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Radio Astronomy
 An Amateur Radio Astronomy Observatory
David Morgan
Part 2B Aperture Synthesis
Development of future global systems
5/24/2017
Website - dmradas.co.uk
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Radio Astronomy
 Total Power Receiver systems - Part 1
Radio
Window
 Interferometers - Part 2 (A&B)
A
B
5/24/2017
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Basic concept
Observing ‘point sources’
Spatial resolution and sensitivity
Multiple baselines & aperture synthesis
Cosmic hydrogen distribution
Fringe visibility functions
< 300,000years after big bang ?
Today’s best instruments
The future global radio telescope - The SKA
Mk1 at Jodrell Bank
VLA New Mexico
Website - dmradas.co.uk
SKA 2020
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Radio Astronomy - Part 2 B Aperture Synthesis
 Recap on interferometers
30m East – West Baseline
Radio Interferometer
Fringe signal from Taurus A
Aperture Synthesis uses an Interferometer to
generate a Radio Picture of the source
Can ‘synthesise’ the effect of a giant dish antenna
using a number of small cheap antennas
5/24/2017
Website - dmradas.co.uk
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Radio Astronomy
 Taurus A - Crab Nebula Radio image @ 327MHz
5/24/2017
Website - dmradas.co.uk
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Radio Astronomy
 By using multiple antennas with variable baselines it is possible
to ‘Synthesise’ the performance of a very large single dish
A two antenna interferometer with a fixed baseline
Wavelength l
Antenna # 1
Baseline b
Antenna # 2
Lets explore what happens if you change the separation between the antennas
5/24/2017
Website - dmradas.co.uk
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Radio Astronomy – interferometer imaging
 Obtaining an image of a source from an interferometer
Source of finite size is moving
East to West
Fringe Visibility
g
Radiation from a source
close to antenna ‘zenith’
E
= fringe amplitude at baseline bn
fringe amplitude at very short baseline
Short baseline
Amplitude
Amplitude
W
Time
Fringe Frequency
Baseline b0
Amplitude
Amplitude
Medium baseline
Baseline b1
Fringe Frequency
Time
Amplitude
Amplitude
Long baseline
Time
Baseline b2
5/24/2017
Website - dmradas.co.uk
Fringe Frequency
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Radio Astronomy – interferometer imaging
 Generating Fringe visibility graph
Amplitude
A
Fringe Visibility
g
= fringe amplitude at baseline bn
fringe amplitude at very short baseline
Fringe Frequency
Baseline b0 (Short)
A/A =1
1
B
Fringe Frequency
Fringe Visibility
Amplitude
g
B/A = 0.8
C/A= 0.6
Baseline b1 (longer)
0
Amplitude
Short
longer Longer still
longest
Baseline length bn
C
Fringe Frequency
bn/l
The shape of this graph tells us about the brightness
as a function of position on the source
Baseline b2 (longer still)
5/24/2017
Website - dmradas.co.uk
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Radio Astronomy – a tricky bit !
 Fringe visibility
g
Chosen source axis
Leads to 2D Fourier transform of source brightness distribution
Orthogonal source axis
Unresolved at any baseline spacing
Single curve falling to 0 at some
long baseline spacing
Sinx /x type curve with zeros at
various baseline spacings
Repeating fixed amplitude maxima
and minima at various baseline
spacings
5/24/2017
Website - dmradas.co.uk
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Radio Astronomy – a tricky bit !
