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Fringe-fitting
Frequency ranges strongly affected by RFI are flagged (not included) before anything else. These ranges are chosen manually.
First we bandpass-correct the phases. For the bandpass we use either the result from a previous iteration, or we vector-average per baseline all times. The mean is subtracted from the bandpass phases to avoid absorbing phase calibration into bandpass calibration. This mean phase is determined from the vector-average of the bandpass over all good channels.
Per time block (e.g. individual 1-sec integrations, 10 sec or 60 sec blocks) are then fitted per baseline and polarisation. The model always includes a phase for the reference frequency freq0 and a (non-dispersive) group delay across the band. We can also add a curvature (sum of dispersive and non-dispersive delay with zero mean slope) and a delay-rate for variations with time.
| parameter | meaning |
|---|---|
| phi0 | phase at freq0 |
| curv | curvature delay |
| group | group delay |
| nondisp | total non-dispersive delay (clocks, atmosphere) |
| disp | total dispersive delay (ionosphere), measured at freq0 |
For a non-dispersive delay, the absolute delay and group delay are equal with equal signs. For a dispersive delay the signs are the opposite. The phase is given by the absolute delay multiplied by 2*pi*freq. With this we can get the following equations:
nondisp = group + curv
disp = curv
group = nondisp - disp
phi0 = (nondisp + disp) * 2pi*freq0
= (group + 2*curv) * 2pi*freq0
Besides explicitly fitting the curvature to distinguish between dispersive and non-dispersive delays, we can thus combine the group delay with the phase to achieve the same result, actually with higher accuracy. Note that we can have arbitrary constants per baseline in each of the parameters (with the exception of phase), because they can be partly absorbed into the bandpass. Before applying the equations one should thus generally subtract the mean.
As a test for this concept we use the dataset (see the list) 1603186576, which is on hour on PKS~1934-638 in 4k mode in band S3. We fringe-fit over 60-sec blocks with curvature and delay rate. As example we use the baseline m045-m060, because it has the strongest dispersive delay variations.
Let us first plot phase against group delay for all data blocks:
