Wide-field and wide-band imaging tutorial

This tutorial will focus mainly on wide-field imaging, covering examples of the issues involved and methods to correct for them. Some examples of wide-band imaging techniques will be given at the end of the tutorial along with some links to further information about the topics covered.

What is wide-field imaging?

Wide-field images are commonly classed as images having large numbers of resolution elements (i.e. beamwidths) across them. They are usually required when surveying large regions of the sky at once, whether for multiple objects or large single objects. There are several issues that need to be addressed when producing wide-field images, which include

Bandwidth smearing
Time-average smearing
Non-coplanar arrays
Confusing sources
Primary beam response

Sample data

This tutorial will utilise MERLIN continuum observations (M82-SSHFT.UVFIX) of the nearby starburst galaxy, M82 at 6343.6 MHz (6 telescopes - Mk2, Defford, Pickmere, Darnhall, Cambridge, and Knockin, no Lovell). This data has been fully calibrated using the MERLIN pipeline and has 29 frequency channels each 0.5 MHz in width and was observed with 3 second sampling. For the purposes of the tutorial the data has been shifted so that the phase centre lies 1 arcminute south of the galaxy we want to image.

To begin with we will make an image of the data. Though there are others, the most sophisticated and commonly used imaging task within AIPS is IMAGR. Imagr can be selected by typing task 'imagr'. The parameters for IMAGR can then be viewed by use of the inp command.

In most cases the default parameters are acceptable, leaving a significantly reduced number that we actually need to set.
task 'imagr' 
inp 
sources  'M82''  
nchav  29 
outname  'M82-ORIG' 
cellsize  0.012  
imsize  2048 2048 
decshift 60,0
uvwtfn  'NA' 
niter  6000 
bmaj  0.06 
bmin  0.06 
minpatch  255
inp 
go 
You can use mca to list the images in the catalogue. You can select the image produced using getn as before and can now use the tval task to view it in the tv window. The following parameters will load the whole image into the window (though you probably won't be able to see all of it).
tblc 0
ttrc 0
tvlo

You can now use the mouse cursor along with a,b,c or d to alter how you view the image as explained in the command window.If you use 'b' to zoom in on the point source in the centre of the image, you can measure its peak brightness using the TVWIN; IMSTAT commands (you will have to have 'quit' the image by pressing d though and don't forget to make a note of this number).

type tvwin;imstat
to make one task immediately follow another. We can also make a contour plot of this source by using the following commands
task 'kntr'
inp
getn #
blc 1000 1017    these work well, but you can choose your own using the tvwin command
trc 1045 1062
clev 2.16E-04    sets the brightness level of the base contour, ~ 3 times the noise level
levs -1,1,1.414,2,2.828,4,5.656,8,11.312,16,22.624,32     sets the contour levels
dotv 1 or -1  will plot the contours to the tvscreen or to a plot file
go
If you made a plot file, you can output it from AIPS as a postscript file using the task LWPLA
task 'lwpla'
inp
getn #
plver 0
outfile '<directory followed by name of file>   e.g. '/home/dmf/contour1.ps*
go
*AIPS will automatically capitalise whatever is written in the single quotes if the trailing quote is included.


Bandwidth Smearing

When observing, we sample the data using a finite bandwidth. This has the effect of averaging the visibilities over a finite region in the u,v-plane. If the visibilities change significantly over this bandwidth and hence over the region sampled, smearing will occur. The averaging over bandwidth in the u,v-plane is radial, resulting in a radial smearing of the image. This effect increases with the distance from the phase-center of the observations. Specific details for MERLIN can be found in the MERLIN Users Guide here, which show the general formulae for calculating the radial distance (and hence limiting field-of-view), &Phi as a function of bandwidth (&Delta&nu) for a given observation.

