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| Version 1.6 Build 363 |
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Kumar Golap and Tim Cornwell
The relationship between the visibility domain to the image plane is given by the Van Cittert-Zernicke theorem. This can be reduced to a Fourier relationship for planar arrays and also for small field of views for non-planar arrays (Thompson, Moran and Swenson). When this happens the Fourier inversion of observed visibilities gives the true image convolved with the Point spread function. Both the true image and the PSF are functions of 2 variables only (l,m). Deconvolving is conceptually simple.
When visibilities are sampled by a non-planar array (u, v and w components), the relationship between them and the image plane can no longer be represented by a Fourier transform. The relationship can be brought to a Fourier transform in 3-D. So deconvolution is to be done in 3-D. Any way the image is truly a two-dimensional, so while viewing such a dirty image in 2-D the PSF function (which is 3-D) appears as being different functions at different places. Deconvolving the 2-D dirty image ideally to use a different PSF for each point in the image. This can be very difficult to achieve if the image has a few million pixels.
It becomes worse when one has to consider that the Field of view for deconvolution is much more than the field of view of interest (at most the primary beam of the antennas). Deconvolution may need to consider the sidelobes and at low frequencies the whole visible sky may have to be considered, especially if strong sources like Cygnus-A or Cas-A are above the horizon. The PSF in the sidelobes suffer both distortion from the 'w' term and the amplitude and gain difference difference of the sidelobes of each antenna. Bandwidth decorrelation is usually a problem in wide field imaging. The solution is to split the whole band of observation into smaller bands and correlate these independently. For a given interferometer pair this constitute several 'uv' points at any time. The number of 'uv' points goes up by the number of spectral bands. The option of 'mfs' (multi-frequency synthesis) allows this to be achieved. One can use the 'channel' option and combine different spectral channels. Combination should be done carefully taking into account the field of view size.
``Wide field imaging'' is different from mosaicing as the whole image
can be had by one pointing of the antenna. WFI is needed when the term
w
varies significantly over the field of
view. Mosaicing is the technique used to combine visibilities (or
images) obtained from different pointings; in effect it increases the
field of view beyond the primary beam pattern.
An important question is how do you know that you need wide field imaging techniques?
One simple way is to make the raw image. If point source responses on the edge of the image have the same shape as those in the center then it is not needed.
A simple criterion (due to Barry Clark) is that:
(Field of view in radians) * (Field of view in beams) > 1
There are in fact a number of different possible approaches to solving the wide-field imaging problem. These are reviewed by Cornwell and Perley. Here we give a brief account:
Calculation of the facet planes can be handled in two ways:
The dragon tool in AIPS++ is a Glish script which depends on the imager and calibrater tools.
The technique of faceting used is the method 2 described above where the a single image plane needs to be dealt with.
For various reasons, one would like to change the number of facets being used when processing an image. For example to optimise on time, one may wish to have few facets when deconvolving bright sources and have many more facets to have deep CLEANing.
Self-Cal part of the imaging process (also called difference mapping as in difmap). The flux levels where phase self-cal and amplitude self are needed can be specified.
The imaging process can be helped by specifying the bright sources by using the components list facility.
If there are bright sources outside the field of interest, their sidelobes can be deconvolved from the image of interest by specifying an outlier region around that source. Inherently there are no limits on the number of facets or number of outlier fields to be specified.
Dragon has a function which advises one on the optimal number of facets, tangent point of image, to be used for given signal to noise and size of image to be made.
The number of facets needed to image a given field of view depend on several factors. Among them are the uv distance, the amount of amplitude loss allowable, the positional error allowable. The number of facets used ultimately depends on what the user wants. If flux information only is needed the number of facets can be much less than if, say, very accurate positions are needed.
The advise function gives both the number of facets needed to get the accurate positions or just accurate flux measurements.
For accurate flux a gradient in the w term phase is not important. advise least squares fit to uvw gives best fitting plane, dispersion in w' gives the beam size in w. Max amplitude loss plus simple geometry gives the facet size. But for accurate positioning the facet size should such that even a gradient in the w term is not important for a given amplitude loss.
The advice for accurate flux may sometimes be too small to the extent of causing artifacts. The positional error might be large enough that sources close to the edge of the facets may end up appearing on 2 facets. In general if one want to get accurate flux values then it would be advisable to use a few more facets than the minimum suggested by advise. Make sure that there is not any source splitting over the image.
If very accurate positions are needed then either one has to image with the large number of facets suggested or try an alternative solution.
The alternative solution is to image with a number of facets which is practical then get the best fit the position of each of the component from the UV-data. The fitting of components in the UV data is yet to be implemented in AIPS++
The self-cal can be set to start at an amplitude level where it is expected that the phase or amplitude errors start to become significant.
