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Subsections

5 Object catalogs

5.1 Source detection and photometry

In a survey like the EIS, where a large variety of astronomical -- and non-astronomical! -- objects of all kinds can be detected and measured over wide areas, one cannot avoid making choices. In the case of EIS, the priority is the detection of objects such as faint stars and galaxies. Brighter objects are generally saturated and/or already cataloged. The source extraction is performed with a new version of the SExtractor software (Bertin & Arnouts 1996) that can be retrieved from "http:/www.eso.org/eis". SExtractor is optimized for large scale imaging survey fields with low to moderate source density, and is therefore perfectly suited to EIS. The processing is done in 3 steps: detection, measurement, and classification, which are briefly described for the single image process.

5.1.1 Detection

  For each image, the detection process in SExtractor begins with the determination of a smooth background map. This is done by computing the modes of histograms built from meshes of $64 \times 64$ pixels, corresponding to $\approx $17 arcsec. This relatively small scale was chosen in order to facilitate the detection of faint objects on top of the strong gradients encountered near the many bright stars in the survey (3 out of the 4 EIS-wide fields are located at moderate galactic latitude). This produces a lower resolution image ($32 \times
32$) of the background (hereafter referred to as miniback). This miniback is median-filtered using a $3 \times 3$ box-car, to avoid the contamination of the background map by isolated, extended objects. The median filtering also helps to reduce photometric bias for bright, "large'' galaxies, to a negligible fraction up to scales $\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle ... $^{\prime\prime}$, which correspond to $I \mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle ... . A full-resolution background map is obtained by interpolating the smoothed miniback pixels, using a bicubic-spline, and is subtracted from the science image.

Background-subtracted images are then filtered before being thresholded, to reduce the contribution of noise on spatial scales of the image where it is dominant. The median seeing (FWHM) of EIS images as a whole is about 0.9 arcsec, a little more than 3 pixels. The data are filtered by convolving with a slightly larger, constant, Gaussian profile with FWHM = 4 pixels. Although the choice of a convolution kernel with constant FWHM may not always be optimum (the seeing may vary by as much as a factor of 3), the impact on detectability is, however, fairly small (see Irwin 1985). On the other hand, it has the advantage of requiring no change of the relative detection threshold. It also simplifies the comparison with the coadded-image catalog, for which the convolution kernel is also fixed.

The detection threshold, $k\sigma$, used in SExtractor is expressed in units of the standard deviation $\sigma$ of the background noise. For single images k = 0.6 is used, which corresponds to a typical limiting surface brightness $\mu_I \sim 24-24.5$ mag/arcsec2. The new SExtractor allows this noise-level to be set independently for each pixel i, using a weight-map wi (Sect. 3.7), which is internally converted to a relative variance: $\sigma^2_i \propto w^{-1}_i$. The variable detection threshold is also used for deciding if a faint detection lying close to a bright object is likely to be spurious or not.

Some pixels are assigned a null weight by Weight Watcher, because they are unreliable: gain too low, charge bleeding, cosmic-ray, etc. The detection routine cannot simply ignore such pixels, because some objects, like those falling on bad columns or charge bleeding features, would be either truncated or split into two. A crude interpolation of bad pixels overcomes this problem. Unfortunately, interpolation creates correlated patterns which are sometimes detected at the very low thresholds applied in the EIS, but as these zones are flagged, they are easily filtered out in the final catalog.

