Intensity Interferometry workshop – Salt Lake City, January 2009 DIGITAL CORRELATORS FOR INTENSITY INTERFEROMETRY AND HIGH-SPEED ASTROPHYSICS Dainis Dravins Lund Observatory, Sweden www.astro.lu.se/~dainis
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 µ 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 CORRELATORS @ 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 µ 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 µ 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 1806-20 : 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 12 Y 15
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
Shadow bands (“flying shadows”) moving across a house in Sicily during a solar eclipse in 1870. Codona, Sky & Tel 81 , 482, 1991 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.
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)
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