&beta = 0.005 &Delta&nu &Phi

where &beta is a dimensionless constant that represents a 1% reduction in peak brightness in the image (and a corresponding level of smearing) with a value of 0.21. This for a bandwidth of 0.5 MHz gives a 1% reduction at 80 arcseconds from the phase centre. Our region of interest is currently well within this limiting field-of-view using the existing setup. Therefore, to illustrate the problem of bandwidth smearing we will now use a copy of the data (M82-SSHFT.BAVG) that has been averaged in frequency, so that instead of 29 channels with 0.5 MHz bandwidth each, there is one channel with 14.5 MHz bandwidth. With the data loaded in the same way as before, we can use the same settings for IMAGR as before either by typing them in again or re-selecting the last used:
task 'imagr'
tget imagr    to select the last-used parameters
getn #        to select the appropriate newly loaded dataset 
outname 'M82-BAVG'
nchav  1      as there is now only one channel 
inp           to check the inputs
go
You can view the image, measure the peak brightness and create a contour plot using the same parameters as before, which can either be output to the same or different postscript file. What is the fractional difference between the peak brightnesses of this and the original datafile image?


Time-average smearing

Time-average smearing as with bandwidth smearing is a consideration to be made when planning the observations. In a similar way to bandwidth smearing, the time interval used when sampling the data takes an average of the visibilities over that interval. Again if the visibility changes significantly over this time-range a smearing will occur. Arrays such as MERLIN, use the rotation of the Earth to sample a greater portion of the u,v-plane, hence we know the visibilities will be constantly changing. The effects of time-average smearing are more complex than bandwidth smearing and are therefore more difficult to describe, though manifest as a distortion of the image. As an example, at a declination of +90, the limiting radial distance from the phase centre &Phi is given by

&Phi &sim &radic&fnof&thetabeam/&tau
where &fnof is the fractional decrease in peak intensity, &theta is the beamwidth and &tau is the integration time in secs (taken from the MUG)

To illustrate the effects of time-average smearing we will image a copy of the data (M82-SSHFT.TAVG) that has been averaged in time, so that the sampling frequency is 25 seconds instead of the original 3 seconds. M82 is a relatively high declination source (+69) so the above equation will give a reasonable estimate of the limiting field-of-view. The previous inputs to IMAGR can be used, but the new datafile needs to be selected and nchav set to 29 again, as the frequency setup is as it was initially.


task 'imagr'
tget imagr
getn #
outname 'M82-TAVG'
nchav 29
inp
go
Again, measure the peak brightness and create a contour image using the original parameters and this new image. Is the degredation in peak brightness worse or better than for the bandwidth smearing?


Non-coplanar arrays

Producing images from radio interferometry data usually involves a 2D Fourier transform of the visibility function V(u,v), which relies on the assumption that the interferometric array (such as MERLIN) lies on a 2D plane. This is usually not the case and the resulting errors increase quadratically with the distance from the phase centre. Serious errors result if

&thetaoffset x &thetabeam > 1
. The visibility function is actually a 3D function V(u,v,w) (usually w=0 is assumed) and to account for the errors fully a 3D Fourier transform is needed, though this is very computationally expensive. The Fourier transform of a 3D visibility function produces a 3D image volume with the sources lieing on a sphere (see image, represented by the red stars). In the standard 2D imaging process, each source is projected onto a tangent plane(blue stars). When the errors introduced by a non-coplanar array become large, there are a number of imaging processes which can be used to account for the 3D geometry.


Facets

In this instance, instead of using one field to produce an image, a number of smaller fields can be used, known as facets. This is currently implemented within IMAGR and when each facet is created, the u,v and w coordinates are recalculated, effectively shifting the phase centre to the centre of each image facet as illustrated in the figure. This essentially can be used to approximate the surface of the image sphere by a number of tangent planes.

We'll now use IMAGR to produce a number of smaller faceted images of the galaxy, to illustrate this methodology. You will need to select the original copy of the dataset that you first used and can set the parameters as indicated, we will now also need to set the following
nfield 3          this will create three facets
overlap 1         this will ensure anything cleaned from one facet is cleaned from all
rashift 15,3,-9,0   this along with 'decshift' tells IMAGR where the centres of the images should be
decshift 62,61,60.5,0  these are offsets from the phase centre in arcseconds
do3dimag 1        ensures the u,v,w's are reprojected in each facet 
imsize 1024 1024
This should have produced three image files and corresponding dirty beams, identified with a 'class' of ICL001 - ICL003.


