principles of interferometry i
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Principles of Interferometry I. CASS Radio Astronomy School R. D. Ekers 24 Sep 2012. WHY?. Importance in radio astronomy ATCA, VLA, WSRT, GMRT, MERLIN, IRAM... VLBA, JIVE, VSOP, RADIOASTON ALMA, LOFAR, MWA, ASKAP, MeerKat, SKA. Cygnus region - CGPS (small). Radio Image of - PowerPoint PPT PresentationTRANSCRIPT
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Principles of Interferometry I
CASS Radio Astronomy SchoolR. D. Ekers24 Sep 2012
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WHY?
Importance in radio astronomy– ATCA, VLA, WSRT, GMRT, MERLIN, IRAM...– VLBA, JIVE, VSOP, RADIOASTON– ALMA, LOFAR, MWA, ASKAP, MeerKat, SKA
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Cygnus region - CGPS (small)
Radio Image ofIonised Hydrogen in Cyg XCGPS (Penticton)
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Cygnus A
Raw dataVLA continuum
Deconvolutioncorrecting for gaps between
telescopes
Self Calibrationadaptive optics
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WHY?
Importance in radio astronomy– ATCA, VLA, WSRT, GMRT, MERLIN, IRAM...– VLBA, JIVE, VSOP, RADIOASTRON– ALMA, LOFAR, ASKAP, SKA
AT as a National Facilityeasy to use don’t know what you are doing
Cross fertilization Doing the best science
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Indirect Imaging Applications
Interferometry– radio, optical, IR, space...
Aperture synthesis– Earth rotation, SAR, X-ray crystallography
Axial tomography (CAT)– NMR, Ultrasound, PET, X-ray tomography
Seismology Fourier filtering, pattern recognition Adaptive optics, speckle Antikythera
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Doing the best science
The telescope as an analytic tool– how to use it– integrity of results
Making discoveries– Most discoveries are driven by instrumental developments– recognising the unexpected phenomenon– discriminate against errors
Instrumental or Astronomical specialization?
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HOW ?
Don’t Panic!– Many entrance levels
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Basic concepts
Importance of analogies for physical insight Different ways to look at a synthesis telescope
– Engineers model» Telescope beam patterns…
– Physicist em wave model» Sampling the spatial coherence function» Barry Clark Synthesis Imaging chapter1» Born & Wolf Physical Optics
– Quantum model» Radhakrishnan Synthesis Imaging last chapter
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Spatial Coherence
van Cittert-Zernike theoremThe spatial coherence function is the Fourier Transform
of the brightness distribution
P1 P2
Q1 Q2
P1 & P2 spatially incoherent sources
At distant points Q1 & Q2 The field is partially coherent
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Physics: propagation of coherence• Radio source emits independent noise from each
element• Electrons spiraling around magnetic fields• Thermal emission from dust, etc.
• As electromagnetic radiation propagates away from source, it remains coherent
• By measuring the correlation in the EM radiation, we can work backwards to determine the properties of the source
• Van Cittert-Zernicke theorem states that the• Sky brightness and Coherence function are a Fourier
pair• Mathematically: dmdlvmuljemlIvuV ..2.),(),(
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Physics: propagation of coherence
• Correlate voltages from the two receiversV1
r .V2r Va
e.g1a Vb
e.g1b Va
e.g2a Vb
e.g2b
Vae.Va
e .g2a .g1
a Vbe.Vb
e .g2b .g1
b
Ia .g2a .g1
a Ib .g2b .g1
b
beb
aea
r
beb
aea
r
gVgVV
gVgVV
222
111
..
..
