projects:mkat_sband:pub:bandpass [Fundamental Physics in Radio Astronomy]

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====== Bandpass ======

The baseline bandpasses can be measured after (phase-only) calibration by averaging the complex visibilities over time and dividing by the source flux per frequency channel. We reduce them to station-based values with full complex fits per frequency and polarisation. The phases for all stations per frequency and pol are shifted to minimise the phase variations. This approach is preferred instead of the more common use of a reference antenna.

Note that there is a degeneracy between some calibration parameters and the bandpass. Because the calibration is performed after applying a guess for the bandpass, phases, delays and curvatures can end up partly in the calibration parameters and partly in the bandpass.

There is an additional complication: We do everything per baseline. The complete solution should 'close' perfectly, which means it can be reduced to station-based parameters. But this may not be true for calibration and bandbass individually. For this reason we apply the remaining (time-averaged) closure errors from the calibration parameters to the baseline bandpasses before reducing them to station-based bandpasses.

Symbolically, we can write (neglecting complex conjugation):
<code>
(true signal) = (baseline-cal) * (baseline-bandpass)
              = (station-cal1 * station-cal2) * (station-bandpass1 * station-bandpass2)
              
                                          (baseline-bandpass) * (baseline-cal)        
(station-bandpass1 * station-bandpass2) = ------------------------------------
                                             (station-cal1 * station-cal2)
</code>

In the end we try to make the bandpass phases as flat 0 as possible, by removing a constant phase, slope (group delay) and curvature per station and polarisation. These are transferred to the calibration solution parameters for consistency.

As described in the [[projects:mkat_sband:pub:fringefit|Fringe-fitting part]], a lower limit in baseline length helps to minimise residual closure errors. For PKS 1934-63 a baseline limit (measured in antenna XY coordinates or in UV) of a few hundre metres works well and keeps a sufficient number of baselines for the fits.
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