Combining Different Arrays Tom Muxlow General introduction Data set alignment Data set weighting Combining data with differing characteristics Image plane.

Combining Different ArraysCombining Different ArraysTom MuxlowTom Muxlow

•General introduction

•Data set alignment

•Data set weighting

•Combining data with differing characteristics

•Image plane combination

•Self-calibrating combination data sets

Combining Different ArraysCombining Different Arrays

General Introduction

•MERLIN covers a unique range of telescope separations, intermediate between that of the VLA and VLBI

•When imaging in a single frequency band, faint extended emission is often only visible with the VLA since the surface brightness is too low to be detected at VLBI angular resolution

•Individual images from the VLA, MERLIN, and VLBI are usually sufficient to show the radio structure changes over large range of scale size

•When would you want to make combination images ??

Combination imaging or separate imaging ??


General Introduction

•Where surface brightness limitations do allow higher resolution imaging of extended structure, MERLIN will add extend the resolution of the VLA, and VLBI extend MERLIN

• In VLA/MERLIN and MERLIN/VLBI combinations, the addition of the shorter-spacing data are required in order to provide otherwise missing spatial frequencies – they also stabilise the de-convolution procedure

•Remember that the largest holes in the u-v coverage will always limit the size of extended region that can be imaged – use MFS where appropriate

Combination imaging or separate imaging ??


General Introduction -- stabilising de-convolution

•MERLIN/VLBI combination stabilises the de-convolution of the VLBI only image and permits high resolution imaging over extended components

3C293 Global VLBI + MERLIN (Beswick et al)


General Introduction -- Separate images

•VLA image shows low surface brightness lobes which are too extended to be succesfully imaged by MERLIN or VLBI

•Separate images are appropriate to show the relationship between regions of low and high surface-brightness

3C293 Global VLBI + MERLIN (Beswick et al)


General Introduction -- Combined/separate images

•VLA

1803+784 Global VLBI + MERLIN (Britzen et al)

VLBA 15 GHz

Global VLBI 5 GHz

Global VLBI+MERLIN 1.7 GHz

MERLIN 1.7 GHz

WSRT 1.4 GHz


General Introduction -- Extended components

•VLA image shows low surface brightness lobes which are too extended to be successfully imaged by MERLIN monochromatically

•Multi-Frequency-Synthesis MERLIN observations alleviate the condition, but the very extended tails show some evidence of break-up during de-convolution procedure

3C401 VLA + MERLIN MFS (Leahy)

L-Band, beam 0.15 arcsec MERLIN User Guide (L-Band) Guidelines:

Maximum component size which can be…

Detected 4 arcsec

Imaged (1 frequency) 2.5 arcsec

Imaged (MFS) 8 arcsec

LAS = 24 arcsec


Data set alignment

•Data sets usually processed separately and then combined

•For MERLIN/EVN data combinations with common baselines (eg Jodrell – Cambridge –Knockin), check amplitude peaks correspond

•For MERLIN/VLA combinations check flux densities found on common phase calibration sources. A full crossing-point analysis may provide insights into interferometry, but rarely helps with imaging since the w-projection is usually significantly different

•Beware variability between combination epochs for both target and calibration sources

Cross-checking amplitude calibration


Data set alignment

•Ensure that both data sets are either B1950 or J2000

•Beware early VLA data sets nominally observed in B1950 – the phase calibrator positions are quoted in equinox 1950, epoch 1979.9

•If the data sets have been phase-calibrated, check the assumed calibrator positions

•Old data sets may suffer from poor phase-calibrator positions

•If the data sets have been self-calibrated only, they are almost certainly not aligned

•Make each image separately and convolve down the higher resolution image to that of the other and check the positions on a compact component within the overall source structure – beware blending

Are the data sets astrometrically aligned?


Data set alignment

•Use J2000. Convert from B1950 where appropriate – use coco

•MERLIN and VLBI data will be equinox 1950.0, epoch 1950.0

•Convert VLA phase calibrator positions from 1950.0, epoch 1979.9

•Check against phase calibrator position used in MERLIN – note offset

•Change the ‘epoch’ label in AIPS uv-data header to J2000 with PUTH

•Modify the ‘RA’ and ‘Dec’ lines in the header with AXDEF to correspond with the correct J2000 position – incorporating any offset

•Run UVFIX to recalculate the u-v-w axes in the data set

•Do not run UVFIX on a B1950 data set – it attempts to convert to J2000 but does not do so to the required precision

B1950 or J2000?


Data set alignment

•If data sets have only been subject to self-calibration or still do not align after careful study of positions and offsets, consider a single pass of self-calibration using high resolution image to correct low resolution data

•Use uvrange to restrict solutions to only match model flux density

Pre-combination self-calibration?

