2 Problems  

The primary method of obtaining high quality images from synthesis arrays is the technique of self-calibration (see Thompson et al. 1986, Chapter 11, Sect. 2, and references therein). In standard self calibration one takes observed visibility data D and model visibility data M for the baselines in the array and, over some time period where one assumes the antenna gains to be uniform over the field of view and constant, one does a least-squares fit to the visibility data to find a complex gain $G_{\rm ant}$ for each antenna in the array. For each baseline in the array a gain relationship G between data and model is then given by

 

D = GM (1)

where,

 

G = G_iG_j^* (2)

and G_i and G_j are the individual antenna gains of the two antennas i and j whose correlated signal gives the visibility on this baseline. By then performing the operation of dividing the data by the gain (D/G) one effectively "adjusts" the data toward the model and hopefully improves the data and the corresponding image.

However there are situations where the assumption of a uniform complex gain is incorrect. At low frequencies, the observed data can be affected by ionospheric irregularities that introduce phase errors which are dependent on position in the field of view (Cotton 1989). The synthesis array itself can also introduce position dependent distortions and therefore position dependent gain errors. Cotton (1989) describes some of the common distortions that affect synthesis data. For example non-coplanar terms must be correctly accounted for in order to produce undistorted images from a non-coplanar array (see also Perley 1989).

The DRAO ST has position dependent distortions because the seven antennas in the array have two different sizes and thus different beam shapes. The two antennas at each end of the array, and thus the pair forming the longest baseline are each 9.15 metres in diameter with a HPBW of 101.8 arcmin at 21 cm wavelength; the remaining five antennas are all 8.54 metres in diameter, with a beam size of 108.8 arcmin. Since each antenna can be correlated with every other antenna, we obtain a total of 21 baselines divided up as follows: 1 baseline of B $\times$ B, 10 L $\times$ L, and 10 B $\times$ L (B = big, L = little antenna). An analysis of overlapping fields from the Canadian Galactic Plane Survey (CGPS) shows that we end up with a weighted mean beam having a HPBW of 107.2 arcmin (Gibson, private communication). Corresponding differences exist at 74 cm wavelength.

The differing sizes of the antennas means that the ST has a point spread function (PSF) that varies radially from the field centre, in contrast to the uniform PSF based on UV coverage that is normally assumed in synthesis imaging techniques. In Sect. 3.1 I shall present an algorithm for adjusting the data associated with that part of an image which lies well inside the main beams of the antennas where the different primary beam responses are well understood. It enables the observer to avoid computing a separate PSF for every direction in the field, and standard self-calibration solutions can then be applied to improve the image.

Another error occasionally affects DRAO ST images if a time variable source is situated in the field of view. If the incoming radio signal is constant one can produce a correct image of the sky from observations made over a variety of time periods. Unfortunately point sources whose signal varies significantly during an observation produce an observed response that does not agree with the PSF calculated under the assumption of an statistically invariant sky. The end result is that one cannot properly clean the effects of such sources from a field with the standard clean algorithm. A number of sources with short period variability have been detected in the CGPS survey. In Sect. 3.2 I describe how the effects due to time variability may be removed by an inversion of the self-calibration procedure.

However, not all instrumental distortions can be removed by an adaption of the self-calibration algorithm. The wide field of view of the ST is both its strength and its weakness. The telescope can easily make wide field images of large scale emission complexes in our galaxy, but at the same time interfering sources such as Cas A, Cyg A or the Sun are likely to be detected in either the main primary beam or in a sidelobe. Grating rings from these objects often run through the area of interest in the field and it is critical to remove the effects of these sources.

If a source is located at a large distance from the field centre its computed model visibility may differ significantly from that observed. This may happen, for example, because the source is located in an antenna sidelobe where the instrumental response has not been properly measured and deviates from that computed on the basis of purely geometric considerations. (The appendix of this paper gives a detailed description of the assumptions and procedures that go into computing model visibilities for the DRAO ST.) It is also possible for instrumental effects to have a baseline dependent origin. If baseline dependent faults, such as bandpass mismatches, are significant, the fundamental assumption of self-calibration, that gain errors can be described by purely antenna based errors, breaks down. Cornwell & Fomalont (1989) list additional causes of of baseline-based errors.

In Sect. 4.1 through Sect. 4.5 I describe an algorithm which has been quite successful at removing sources affected by distortions due to either unknown or baseline-based errors.