Confusing sources and peeling

When observing a large field, it is likely that there will be multiple sources in the data, some of which you may not be interested in. However, if these sources are sufficiently bright, they can produce artifacts in the images you make of the source you are interested in, from the side-lobes of the confusing source. If this is the case, the faceted imaging can be used to produce images of the confusing sources as well as the target sources, removing their effect on the rest of the images. When neccessary, the confusing source can then be completely removed from the data by subtraction using the images produced, this is one form of peeling and can be repeated for multiple sources.

We can use these observations as an example of the effects of a 'confusing source' and how to remove it. We will produce an image using the first datafile and the first list of parameters, but this time create a 1024x1024 imageusing the following parameters.

imsize 1024 1024
do3dimag 1
cellsize 0.015
If you look at this image you should see a large number of ripples toward the left hand edge of the image. This is the rippling effect, in this case being produced by one of the brighter supernova remnants, situated just to the left of the image.

In order to get rid of this effect we will now image the 'confusing source' as well as the 1024x1024 field using the following parameters
nfield  2
rashift  0,0
decshift 0,0
fldsize 1024,1024,512,512
imsize 512 512
overlap 1
do3dimag 1
This should have now removed the rippling from the larger image.

In some cases the confusing source can be sufficiently far from the phase centre of the observations, that they can no longer be considered to be experiencing the same phase distortions due to the Earths atmosphere. Hence, any phase corrections applied to the data during calibration may not be correct for the confusing source. In this case, self-calibration on the confusing source may be required to fully remove its effect from the data.

We can use the image of the 'confusing source' from above to illustrate how to subtract a source from the data using the task UVSUB. You need to select both the datafile and the image file to perform this process. Associated with each image file will be a cc extension table which contains a list of the components 'cleaned' from the facet in the imaging procedure (you can view the header information of a file along with the extension tables by typing imh into the command line). These clean-components will be used to subtract the source from the data.
task 'uvsub'
inp
getn #      select the original datafile
get2n #     select the smaller image file
invers 0
opcode ''

If you now repeat the last imaging process using 'tget imagr' and 'getn # to select the UVSUB datafile, you should see that the source has been removed from the smaller facet. This imaging and subtraction process can be performed together using the task 'SCIMG', which will perform some self-calibration as well.


Primary beam response

The ultimate limiting factor in wide-field imaging is the primary beam response of the telescope, given by the diffraction limit. An approximate formula is

&thetaFWHM = 1125/(d &nuGHz) arcmins 
When, as is the case for MERLIN, the antennas are mixed in size, the FWHM is given by a combination of the antenna power patterns. Tasks exist within AIPS to correct for the primary bean response such as PBCOR and can even be included within IMAGR when imaging.




Images and plots

A copy of all of the images produced during this tutorial can be found here, as well as the contour plots from each stage and a list of flux density values.


Wide-band imaging

Many new interferometers are making use of the benefits of large bandwidths to imporve their sensitivity and performance. However, this takes them well ot of the range where the fractional bandwidth (i.e.) the bandwidth with respect to the observing frequency is small and so the source brightness can no longer be considered fixed over the whole bandwidth used. Most radio sources can be characterised as varying in brightness with frequency with a power-law for example

S = S0(&nu/&nu0)&alpha
where &alpha is the spectral index. Parameters within IMAGR can be used to correct for a generic linear spectral index (and curvature), however it is often the case where there is more than one source (or parts of a source) that have differing spectral indices.
You can test the effect of setting a linear spectral index into the cleaning process using the IMAGRPRM(2) parameter, see HELP IMAGPRM for more details. The first copy of the datafile and imaging parameters can be used to try this.

Full characterisation of the spectral variation within the imaging process is under development for use with e-MERLIN (using AIPS and python) and for the EVLA (using CASA).




Further information

More information on all of these topics can be found in
The AIPS cookbook - a guide to using the software package.
An AIPS helpsheet - some basic help for using AIPS, written by Megan Argo.
The MERLIN Users Guide - provides information on the array, how to plan observations and the data reduction process.
Lectures from the NRAO Synthesis Imaging Workshop - An interferometry summer school run by the NRAO every two years.
Previous European interferometry schools - This links to lectures and tutorial information from the 2007 ERIS in Bonn.