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Image Analysis

Jim Lovell
ATNF Synthesis Imaging Workshop May 2003


(What you want to do and how to do it.)
Flux density of components Absolute positions Relative positions and motions Flux density variability Spectral index, rotation measure etc (image combination). ! Overlay with other wavelength images ! Putting it all together ! ! ! ! !

What Do You Want to Measure?


Image Analysis Software
! ! ! ! Miriad AIPS The package formerly known as Aips++ Difmap:

! Imaging (spectral line & continuum), model fitting, self-cal. ! Very good user interface. ! Not suitable for mosaicing or wide-field imaging.


Miriad ta s k Vis ib ility p la n e m o d e l fittin g Imag e p lane m o de l fittin g Imag e plane in te g ra te d flu x

Tasks, commands
Difmap c o mm and Mo d e lfit AIP S ta s k Uvfit, (s lime ) Im s ta t, "S " in ma p p lo t Ma xfit, jmfit, imfit, s a d Ime a n, ims ta t, tvs ta t, b ls um

Aips ++ fu nc tio n (s p a tia l), ima g e .ma xfit, imag e.fitp ro file , ima g e p ro file r ima g e .s ta tis tic s imag e.g e tc hunk, im a g e.g e treg io n, im a g e .p utc hunk, im a g e .p utre g io n ima ge .m od ify ima g e .va rious im ag ep o l.ro tatio nmeasure, imag e.fo urie rro tatio nmeasur e imag e.c a lc ima g e .c a lc

Uvfit, uvmo d e l

Ma xfit, im fit Ims ta t

E llint S lices p con tin u u m Uvs ub, im lin, uvlin, uvmode l su b tra c tio n Fo rmin g p o la ris a tio n Impol ima g e s

S e tcont multi_ mode l true ; polve c ; ma pl pc ln

S lfit, xg a us Uvmod, uvs ub C omb

Ro ta tio n me a s u re S p ectra l In d e x Oth e r im a g e com b in a tio n s

Im rm Ma ths Ma ths

-

C omb C omb C o mb , s umim


Resources
! Follow the links from the ATNF Software And Tools page: www.atnf.csiro.au/computing/software ! TPFKA Aips++: see the Getting Results documentation for an overview of image analysis. ! Miriad: see Chapter 18 of the Users Guide ! Difmap: see the Difmap Cookbook ! AIPS: see chapter 7 of the AIPS Cookbook


TPFKA Aips++ has good image analysis capabilities. Can do almost everything that Miriad, AIPS and Difmap can plus more. !Paths of least resistance (i.e hassle): ! ATCA data:
!

Personal Bias/Ignorance

! Calibrate in Miriad ! Imaging or model fitting in Difmap. If mosaicing or bandwidth smearing effects are important use Miriad.

! VLBI/SVLBI data:
! Calibration and fringe-fitting in AIPS ! Imaging/model fitting in Difmap. Wide-field imaging with IMAGR in AIPS.

! Detailed image analysis in Miriad or AIPS


Errors
! Errors given by fitting software should be treated with scepticism ! Generally assumed errors are stochastic ! No accounting for on-source errors etc ! Components are not necessarily independent. e.g. Usually a strong correlation between intensity and diameter. Extreme example is one (u,v) point:
Amp

(u,v) dist


Component Fluxes
1 Discrete Components: Model Fitting ! Model fitting is suitable for relatively discrete, isolated features. ! Usually not a unique solution, so choose the simplest possible model (fewest components, simplest shapes) !

! Point source -> circular Gaussian -> elliptical Gaussian.

Model components tend to be too simple for more complex structures.


Component Fluxes cont.
!
!

Extended Sources
Reducing the dimensionality can help.

PKS 1333-33

Killeen, Bicknell & Ekers 1986


Reducing the dimensionality
! Fit to jet width vs distance

Width (arcsec)

RA (arcsec)


Component Fluxes cont.
! Extended Sources
! ! Reducing the dimensionality can help. Integrated intensity.
! Sum the intensity within a given region


! Depends on the quality of calibration: ! Precision of the position of the phasecal ! Separation of source from phase-cal (closer the better) ! Weather, phase stability ! Signal to noise

Absolute Positions

Relative positions and motions
! Limited by signal-to-noise


Flux Density Variability
! Between epochs: easy. ! Within epochs: difficult.
NOTE: Check your secondary cal isn't an Intra-Day Variable!

! At any given time ~10% of flat spectrum sources show IDV of a few % or more at cm-wavelengths. ! Can seriously harm amplitude calibration. ! IDV can be episodic


Flux Density Variability
! Between epochs: easy. ! Within epochs: difficult.
NOTE: Check your secondary cal isn't an Intra-Day Variable!

! Imaging algorithms assume the source stays constant during the observation
1 2 3 4

! A similar procedure may be required before combining data from different arrays or array configs.

Split data into N segments and image each one separately Measure S(t) of variable component(s) Subtract variable component from the visibility data. Image whole dataset


Image Combination
! Often desirable to combine images to
! ! ! ! ! Measure Measure Measure Look for Compare polarisation, spectral index, rotation measure, differences, with optical, X-ray etc.

! When combining radio images, restore all images with the same beam first.


Polarisation
! Alignment should not be a problem as any selfcal solutions from imaging I can be passed directly to Q and U. ! Polarised intensity:

IP = I + I
! Linear polarisation position angle:

2 Q

2 U

IU = 0.5 arctan I Q


Low S/N, Misalignment
! Beware of edge effects due to low S/N or image misalignment.
! In spectral index measurements you can end up with a fake gradient.

S1 1 = S2 2
A B A/B

A B A/B


Low S/N, Misalignment
! Beware of edge effects due to low S/N or image misalignment.
! Extreme rotation measures are possible
RM =
A B A-B

( 1 ) - ( 2 )



2 1

-



2 2

A B A-B


Image Overlays
! Can be tricky if X-ray/optical/radio have different astrometric precision. ! Two approaches:
1 Accept the uncertainties 2 Make some assumptions. If there are multiple components in each image, look for an alignment with the best correlation.


Example: PKS 0637-752
Quasar, z=0.651 (Montage from Difmap image and overlays in Miriad) Space VLBI (VSOP)

ATCA 8.6 GHz (contours) Chandra (pixels)

ATCA/HST overlay


PKS 0637-752 cont.

ATCA 8.6 Ghz Contours: total intensity Pixels: fractional polarisation Lines: polarisation E-vectors (Imaged in Difmap, polarisation and overlays in Miriad)


PKS 0637-752 cont.

(Slice along radio jet in AIPS)


PKS 0637-752 cont.
VLBI Component motion (separation vs time).

(Model fit to VSOP and ground-only VLBI data in Difmap)