 Build up a 2D g plot for multiple spatial frequencies (baselines)
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Then calculate 2D Fourier transform
Example of 2D
g
v
spatial frequency (b/l) plots (from different baselines on various axies)
Orthogonal Axis
Fringe Visibility
(by/l)
g
g values are the white levels
Fourier Transforms
to sharp edged source
Spatial frequency b/l (for Axis 1)
Source brightness
function (Top Hat)
Repeat measurements for
each axis
Axis 1
5/24/2017
Website - dmradas.co.uk
(bx/l)
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Radio Astronomy
 How to understand Spatial Fourier Transforms – musical harmonics analogy
Brightness
Uniformly bright source
of Diameter D
Source brightness
function (Top Hat)
Can be built up from
Spatial components
Position
A square wave
Third harmonic wave F3
fundamental
wave F1
Fith harmonic wave F5
Sum of wave components
5/24/2017
At = S (AF1 + 1/3 AF3 + 1/5 AF5 + - - - )
Website - dmradas.co.uk
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Radio Astronomy
 Components of a Fourier Series
Component Amplitude
g
Square wave
Sharp edged disc
A
1/3
A
1/5
F1
F3
F5
A
Spatial Frequency
FN
Increasing fidelity
Increasing resolution
5/24/2017
Website - dmradas.co.uk
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Radio Astronomy
 Harmonic analysis
• Just as complex sound waves can be built up from harmonic
frequencies
• So can a source brightness picture be built up from ‘spatial
frequencies’
• It is the amplitude of these spatial frequencies that are
measured at each baseline setting of the interferometer
• These are the g values
• The Fourier Transform process simply reconstructs the
brightness picture from all the g components
(by/l)
g values are the white levels
Orthogonal Axis
Fourier Transforms
to sharp edged source
(bx/l)
Website - dmradas.co.uk
Axis 1
5/24/2017
Source brightness
function (Top Hat)
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Radio Astronomy – Aperture synthesis
 Measuring enough baselines by tracking the source
Baseline length changes as source transits
b3
b1
b0
Baseline length
b2
Source transit
b2
b1
b3
b0
t0
t1
t2
t3
time
Tracking cuts down the time to acquire all the baselines needed
The baseline length changes with time as a matter of course
Can get data on g as function of b/l automatically –
If the antennas point and track the source
5/24/2017
Website - dmradas.co.uk
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Radio Astronomy
 Multiple baseline interferometers - today’s Radio Telescopes
 Measuring g sequentially at many baseline spacings
Interferometric fringes are obtained simultaneously for baselines
from every antenna to every other antenna
They can be moved to create a new set of baselines
The results can all be put together to give a high resolution
‘picture’ of source brightness
This requires significant fast data gathering and computing power
The Very Large Array in New Mexico
Images can be produced with greater angular resolution than
large optical telescopes if arrays are on a very large scale
Sagittarius A
using VLA
Using a multiple Interferometer it is possible to ‘Synthesise’ a very large
antenna aperture – one that could not physically be built from a solid surface
5/24/2017
Website - dmradas.co.uk
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Radio Astronomy
 Antenna discussion - gain v beamwidth v bandwidth
• Any antenna design is optimised for particular factors
Performance
Type
Gain
BeamW
BandW
Large
Dish + Feed
H
N
W
YAGI
M
M
M
Dipole
L
W
W
Complex
X
Must compromise on parameters
Can get high gain + narrow beams + wide bandwidth
with interferometers using dipoles
5/24/2017
Website - dmradas.co.uk
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Radio Astronomy
 The next generation Radio Telescopes
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Square kilometre array – a continent wide instrument !
Multi frequency , multi source, imaging Aperture Synthesis
Used thousands of broad band simple antennas
Real-time digitisation of each broadband antenna signal
Fibre-optic communications to processor
Significant computer power to produce multi target images
For sources A,B, C etc
simultaneously
Frequency F1,F2, to Fn
simultaneously
Source A
thousands of antennae
1km
All the work is done in the software – a huge advance in image resolution and saving in time
5/24/2017
Website - dmradas.co.uk
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Radio Astronomy - the future SKA
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$ 1.5 billion multi national collaboration
2015 – 2020
Many radio telescopes in one system 100MHz to xx GHz
South Africa or Australia - A global instrument !
Central cluster of antennas with ‘outliers’ thousands of miles away
Improved sensitivity enable to see back to ‘darkages’ 300,000yrs
Image resolution better than any optical instrument
Investigate distribution of dark matter & nature of dark energy
Dark Ages
5/24/2017
Website - dmradas.co.uk
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Radio Astronomy - the future
 Science goals of SKA
The Unknown
While this is truly exciting and transformational science
History has shown that many of the greatest discoveries
happen accidentally
The unique sensitivity and versatility of the SKA make it a
Discovery Machine
We should be prepared for the possibilities !
5/24/2017
Website - dmradas.co.uk
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Radio Astronomy
End of Part 2
5/24/2017
Website - dmradas.co.uk
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