Usually the user will set the phase self-cal to be switched on first and the phase and amplitude to be turned on at a much lower level of residuals.
Outlier fields are regions outside the main image where there are sources that whose sidelobes fall into the field of view. Such regions would be around bright radio sources e.g Cyg-A, Vir-A, the Sun etc. Such sources have to be included in the CLEAN and self-cal loops so as to achieve good dynamic range. A special outlier field is the pole regions where interference tend to pile up in rotation synthesis arrays. This can be treated as an outlier field and the effect of such interference can thus be somewhat reduced from field of view.
The position of the center of field can be given manually or can be looked up from a catalog by using the measures tool (see users guide)
The componentlist tool, as its name suggests, allows one to make a compendium of sources or skycomponents. We can use this tool to make model of the image which can be used by dragon. Skycomponents have to be made for each of the source that one want to include in the model and added to the componentlist.
A componentlist can be created from an image using the imagefitter tool. This tool allows the user to interactively select regions where there are components and estimate its parameters.
For interference handling see the Getting Results in AIPS++ chapter on the topic
- Parameter recommendations for all VLA configurations
Here is an example of a Glish script which was used to image the coma
cluster at 74MHz with data from the VLA in the B and C configurations.
include 'dragon.g'
#Converting UVFITS to measurement set
myms:=fitstoms('coma.ms','COMA-4CB-CUT.FITS',T,F)
myms.close()
myms.done()
# creating dragon tool
mydrag:=dragon('coma.ms')
#setting the wanted image parameters
mydrag.setimage(name='coma',nx=1800, ny=1800, cellx='30arcsec',
celly='30arcsec', doshift=F, phasecenter=dm.direction('J2000','0deg',
'0deg'), mode='mfs', facets=25)
#setting an outlier field towards Centaurus-A
ok :=mydrag.setoutlier(name='cent-A' , nx=400, ny=400,
cellx='37arcsec', celly='37arcsec' , doshift=T,
phasecenter=dm.direction('J2000','201.3deg','-42.6deg'),
mode='mfs' , nchan=1, start=1, step=1, spwid=1, fieldid=1);
#setting an outlier field towards Virgo-A; note for direction we have
# made use of the inbuilt radio catalog
ok :=mydrag.setoutlier(name='virg-A' , nx=400, ny=400,
cellx='37arcsec',
celly='37arcsec' , doshift=T, phasecenter=dm.source('VIRGOA'),
mode='mfs' , nchan=1, start=1, step=1, spwid=1, fieldid=1);
# deciding on uv to be used
ok :=mydrag.uvrange(uvmin=0, uvmax=10000000);
# Selecting the weighting scheme
ok :=mydrag.weight(type="uniform", rmode="robust", noise="0Jy",
robust=0, fieldofview="0rad", npixels=1000);
# Setting the padding for the Fourier Transform
ok:=mydrag.setoptions(padding=1.5, cache=0)
# Get the imaging and self-cal loops going
mydrag.image(levels='1Jy 0.3Jy 0.1Jy',amplitudelevel='0.2Jy',
timescales='200s 200s 100s', niter=50000, gain=0.05,
threshold='0.05Jy', plot=F, display=F)
#Closing up the tool
mydrag.close()
mydrag.done()
To deal with very bright and compact source:
NNLS algorithm (Briggs) can be used to deconvolve bright the source then the residual visibility is imaged using wide field imaging.
Bright source in the sidelobes:
This is a tricky problem as the phase and amplitude of sidelobes are
very different from the main lobe. No exact cure is yet available but
it can be considered as an outlier field problem and the actual
widefield imaging will correct an ``averaged'' quantity. This will
reduce the effect of the bright interfering source but may still leave
some artifacts.
Mosaicing and wide-field is possible:
This is a very special and
rare case when each pointing is wide enough to warrant the usage of
widefield imaging and the object under observation is large enough to
need many such pointings. Mosaicing and widefield imaging can be
achieved simultaneously.
The solution to this is to image with self-cal corrections starting at much higher flux levels. One should be aware of the time scale of the non-isoplanar changes. If one passes a too low time scale than necessary to self-cal, the signal to noise of the self-cal estimates will be worse for nothing. If it is much larger than necessary then its equivalent to no self-cal.
The capability to correct for directional dependent part of phase and amplitude errors is going to be implemented soon. This should be able to take care of assymetric primary beam and effect of the atmosphere/ionosphere which are direction dependent.
The problem is most probably the effect of ringing on the edge of the facets which can be reduced by padding. So in the setoptions function the padding factor can be given a value of more than 1 (usually 1.2 to 1.5) depending on how severe the edge get picked up by clean. The more the padding the longer will FFT take.