5.1.2 Measurement

  Basic positional and shape parameters are computed for each detection on the convolved image. These include the barycenter, major, minor axes and position angle derived from the second-order moments of the light distribution and the associated error-estimates, which take into account the weighting of each pixel. The photometry is performed on the un-convolved, un-interpolated image. Photometric parameters measured on the images include isophotal magnitudes, fixed-disk aperture magnitudes with diameters ranging from 2.7 to 14 arcsec (14 arcsec is the typical "Landolt aperture''), and SExtractor's estimate of "total'' magnitude: MAG_AUTO. The latter is a Kron-like elliptical aperture magnitude. It is computed in a way similar to that proposed by Kron (1980), except that the aperture is required to be elliptical, with aspect-ratio and position angles derived from the second-order moments. For the measurement of magnitudes, pixels with zero-weight and those associated with the isophotal domain of some neighbor are handled in a special way by the new SExtractor: when possible, they are replaced by the value of the pixel symmetrical to the current one, with respect to the barycenter of the object. Although this simple algorithm is certainly crude, it proves to yield fairly robust results and replaces advantageously the MAG_BEST estimator used in the old SExtractor (Bertin & Arnouts 1996). One particular aspect of EIS is the large variation in the seeing from frame to frame. Simulating EIS images of point sources under different observing conditions, it is found that the MAG_AUTO magnitudes are fairly robust with respect to seeing variations: systematics of only $\approx $1% peak-to-peak are expected for the bright stars used in the photometric solution.

5.1.3 Classification

The standard SExtractor star/galaxy classifier is a multilayered back-propagation neural-network fed with isophotal areas and the peak intensity of the profile. The classifier was trained with simulated ground-based, seeing-dominated, optical images. It will therefore perform well on images close to the conditions met in the original simulations. This is so for EIS images in patch A, but it is no longer the case for other patches, where very good seeing and strong optical distortions yield significantly elongated and skewed stellar profiles, varying over the frame. A new, more general, star/galaxy separation scheme is therefore needed for these fields, and is currently being implemented in SExtractor.

The current classifier returns a "stellarity index'' between 0 and 1. A value close to 0 means the object is extended (galaxy), while a value close to 1 indicates a point-source (star). It can be shown that the neural network output is approximately the probability that an object is a point-source. This is only valid for a sample of profiles which would be drawn from the same parent population as the training set. Because the neural classifier is a finely tuned system, these conditions are almost never met with real images, and care has to be taken when interpreting the stellarity index. Nevertheless, it is fair to adopt a stellarity index value of 0.5 as a default limit between point-sources and elongated objects. At faint levels ($I~\rlap{$\gt$}{\lower 1.0ex\hbox{$\sim$}}\ 21$), star/galaxy separation begins to break down for frames obtained under the least favorable seeing conditions in patch A. A clump begins to form around a stellarity index of 0.5, indicating that the algorithm cannot provide a reliable classification for most objects.

In the discussion below two values of the stellarity index are adopted to separate stars and galaxies: the conservative value of 0.5, which tends to favor more complete star catalogs, and a value of 0.75, which assumes that beyond the classification limit galaxies largely outnumber stars.

5.2 Single frame catalogs

  The most basic catalogs are the single frame catalogs which are generated by SExtractor. These are produced by default by the pipeline in a two-step process. First, SExtractor is run with a high threshold to identify stars and determine a characteristic value of the FWHM for each frame. This value of the FWHM is then used as input to a second run of SExtractor with a low-threshold for detection which also provides the classification of the detected objects by computing the stellarity-index.

During the extraction SExtractor sets several flags to describe any anomalies encountered. The meanings of these flags, $f_{\rm s}$, are summarized in Table 2. Information available in the flag-maps generated by the Weight Watcher program are also propagated to the catalog. Flags are set to indicate that a given object is affected by bad pixels in the CCD-chip or by artifacts in the image that have been marked either by the artificial retina or by the polygon-masking during visual inspection (Sect. 5.4). Table  3 summarizes the meaning of the flags in the catalog set from the information contained in the flag-maps, $f_{\rm w}$.


