Primary beam correction at 6 cm

[len067]

Hi All,

I've been thinking a bit more about the effect of correcting a 6 cm wide-band observation using the primary beam associated with the central frequency and the effects on the sources in the field. To test the effect I ran a few simulations. Attached is a spreadsheet that summarises a number of scenarios for different source types with spectral index +1, +0.5, 0.0, -0.5, -1.0, -1.5 and -2.0. In each case I determined the fractional primary beam power at various central frequencies and various offsets in the field (the black text). I then estimated what the flux of the source would be in an uncorrected image for the various 0.5 GHz bands, a narrow band observation exactly at 5.5 GHz and the 2GHz wide band (blue text) - in the case of a non-flat SED I also take into consideration of the SED across the band of interest. Finally, I correct the flux measurements based on the primary beam at the central frequency i.e. just a single correction regardless of the width of the band just like what linmos would do (red text).

To my surprise (assuming my calculations are correct), for a flat-spectrum source this is sufficient to recover the original flux to within ~1% if 0.5 GHz bands are used and to within ~2% if the 2 GHz band is used if the source is within the half-power point of the 4.5 GHz beam. It seems that the losses at the high frequency end (which are under-corrected by the 5.5 GHz primary beam correction) are closely offset by the gains at the low frequency end (which are over-corrected by the 5.5 GHz primary beam correction). However, the situation is worse for steep spectrum sources where the source flux densities are grossly over-estimated by 5-10% (with alpha=-1.0 and -2.0) ... these errors grow dramatically as you move past the half-power point.

So, to cut a long story short, it looks like you can probably get by with correcting a full-band (2GHz) image as long as you're happy with errors of about 5-10% in the more steep spectrum sources and as long as you keep only within the half-power point of the 4.5 GHz beam.

If anyone can see an error in my reasoning/calculations please let me know.

Cheers,

Emil.

[Mark.Wieringa]

Hi Emil,

that's an interesting analysis. Thanks for posting the spreadsheet.
I added some columns with the 'average PB correction' over the 4 x .5GHz bands and used that to correct the measured 2GHz fluxes and calculated the errors. In all cases they come out lower than linmos' current result, generally keeping errors more in line with the sub band results. Of course the extremes of spectral index still give the largest errors.

So it looks to me we can improve the linmos accuracy by correcting not with the PB response at the central frequency, but instead with a frequency averaged response.

I might look at adding an mfs option to linmos to take the bandwidth into account in the correction. It will be slower because of the extra evaluations of the PB response needed.

Cheers,

Mark

[len067]

Hi Mark,

That would be great - as it is linmos is the fastest part of the whole mosaicing stage so a hit in speed in that task would not concern me all that much. When I get a chance I'll have to repeat the test with the new LS receiver - that's where things will really get interesting!

Cheers,

Emil.

[len067]

Hi Mark (and anyone else that might be reading),

I just realised that it might be useful for others to see the script I used to calculate my initial data for the spreadsheet. I've attached the python script (beam.py) that I put together. I've also recently updated it so that it works with any of the ATCA bands (including L-S) with an approximation to the beam made at each frequency based on information from PBCOR in AIPS. It can be called from the command line and set up with command line arguments - running without parameters (or the right number of parameters) should print out basic help describing the usage of the script.

Cheers,

Emil.