I CASS Radio Astronomy School R D Ekers 24 Sep 2012 292Sep 2012 R D Ekers 2 WHY Importance in radio astronomy ATCA VLA WSRT GMRT MERLIN IRAM VLBA JIVE VSOP RADIOASTON ALMA LOFAR MWA ASKAP MeerKat SKA ID: 1044560
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1. Principles of Interferometry ICASS Radio Astronomy SchoolR. D. Ekers24 Sep 2012
2. 292Sep 2012R D Ekers2WHY?Importance in radio astronomyATCA, VLA, WSRT, GMRT, MERLIN, IRAM...VLBA, JIVE, VSOP, RADIOASTONALMA, LOFAR, MWA, ASKAP, MeerKat, SKA
3. 29 Sep 2008R D Ekers3Cygnus region - CGPS (small)Radio Image ofIonised Hydrogen in Cyg XCGPS (Penticton)
4. 29 Sep 2008R D Ekers4Cygnus ARaw dataVLA continuumDeconvolutioncorrecting for gaps between telescopes Self Calibrationadaptive optics
5. 29 Sep 2008R D Ekers5WHY?Importance in radio astronomyATCA, VLA, WSRT, GMRT, MERLIN, IRAM...VLBA, JIVE, VSOP, RADIOASTRONALMA, LOFAR, ASKAP, SKAAT as a National Facilityeasy to usedon’t know what you are doingCross fertilizationDoing the best science
6. 24 Sep 2012R D Ekers6Indirect Imaging ApplicationsInterferometryradio, optical, IR, space...Aperture synthesisEarth rotation, SAR, X-ray crystallographyAxial tomography (CAT)NMR, Ultrasound, PET, X-ray tomographySeismologyFourier filtering, pattern recognitionAdaptive optics, speckleAntikythera
7. 29 Sep 2008R D Ekers7Doing the best scienceThe telescope as an analytic toolhow to use itintegrity of resultsMaking discoveriesMost discoveries are driven by instrumental developments recognising the unexpected phenomenondiscriminate against errorsInstrumental or Astronomical specialization?
8. 29 Sep 2008R D Ekers8HOW ?Don’t Panic!Many entrance levels
9. 29 Sep 2008R D Ekers9Basic conceptsImportance of analogies for physical insightDifferent ways to look at a synthesis telescopeEngineers modelTelescope beam patterns…Physicist em wave modelSampling the spatial coherence functionBarry Clark Synthesis Imaging chapter1Born & Wolf Physical OpticsQuantum modelRadhakrishnan Synthesis Imaging last chapter
10. 29 Sep 2008R D Ekers10Spatial Coherencevan Cittert-Zernike theoremThe spatial coherence function is the Fourier Transform of the brightness distributionP1P2Q1Q2P1 & P2 spatially incoherent sourcesAt distant points Q1 & Q2 The field is partially coherent
11. 11Physics: propagation of coherenceRadio source emits independent noise from each elementElectrons spiraling around magnetic fieldsThermal emission from dust, etc.As electromagnetic radiation propagates away from source, it remains coherentBy measuring the correlation in the EM radiation, we can work backwards to determine the properties of the sourceVan Cittert-Zernicke theorem states that theSky brightness and Coherence function are a Fourier pairMathematically:
12. 12Physics: propagation of coherenceCorrelate voltages from the two receiversSimplest examplePut two emitters (a,b) in a planeAnd two receivers (1,2) in another planeCorrelation contains information about the source ICan move receivers around to untangle information in g’s
13. 23 Sep 2012R D Ekers13Analogy with single dishBig mirror decomposition
14. 14
15. 15
16. 16( Vi )2Free spaceGuided
17. 17( Vi )2Free spaceGuided
18. 18( Vi )2Phased arrayFree spaceGuidedDelay
19. 19( Vi )2Free spaceGuidedPhased arrayDelay
20. 20( Vi )2 = (Vi )2 + (Vi Vj )Free spaceGuidedPhased arrayDelay
21. 21( Vi )2 = (Vi )2 + (Vi Vj )Free spaceGuidedPhased arrayDelayCorrelation arrayRyle & Vonberg (1946) phase switch
22. 22
23. 23IPhasedArrayx2x2x2x2x2x2Split signalno S/N losstPhased array ( Vi )2I() ( Vi )2
