Interferometry in Radio Astronomy

1
Interferometry in Radio Astronomy

• Tony Wong, ATNF
• Synthesis Workshop
• 13 May 2003

2
Basic Concepts

• An interferometer measures coherence in the
  electric field between pairs of points
  (baselines).

Direction to source
wavefront
ct
Bsin?
?
B
T1
T2
(courtesy Ray Norris)
Correlator

• Because of the geometric path difference ct, the
  incoming wavefront arrives at each antenna at a
  different phase.

3
Basic Concepts

• Youngs double slit experiment constructive
  interference occurs when path difference is an
  integer number of wavelengths.

from Dave McConnell
4
Basic Concepts

• Consider a 2-element east-west interferometer.
• By analogy to the double slit experiment, regions
  which would cause constructive and destructive
  interference can be considered stripes in the
  sky.

meridian
east
west
5
Basic Concepts

• The angular resolution of the interferometer is
  given by the fringe half-spacing l/(2B).

meridian
east
west
6
Basic Concepts

• As the source moves through the fringe pattern,
  it produces an oscillating output signal from the
  interferometer.

meridian
east
west
7
Basic Concepts

• If the source is very small compared to the
  fringe half-spacing l/(2B), we say it is
  unresolved. The output signal is just the fringe
  pattern, and the source structure cannot be
  determined.

meridian
east
west
8
Basic Concepts

• If the source is comparable to the fringe
  half-spacing l/(2B), then the output signal is
  the fringe pattern smoothed by the finite size of
  the source.

meridian
east
west
9
Basic Concepts

• If the source is large enough to span both a peak
  and a trough in the fringe pattern, the output
  signal is nearly constant. The source is
  over-resolved or resolved out, and its
  structure poorly determined.

meridian
east
west
10
Basic Concepts

• If you are interested in source structure that is
  being resolved out, then observe with a shorter
  baseline B to make the fringe spacing l/B larger.

meridian
east
west
11
Basic Concepts

• The primary beam of each antenna has a diameter
  l/D, which is always larger than the fringe
  spacing because DltB. The primary beam gives the
  FOV.

meridian
east
west
12
The 2nd Dimension

• With a single baseline it would appear that we
  only get information about the source structure
  in one dimension!

How do we know its not like this?
13
The 2nd Dimension

• However, for circumpolar objects the source
  traces a circle with respect to the fringe
  pattern, so 2D info can be obtained, if you
  observe long enough.

SCP
14
The 2nd Dimension

• For sources closer to the celestial equator, the
  path is less curved and one obtains little
  information on N-S structure (for a pure E-W
  array).

15
Bandwidth smearing

• Since the fringe spacing is proportional to
  wavelength, different frequencies in the
  observing band will have slightly different
  fringe patterns.

meridian
east
west
1420 MHz
16
Bandwidth smearing

• Since the fringe spacing is proportional to
  wavelength, different frequencies in the
  observing band will have slightly different
  fringe patterns.

meridian
east
west
1430 MHz
17
Bandwidth smearing

• As a result, constructive interference
  (coherence) is only strictly maintained at the
  meridian, where the path lengths to the two
  telescopes are equal.

meridian
east
west
White light fringe
18
Delay tracking

• To counter this problem, a variable delay is
  added to the signal from one dish, causing the
  white light fringe to follow the source across
  the sky.

Extra delay ct added in electronics for T2
19
Delay tracking

• However, by having the fringes move with the
  source, less information is available about the
  source structure.

Phase centre
20
Delay tracking

• So, a phase shift of p/2 is periodically inserted
  to effectively shift the fringe pattern (this is
  done automatically by using a complex correlator).

Phase centre
21
Delay tracking

• So, a phase shift of p/2 is periodically inserted
  to effectively shift the fringe pattern (this is
  done automatically by using a complex correlator).

Phase centre
22
Fringe rotation

• Delay tracking can also cause the fringes to
  rotate!

Phase centre
0000
23
Fringe rotation

• Delay tracking can also cause the fringes to
  rotate!

0300
24
Fringe rotation

• Delay tracking can also cause the fringes to
  rotate!

