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

2. But first a little history…
Photon Correlators !
But first a little history…

3. EARLY PHOTON-CORRELATION SPECTROSCOPY
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.

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

5. FIRST APPLICATION USING
PHOTON CORRELATORS
1980’s state-of-the-art:
MALVERN photon correlator

6. 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)

10. PRINCIPLE OF A DIGITAL PHOTON CORRELATOR

12. 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

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

14. 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

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

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

17. A screenshot of the PhoCorr photon correlator user interface for Flex01-05D, showing the 100 Hz modulation of light from an incandescent lamp. (Ricky Nilsson, MSc thesis, Lund Observatory 2005)

18. 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

19. Alexander Stefanescu (MPE) Tasos Kougentakis (Heraklion)
Skinakas
Observatory
Operating
QVANTOS
& OPTIMA:
Alexander Stefanescu (MPE)
Tasos Kougentakis (Heraklion)
Helena Uthas
(Lund)
Gottfried Kanbach
(MPE)

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

21. 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.

22. Ricky Nilsson, MSc thesis,
CRAB PULSAR
SIMULATION
Ricky Nilsson, MSc thesis,
Lund Observatory 2005

23. Comparison a between simulated and measured (3,000-s integration) auto-correlation of the Crab pulsar light-curve. The scaling differs for delay times above milliseconds, since the hardware correlator uses a different normalization than the simulation. (Ricky Nilsson, MSc thesis, Lund Observatory 2005)

24. 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, (2003)

25. CRAB PULSAR SIMULATION FOR MAGIC 17-m telescope Integrations of
1, 10, & 30 seconds
Period-folded light curves
& autocorrelations
(Ricky Nilsson, Lund Observatory

26. 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)

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

28. 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?

29. 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)
Surface patterns for torsional modes that may have been excited by the hyperflare.
Colors and arrows indicate the magnitude of the vibrations.
(Max Planck Institute for Astrophysics)

30. p-mode oscillating neutron star

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

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

33. Binary accretion systems
Artwork by Catrina Liljegren D. Dravins, ESO Messenger 78, 9

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

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

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

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

38. 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)

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

40. 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.

41. 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)

42. 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)

43. 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)

44. Simulated “flying-shadow” pattern on an extremely large telescope
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

45. 60-cm telescope on La Palma, and the setup used for scintillation measurements

46. Atmospheric Intensity Scintillation of Stars.
Statistical
Distributions and Temporal
Properties
D.Dravins, L.Lindegren, E.Mezey & A.T.Young, PASP 109, 173 (1997)
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.

47. Atmospheric Intensity Scintillation of Stars.
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 sigma2.
Each curve represents a 2-min integration.
Scintillation changes on timescales of typically tens of minutes.

48. Atmospheric Intensity Scintillation of Stars.
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.

49. Atmospheric Intensity Scintillation of Stars.
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).

50. Atmospheric Intensity Scintillation of Stars. II.
Dependence on Optical Wavelength
D.Dravins, L.Lindegren, E.Mezey & A.T.Young, PASP 109, 725 (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.

51. Atmospheric Intensity Scintillation of Stars. II.
Dependence on Optical Wavelength
D.Dravins, L.Lindegren, E.Mezey & A.T.Young, PASP 109, 725 (1997)
Atmospheric chromatic dispersion & flying shadows
Cross covariance between intensity fluctuations at 400 and 700 nm, measured with
a 20-cm diameter aperture, and its zenith-angle dependence. 
Near zenith, the fluctuations are simultaneous, but with increasing Z a time delay
develops, seen as a difference from the autocovariance function for 700 nm. 
The effect is due to atmospheric dispersion, which stretches the "flying shadows"
into "flying spectra" on the ground.

52. 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. 

53. 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

54. 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)
Power spectral content of scintillation in different apertures, i.e. the amount of
integrated power, as function of frequency. 
For smaller apertures, the power shifts towards higher frequencies.
This trend continues until  5 cm, where the "flying shadows“ become resolved.

55. 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 depends on wind direction (source position on the sky)
and on central obscuration (secondary mirror).
For a circular and open 20 cm aperture, the calculated function is shown
for the zenith, and for two wind-azimuth angles at Z = 35 deg.
The scintillation in a 2.5 m telescope is much less but has a complex structure,
caused by its 90 cm secondary mirror.
Autocovariance + epsilon is plotted; true zero levels are marked.

56. 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.

57. Photon Statistics Change by Adaptive Optics
Probability intensity
distribution of light
intensity at the PSF
core of an AO-
compensated image
for three different
D/r0 values.
V.F.Canales, M.P.Cagigal, Opt.Lett. 26, 737 (2001)

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

59. Avalanche Photo-Diodes
Silicon
Single-Photon
Counting
Module
PerkinElmer

60. Avalanche diode dead-time and afterpulsing
in passively and actively quenched APDs
(Dravins, Faria & Nilsson, SPIE 4008, 298, 2000)

61. Avalanche diode “afterglow” (post-detection light emission)
(Dravins, Faria & Nilsson, SPIE 4008, 298, 2000)

62. APD dark signal bistability. Measured (top) & simulated random
(Dravins, Faria & Nilsson, SPIE 4008, 298, 2000)

63. 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 !
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

64. 5 x 5 array of 20 μm diameter APD detectors (SensL, Cork)

67. “REALISTIC” DATA RATES ?
* 1024 x 1024 imaging elements
one wavelength channel at a time
* Each channel photon-counting
@ 10 MHz with 1 ns time resolution
* 1013 photon time-tags per second
= 10 TB/s (Terabyte, 1012 B)
≈ 1 PB/min (Petabyte, 1015 B)
≈ 1 EB/few nights (Exabyte = 1018 B)

68. “ULTIMATE” DATA RATES ? * 1024 x 1024 imaging elements
@ 100 spectral & polarization channels
* Each channel photon-counting
@ 10 MHz, 1 ns time resolution
* 1015 photon time-tags per second
= 1 PB/s (Petabyte, 1015 B)
= some EB/h (Exabyte = 1018 B)

69. PRELIMINARY OPTICAL DESIGN FEASIBILITY OF CONCEPT
PRELIMINARY OPTICAL DESIGN FEASIBILITY OF CONCEPT * Slice ELT pupil into 100 segments * Focus light from each pupil segment into one of an array of 100 lenses * Detect with an array of 100 APD’s (enables 1 GHz count rate)

70. Light collection with a lens array
Each lens has a square aperture, 10 mm side
The beam section is an annulus, with 100 mm external diameter

71. Array lens mounting concept

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

74. Digital Intensity Interferometry
Laboratory setup at Lund Observatory (2006)

75. The four 12-meter telescopes of the VERITAS array in Arizona offer baselines between 34-109 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)

76. Steps towards a km2 optical telescope
Full-scale test observations with VERITAS, Oct. 2007
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

78. 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

79. CTA, Cherenkov Telescope Array