Scintillation of Stars. I. Statistical Distributions and Temporal Properties D.Dravins, L.Lindegren, E.Mezey & A.T.Young, PASP 109, 173 (1997)

Aperture dependence of autocovariance, measured at different times during a night. Left: Early evening at moderate zenith angles Right: Closer to midnight at small zenith angles. Anti-correlation dips indicate a high temporal stability in the flying shadows. Atmospheric Intensity Scintillation of Stars. I. Statistical Distributions and Temporal Properties D.Dravins, L.Lindegren, E.Mezey & A.T.Young, PASP 109, 173 (1997)

Non-zero scintillation on very short timescales The break in the curve near 300  s may be connected to the inner scale of atmospheric turbulence (linear size 3 mm at windspeeds of 10 m/s). Atmospheric Intensity Scintillation of Stars. I. Statistical Distributions and Temporal Properties D.Dravins, L.Lindegren, E.Mezey & A.T.Young, PASP 109, 173 (1997)

Autocorrelation at 400 and 700 nm, for different telescope apertures. At shorter optical wavelengths, the fluctuations are more rapid. The effect is most pronounced for the smallest apertures. Atmospheric Intensity Scintillation of Stars. II. Dependence on Optical Wavelength D.Dravins, L.Lindegren, E.Mezey & A.T.Young, PASP 109, 725 (1997)

Cross correlations of scintillation between pairs of colors Time delays at larger zenith angles depend upon the difference in wavelength. With increasing wavelength difference, (a) the degree of correlation between different colors decreases, and (b) the time delay increases In the violet, the dispersion of air changes rapidly with wavelength, explaining the significant differences between the nearby wavelengths of 365 and 400 nm. Atmospheric Intensity Scintillation of Stars. II. Dependence on Optical Wavelength D.Dravins, L.Lindegren, E.Mezey & A.T.Young, PASP 109, 725 (1997)

Cherenkov telescopes have narrow gaps between mirror facets, making them sensitive to small spatial scales of scintillation. The gap orientation makes them sensitive to also the direction of flying shadows, i.e., to the atmospheric windspeed vectors. MAGIC, Roque de los Muchachos, La Palma

Atmospheric Intensity Scintillation of Stars. III. Effects for Different Telescope Apertures D.Dravins, L.Lindegren, E.Mezey & A.T.Young, PASP 110, 610 & 1118 (1998) Scintillation through masks with two apertures, at different spacings and angles. If the same pattern crosses both apertures, a secondary peak appears, revealing the flying-shadow speed and direction. For apertures separated by 30 cm, typical delays of 20 ms indicate a flying-shadow speed of about 15 m/s.

Photon Statistics Change by Adaptive Optics V.F.Canales, M.P.Cagigal, Opt.Lett. 26, 737 (2001) Probability intensity distribution of light intensity at the PSF core of an AO- compensated image for three different D/r 0 values.

Understanding detectors Afterpulsing, afterglow and other detector signatures can mimic intensity correlations

D. Dravins 1, C. Barbieri 2, V. Da Deppo 3, D. Faria 1, S. Fornasier 2, R. A. E. Fosbury 4, L. Lindegren 1, G. Naletto 3, R. Nilsson 1, T. Occhipinti 3, F. Tamburini 2, H. Uthas 1, L. Zampieri 5 (1) Lund Observatory, (2) Dept. of Astronomy, Univ. of Padova (3) Dept. of Information Engineering, Univ. of Padova (4) ST-ECF, ESO Garching, (5) Astronomical Observatory of Padova ESO Instrument Studies for Extremely Large Telescopes (2005) HIGHEST TIME RESOLUTION, REACHING QUANTUM OPTICS Other instruments cover seconds and milliseconds QuantEYE will cover milli-, micro-, and nanoseconds, down to the quantum limit !

“REALISTIC” DATA RATES ? * 1024 x 1024 imaging elements one wavelength channel at a time * Each channel 10 MHz with 1 ns time resolution * photon time-tags per second = 10 TB/s (Terabyte, B) ≈ 1 PB/min (Petabyte, B) ≈ 1 EB/few nights (Exabyte = B)

“ULTIMATE” DATA RATES ? * 1024 x 1024 imaging 100 spectral & polarization channels * Each channel 10 MHz, 1 ns time resolution * photon time-tags per second = 1 PB/s (Petabyte, B) = some EB/h (Exabyte = B)

Correlating for intensity interferometry Real-time correlators already permit verifying various observational modes, both in the lab, and at telescopes

Digital Intensity Interferometry Laboratory setup at Lund Observatory (2006)

The four 12-meter telescopes of the VERITAS array in Arizona offer baselines between m S.LeBohec, M.Daniel, W.J.de Wit, J.A.Hinton, E.Jose, J.A.Holder, J.Smith, R.J.White Stellar Intensity Interferometry with Air Cherenkov Telescope Arrays in D.Phelan, O.Ryan & A.Shearer, eds., The Universe at sub-second timescales, AIP Conf.Proc. 984, 205 (2008)

Steps towards a km 2 optical telescope Full-scale test observations with VERITAS, Oct Dainis Dravins (Lund Observatory) Stephan LeBohec (University of Utah) Michael Daniel (University of Leeds) Digitally correlated pairs of 12-meter telescopes * Photon rates > 30 MHz per telescope * Real-time cross correlation,  t = 1.6 ns

CTA, Cherenkov Telescope Array