Calibration

Calibration is performed by fitting observed visibilities to a model visibility. The least squares fit algorithm uses

an iterative substitution (or relaxation) algorithm from Larry D’Addario in the late seventies.

The equation to be minimised is:

\[S = \sum_{t,f}^{}{\sum_{i,j}^{}{w_{t,f,i,j}\left| V_{t,f,i,j}^{\text{obs}} - J_{i}{J_{j}^{*}V}_{t,f,i,j}^{\text{mod}} \right|}^{2}}\]

Calibration control is via the arl.calibration.calibration_context. This supports the following Jones

matrices:

. T - Atmospheric phase
. G - Electronics gain
. P - Polarisation
. B - Bandpass
. I - Ionosphere

This is specified via a dictionary:

contexts = {'T': {'shape': 'scalar', 'timeslice': 'auto', 'phase_only': True, 'first_iteration': 0},
            'G': {'shape': 'vector', 'timeslice': 60.0, 'phase_only': False, 'first_iteration': 0},
            'P': {'shape': 'matrix', 'timeslice': 1e4, 'phase_only': False, 'first_iteration': 0},
            'B': {'shape': 'vector', 'timeslice': 1e5, 'phase_only': False, 'first_iteration': 0},
            'I': {'shape': 'vector', 'timeslice': 1.0, 'phase_only': True, 'first_iteration': 0}}

Model Partition Calibration

The Model Partition Calibration approach is described in SDP memo 97.