Transcript Interferometry in Radio Astronomy

Interferometry in Radio
Astronomy
Tony Wong, ATNF
Synthesis Workshop
13 May 2003
Basic Concepts
• An interferometer measures coherence in the
electric field between pairs of points (baselines).
Direction to source
ct

B
T2
T1
(courtesy Ray Norris)
Correlator
• Because of the geometric path difference ct, the
incoming wavefront arrives at each antenna at a
different phase.
Basic Concepts
Young’s double slit experiment: constructive
interference occurs when path difference is an
integer number of wavelengths.
from Dave McConnell
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.
west
meridian
east
Basic Concepts
The angular resolution of the interferometer is
given by the fringe half-spacing l/(2B).
west
l/(2B)
radians
meridian
east
Basic Concepts
• As the source moves through the fringe pattern, it
produces an oscillating output signal from the
interferometer.
west
meridian
east
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.
west
meridian
east
output signal
Basic Concepts
• If the source is comparable to the fringe halfspacing l/(2B), then the output signal is the fringe
pattern smoothed by the finite size of the source.
west
meridian
east
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.
west
meridian
east
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.
west
meridian
east
Basic Concepts
• The primary beam of each antenna has a diameter
~l/D, which is always larger than the fringe spacing
because D<B. The primary beam gives the FOV.
west
meridian
east
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 it’s not like this?
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
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).
Bandwidth smearing
• Since the fringe spacing is proportional to
wavelength, different frequencies in the observing
band will have slightly different fringe patterns.
west
meridian
1420 MHz
east
Bandwidth smearing
• Since the fringe spacing is proportional to
wavelength, different frequencies in the observing
band will have slightly different fringe patterns.
west
meridian
1430 MHz
east
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.
west
meridian
east
White light fringe
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.
Phase
centre
Extra delay ct added
in electronics for T2
ct
B
T2
T1
Correlator
Delay tracking
However, by having the fringes move with the source,
less information is available about the source structure.
Phase
centre
structures here
would be invisible!
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
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
Fringe rotation
Delay tracking can also cause the fringes to rotate!
Phase
centre
00:00
Fringe rotation
Delay tracking can also cause the fringes to rotate!
03:00
Fringe rotation
Delay tracking can also cause the fringes to rotate!
06:00
Fringe rotation
Delay tracking can also cause the fringes to rotate!
09:00
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.
ct
T1
B
T2
12:00
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.
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)
Aperture Synthesis
• As the source moves across the sky (due to Earth’s
rotation), the baseline vector traces part of an
ellipse in the (u,v) plane.
v (kl)


T1
B
T1
B sin  = (u2 + v2)1/2
T2
u (kl)
T2
• Actually we obtain data at both (u,v) and (-u,-v)
simultaneously, since the two antennas are
interchangeable. Ellipse completed in 12h, not 24!
Aperture Synthesis
• Example: 5 moveable antennas of ATCA, in
the EW214 configuration.
north
214m
31m
east
10 baselines ranging from 31m to 214m
 9.1 to 63 kl at 88 GHz
Aperture Synthesis
• Instantaneous
(u,v) coverage
near transit
• 10 baselines, 20
(u,v) points
Aperture Synthesis
• (u,v) coverage
for full 12 hour
observation at
declination –80.
Aperture Synthesis
• Simulated (u,v)
coverage for a
single dish
telescope of
diameter 200m.
Aperture Synthesis
Hence the term
“aperture
synthesis”!
Visibility Function
1. The output of the interferometer, after multiplying
each pair of signals, is the complex visibility, V =
|V|ei, 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.
V (u , v)   I (l , m)e 2pi (ul  vm) dldm
I (l , m)   V (u , v)e 2pi ( ul  vm) dudv
Sampling of Visibility Plane
• If the (u,v) plane is incompletely sampled, the point
spread function (PSF) has artefacts (“sidelobes”).
FT
Point source response of 3 antennas (3 baselines)
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.
FT
Point source response of 5 antennas (10 baselines)
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.
Högbom’s 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.
Deconvolution
Dirty map
CLEANed map
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.
Centimetre Arrays
Westerbork
Synthesis
Radio
Telescope,
Netherlands
14 antennas (4
moveable) x
25m diameter,
300 MHz – 9
GHz
Centimetre Arrays
Very Large Array, Socorro NM USA
27 moveable antennas x 25m diameter, 73 MHz – 50
GHz
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)
Centimetre Arrays
Ryle Telescope, Cambridge, UK
8 antennas (4 moveable) x 13m diameter, 15 GHz
Centimetre Arrays
Molongolo Observatory Synthesis Telescope,
Canberra ACT
2 fixed cylindrical paraboloids 778m long, 843 MHz
Centimetre Arrays
DRAO Synthesis Telescope, Penticton BC Canada
7 antennas (3 moveable) x 9m diameter, 408 & 1420
MHz
Centimetre Arrays
Mauritius Radio Telescope, Mauritius
1088 helical antennas, 151 MHz
Centimetre Arrays
Giant Metrewave Radio Telescope, Pune, India
30 fixed antennas x 45m diameter, 150 – 1420 MHz
Millimetre Arrays
Plateau de Bure Interferometer, France
6 antennas x 15m diameter, 80 – 250 GHz
Millimetre Arrays
Caltech Millimeter Array, CA USA
6 antennas x 10.4m diameter, 86 – 270 GHz
Millimetre Arrays
Berkeley-Illinois-Maryland Association, CA USA
10 antennas x 6m diameter, 70 – 270 GHz
Millimetre Arrays
Nobeyama Millimeter Array, Japan
6 antennas x 10m diameter, 85 – 237 GHz
Millimetre Arrays
Sub-Millimeter Array, Hawaii USA
8 antennas x 6m diameter, 190 – 850 GHz
Under construction
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.
Proposing for
Observations
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 l=21 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.
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 source’s redshift, and
the telescope automatically calculates the
right observing frequency.
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?
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.
Lecture Summary - II
•
The resolution is set by the average baseline
length: D ~ 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.