0600
25
Fringe rotation

• Delay tracking can also cause the fringes to
  rotate!

0900
26
Fringe rotation

• The basic reason is that by inserting additional
  delays, you are effectively moving one of the
  antennas closer or further from the source.
  Moving the baseline produces a change in the
  fringe pattern.

1200
27
Getting Confusing?

• Clearly, tracking a source across the sky
  provides a great deal more information than a
  snapshot observation, because the source is
  sampled with a variety of fringe spacings, which
  are at different angles to the source.
• One way to formalise this is to adopt the view
  from the source, which sees the array rotating
  beneath it.
• This leads to the concept of the visibility
  plane, and the powerful technique of aperture
  synthesis.

28
The Visibility Plane

• The projection of a baseline onto the plane
  normal to the source direction defines a vector
  in (u,v) space, measured in wavelength units.

(u,v)
29
Aperture Synthesis

• As the source moves across the sky (due to
  Earths rotation), the baseline vector traces
  part of an ellipse in the (u,v) plane.

B sin ? (u2 v2)1/2
v (kl)
Bsin?
?
T2
u (kl)
?
B
T1
T2
T1

• Actually we obtain data at both (u,v) and (-u,-v)
  simultaneously, since the two antennas are
  interchangeable. Ellipse completed in 12h, not
  24!

30
Aperture Synthesis

• Example 5 moveable antennas of ATCA, in the
  EW214 configuration.

north
east
10 baselines ranging from 31m to 214m ? 9.1 to 63
kl at 88 GHz
31
Aperture Synthesis

• Instantaneous (u,v) coverage near transit
• 10 baselines, 20 (u,v) points

32
Aperture Synthesis

• (u,v) coverage for full 12 hour observation at
  declination 80.

33
Aperture Synthesis

• Simulated (u,v) coverage for a single dish
  telescope of diameter 200m.

34
Aperture Synthesis

• Hence the term aperture synthesis!

35
Visibility Function

1. The output of the interferometer, after
   multiplying each pair of signals, is the complex
   visibility, V Vei?, which has an amplitude
   and phase.
2. The Fourier transform of the complex visibility
   with respect to (u,v) gives the sky intensity
   distribution. Hence (u,v) spatial frequencies.

36
Sampling of Visibility Plane

• If the (u,v) plane is incompletely sampled, the
  point spread function (PSF) has artefacts
  (sidelobes).

Point source response of 3 antennas (3 baselines)
37
Sampling of Visibility Plane

• Adding one antenna to an N element array adds N-1
  baselines! Imaging quality increases faster than
  linearly with array size.

Point source response of 5 antennas (10 baselines)
38
Data Reduction

• After obtaining raw visibilities, the usual
  procedure is
• Calibration of visibilities using data from one
  or more bright point sources, observed at regular
  intervals during the observation.
• Establish the flux density scale (Jy) using a
  standard source.
• Inverse Fourier transform to make a dirty map.
• Deconvolution to remove artefacts due to the PSF.

39
Högboms CLEAN algorithm

• Locate the peak in the map.
• Subtract off a scaled version of the PSF or
  dirty beam.
• Repeat until only noise left in image.
• Add back the subtracted components in the form of
  Gaussians (clean beams) with size comparable to
  the centre of the PSF.

40
Deconvolution
Dirty map
CLEANed map
41
Advantages of interferometers

• Can achieve much higher angular resolution than
  single-dish telescopes.
• Less affected by pointing errors position of the
  phase tracking centre determined by the
  observatory clock, and is independent of the
  pointing of the individual antenna elements.
• Less affected by gain fluctuations on an
  individual antenna, as long as they are
  uncorrelated with other antennas. Long
  integrations possible.
• Spectral baselines usually flat for same reason.
• Can adjust the resolution of the map by
  re-weighting the visibilities in software.

