Linmos Primary Beam

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nseymour
Posts: 6
Joined: Wed Feb 29, 2012 3:29 pm

Linmos Primary Beam

Post by nseymour »

Hello,

Linmos applies a frequency dependent primary beam correction when mosaicing a number of pointings.

- is there an analytical expression for this PB correction as a function of radius and frequency?
- how was this calculated? At certain frequencies and then interpolated?

thanks,

Nick
Mark.Wieringa
ATCA Expert
Posts: 297
Joined: Mon Feb 08, 2010 1:37 pm

Re: Linmos Primary Beam

Post by Mark.Wieringa »

Hi Nick,

The corrections are calculated by the routine miriad/subs/pb.for - there are separate fits to the primary beam for the different observing bands, all using the 'inverse polynomial' fit:
PB(r) = 1/(1+a1*r^2+a2*r^4+a3*r^6+a4*r^8), where r = freq * dist

Most of these fits were done in the distant past (see http://www.atnf.csiro.au/observers/memos/d96b7e~1.pdf ), but more recent ones have been added for the mm bands.

So the nearest band for your image frequency is determined, this sets the PB parameters to use, then the distance from the pointing centre is scaled with the actual frequency.

If you use the bw parameter the wide bandwidth response is approximated by dividing the band up in 10 bins around the centre frequency.

Cheers,

Mark
nseymour
Posts: 6
Joined: Wed Feb 29, 2012 3:29 pm

Re: Linmos Primary Beam

Post by nseymour »

Hi Mark,

Thanks for that.

The question relates from our work on the ATLAS field where we are mosaicing many deep pointings from observations across 1.1-1.8GHz (earlish CABB data). We are imaging with mfclean and then mosaicing with linmos. Obviously, mfclean deals with the wide bandwidth appropriately and you don't have to worry about bandwidth smearing. The question is how to get the fluxes and spectral indices primary beam corrected give the wide frequency range. Also we want to clean using the full frequency range at once to get the best sensitivity (rather than separating it into chunks).

(1) Fluxes: I think what you get from linmos (mosaicking images from the full frequency range) is correct as fluxes are monochromatic at the central/reference frequency and therefore the primary beam correction at that frequency is valid, as the flux is the same at the central frequency regardless of the spectral index.

"If you use the bw parameter the wide bandwidth response is approximated by dividing the band up in 10 bins around the centre frequency."

I don't quite understand this. Does this take the output of mfclean (flux map and flux*spectral index map), use the spectral index map to create 10 submaps of flux? Corrects each for the PB and then combines them linearly? Otherwise, I don't see how you divide a 2d sky image by frequency.

(2) Spectral index: it appears that the task 'mfspin' will sort this out for you using the flux and flux*spectral and give you a spectral index map. So the questions is can you give mfspin the output of linmos (a mosaicked map with these two planes in the 3rd dimension) and get a spectral index map of the full mosaic? That seems like it should work, but perhaps I'm missing something.

many thanks for your help,

Nick
Mark.Wieringa
ATCA Expert
Posts: 297
Joined: Mon Feb 08, 2010 1:37 pm

Re: Linmos Primary Beam

Post by Mark.Wieringa »

Hi Nick,

Some previous discussion on this can be found here http://atcaforum.atnf.csiro.au/viewtopic.php?f=9&t=54. Emil worked out the errors are pretty small for flat spectrum sources, but rise to 10% or so for steeper spectrum sources (his analysis was at 6cm).
To get the best results for average flux over the band you need to do the primary beam correction in narrow frequency bands and add all the results together. The compromise implemented in linmos uses the average primary beam correction over the band at each point in the image. This reduces the errors, but is still not optimal for steep (or inverted) spectrum sources.
In a mosaic the problem is less severe, since most sources are within half a beam of a pointing centre.

(1) Yes, near the pointing center that is probably right - it clearly fails near nulls in the monochromatic beam (there are no nulls in the wide band beam)
Re bw: As mentioned above, it just does one side of the equation, it averages the beam response over frequency before dividing by it.This help to reduce the error near the edge of the beam (removes the null in the monochromatic beam). However it doesn't try to work out the corresponding maps at each frequency - it can't really since you need to feed linmos restored images (which only have a single plane).

(2) Hmm, you could use linmos to mosaic together mfclean's component images (with 2 planes) but it will apply the same primary beam correction to both planes - if you then fed that to mfspin you will get an incorrect spectral index out (composed mostly of beam spectral index). Mfspin can compute the primary beam corrected spectral index image from mfclean's component image, but it currently only deals with a single pointing. I don't think there is an easy way to get a mosaic of the spectral index.

So, it doesn't look like miriad can do what you want, CASA possibly can (it has a combined MFS and Mosaic imager, but how well it works I don't know.)
The best you can do in miriad is to use the mfclean approach or split up the band, image, clean and restore the narrow band images and then linmos it all together. To get the spectral index image you could repeat the process for the top and bottom half of the band.
It is clearly not optimal, but that is one of the reasons the new algorithms in CASA and ASKAPSoft are being developed.

Cheers,

Mark
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