Propagation effects (tropospheric and ionospheric phase calibration)

Transcription

1 Propagation effects (tropospheric and ionospheric phase calibration) Prof. Steven Tingay Curtin University of Technology Perth, Australia With thanks to Alan Roy (MPIfR), James Anderson (JIVE), Tasso Tzioumis (ATNF) and Emil Lenc (Swinburne), for material (+ stuff stolen from Rick Perley, Tom Osterloo, and Tony Beasley)

2 Outline Propagation in radio astronomy in general terms; Introduction to troposphere and ionosphere; Propagation effects in the ionosphere; Propagation effects in the troposphere; Correction of phase at phase centre (narrow-field calibration); Correction of phase away from phase centre (wide-field calibration);

3 Propagation in general Propagation effects in astronomical source (absorption, masers etc); Propagation through space (Faraday rotation, dispersion etc) Propagation through solar system (solar wind) Propagation through troposphere and ionosphere; Propagation through antenna system and electronics.

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5 Propagation through an ionised medium (pulsars)

6 Time PSR Dynamic spectrum 0.6 AU Frequency Pulsar scintillation and the structure of the ISM: Walter Brisken (NRAO) Arecibo, GBT, Jodrell Bank, Westerbork: correlated at Swinburne (32768 spectral channels for each of four 8 MHz bands, pulsar gated, 1.25 s integrations)

7 Free-free absorption

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9 Introduction to the troposphere and ionosphere Troposphere: < 12 km: Neutral (not ionised); Wet component - contains water (precipitable and vapour); Complicated and highly variable structure. Ionosphere: ~ km: Ionised atmosphere (by cosmic radiation - mainly solar uv and X-ray radiation) A number of layers (D, E, F); Complicated and highly variable structure.

10 Troposphere and ionosphere beneficial to life - protects us from high energy radiation; Complication for most astronomy;

11 Phase and amplitude change to radio astronomy signals Propagation through the ionosphere and troposphere alters the amplitude and phase of the radio waves; Phase (delay) causes a change in the relative arrival times of the wavefront at two locations on Earth (radio telescopes in an interferometer), altering the amplitude and phase of the visibility output of the correlator (see lectures tomorrow); This introduces antenna-based errors into the data that must be removed, in order to recover the true visibilities that describe the structure of the radio source being imaged.

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13 target θ Calibrator

14 The ionosphere Ionised medium has a index of refraction that is a function of frequency at radio wavelengths => the ionosphere is a dispersive medium for radio waves. VTEC STEC TEC = Total Electron Content; STEC = Slant TEC (line of sight); VTEC = Vertical TEC (STEC at zenith); ζ TECU = TEC units (10 16 electrons/m 2 )

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16 STEC varies on short and long timescales within the different layers of the ionosphere: Diurnal variations; Seasonal variations; Variations with solar cycle; Complicated variations on timescales of seconds to hours; Depends on solar output of uv and X-rays. TEC varies with latitude.

17 Scintillation Refractive wedge At dawn Midnight wedge Quiescence TIDs

18 QuickTime and a Cinepak decompressor are needed to see this picture.

19 Milky Way Ionosphere

20 On long baselines and for large fields of view, assumptions of static structures and fixed gradients break down.

21 Movie of VLBA 327 MHz ionospheric phase errors

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23 The troposphere The troposphere is neutral and has wet and dry components. Additional path length (m): P o = total atmospheric pressure at surface; P w = partial pressure due to water vapour at surface; T = surface temperature; f = factor of order unity dealing with gravity variations (with latitude and height); Dry component (depends only on P o ) dominates change in path length but can be modelled to 0.05 cm (1/20th of wavelength at 22 GHz). P w can only be modelled to ~2 cm (2 wavelengths at 22 GHz) => wet atmosphere dominates phase errors NB: Not a function of frequency (non-dispersive)

24 Phase goes as: φ = 2πνδ For ionosphere: δ ν -2 => φ ν -1 For troposphere: δ ν 0 => φ ν +1 Frequency that (generally) minimises total phase error variations is ~ 1 GHz. Log phase ~ 1 GHz Log f

25 Phase monitor at the Australia Telescope Compact Array

26 Phase errors in VLBA observations of Centaurus A: VLBA, a Northern Hemisphere (latitude ~ +30) long baseline array; Centaurus A, a Southern Hemipshere (declination = -44) radio galaxy; Low elevation for a few hours, 8.4 GHz, so tropospheric phase errors are significant

27 Phase errors in ATCA observations of NGC 4945 ATCA 6 km, east-west array; 22 GHz observation, moderate weather; Significant tropospheric phase errors;

28 Correction of phase errors: 1 Ionosphere - GPS satellites: Many satellites monitored at many locations on Earth; Dual-frequency measurement of delay as function of frequency; Grids in (lat,long) and (RA,Dec) are not fine enough to be generally useful. Troposphere - Water Vapour Radiometers: Measure radio power radiated from water vapour and convert to path length to correct phase; Only works when the water is vapour - not applicable to precipitable water (i.e. clouds)

29 QuickTime and a YUV420 codec decompressor are needed to see this picture. QuickTime and a YUV420 codec decompressor are needed to see this picture.