• Simplest example– Put two emitters (a,b) in a plane– And two receivers (1,2) in another plane
• Correlation contains information about the source I• Can move receivers around to untangle information
in g’s
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Analogy with single dish
Big mirror decomposition
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( Vi )2
Free space
Guided
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( Vi )2
Free space
Guided
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18( Vi )2Phased array
Free space
Guided
Delay
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19( Vi )2
Free space
Guided
Phased array
Delay
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20( Vi )2 = (Vi )2 + (Vi Vj )
Free space
Guided
Phased array
Delay
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21( Vi )2 = (Vi )2 + (Vi Vj )
Free space
Guided
Phased array
Delay
Correlation array
Ryle & Vonberg (1946) phase switch
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24I
PhasedArray
x2 x2 x2 x2 x2 x2Split signalno S/N loss
t
Phased array ( Vi )2
I()
( Vi )2
Tied arrayBeam former
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<Vi Vj>
t
= t/
correlator
Fourier Transform
I(r)
van Cittert-Zernike theorem
Synthesis Imaging
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Analogy with single dish
Big mirror decomposition Reverse the process to understand imaging with a
mirror– Eg understanding non-redundant masks– Adaptive optics
Single dishes and correlation interferometers– Darrel Emerson, NRAO– http://www.gb.nrao.edu/sd03/talks/whysd_r1.pdf
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Filling the aperture
Aperture synthesis– measure correlations sequentially– earth rotation synthesis– store correlations for later use
Redundant spacings– some interferometer spacings twice
Non-redundant aperture Unfilled aperture
– some spacings missing
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1 2 3 4 5 6
1unit 5x2units 4x3units 3x4units 2x5units 1x 15n(n-1)/2 =
Redundancy
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1 2 3 4 5 6 7 8
1unit 1x2units 1x3units 1x4units 1x5units 0x6units 1x7units 1xetc
Non Redundant
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Basic Interferometer
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Storing visibilities
Storage
Can manipulate the coherence function and re-image
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Fourier Transform and Resolution
Large spacings– high resolution
Small spacings– low resolution
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Fourier Transform Propertiesfrom Kevin Cowtan's Book of Fourier
http://www.ysbl.york.ac.uk/~cowtan/fourier/fourier.html
FT
FT
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Fourier Transform Properties
http://www.general.uwa.edu.au/u/vpatrick/fourier/magic.html
FT
10% data omitted in rings
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Fourier Transform Properties
http://www.general.uwa.edu.au/u/vpatrick/fourier/magic.html
Amplitude of duckPhase of cat
FT
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Fourier Transform Properties
http://www.general.uwa.edu.au/u/vpatrick/fourier/magic.html
Amplitude of catPhase of duck
FT
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In practice…1. Use many antennas (VLA has 27)2. Amplify signals3. Sample and digitize4. Send to central location5. Perform cross-correlation6. Earth rotation fills the “aperture”7. Inverse Fourier Transform gets
image8. Correct for limited number of
antennas9. Correct for imperfections in the
“telescope” e.g. calibration errors10.Make a beautiful image…
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Aperture Array or Focal Plane Array?
Why have a dish at all?– Sample the whole wavefront– n elements needed: n Area/( λ/2)2
– For 100m aperture and λ = 20cm, n=104
» Electronics costs too high!
Phased Array Feeds– Any part of the complex wavefront can be used– Choose a region with a smaller waist– Need a concentrator
Computer
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Find the Smallest Waistuse dish as a concentrator
D1 < D2
n1 < n2
D1
D2
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Radio Telescope Imagingimage v aperture plane
Computer
Computer
Dishes act as concentratorsReduces FoV
Reduces active elementsCooling possible
λ
Increase FoV Increases active elements
Active elements ~ A/λ2
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Analogies
RADIO
grating responses
primary beam directionUV (visibility) plane
bandwidth smearing
local oscillator
OPTICAL
Û aliased orders
Û grating blaze angleÛ hologram
Û chromatic aberration
Û reference beam
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Terminology
RADIO
Antenna, dish
Sidelobes
Near sidelobes
Feed legs
Aperture blockage
Dirty beam
Primary beam
OPTICALÛ Telescope, elementÛ Diffraction patternÛ Airy ringsÛ SpiderÛ VignettingÛ Point Spread Function (PSF)Û Field of View
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Terminology
RADIO
Map
Source
Image plane
Aperture plane
UV plane
Aperture
UV coverage
OPTICALÛ ImageÛ Object
Û Image planeÛ Pupil planeÛ Fourier planÛ Entrance pupilÛ Modulation transfer function
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Terminology
RADIO
Dynamic range
Phased array
Correlator
no analog
Receiver
Taper
Self calibration
OPTICAL Û ContrastÛ Beam combinerÛ no analogÛ CorrelatorÛ DetectorÛ ApodiseÛ Wavefront sensing (Adaptive optics)