1 Introduction

  When one telescope of a VLBI network is very displaced from the others, a large hole results in the u-v coverage. An example is in observations where one telescope is on a satellite: the baselines between two ground stations will be much shorter than those between a ground station and the satellite. The hole in the u-v coverage appears between the baselines connecting pairs of ground based stations and those much longer connecting each ground station with the orbiting telescope. Such a hole may also occur in observations using EVN telescopes in China and Europe or using both EVN and VLBA telescopes. By studying simulations of orbiting VLBI projects, Linfield (1986) showed that the hybrid mapping procedure usually used to self calibrate ground-based VLBI observations created artificial structures when significant holes were present in the u-v data. These structures tended to be symmetric with real structure and were not removed by the standard processing despite many iterations of the process.

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

 

$$L= \sum_{i\not= k} w_{ik} \left\vert A_{{ik}_{\rm o}} {\rm e... ..._{\rm m}} + \left( E_i - E_k \right) \right]} \right\vert ^2, ~$$ (1)

where w_ik are the baseline weights, $A_{{ik}_{\rm o}}$and $A_{{ik}_{\rm m}}$ are the observed and model visibility amplitudes, $\psi_{{ik}_{\rm o}}$ and $\psi_{{ik}_{\rm m}}$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.

  

Figure 1: Hybrid mapping scheme

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.