3C147_Band0

3C147_spw0.MS

A quick calibration produced some curious results (NB: still need to upload these images), so I have decided to take a step back and proceed slowly.

Initial flagging

13/10/08:

Here's a typical time/freq image (amplitude on right, phase on left.) Note that channel numbers increase right-to-left.

ImageLink(timefreq_0-B.png,height=256)

Note odd signal (RFI?) in channels 1,5,7,53,55,61,63. Given that we use Hanning tapering (which will "smear" the RFI by one channel in each direction), it makes sense to flag the even channels, plus channels 5,7,53,55, then use channels 3-59 for calibration. This will ensure that every channel actually used has a "good" neighbouring channel.

Looking at DATA visibilities now:

ImageLink(data-amplitudes.png,height=256)

Baselines with RTC have a lot of interference, but it's gone after one bout of flagging with

{{{af:=autoflag('3C147_spw0.MS') af.setdata() af.settimemed(hw=50,rowhw=50) af.setfreqmed(hw=50,rowhw=50) af.setuvbin(plotchan=T,nbins=100,thr=.01) af.run(plotdev=[2,2]) }}}

the flagged visibilities look like this:

ImageLink(data-amplitudes-flag1.png,height=256)

Calibration

14/10/08:

Performed solutions in the following order:

G (time tile 1, freq tile None)
B (time tile 60, freq tile 1)
G again
B (now with 1st-degree polc in time)
G again
interferometer gains (note potential gotcha: if you ignore short baselines for per-antenna solutions, you may want to include them here)
E for NEWS1000 NEWS1009 NEWS7 NEWS1003 NEWS1037, tile size 60, no time/freq dependence Using sources 0:49, smearing enabled for first 50 sources, baselines shorter than 144m ignored. Resulting image (50 sources subtracted):

ImageLink(residual-cal1.png,height=256)

The residual plots look very good, so it looks like the initial flagging given above was sufficient:

ImageLink(data-amplitudes-residual1.png,height=256)

What worries me is the grating rings left over from 3C147 itself. It seems the WSRT bandpass is not sufficiently stable to do my kind of solution (B ~ 60 timeslots). Note that the last images in my [:../:band 1 calibrations] suffer from a similar problem.

For comparison, I will try a per-channel selfcal like Ger uses.

Per-channel selfcal

Performed solutions in the following order (all other options are the same as for previous calibration):

G (time tile 1, freq tile 1), so effectively per-channel selfcal
interferometer gains
E for NEWS1000 NEWS1009 NEWS7 NEWS1003 NEWS1037, tile size 60, no time/freq dependence Here's a map of the residuals (50 sources subtracted). The central source subtracts a lot better:

ImageLink(residual-cal2.png,height=256)

Comparison of calibration techniques

I have made four residual images (and the associated histograms) with all 298 sources subtracted:

(A, top left) is made via NEWSTAR
(B, top right) is made via Calico, using the first calibration above (separate G/B terms)
(C, bottom left) is made via Calico, using the second calibration method above (per-channel selfcal), without differential gains
(D, bottom right) is made via Calico, using the second calibration method above, with differential gains for NEWS1000 NEWS1009 NEWS7 NEWS1003 NEWS1037. These are the full maps:

ImageLink(residual4-full.png,height=256)

And these are the maps zoomed into the central region:

ImageLink(residual4-zoomed.png,height=256)

Discussion:

