The standard hybrid mapping scheme is sketched in Fig. 1. Some initial model for the source is chosen, typically a point source. Model visibilities are derived and self calibration determines antenna based corrections to the u-v data by minimizing the expression
where wik are the baseline weights, and are the observed and model visibility amplitudes, and are the observed and model visibility phases, gi and Ei are the amplitude and phase corrections for antenna i. The corrected data are Fourier transformed and a new model is determined by applying the CLEAN algorithm to the resultant image. New model visibilities are generated, and Eq. (1) is again used to determine a new set of corrections. This process is repeated (called Loop "A'' in Fig. 1) until convergence to a constant model is achieved.
We will show in Sect. 4 that for small values of the closure phase the self calibration process is non-linear and is most sensitive to the choice of initial model. Therefore, we suggest a modification to the standard hybrid mapping procedure in that the model derived by CLEAN be used as the initial model for the original data, replacing the point source used the first time through the process. We call this Loop "B'' in Fig. 1. We show empirically in Sect. 2 that this modified procedure eliminates the spurious structures created by standard hybrid mapping, enabling the calibration to efficiently converge to an acceptable solution.
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