7 Conclusions

We have presented some approaches to forming wide-field polarimetric images. One approach does the deconvolutions of the Stokes images separately, and the other does a joint deconvolution of all Stokes images. In our example, we found that including polarized-intensity single-dish data added little to the deconvolution process over the interferometer data. Also we found that the joint deconvolution approach produced images which were mildly inferior to the separate deconvolution of the Stokes images. However, the relative merits of the joint versus separate approaches will depend very much on the data. The separate approach avoids error propagation from total intensity to the polarized intensity images, whereas the joint approach would be preferable when it can provide extra information in the deconvolution process. Certainly in instances where the Fourier-plane coverage differs between the Stokes images, a joint deconvolution would be advantageous. Indeed, where Stokes visibilities could not be formed (because instantaneously fewer than the four possible polarization cross-correlations were measured), a joint deconvolution is the only possible approach. In our example, we note that the Fourier-plane coverage of the four Stokes parameters was identical, and essentially complete between the shortest and longest spacing. With good and identical Fourier plane coverage, a joint approach is probably less advantageous.

It is interesting to consider the importance of the data constraints implicit in the joint deconvolution: that the total intensity must be positive and that the fractional polarization must be less than 100%. As we noted above, in the runs without the single-dish constraint, the maximum entropy deconvolutions substantially overestimated the total intensity in the spacings that were shorter than those well constrained by the interferometer data. That is, although the deconvolutions were plausible (i.e. positive valued), they were no more "correct'' than the Steer CLEAN algorithm. While the CLEAN algorithm left a negative bowl, the maximum entropy results contained a "positive bowl''. This should not be surprising - positivity is a fairly weak constraint in that it provides only a lower bound. Similarly, the constraint that the fractional polarization must be less than 100% is also weak, as it too only provides a bound. Even though the fractional polarized emission was comparatively high at 60%, the bound constraint was not a particularly strong one.

Acknowledgements

The Australia Telescope is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO. ARD is an Alexander von Humboldt Fellow and thanks the Stiftung for their support. We thank M.H. Wieringa for comments on the manuscript.