This section briefly describes the photometric software used in the data analysis (SExtractor: Source Extraction software). A complete description is given in Bertin & Arnouts (1996, hereafter BA96).
The photometric analysis is done in four steps:
The background map is derived by binning the frame into large
meshes (32 
32 or 64 
64 pixels), and removing the possible
overestimations due to
bright objects using a 
-sigma clipping algorithm.
This sky background map is subtracted from each frame.
The detection algorithm determines a group of connected pixels above a given
threshold. A minimum number of connected pixels is chosen in order to avoid
spurious objects (bad pixels, un-removed cosmic rays,...). Convolution with a
gaussian with a FWHM close to the seeing improves the detection of
objects by decreasing the background noise.
The typical threshold used is 
above the background value
(
is measured from the unsmoothed background) corresponding to a
surface brightness equal to 27 mag arcsec
in B, 26.5 mag
arcsec
in V
and 26 mag arcsec
in R.
When such a low threshold is used, large spurious faint objects can appear in the wings
of objects with shallow profiles. This effect is seen around elliptical galaxies or
bright stars where the local background noise increases and can exceed the detection
threshold.
A cleaning procedure is therefore applied to check if the detected objects are real.
For the faint objects in the vicinity of bright objects, a new estimation of the
local background is obtained by assuming that the dominant central object has
large gaussian wings. If the mean
surface brightness of the faint object is lower than the calculated local threshold,
the object is rejected.
Each detection of a connected set of pixels is processed through a deblending algorithm based on multi-thresholding as described in BA96.
Three kinds of magnitudes are used: isophotal, "corrected isophotal''and "adaptive aperture''.
The "corrected isophotal'' retrieves the lost flux in the isophotal magnitude by assuming that the wings of objects outside the limiting isophote are nearly gaussian (see Maddox et al. 1990a). This estimation of the "total'' magnitude could be improved by assuming that the profile of objects follows the more realistic Moffat profile. However, if the value of the threshold is low, the gaussian profile provides an adequate correction as demonstrated by the tests on simulated frames (see Sect. 4.2).
The "adaptive aperture'' magnitude is the best estimation of the "total'' magnitude. The algorithm is similar to the "first-moment'' measure designed by Kron (1980). This magnitude is calculated in two steps:
(1) The object's light distribution above the isophotal threshold is used to
measure an isophotal elliptical aperture
characterized by the elongation 
and position angle 
.
(2) The first moment 
is calculated in an aperture 2 
larger than the
isophotal aperture in order to reach the light profile information below the isophotal
threshold.
The first moment is used to define the "adaptive aperture'' of radius 
inside which we measure the "total'' magnitude.
The principal axes of each object are defined by 
and 
.
Kron (1980) uses a circular aperture of radius 
with k=2
which measures 90% of
the total flux from the objects. To converge near the "total''
magnitude we can increase the k value, but a compromise must be found between the
added measured flux and the increasing noise in larger apertures.
As Metcalfe et al. (1991), we choose k=2.5, yielding 94% of the total
flux inside the adaptive aperture (this value was calculated using simulated frames with a large variety of
galaxy profiles).
In contrast to the isophotal magnitude which operates at fixed signal-to-noise,
the "adaptive aperture'' magnitude may be determined at very low
signal-to-noise. Sometimes for faint objects, 
may converge to
erroneously small apertures.
We therefore constrain the apertures to a minimum value of 
(where 
is the mean standard deviation of the bivariate gaussian profile defined by the
second order moments of the object profile (BA96)).
To test the quality of the photometry for objects with different magnitudes,
we use simulated frames provided by E. Bertin (BA96) and
generated according to the following scheme.
A sky background is defined by a sky surface brightness (
mag/
), and Poisson noise is added according to a gaussian
distribution as observed on real CCD frames.
A set of stars with a Moffat profile
(Moffat 1969) are generated.
Galaxies are produced with a large variety of shapes and sizes.
The pixel size and seeing disk are adjusted to resemble as much as possible
the real frames.
The frames are defined through the R band corresponding to the band used here for
the selection of the spectroscopic sample and for the star/galaxy separation.
The results of the tests on several simulated images are based on 
6000
galaxies and 
600 stars in total.
In Fig. 1 (click here), we compare the mean difference between the
different measured magnitudes and the true magnitude for the galaxies. The mean
difference is calculated in bins of 
of the true magnitude.
The error bars represent the rms scatter around the mean.
As expected, the isophotal magnitude which measures the flux inside the
defined isophote looses the flux in the wings outside this isophote.
Figure 1 (click here) shows that an increasing fraction of flux is lost for
fainter magnitudes.
The "corrected isophotal'' magnitude (defined in Sect. 4.1.4) provides a
significant improvement.
Figure 1 (click here) also confirms that the "adaptive aperture'' magnitude
(Kron magnitude) measures 
of the flux of objects over the entire
magnitude range (the systematic offset of 
is indicated by the dashed line in
Fig. 1 (click here)).
To reach the "total'' magnitude, we then subtract a constant value of
to all magnitudes.
The error bars in Fig. 1 (click here) are 
for galaxies with
, and up to 
at fainter magnitudes.
The interest of the "adaptive aperture'' magnitude over the
isophotal magnitude originates in it insensitivity to seeing and redshift
(Kron 1980).
Because a large fraction of the detected objects in our survey are stars, we also
compare in Fig. 2 (click here) the different magnitudes for the simulated stars.
