next previous
Up: Deconvolution of interferometric

6. Example: 3C 309.1

Dr. A. Kus of Toruń kindly supplied us with VLBI visibilities of 3C 309.1. The observations were done on 08/06/1986 at 5 GHz, involving the 12 telescopes Onsala, Medicina, Effelsberg, WSRT, Jodrell Bank, Haystack, NRL, NRAO 42 m, VLA E8, OVRO, Hat Creek, and Torun.

A total of 18870 CVs were provided. The u,v coverage is shown in Fig. 1 (click here)b. The smallest frequency is about 0.8, the largest tex2html_wrap_inline1139. Due to the lack of small frequencies, all features larger than about tex2html_wrap_inline1141 mas are lost. That means that only the fine structure near the central compact source (Wilkinson et al. 1984) can be seen. The natural beam size is about tex2html_wrap_inline1143 mas. It follows that a reasonable pixel size should be between about .2 and .8 mas. The DM (Fig. 4 (click here)a), the DB (Figs. 1 (click here)c,d) and the deconvolution result as given in Figs. 4 (click here)c+d refer to a 0.2 mas pixel size. The central source (top right) is unresolved. It must be deconvolved with removed smoothing in order to avoid apparent Gibbs phenomena. It is surrounded by a roughly circular extended emission with half power width of about 1.0 mas and a total width of about 2.0 mas, the center of which is slightly shifted in the direction of the adjacent jet by about 0.1 to 0.2 mas. The southern part of the jet is quite faint and appears to contain indications of weak remaining Gibbs rings caused by the strong central source. A second source near the center of Fig. 4 (click here)c is barely resolved in the source center and has surrounding extended emission. The brightest pixel is 6.8 mas east and 23.2 mas south of the central point source. A third source (upper bottom) is smoothly extended. The fourth one (lower bottom) has very low level intensity that tends to look knotty but this appears to be an artifact of the deconvolution.

The intensities (in units of the point source which has about 0.2 Jy) are approximately as follows:


central point source1.0
central extended source: maximum pixel0.08
second source: maximum pixel0.04
third source: maximum pixel0.004
fourth source: maximum pixel0.001
Table 1:   Maximum intensities


central source: inner part 1.2 within about 1 mas2
total 1.8 within about 3 mas2
jet (total) 0.7 within about 8 mas2
second source: center 0.8 within about 1 mas2
2.9 within about 10 mas2
3.9 within about 20 mas2
total 5.9 within about 100 mas2
third source: total 2.0 within about 40 mas2
fourth source: total 1.7 within about 90 mas2
Table 2: Extended intensities

Not much is gained by still smaller pixels of 0.1 mas (not shown) except that the central source still does not show any sign of being resolved. Much larger pixels (2 mas, also not shown) will force the central point source to be smeared out over more than 1 beam which implies the appearance of strong Gibbs rings. Dr. Kus also supplied us with an 0.1 mas pixel size deconvolution of the same data with a modified CLEAN (Kus et al. 1990). The two maps are remarkably similar. However, the final smoothing with the main beam, necessary in CLEAN, results in a slightly decreased resolution. This is, of course, particularly obvious near the central source but is also noticeable in the deconvolution of the jet, and the brightest part of the second source. We show in Fig. 4 (click here)b a part of the difference map (MIM minus CLEAN). The inner parts of the sources appear dark (MIM is brighter) and are surrounded by regions where MIM is fainter, a clear sign of the better resolution by MIM. While the details of the jet appear similar in both deconvolutions, some of them might nevertheless be not more than artifacts common to both methods.


We thank Andrzej Kus for stimulating discussions, for giving us his data on 3C 309.1, and for comments on the manuscript. We acknowledge support by the Österreichische Akademie der Wissenschaften (East-West program) and by the Fonds zur Förderung der Wissenschaftlichen Forschung (project P8568).

next previous
Up: Deconvolution of interferometric

Copyright by the European Southern Observatory (ESO)