Inversion and deconvolution of GMRT data

The 325-MHz primary beam of GMRT antennas has a full width at half maximum (FWHM) of $\sim1{^\circ}.4$. The central square provides a maximum baseline of $\approx 1$ km equivalent to an angular resolution of $\sim3$ arcmin. At this resolution, the full GMRT primary beam can be mapped without severe degradation due to non-coplanar effects. As a first step, with the dual purpose of gauging the data quality and locating strong confusing sources, single facet images were made at a resolution of $\approx 1$ arcmin using the task IMAGR.

Having identified the sources in the field of view from this lower resolution image, higher resolution imaging was attempted. Typically, a maximum baseline of $20$k$\lambda$ was used corresponding to an angular resolution of $\sim 15$ arcsec. Most of the fields had strong extended sources all over the field of view forcing the mapping of the full primary beam. At these resolutions, the number of planes required along the n-axis is 8. Hence, a 3D inversion was required. The IMAGR task of AIPS performs a 3D inversion using the polyhedron imaging algorithm. In this, the entire field of view is divided into a two dimensional grid of facets. A small part of the sky (corresponding to the size of the facet) centred around each facet is then imaged by first shifting the phase centre of the visibility to the centre of the facet and then performing the normal 2D inversion and CLEANing. Since, the 2D approximation is assumed to be valid within the facet, it is important to make sure that the facet is not so big as to re-introduce distortions at the edges of the facets.

The number of facets required for 3D inversion using IMAGR and the appropriate RA and DEC shifts for the centre of each facet, were computed using the relatively new task in AIPS called FCSET. Essentially, given the size of each facet, the size of the field of view and the RA and DEC of the phase center, this task writes out a IMAGR readable list of field specifications (the field number, its RA and DEC shifts and its size in number of pixels along the RA and DEC axis). Typically, this resulted in a $5\times 5$ grid of facets, each of size $256 \times 256$.

After the inversion of each of the facets, the IMAGR task uses the usual 2D Clark CLEAN (Clark1980) on each facet. The class of CLEAN and MEM based deconvolution algorithm treats each pixel in the image as a degree of freedom. Even when mapping in the Galactic plane (or close to it), it is clear from the images that most of the pixels do not have any physical emission associated with them. Reconstruction of the physical emission in the field of view should therefore be somehow constrained to use only those pixels where there is significant physical emission from the sky. Not doing so is equivalent to giving more freedom to a non-linear fitting process (the deconvolution process), than is justified by the data. CLEAN based algorithm (and its variants) are themselves unconstrained. This constraint must therefore be provided externally by setting boxes around the dominant sources in the field of view at each cycle of CLEAN. It has been shown by Briggs (1995) that the best results are obtained by putting as tight a box as justified by the data (essentially by inspection). During the deconvolution process, the IMAGR task provides a facility to dynamically define boxes for each field for every cycle of CLEAN. However, since the emission was usually of complex morphology making it difficult to define tight boxes, simple square boxes enclosing the source of emission were used. This was manually done for each facet.

The resulting set of facet images were put together to reconstruct the sky using the task FLATN. The FLATNed image was then primary beam corrected using the task PBCOR. The GMRT visibilities correspond to the date-epoch at the time of observations. The final image was therefore rotated to the J2000 epoch using the task REGRD.