3 Catalogue preparation

   
3.1 Construction of merged catalogues

To prepare merged catalogues with UBVI colours for each object we derive a "detection'' image to locate objects and then perform aperture photometry on each separate filter at the positions defined by the detection image. This procedure avoids the difficulties associated with merging separate single-band detection images (such as differences in object centroids between U- and I-band images, for example). This detection image is constructed using a $\chi ^2$ image technique (Szalay, Connolly, & Szokoly Szalay et al. 1999), expressed in equation (2), where a_i represents the background-subtracted pixel value in filter i, $\sigma_i$ the rms noise at this pixel and n is the number of filter,

$$\chi^2 = {1\over n} \sum_{i=1}^{i=n}(a_i/\sigma_i)^2 .$$ (2)

This image has the advantage over other (more arbitrary) combinations of images such as (V+I) in that it has a simple physical interpretation, namely that each pixel of this image represents the probability of detecting an object at that location. We compute a_iand $\sigma_i$ for each pixel in each of the stacks using sextractor; this procedure allows us to correctly account for regions of varying signal-to-noise such as the overlap regions at the CCD boundaries. This resulting image is then used as input to sextractor as a detection image in the dual-image mode. We note that this method requires that both images are convolved to have the same full-width at half maximum and furthermore that they have a positional accuracy between filters of better than 1 pixel (as we have demonstrated in Sect. 2.3 our internal positional accuracy is $\sim$0.3 pixels, which meets this objective). We use an empirical approach to set the detection threshold in the chisquared image, similar to that employed in da Costa et al. (1998). Based on the numbers of objects detected in "blank'' images (frames which have the same background noise as our real images), the noise threshold is lowered in the chisquared image until the the number of additional sources detected is less than twice the number of sources detected in the blank images for the same change in the threshold. We emphasise however that the exact choice of the threshold is unimportant in this work as the range of variations considered in this procedure ($\sim$$2.0\sigma$) does not affect object detection even at the faintest magnitude limit where we carry out our scientific analysis ( $I{_{AB}\sim25}$).

   
3.1 Effect of $\chi\mathsfsl{^2}$-technique on galaxy magnitudes

As object parameters crucial to galaxy photometry, such as half-light radius, are extracted from the detection image when using sextractor in dual-image mode (in addition to the normal (x, y) centroids) we wished to ensure that the use of the $\chi ^2$image did not bias our derived (total) magnitudes. In Fig. 8 we plot the difference in galaxy total magnitudes between the single band 03 hr image and the dual-image mode method ($\chi ^2$ image and stacked image) as a function of total ABmagnitude in the single-band image. The filled shaded points show the median magnitude difference in half-magnitude intervals. Until $I_{AB}\sim24$, $I_{AB}~({\rm direct})-I_{AB}(\chi^2) \lesssim 0.02$; for 24 < I_AB < 25.5, $I_{AB}~({\rm direct})-I_{AB}(\chi^2) \lesssim 0.1$. Beyond $I_{AB}\sim24$ magnitudes computed using the direct image become systematically brighter than the chisquared image, which is most likely a consequence of the more reliable object profile information contained in the chisquared image (which is comprised of effectively a sum of object fluxes over all filters). In any case our galaxy colour measurements, which use aperture magnitudes, are unaffected by the application of this technique.

Our final catalogues consist of matched V,I band catalogues for all fields. For fields 14 hr, 22 hr and 03 hr we have additional B and Uband imaging. Magnitudes in our catalogues are Kron (Kron 1980) ``total'' magnitudes computed using the sextractor $mag_{\rm auto}$ parameter. We have also carried out a comparison between these magnitudes and those computed using the software employed in Le Fèvre et al. (1986) and the "Oxford'' galaxy photometry package described in Metcalfe et al. (1991). We find no evidence of any systematic differences between these three softwares. Throughout this paper we measure colours in an aperture of 1.5'' radius.

We also perform star-galaxy separation using the $r\rm _h$ parameter from sextractor, which is carried out on the I-band catalogue. This parameter measures the radius which encloses half the object flux. Star-galaxy separation is not carried out faintwards of $I_{AB}\sim21.5$; in any case for high galactic latitude fields like ours galaxies outnumber stars by a large fraction at these faint magnitudes (Reid et al. 1996). The bright limit of our catalogue (above which all galaxies and stars are saturated) is $I_{AB}\sim18.5$.

Figure 8: The difference between Kron (1980) total magnitudes computed in the direct 03 hr I-band image and using the $\chi ^2$ technique ($\chi ^2$ detection image combined with I-band photometry image) as a function of total magnitude measured in the I-band direct image (for clarity only 1/4 of all points are shown). The filled shaded points line shows the median difference in half magnitude intervals.