24. 24IPhasedArrayx2x2x2x2x2x2Split signalno S/N losstPhased array ( Vi )2I() ( Vi )2Tied arrayBeam former
25. 25<Vi Vj>t= t/correlatorFourier TransformI(r)van Cittert-Zernike theoremSynthesis Imaging
26. 23 Sep 2012R D Ekers26Analogy with single dishBig mirror decompositionReverse the process to understand imaging with a mirrorEg understanding non-redundant masksAdaptive opticsSingle dishes and correlation interferometersDarrel Emerson, NRAOhttp://www.gb.nrao.edu/sd03/talks/whysd_r1.pdf
27. 29 Sep 2008R D Ekers27Filling the apertureAperture synthesismeasure correlations sequentiallyearth rotation synthesisstore correlations for later useRedundant spacingssome interferometer spacings twiceNon-redundant apertureUnfilled aperturesome spacings missing
28. 1 2 3 4 5 61unit 5x2units 4x3units 3x4units 2x5units 1x 15n(n-1)/2 = Redundancy
29. 1 2 3 4 5 6 7 81unit 1x2units 1x3units 1x4units 1x5units 0x6units 1x7units 1xetcNon Redundant
30. 29 Sep 2008R D Ekers30Basic Interferometer
31. 29 Sep 2008R D Ekers31Storing visibilitiesStorage Can manipulate the coherence function and re-image
32. 29 Sep 2008R D Ekers32Fourier Transform and ResolutionLarge spacingshigh resolutionSmall spacingslow resolution
33. Fourier Transform Propertiesfrom Kevin Cowtan's Book of Fourierhttp://www.ysbl.york.ac.uk/~cowtan/fourier/fourier.htmlFTFT
34. Fourier Transform Propertieshttp://www.general.uwa.edu.au/u/vpatrick/fourier/magic.htmlFT10% data omitted in rings
35. Fourier Transform Propertieshttp://www.general.uwa.edu.au/u/vpatrick/fourier/magic.htmlAmplitude of duckPhase of catFT
36. Fourier Transform Propertieshttp://www.general.uwa.edu.au/u/vpatrick/fourier/magic.htmlAmplitude of catPhase of duckFT
37. 37In practice… Use many antennas (VLA has 27)Amplify signalsSample and digitizeSend to central locationPerform cross-correlationEarth rotation fills the “aperture”Inverse Fourier Transform gets imageCorrect for limited number of antennasCorrect for imperfections in the “telescope” e.g. calibration errorsMake a beautiful image…
38. 29 Sep 2008R D Ekers38Aperture Array or Focal Plane Array?Why have a dish at all?Sample the whole wavefrontn elements needed: n Area/( λ/2)2For 100m aperture and λ = 20cm, n=104Electronics costs too high!Phased Array FeedsAny part of the complex wavefront can be usedChoose a region with a smaller waistNeed a concentratorComputer
39. 29 Sep 2008R D Ekers39Find the Smallest Waistuse dish as a concentratorD1 < D2n1 < n2D1 D2
40. 29 Sep 2008R D Ekers40Radio Telescope Imagingimage v aperture planeComputerComputerDishes act as concentratorsReduces FoV Reduces active elementsCooling possibleλIncrease FoV Increases active elementsActive elements ~ A/λ2
41. 29 Sep 2008R D Ekers41Analogies RADIOgrating responsesprimary beam directionUV (visibility) planebandwidth smearinglocal oscillator OPTICAL aliased orders grating blaze angle hologram chromatic aberration reference beam
42. 22 Sep 2012R D Ekers42Terminology RADIOAntenna, dish SidelobesNear sidelobesFeed legsAperture blockageDirty beamPrimary beam OPTICAL Telescope, element Diffraction pattern Airy rings Spider Vignetting Point Spread Function (PSF) Field of View
43. 22 Sep 2012R D Ekers43Terminology RADIOMap SourceImage planeAperture planeUV planeApertureUV coverage OPTICAL Image Object Image plane Pupil plane Fourier plan Entrance pupil Modulation transfer function
44. 22 Sep 2012R D Ekers44Terminology RADIODynamic rangePhased arrayCorrelatorno analogReceiverTaperSelf calibration OPTICAL Contrast Beam combiner no analog Correlator Detector Apodise Wavefront sensing (Adaptive optics)