3C459 VLA 5 GHz

3C459 MERLIN MFS 5 GHz


Data set weighting•Statistical weights associated with each integration differ between arrays and depend on processing route

•Inspect weights with PRTUV

task time messages for user 666

IMAGR1 16:30:38 GRDMEM: Frequency 4.866000E+09 Hz

IMAGR1 16:30:38 Field 1 Sum of gridding weights = 2.40224E+07

IMAGR1 16:30:38 Field 1 Beam min = -198.5 MilliJy, max = 1.0 Jy

IMAGR1 16:30:38 Field 1 fit FWHM = 93.611 x 50.207 Milliarcsec, PA= 28.3

Source= 3C459 RA = 23 14 2.31 DEC = 03 48 55.2 IF = 1

Freq= 4.865999862 GHz Ncor= 4 No. vis= 78598 Sort order= TB

Source= 3C459 Freq= 4.865999862 Sort= TB 1 RR 1 LL 1 RL 1 LR

Vis # IAT Ant Su Fq U(klam) V(klam) W(klam) Amp Phas Wt Amp Phas Wt Amp Phas Wt Amp Phas Wt

1 0/23:12:25 1- 2 1 0 -446 96 0 0.470-105 0.6928 0.386 -99 0.6928 0.217 117 0.6928 0.050 32 0.6928

2 0/23:12:25 1- 3 1 0 -869 -832 0 0.609 36 0.4123 0.636 45 0.4123 0.170 -79 0.4123 0.165 27 0.4123

3 0/23:12:25 1- 4 1 0 -1452 -1197 0 0.533 22 0.4123 0.355 27 0.4123 0.145 28 0.4123 0.081-103 0.4123

4 0/23:12:25 1- 5 1 0 -1594 -1265 0 0.339 29 0.3162 0.421 9 0.3162 0.060 157 0.3162 0.147 120 0.3162

•In order to assign similar weights to each array – check sum of gridded weights in IMAGR

•Modify weights with REWEIGHT in routine DBCON


Combining data with different characteristics

•Process each array dataset as multi-source data files retaining characteristics of that data set

•Convert to single-source data files containing fully calibrated, astrometrically aligned target data

• Do any epoch conversions, position offset corrections, u-v-w re-calculation before combining

•Data sets should contain identical numbers of Ifs and frequency channels before combination – split out each IF and pre-combine to form a nominally time sequential single IF data set with separate sub-arrays

•Multi-channel data sets can be problematical. They should contain identical reference frequencies, channels numbers and channel bandwidths otherwise gridding errors will cause smearing in wide-field images – consider SPECR and BLOAT in aips

1 2

2 IF data set

1 IF data set

1

2


Data plane combination•Use DBCON in aips to concatenate each single-source data set

Positions:•Provided each data set is astronomically aligned, different pointing centres can be accommodated within DBCON by shifting the pointing centre of the second data set to that of the first (DOPOS parameter)

•If the data sets are not astronomically aligned, they can still be combined within DBCON and shifted to a single nominal pointing centre. However further cycles of self-calibration will be required in order to align the data set. It is usual to start with the high-resolution model for the first round of self-calibration

•Provided the data sets are single channel, all should be ok

•Recalculating u-v-ws in UVFIX after combination is not recommended – the data set may have originated from several different frequencies


Data plane combination

u-v-w values:

•The u-v-w values associated with each integration are the projected baseline in wavelengths of the reference frequency in the file header of the original data file prior to combination

•The combination data set may be constructed from individual files with different reference frequencies. Don’t mess with them unless you have to !!

•For multi-channel data, the u-v-w value refers to the reference channel

•DBCON will have ensured that the combination data set has a single defined reference frequency and reference channel – you can override frequency checks if the reference frequency and channel bandwidths differ

•IF you do – beware gridding errors in wide-field images since IMAGR will grid each channel stepping out from the reference assuming the reference frequency and channel bandwidth contained in header


Image plane combination

•Since the Fourier transform is a linear transform, one can make use of the equivalence principle which states that the transform of the sum of two distributions is equivalent to the sum of the separate transforms

FT=>+ Standard data-plane combination

FT=>

FT=>

+ => Image-plane combination



•This is the standard method for deep field VLA+MERLIN combinations

•The VLA and MERLIN data sets are each Fourier transformed to separate dirty maps and dirty beams with appropriate image and pixel sizes

•The VLA dirty map and dirty beam are then re-gridded with HGEOM to the geometry of the MERLIN images

•Combination dirty maps and dirty beams are constructed with COMB prior to conventional de-convolution via and image-based algorithm

VLA dirty beam MERLIN dirty beam VLA dirty beam re-gridded to MERLIN geometry



•The sensitivity of the combination image may be maximised by altering the relative weighting in COMB to reflect the array sensitivities

•Test image performed from HDF-N field (Muxlow et al 2005) for 307µJy source J123649+620738, which lies 320 arcsec from field centre. Data rotated and averaged to single channel before imaging

