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)

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-fieldcalibration);

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.

Propagation through an ionised medium (pulsars)

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)

Frequency

Time

0.6 AU

PSR 0834+06

Dynamic spectrum

Free-free absorption

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: ~50 - 500 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.

• Troposphere and ionosphere beneficial to life -protects us fromhigh energy radiation;

• Complication for most astronomy;

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 datathat must be removed, in order to recover the truevisibilities that describe the structure of the radio source being imaged.

target

Calibrator

θ

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.

TEC = Total Electron Content;STEC = Slant TEC (line of sight);VTEC = Vertical TEC (STEC at zenith);

TECU = TEC units (1016 electrons/m2)

VTEC STEC

ζ

• 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.

ScintillationRefractive wedge

At dawn

Quiescence‘Midnightwedge’

TIDs

QuickTime™ and aCinepak decompressor

are needed to see this picture.

Milky Way

Ionosphere

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

• Movie of VLBA 327 MHz ionospheric phase errors

The troposphere

• The troposphere is neutral and has wet and dry components. Additional path length (m):

Po = total atmospheric pressure at surface;Pw = 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 Po) dominates change in path length but can be modelled to 0.05 cm (1/20th of wavelength at 22 GHz). Pw 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)

Phase goes as: φ = 2πνδ

– For ionosphere: δ ≈ ν-2 => φ ≈ ν-1

– For troposphere: δ ≈ ν0 => φ ≈ ν+1

– Frequency that (generally) minimises total phase error variations is ~ 1 GHz.

Log f

Log phase

~ 1 GHz

Phase monitor at the Australia Telescope Compact Array

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

Phase errors in ATCA observations of NGC 4945

– ATCA 6 km, east-west array;

– 22 GHz observation,moderate weather;

– Significant tropospheric phase errors;

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)

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

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.

target

Calibrator

θ

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.

Calibrationscans

Targetscans

CAL 1CAL 3

CAL 2

Target

Target - calibrator angular separation depends on the application:

Detection of weak sources: ~ 1 - 2 degrees;Precision astrometry: ~ arcminutes;

Multiple phase-reference sources per targetimproves the interpolation (if possible)

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 (~2.2 - 2.5 GHz) and X band (~7.8 - 9.0 GHz).

=>

Determine tropospheric and ionospheric components of the phase errors

VERA (VLBI Exploration of

Radio Astrometry)

Self-calibration (quick example)

ATCA; NGC 4945 (starburst galaxy):

21 GHz, 375m + 6 km, reference calibration every 5 minutes

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 phase-referencing and self-calibration is that:– FoV < isoplanatic patch size

• For some applications, violation of this assumption limits the quality of images

• Mainly a problem at low frequency (< fewhundred 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.

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)

“Peeling”From Tom Osterloo’s presentation (SKA wide-field imaging meeting, Dwingeloo [June 2005])

Normal assumption for the whole field:

However, when the field containsseveral isoplanatic patches:

)b( a(t) )g(t,g

ggVV

νννννννν ==

⋅= *21obs2,-1true2,-1

)b( )a(t )g(t,g

ggVV

patchpatchpatch

*21obs2,-1true2,-1

||||νννν|||| ||||νννν ==

⋅=For each patch:

so:

Subtract sources and calibrate what is left

3C343 & 3C343.1 WSRT L band

selfcal on entire field

1 degree

subtract “central” sources� only off-axis source left

define central field

subtract “central” sources� only off-axis source left

selfcal on off-axis source gives extra gainsfor off-axis patch so off-axis errors disappear

errors due to central sources unchanged !

Peeling: 1. apply extra gains to data2. subtract off-axis source3. undo extra gains

�off-axis source (+ its errors!!!) gone

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

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

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.

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;

• 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.