In order to perform a co-addition with the full mosaic, what we need is to place every pixel of any science images into sky coordinates, i.e. define a World Coordinate System (WCS) for a dithering set. A source which happens to fall in the gaps between adjacent CCDs in some frames of a data set, is successfully retrieved during the final stacking.
For the astrometric solution of the OACDF data, we used the mscred package in IRAF and the procedure adopted by Dr. H. McCracken (Private communication). The various steps where then implemented in a single automatic algorithm. We briefly summarise the main steps in what follows.
The best absolute astrometric precision that one can achieve with the procedure described above is limited to that of the catalogue used; in our case it is about 0.3'', corresponding to the intrinsic accuracy of the USNO catalogue. However, the relative astrometric precision is better, as one can see from Figure 3, where the relative astrometric errors of the fourteenth dithering relative to the first one for the R band are shown. Moreover, the coordinate residuals of a given dithering with respect to each other show that there are no systematic errors in the coordinates over the entire mosaic of 0.25 deg2 (c.f. Fig. 3 right panel). Thus, we conclude that the average relative error of the coordinates in the OACDF data is of the order of 0.15''. This is in perfect agreement with the result by Wolf et. al. (2001), who used a different procedure (within MIDAS) for their astrometric solution.
All frames (which are still in the multi-extensions fits file format after pre-reduction and astrometry calibrations), obtained in a dithering sequence and for a given pointing and filter, are projected into monolithic 8k x 8k images. The stars in common to all frames are used to determine the air mass and transparency variations from one frame to the other. These weights and offsets are determined with respect to the frame with the lowest airmass, and are stored in the image headers. The dithered 8k x 8k images for a given filter and pointing are then stacked using a ccd-clipping algorithm for cosmic-rays/bad pixel-column removal, and applying the corresponding weights and offsets to compensate for air-mass and transparency relative to the lowest airmass frame.
The accuracy of the astrometric calibration and of the co-addition was checked by testing the PFS characteristics before and after stacking of a dithering set. Even a small error in the astrometric solution yields a deformed PSF after the combination of the images. In Figure 4, the contour maps of two stars in the combined R band mosaic are shown. The ellipticity of these objects is less than 0.02. Furthermore, it is important to verify that the Poissonian character of the noise is maintained. In all cases were we have produced mosaics the noise of the combined mosaic was indeed Poissonian.