The NEWSTAR map is dominated by residuals from off-center sources in the 10~30 mJy range (e.g. NEWS1000, NEWS7, NEWS1009) caused by, presumably, pointing errors. Note that these "Cat II" sources (to use Jan's LOFARian terminology) are ~1000 times fainter than 3C147 (22 Jy), yet ~1000 times brighter than the noise (30 uJy). So even a .5% gain error due to pointing would be quite visible above the noise.
Map B gets to the thermal noise. The noise histogram is broader than that of NEWSTAR due to a different selfcal bias. The NEWSTAR solution has a 1:5 solvables-to-measurements ratio, map B has about 1:25, so the noise is less attenuated.
Map B is dominated by odd ring-like structure left over from the grating rings of 3C147, which the NEWSTAR map does not suffer from. The regularity of the pattern suggests that the actual cause is the bandpass solution being stepwise in time (which in this case is once per 60 timeslots, 1-deg polc in time). The conclusion would then be that the WSRT bandpass is not stable enough for this stepwise model. The residual structure is ~~200 uJy, 1e-5 fainter than 3C147. Hence a bandpass instability of .001~~0.01% within 30 minutes is sufficient to introduce such residuals. It looks like there's no getting around per-channel self-calibration here (although I have yet to experiment with even shorter bandpass solution intervals.)
Map C should roughly correspond to the NEWSTAR solution (map A), since this has the same calibration model -- per-channel selfcal. (Although map C also had a solution for interferometer gains -- not sure whether the NEWSTAR solution did.) I have no explanation for the qualitative difference between the two maps -- perhaps different imaging weights?? At least the noise distribution matches up, and the residual rings are all in the same places.
Map D has eliminated grating rings from all five sources for which a differential E gain solution was derived. New candidates for an E solution are NEWS9 (13mJy) & NEWS1001 (8mJy), NEWS1041 (5mJy), NEWS1043 (6mJy), NEWS1065 (4mJy), MEWS1073 (4mJy), NEWS1005 (3mJy -- the unlabelled cross towards the bottom of the map.) It would be interesting to see how far these could be pushed.

On the convergence of E (differential gains)

In one of the final steps of my [:../:band 1 calibration], I went through the rather cumbersome procedure of subtracting sources 0-5 and 25-298, then solving for E on the residuals (somewhat like peeling). I have tried to avoid this procedure for band 0, and just solve for E directly. Initially, the convergence crtiterion was set to 1e-5, but this produced a poor map (it was something of an improvement on map C above, but not much). When I set convergence to 1e-6, I got the much better map D above. Here's a side-by-side comparison. Map D (convergence 1e-6) is on the left, the previous map (convergence 1e-5) is on the right.

ImageLink(residual-Econv.png,height=256)

The conclusion is pretty clear, E solutions (without peeling, at least) need a tighter convergence criteria (or to put it another way, need to be iterated more.) Note that converging to 1e-6 took roughly twice as long as to 1e-5 (30 mins vs 15 mins on my laptop), but it's worth it, if only to avoid the hassle of peeling.

Primary beam problems half-solved

15/11/08:

The inconsistency of my primary beam corrections w.r.t. NEWSTAR's corrections (see CalibrationEfforts) appears to come down to the fact that the NEWSTAR sky models define their own "model centre" which is slightly different from the phase centre (which I'd been using as the centre of my primary beam). The diffrence is tiny -- 1e-2~1e-3 acrsec -- but simple calculations show that this is enough to introduce a ~1% difference in the power beam for off-center sources.

I'm now getting more consistent results when applying the primary beam within Calico (I have added options to wsrt_beams.py to override the beam centre with user values. For now, I'm transferring the model centre coordinates by hand. Need to think of a way to propagate this using the MS.) However, there's still the mystery of why the spectral index in Ger's beamed and unbeamed models is the same. Following up on that now.

Actually, looking at the NEWSTAR source, I don't see the spectral index corrected anywhere during de-beaming. I can try to apply a correction manually as follows:

the power beam at frequency f is E=cos^6(Bfr)
dE/df = -6cos^5(Bfr)sin(Bfr)Br
spectral index correction at frequency f is S=(f/f0)^spi
dS/df = (spi*(f/f0)^(spi-1))/f0
at frequency f0, the beam imparts an "apparent" spectral index given by the equation dE/df(f0) = dS/df(f0)
which works out to spi = -6cos^5(Bf0r)sin(Bf0r)Br*f0
Just to check this, with B=65, f0=1.4 GHz, r=.5 deg, we end up with spi=-0.57489836045682907, which seems reasonable.

OK, nevermind all that, as I think I've figured out the whole spectral index issue. I'm now using PURR to generate further calibration logs automatically, so please see

http://www.astron.nl/meqwiki-data/users/oms/purrlog-3C147_spw0/index.html

for further details.

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