  
Table 2: Description of SExtractor flags ($f_{\rm s}$)

\begin{tabular}
{rp{7cm}}\hline
Value & Description \\  \hline
1 & The object ha...
 ...ding \\ 128 & A memory overflow occured during extraction \\ \hline\end{tabular}


  
Table 3: Description of Weight Watcher flags ($f_{\rm w}$)

\begin{tabular}
{rp{7cm}}
\hline
Value & Description \\  \hline
1 & The object c...
 ...ixels \\ 32 & The object was masked out during eye-balling\\ \hline\end{tabular}

The contents of the catalogs include: J2000.0 right ascension and declination, x and y coordinates in the chip; total magnitude (MAG_AUTO) and error; major and minor axes; position angle; stellarity index; SExtractor flag $f_{\rm s}$ (see Table 2); Weight Watcher flag $f_{\rm w}$ (see Table 3); total number of pixels above the analysis threshold (npix); total number of pixels that are flagged by Weight Watcher (nflag). Further information can be found at "http:/www.eso.org/eis".

5.3 Derived catalogs

  During the processing of a patch through the pipeline the single frame catalogs are merged together into a "patch'' catalog which contains information of all objects identified in the individual frames. Note that objects may have multiple entries if they are in overlapping frames. From this patch catalog several single entry catalogs may be derived, for instance, the even/odd catalogs containing all objects detected in the even/odd frames. Objects detected in more than one frame are identified to produce a single-entry in the final catalog, choosing the parameters as determined from the best-seeing image. Objects in regions of overlap are paired whenever the barycenter of the smallest falls within an ellipse twice the size of the object ellipse of the larger one. Details on this procedure will be presented elsewhere (Deul et al. 1999).

From the flag information available in the single-entry catalog, filtered catalogs can be produced for analysis purposes (see Sect. 6). The filtering is required to eliminate truncated objects and objects with a significant number of pixels affected by cosmics and/or other artifacts. Objects with the following characteristics are discarded: $f_{\rm s} \geq 8$ or nflag/npix $ \ge 0.1$,where $f_{\rm s}$ is the SExtractor flag, npix the number of pixels above the analysis threshold and nflag the number of pixels flagged by Weight Watcher. The two-dimensional distribution of stars and galaxies from the resulting catalog are shown in Figs. 15 and 16, for different limiting magnitudes.

  
\begin{figure}
\resizebox {8.8cm}{!}{\includegraphics{7652f15a.eps}}

\resizebox {8.8cm}{!}{\includegraphics{7652f15b.eps}}\end{figure} Figure 15: Distribution of stars detected in the even frames covering patch A at magnitudes brighter than I=20 (12355 objects, upper panel) and I=21 (18529, lower panel). Objects with a stellarity index >0.5 were classified as stars. Note the two bad frames in the upper part of the patch, yielding nearly empty regions. As pointed out in the text this region is usually discarded from the analysis

  
\begin{figure}
\resizebox {8.8cm}{!}{\includegraphics{7652f16a.eps}}

\resizebox {8.8cm}{!}{\includegraphics{7652f16b.eps}}\end{figure} Figure 16: Same as in previous figure showing the distribution of 9006 (upper panel) and 23129 (lower panel) galaxies for the same two limiting magnitudes as in Fig. 15. Again note the empty regions in the upper part of the patch caused by bad frames

5.4 Visual inspection

 

The visual inspection of the catalogs was done using the new version of ESO SkyCat which also provides the possibility of accessing the EIS catalogs through the on-line server. Further information on the SkyCat setup can be found at "http:/www.eso.org/eis". This setup interprets the parameters and flags available in the EIS catalogs. To distinguish between the different object classes and flags, the following plot symbols and colors have been used:

This tool has been extensively used to fine-tune the configuration parameters used by SExtractor and Weight Watcher as well as to inspect the performance of the filtering of the catalogs (see Sect. 5.3). Users of the catalogs should be aware of the following features:

The visual inspection shows that, by adopting the filtering criteria described in the previous section, most of the spurious objects are appropriately removed.

5.5 Uniformity of the detections

As a first check on the quality of the object catalogs produced by the pipeline it is important to examine the uniformity of the detections across the effective area (excluding the regions masked out) of the EMMI-frame. This is shown in Figs. 17 and 18, where the normalized average counts of stars and galaxies as a function of the east-west (Fig. 17) and north-south position (Fig. 18) on the chip are displayed. The upper panels show the star counts brighter than I = 21, which is the limiting magnitude for reliable classification in patch A as a whole. The lower panels show the galaxy counts to the same limiting magnitudes.