•Test shows that images are the same for dynamic ranges ~300:1

Combining Different ArraysCombining Different ArraysImage plane combination – HDF North

•MERLIN – 18 days, 1 IF (1420 MHz, 31x0.5 MHz channels

•VLA – 42 hours, 2 IFs (1365&1435 MHz, 7x3.125 MHz channels

Sensitivity (rms µJy/beam)

MERLIN ~ 5.9

VLA ~ 5 (7.5)

Combined ~3.2 (Equal weight)

J123725+621128 VLA

J123725+621128 Combined

Beam 2 arcsec

Beam 200 mas

Data Weighting and ImagingData Weighting and Imaging

Wide-Field Imaging Non-coplanar baselines

Corner of image 0.00206 radians from phase centre

Combination Beam = 0.2 arcsec – 2120 beam offsets

2120x0.00206= 4.37

– need to mosaic with many smaller images

7 arcmin

HDF North VLA 1.4 GHz


•Radial smearing parameterized by the product of the fractional bandwidth and the source offset in synthesised beamwidths – Worst case 7 arcmin from phase centre

•VLA: 212 x 3.125/1400 = 0.47 4% of 2000 = 80 mas

•MERLIN 2120 x 0.5/1420=0.7511% of 200 = 22 mas

Wide-Field Imaging Bandwidth smearing

Chromatic Aberration

0.00

20.00

40.00

60.00

80.00

100.00

120.00

0.00 0.50 1.00 1.50 2.00 2.50

Fractional Bandwidth x Source Offset

Pe

rce

nta

ge

Smearing

Peak

δυ /υ0 x θ/θHPBW

•80% of field lies within 5 arcmin smearing now down to 40 mas and 10 mas

•Beyond 7 arcmin chromatic aberration become very significant for combination imaging

Combination images – 200, 300, & 500 mas

Some smearing at full angular resolution


Wide-Field Imaging Bandwidth smearing•Beyond 7 arcmin chromatic aberration become very significant for combination imaging with the VLA configuration chosen (correlator limitations)

•VLA-only imaging ok out to edge of field and MERLIN-only imaging ok over most of field from 4 pointing centres

•Combination imaging only possible over inner region – need 4 separate VLA pointings in order to image most of field in combination

VLA pointing centre

MERLIN pointing centres

10 arcmins

7 arcmins


Wide-Field Imaging - 3 Time-averaging smearing

•For the worst case (7 arcmins from the phase centre) this represents ~2100 MERLIN beams – assume this number of turns in 6 hours 6 turns / minute – 1 turn in 10 seconds

•MERLIN integration time is 2 seconds – so this is 5 samples per turn (rule of thumb says we need at least 4 samples per turn) – so this is ok

•Time-average smearing (decorrelation) will produce tangential smearing – only really a problem for the MERLIN data set


Self-calibrating combination data sets

•Only possible if the same structure is seen on both arrays – take care to restrict u-v range and source model during self-calibration – aligns data sets

•For difficult combinations where the common structure is minimal (usually when there are no, or very few common baselines, and very little u-v range overlap) – the data sets should be processed separately, aligned, and then combined – this can sometimes go wrong !!!•MERLIN and global VLBI observations of the nucleus of the giant radio-galaxy 3C236

•Global VLBI September 1984 1.663 GHz with 16 antennas

•MERLIN September 1991 1.658 GHz with 6 antennas (including Cambridge 15m)

•Neither data set phase calibrated – only self-calibration possible


Separate self-calibrated combination data sets

•MERLIN partially resolves A and B1/B2/C complex.

•MERLIN aligned under core candidate B2 (compact, α=+0.05)

•Shows two-sided jet structure in B1/B2/C complex + extended emission in A offset NW from knot feature

A

B2C

B1

Combination image – beam=10 mas


Schilizzi et al. 1988, IAU Symposium 129, 127-128

Combining Different ArraysCombining Different ArraysSeparate self-calibrated combination data sets

•Extended emission in SE complex now only associated with component C

•Jet from B2 now mostly one-sided through B1 – enters A at bright knot

•Receding counter-jet disrupted by cloud interaction in component C

Subsequently MERLIN data re-aligned to overlay component C (NOT B2)



Combining Different ArraysCombining Different ArraysSeparate self-calibrated combination data sets

•Alignment problems can usually be cured by combined self-calibration

•Otherwise BEWARE – errors can come back to haunt you years later !!!!

Subsequently MERLIN data re-aligned to overlay component C (NOT B2)



Schilizzi et al. 2001, A&A 368, 398-407

Combining Different Arrays Tom Muxlow General introduction Data set alignment Data set weighting Combining data with differing characteristics Image plane.

Documents

global vlbi merlin

separate imaging

ghzglobal vlbi

appropriatecombination

vlbiwhen imaging

extended tails

synthesis merlin observations

high resolution imaging