$\begin{figure} \resizebox {7.8cm}{!}{\includegraphics{mm7911f2.eps}}\end{figure}$

Figure 2: The u-v coverage of a simulated array consisting of selected EVN and VLBA telescopes

Using the program FAKE of the Caltech VLBI package, we simulated an observation of a source with a simple core-jet morphology using the u-v coverage shown in Fig. 2. This coverage is generated by an array of selected EVN stations and two VLBA telescopes (MK and KP). The presence of the latter two telescopes provides, together with long baselines to the western EVN telescopes, one baseline at intermediate spacings in the u-v plane.

We introduced random, antenna-based phase errors into the u-v data, which will be removed by the hybrid mapping sequence. The aim of our tests will be, in case of two slightly different uv coverages, to try to reproduce the map of Fig. 3 (obtained by using the true model as input model).

First, we processed the corrupted data using the standard procedure described in Sect. 1, , repeated iterations of self calibration using Loop "A'' with a point source as an initial model. We will refer to this as Test-1 below. The result is shown in Fig. 4. As one can see the hybrid mapping sequence is able in this case to reproduce the map of Fig. 3. No artificial features have been added.

Next, we deleted the single intermediate spacing baseline from the u-v data, and again processed the data with the standard procedure. We will refer to this as Test-2A. We find the image shown in Fig. 5. Spurious structure now appears in the image, extending southwest of the core. As will be shown in Sect. 4, this effect is entirely due to the lack in the self calibration solution of closure phase values related to those triangles of baselines previously using the now flagged intermediate baseline.

A surprising discovery is that excluding the spurious emission region from the clean model does not remove it from the corrected data. Even in this case, in which one can distinguish the spurious features from the real features, Loop "A'' continues to generate spurious emission. After 10 iterations with Loop "A'', using CLEAN boxes to exclude the spurious feature, we are still left with traces of artificial symmetrization, as we show in Fig. 6.

Finally, with the intermediate baseline deleted, we processed the u-v data using our modified procedure (Loop "B''), which we refer to as Test-2B below. The result after 3 iterations is shown in Fig. 7. We again have an image that agrees well with the true structure of the simulated source.

$\begin{figure} \centerline{ \psfig {figure=mm7911f3.eps,width=5cm} }\end{figure}$

Figure 3: Map for comparison with the successive tests. The image has been produced by using the true model as input model

$\begin{figure} \psfig {figure=mm7911f4.eps,angle=-90,width=5cm}\end{figure}$

Figure 4: Test-1: the final image obtained with the full u-v coverage of the sample data set

$\begin{figure} \psfig {figure=mm7911f5.eps,angle=-90,width=5cm}\end{figure}$

Figure 5: Test-2A: the final image obtained using the standard self calibration technique on the u-v data from which the lone intermediate length baseline has been deleted

$\begin{figure} \psfig {figure=mm7911f6.eps,angle=-90,width=5cm}\end{figure}$

Figure 6: Same as Fig. 5 but setting (for 10 iterations) CLEAN boxes excluding spurious emission

$\begin{figure} \psfig {figure=mm7911f7.eps,angle=-90,width=5cm}\end{figure}$

Figure 7: Test-2B: the final image obtained using our modified self calibration algorithm (see text) on the same u-v data as previously

The total calibration at the end of repeated iterations of Loop "A'' consists of the sum of the corrections derived in each iteration. That this does not converge to the proper result implies the process is non-linear and sensitive to the choice of the initial model. We will show this analytically in Sect. 4.

2 Simulation results