30 Phase error correction at the centre of the FoV External calibration: Phase referencing; Refer to a nearby celestial source for which position and structure are accurately known, to solve for amplitude and phase errors on all antennas (needed for weak target sources). Internal calibration: Self-calibration; Use an iterative approach to solve for the parameters of the source as well as the amplitude and phase errors (only possible for strong target sources). Covered in lecture yesterday.

31 target θ Calibrator

32 Phase referencing works if you can switch between target and calibrator quickly enough (to properly sample temporal changes) AND the target and calibrator are close enough to minimise the spatial changes. Target scans Calibration scans

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34 Target - calibrator angular separation depends on the application: Detection of weak sources: Precision astrometry: ~ 1-2 degrees; ~ arcminutes; Multiple phase-reference sources per target improves the interpolation (if possible) CAL 2 Target CAL 1 CAL 3

35 Determine the antenna delays accurately by measuring phase vs frequency over a wide frequency range. Accurate astrometry and geodesy VLBI uses ~16 simultaneous frequencies spanning S band (~ GHz) and X band (~ GHz). => Determine tropospheric and ionospheric components of the phase errors

36 VERA (VLBI Exploration of Radio Astrometry)

37 Self-calibration (quick example) ATCA; NGC 4945 (starburst galaxy): 21 GHz, 375m + 6 km, reference calibration every 5 minutes

38 Isoplanatic patchs - ionosphere and troposphere Isoplanatic patch: the angular size of a patch of sky for which the phase errors due to troposphere and/or ionopshere are highly correlated. Assumption used for simple phasereferencing and self-calibration is that: FoV < isoplanatic patch size For some applications, violation of this assumption limits the quality of images

39 Mainly a problem at low frequency (< few hundred MHz): Beam FWHM are larger; Ionosphere is far away (100 s of km); Isoplanatic patch size is ~10 km; Beam covers more than one patch typically; Different patch over each antenna in long baseline arrays. VLA (74 MHz); VLBA (327 MHz); LOFAR/MWA/SKA.

40 Phase correction across the full FoV Field-based calibration: Take snapshot image of bright sources in field; Measure positions relative to known positions; Fit a Zernicke polynomial to estimate a set of corrections to the phase across the field; Works best on short baselines and simple ionospheric structures (i.e. wedges)

41 Peeling From Tom Osterloo s presentation (SKA wide-field imaging meeting, Dwingeloo [June 2005]) Normal assumption for the whole field: V = V g g* 1-2,true 1-2,obs 1 2 g = g(t, ν ) = a(t) b( ν) However, when the field contains several isoplanatic patches: For each patch: so: V = V g g* 1-2,true 1-2,obs 1 2 g = g(t, ν patch) = a(t patch) b( ν patch)

42 Subtract sources and calibrate what is left 1 degree selfcal on entire field subtract central sources only off-axis source left define central field 3C343 & 3C343.1 WSRT L band

43 subtract central sources only off-axis source left selfcal on off-axis source gives extra gains for off-axis patch so off-axis errors disappear errors due to central sources unchanged!

44 Peeling: 1. apply extra gains to data 2. subtract off-axis source 3. undo extra gains off-axis source (+ its errors!!!) gone

45 off-axis source (+ errors!!!) gone selfcal centre again good calibration for central field

46 By solving for extra gains for off-axis source off-axis errors gone; dyn range > 10000

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48 MIM (Minimum Ionosphere Model) Due to Jan Noordam (ASTRON); Worked on by James Anderson (JIVE); Experimental technique to calibrate the ionosphere for LOFAR; Takes advantage of many piercing points from the LOFAR stations and attempts to fit minimum parameters to the dynamic ionosphere; Subject for another lecture.

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50 Summary When instrumental effects are under control (clocks, antenna positions etc), the troposphere and ionosphere provide the largest sources of phase error for interferometers; Phase errors translate into errors in the structure seen in images of radio sources, the derived positions of radio sources, and can limit the dynamic range of interferometric images - the errors must be controlled; Ionosphere generally dominates at low frequencies (< 1 GHz); Troposphere generally dominates at high frequencies (> 1 GHz); Both troposphere and ionosphere are dynamic and vary to different degrees on different timescales;

51 Phase reference calibration + self-calibration works well near the phase centre and can be routinely utilised; More complicated phase calibration techniques are required over wide fields of view, especially for long baseline arrays at very low frequencies, such as for the next generation instruments like LOFAR, MWA, and SKA.