Even when a gaussian profile is used to correct the flux lost in the wings of
stellar objects with Moffat profile, the "corrected isophotal'' is very close to
the total magnitude for 
.
Because the fraction of flux measured in a fixed aperture is constant for stars,
we check the reliability of the second order moments by comparing the
"adaptive'' magnitudes to the "aperture'' magnitudes.
The aperture radius is defined by 
where 
is the second order moment along the major axis, estimated by using unsatured
stars with high signal-to-noise (typically 
). The lost flux
is stable in the full magnitude range and is close to 
.
This value is in good agreement with the "adaptive'' aperture obtained by using
a minimum radius defined as 
(where 
is calculated for each object). We can then conclude
that the second order moments can be
reliably estimated down to very low
signal-to-noise ratios and the "adaptive'' magnitude is a good measure of the
total magnitude.
Despite the reliability of "adaptive'' magnitude for stars, we use
the "corrected isophotal'' magnitude as being the best magnitude to estimate
the "total'' magnitude.
Because, we make the star/galaxy separation only for 
, we use the
"corrected isophotal'' magnitude up to this cut-off for the stellar sample
and the "adaptive'' magnitude for the galaxy sample. At fainter magnitudes,
no classification is done, thus we use the "adaptive'' magnitude for all
objects.
Figure 1: Mean
difference in 
bins between the measured magnitudes
and the true magnitudes for galaxies in simulated R frames. The symbols for
the different
magnitudes used are given inside the graph. The error bars show the rms
scatter around the mean. The dashed line represents the expected
position of magnitude difference for the "adaptive aperture'' magnitude
corresponding to the 94% enclosed flux
Figure 2: same as Fig. 1 (click here) for stars. The dashed line represents
the flux measured inside a radius defined as 
,
where 
is derived from stars with high signal-to-noise
(as described in text)
The results of the tests applied to the simulated images show that:
(1) For galaxies,
the "adaptive aperture'' magnitude is a robust estimate of the
"total magnitude'' (after correction for an offset of 
) down to
. The uncertainty in the measure is close to 
up to 
and increases to 
up to 
.
However, this is an aperture magnitude and it is sensitive to crowding by
close neighbours. Therefore, when an object has a
neighbours closer than 2 isophotal radii, we use by default the
"corrected isophotal'' magnitude.
(2) For stars, the "corrected isophotal'' magnitude is a reliable estimate
of the "total magnitude'' for 
.
(3) Because we measure "total'' magnitudes,
the colours can be calculated as the difference between the "total'' magnitudes
in each passband. The colour error can be estimated
as the quadratic sum of the error in each band. For objects brighter than
, the colour error is 
and at fainter magnitudes the
colour error is 
.
To build the spectroscopic catalogue, it is important to exclude the stellar
objects. The star/galaxy separation is performed using the neural network
included in the photometric software SExtractor. For a complete description of the
principle, the training (with using simulated frames containing stars and
galaxies), and various tests of this neural network,
the reader can refer to BA96.
Here, we describe the input and output parameters used for the separation.
For each image, the classifier works in a ten-parameter space containing 8
isophotal areas defined by dividing the peak intensity in 8 levels equally spaced
in logarithmic scale, the central peak intensity, and one control-parameter which
defines the fuzziness of the frame and is chosen to be the seeing (in pixels).
This set of input
parameters is shown to provide an "optimal'' description of the characteristics of
each image (BA96).
The neural network provides an output parameter defined as a
"stellarity-index''. Because the p.s.f. of a frame is the parameter which
determines the quality of the performance of the neural network, SExtractor
estimates on each frame the FWHM of the p.s.f. using the unsatured bright stars and
uses it for the neural network.
The "stellarity-index'' output parameter is a measure of the
confidence level in the classification of each image. The value varies
between 1 for stars and 0 for galaxies.
In Fig. 3 (click here), we show the stellarity index as a function of magnitude for
a R frame. For our 50 R frames, a reliable
classification can be done for 
with a success rate for the galaxies
close to 95% (BA96). A fainter magnitude limit can be reached
for several frames with good seeing quality (such a frame is shown
in Fig. 3 (click here)).
To be sure that galaxies are not mis-classified as stars,
we define as stars all objects with a stellarity index greater than 0.8.
The corresponding magnitude limit for classification is 1.5 magnitude deeper
than our spectroscopic limit of R=20.5, and thus guarantees that our spectroscopic
sub-sample is poorly biased by mis-classified objects.
Figure 3 (click here) shows that at faint magnitudes 
, the stellarity index
approaches 0.5 because no distinction can be made between the two classes when
the profiles are dominated by the seeing disk. On the other hand, at bright
magnitudes, for the largely saturated stars (
) the stellarity index may
drop below 0.8.
When we started the spectroscopic observations, the photometric software
by E. Bertin was not avalaible. We thus used INVENTORY, the photometric software
developed by A. Kruszweski
(West & Kruszewski 1981) and avalaible in
the MIDAS environment.
INVENTORY provides a reliable star-galaxy separation for 
and was used to generate the entry catalogue for the first half of
the spectroscopic observations. The good success
rate in the separation is confirmed by only 15 spectra of stars observed out of a
total number of 521 reduced spectra (i.e. 
)
(Bellanger et al. 1995a).
Figure 3: Star/galaxy separation for a science frame observed in the
R band with a seeing of 0.9 arcsec. The ordinate shows the output parameter of neural
network, the "stellarity index'' which provides an estimate of the confidence
level in the classification of each object as a star (CLASS = 1) or a galaxy
(CLASS = 0)