42
Centimetre Arrays

• Westerbork Synthesis Radio Telescope, Netherlands
• 14 antennas (4 moveable) x 25m diameter, 300 MHz
  9 GHz

43
Centimetre Arrays

• Very Large Array, Socorro NM USA
• 27 moveable antennas x 25m diameter, 73 MHz 50
  GHz

44
Centimetre Arrays

• Australia Telescope Compact Array, Narrabri NSW
• 6 antennas (5 moveable) x 22m diameter, 1 9 GHz
  (being upgraded to 22 and 100 GHz)

45
Centimetre Arrays

• Ryle Telescope, Cambridge, UK
• 8 antennas (4 moveable) x 13m diameter, 15 GHz

46
Centimetre Arrays

• Molongolo Observatory Synthesis Telescope,
  Canberra ACT
• 2 fixed cylindrical paraboloids 778m long, 843 MHz

47
Centimetre Arrays

• DRAO Synthesis Telescope, Penticton BC Canada
• 7 antennas (3 moveable) x 9m diameter, 408 1420
  MHz

48
Centimetre Arrays

• Mauritius Radio Telescope, Mauritius
• 1088 helical antennas, 151 MHz

49
Centimetre Arrays

• Giant Metrewave Radio Telescope, Pune, India
• 30 fixed antennas x 45m diameter, 150 1420 MHz

50
Millimetre Arrays

• Plateau de Bure Interferometer, France
• 6 antennas x 15m diameter, 80 250 GHz

51
Millimetre Arrays

• Caltech Millimeter Array, CA USA
• 6 antennas x 10.4m diameter, 86 270 GHz

52
Millimetre Arrays

• Berkeley-Illinois-Maryland Association, CA USA
• 10 antennas x 6m diameter, 70 270 GHz

53
Millimetre Arrays

• Nobeyama Millimeter Array, Japan
• 6 antennas x 10m diameter, 85 237 GHz

54
Millimetre Arrays

• Sub-Millimeter Array, Hawaii USA
• 8 antennas x 6m diameter, 190 850 GHz
• Under construction

55
ATCA The Only Southern Millimetre Interferometer

• 3mm (85-105 GHz) and 12mm (16-25 GHz) upgrades in
  progress future provision for 7mm (35-50 GHz)
  upgrade.

56
Proposing for Observations
57
Array configurations

• The maximum baseline B in an array has a
  resolution of l/(2B) radians, but when combined
  with shorter baselines the effective resolution
  is usually l/B.
• If you want 10 resolution at l21 cm, the
  maximum baseline should be 4 km.
• For good u-v coverage you may wish to combine
  data from several configurations.
• For objects north of DEC 30, consider ATCA
  configurations with N-S baselines.

58
Frequency Setup

• Most arrays provide both a continuum and a
  spectral line observing mode, just like
  single-dish telescopes.
• Bandwidth usually comes at the expense of reduced
  frequency resolution.
• Check if the observatory employs Doppler
  tracking. This allows you to give the rest
  frequency and the sources redshift, and the
  telescope automatically calculates the right
  observing frequency.

59
How much time to request?

• The relevant questions to ask are
• How bright is the source (flux density)?
• How complex is the source? Is good (u,v)
  coverage needed?
• How large is the source? If it is comparable to
  the primary beam (l/D), you should mosaic several
  fields.
• How much time will be needed for calibrations?

60
Lecture Summary - I

• An interferometer samples spatial frequencies in
  the sky given by the length(s) of its projected
  baseline(s), in wavelengths.
• With no delay tracking, the interferometer output
  can be interpreted as the source moving through
  the peaks and troughs of a fringe pattern
  projected onto the sky.
• With delay tracking, the fringe pattern moves
  with the source, but the fringe spacing changes
  and the fringes rotate as the source moves across
  the sky.
• In both cases we learn the most about emission on
  scales comparable to the fringe half-spacing,
  which is l/(2B) near the meridian.

61
Lecture Summary - II

• The resolution is set by the average baseline
  length Dq l/B.
• The field of view is set by the antenna diameter.
• Maximum coverage of the visibility plane can be
  achieved by increasing the number of baselines
  and tracking the source for 12 hours.
• A dirty image can be produced by Fourier
  transforming the measured complex visibilities.
• Deconvolution methods such as CLEAN can be used
  to remove artefacts due to incomplete sampling of
  the visibility plane.