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

(1) |

where *w*_{ik} are the baseline weights, and are the observed and model visibility amplitudes,
and are the observed and model visibility phases, *g*_{i} and
*E*_{i} 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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