6.4 Stacking of GAIA BBP Observations

The general problem of the superposition, or stacking, of different images of the same sky region into a global image can be referred to as mapping. In the context of the GAIA mission, where the observations will generally be essentially one-dimensional, this problem is of interest not only in connection with galaxy observations, but also whenever a two-dimensional study may be required. This is the case e.g. for the observation of stars in the PSM, where a two-dimensional map of the sky region near each detected star will be needed in order to correct the brightness of the detected star for nearby, fainter disturbing stars, but also for the study of resolved binary systems. The latter issue, in particular, was already discussed by [Høg et al. 1998b] in the context of the construction of the Tycho 2 catalogue. In the following, observation will indicate the image of a given sky region obtained at a given epoch, whereas flux map will indicate the image resulting from the stacking of a given number of observations of the same sky region taken at different epochs.

The stacking of a single simulated observation into a one-scan flux map was carried out through the following steps:

1. Subsampling of GAIA observation: in order to partly recover some of the resolution lost in the wide CCD binning of GAIA observation, each sample is considered as consisting of a mosaic of square subsamples of 37.2 mas side, each containing the same fraction of the sample electron count, much like it is done in Section 6.3 and shown in Figure 6.4 for the subpixeling. The value of 37.2 mas, i.e. the Astro CCD pixel size in the along scan direction, was chosen so as to be smaller than the side of the flux map elements and to be an integer submultiple of the sample size along both directions, so that each sample can be divided into an integer number of subsamples.
2. Translation and rotation of GAIA subsamples: the mosaic of subsamples is counter-translated and counter-rotated to superpose it onto the flux map, which is a mosaic of step equal to HST pixel size and half HST pixel size for PC and WFCs respectively, having the same orientation and the same center as the original HST image. Note that, due to the extremely accurate astrometric calibration that will be available at the end of the mission, the errors in the determination of the center and scan direction of the observations are negligible with respect to the sample size and the expected angular resolution.
3. Rebinning of GAIA subsamples into GAIA flux map: each GAIA subsample electron count is assigned to the flux map element containing its center.

This procedure returns a one-scan flux map. The all-mission flux map is then simply obtained by adding up all the one-scan flux maps from observations of a given sky region.

This stacking technique, accurately preserves the total number of electrons of the original image, thus allowing an easy photometric calibration of the flux map on the basis of the HST WFPC2 photometric calibration obtained by [Holtzman et al. 1995b].

A second stacking method, slightly different but much more efficient than the baseline technique described above, was also developed, consisting in assigning to a given flux map element the electron counts corresponding to the subsample nearest to its center. On the basis of visual inspection, this stacking method appears to deliver much the same results as the baseline method described above. Since the subsamples are smaller than the flux map elements, some subsamples happen not to be assigned to any flux map element, thus reducing the total number of electrons in the flux map. On average, this effect can be taken into account by multiplying the electron counts in the flux map by the ratio between the sizes of the flux map elements and the subsamples. Owing to its recent development this method has not been thoroughly tested yet, but owing to its efficiency is metioned here as a suggestion as to how the data reduction of galaxy observations could be carried out in practice. Note also that, although the possible use of drizzling, a stacking technique developed for use in the superposition of HST WFPC2 images in the Hubble Deep Field North campaign ([Williams et al. 1996]), was considered for use in the stacking of GAIA galaxy observations, it was finally discarded for reasons described in Appendix F. The simulated images presented in Chapter 7 and in Appendix B have therefore been derived using the previously described baseline stacking method.