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50% completeness are given for point-like (star or bulge) and for extended (disks) sources.
The 80% and 50% completeness values are calculated from an automated fitting process applied to the
catalogues of real and simulated sources without tuning. The limiting magnitudes are derived automatically
by an empirical two parameter (x 0 ; α) fitting function
(
y = 100.0 × 1 − erf [x − x 0] α )
+ 1.0
2.0
where x 0 provides the turn-over position of the completeness function and α is the function slope at x 0 .
The parameters (x 0 ; α) are found from a standard χ 2 minimization. The 50% and 80% completeness
limits are derived from a linear interpolation. An example of fit is given in Fig. 28. In some cases, the fit
and the interpolation are not good and the completeness value is then poorly estimated.
The completeness distributions over all the Wide fields and inside a Wide field are presented in Table 6.
The left panel of Figure 29 shows the completeness distribution for the entire Wide survey for all four
fields. Figure 30 shows the completeness distributions for each of the four Wide patches.
The histograms coupled to a detailed inspection of the data show that the mean scatter in completeness
is ±0.20 magnitudes, with significant variations from filter to filter. The completeness distribution in
z-band is broader than other filters, with a tail that extends over one magnitude. In contrast, the r band
distribution is narrower (± 0.15 mag.). This is due primarily to the large variations of the sky brightness
through the years in that photometric band (OH emission lines), causing the variable depth on observations
following a fixed exposure time model. Erratic behavior of the OH emission lines also leads to
poorer correction of the fringes, aggravating the situation in the z-band.
Figure 32 shows a series of completeness maps over the entire Wide fields. The maps are produced for
each Wide field and for each filter.
The left and right panels of Figure 31 shows that the completeness distribution are dominated by seeing,
both for point sources and extended objects : better image quality corresponds to deeper images.
Compared to the seeing contribution, the exposure time (even with double exposure time) has a smaller
influence on the final depth measurement. For the u ∗ band, the range of limiting depth is likely broadened
by the diversity of observing conditions (Moon, extinction, seeing). Nevertheless, (other than exposure
time) the main factor affecting image completeness is the Seeing FWHM.
The comparison with T0006 completeness is not straightforward. In T0006, the simulations were produced
using a PSF of fixed FWHM equal to 0.9 arcsec. In T0007, the simulated PSF size matches the real
PSF size of each tile. Since the actual seeing distribution peaks at an image quality better than 0.9 arcsec,
the T0007 measured completeness of point sources is deeper than T0006. This increase in depth (around
0.02 to 0.03mag in riyz) is therefore largely due to the measurement technique rather than changes in the
images.
Finally, Figure 33 shows the galaxy counts for the four Wide patches for each of the six bands, appropriately
normalized in each case to the effective area after masking. The field-to-field agreement between
the different patches is excellent, as is the match to the literature values.
(12)
4.4 Photometric accuracy
In this Section we attempt to make a robust estimate of the internal photometric errors of the CFHTLS
using a variety of methods. Although Scamp provides an estimate of the internal photometric error
(between individual MegaCam images), we instead focus on the photometric errors in the final tiles.
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