The overall uniformity of the detections at magnitudes $I \leq 21$ is good. A small decrease in the number of stars is seen at the upper edge of the chip and is almost compensated by an increase in the galaxy counts. This behavior is likely to be due to misclassifications caused by the increase in size of the PSF as shown in Sect. 3.5.

  
\begin{figure}
\resizebox {8.8cm}{!}{\includegraphics{7652f17.eps}}\end{figure} Figure 17: The uniformity of the detections in the east-west direction. The top panel shows the detected stars brighter than I=21 for a stellarity index $\ge$ 0.75 (dotted line) and stellarity index $\ge$ 0.5 (dashed line). For fainter magnitudes the classification breaks down. The bottom panel shows the detected galaxies brighter than I=21 stellarity index < 0.75 (dotted line) and stellarity index <0.5 (dashed line). It is seen that the star counts show a dip at the "right" edge of the chip, and a corresponding increase in the galaxy counts. This feature is attributed to the image distortions, see text for details

  
\begin{figure}
\resizebox {8.8cm}{!}{\includegraphics{7652f18.eps}}\end{figure} Figure 18: As Fig. 17 but showing the detections in the north-south direction. Again at the "upper" edge of the chip we see a dip in the star counts and a corresponding increase in galaxy counts, which is due to the image distortions, see text for details

5.6 Completeness and reliability

To verify the pointing of the telescope, a reference field has been observed before the start of each row (150 s) and, in some cases, the start of sub-rows (50 s). These exposures, which for patch A total 2250 s, were used to determine the offset required to compensate for the problems detected with the NTT pointing model. Using the EIS pipeline these images have been coadded and an object catalog was produced extending to fainter magnitudes. This catalog has been used to empirically determine the completeness of the detections in typical single-frame EIS catalogs. This was done by comparing the catalog produced from the coadded image of the reference field to the individual catalogs derived for the various exposures of that field. Since the limiting magnitude of the coadded image is much fainter than that of the single frames, one can assume that the coadded catalog is complete and that it is not significantly contaminated with false objects at least to the limiting magnitude of the single-frame catalogs. Keeping this in mind a match was made between all the objects in the coadded catalog and those found in the single-frame catalogs. The ratio between the number of paired objects and the total number of objects in the coadded catalog provides a measure of the differential completeness as a function of magnitude, which is shown in Fig. 19. The completeness defined in this way only measures the fraction of objects actually found, but does not tell anything about the reliability of their properties. It is seen from the figure that for objects of magnitude $I \sim 23 $ the completeness is $\sim$80%. At this magnitude the integrated completeness of the catalog is 94%. The completeness does not vary for seeing between 0.7 and 1.3 arcsec. For a seeing of 1.5 arcsec the 80% differential completeness limit is at $I \sim
22$.

  
\begin{figure}
\resizebox {\columnwidth}{!}{\includegraphics{7652f19.eps}}\end{figure} Figure 19: Top panel: Completeness of the single-frame catalogs as determined from the comparison with the reference field. The plot shows the ratio between the number of objects found in both the coadded image and a single frame and objects found in the coadded image as a function of magnitude. The figure shows that at $I \sim 23 $ the single-frame catalogs are 80% complete. Bottom panel: The number of paired objects, to give an idea of the statistical errors in the comparison

The number of false detections can be estimated in a similar way. Figure 20 shows the ratio between objects that were found in a single-frame catalog but not in the coadded one and the total number of objects in the single-frame catalog. The figure is based on a comparison obtained using a single frame with a seeing of 1.07 arcsec, which is close to the median seeing of the observations for the patch. It is seen that at $I \sim 22.5$ 10% of the objects are false detections and 20% of the objects with magnitude $I \sim 23 $ are spurious. The integral fraction of spurious objects up to the limiting magnitude of I=23 is $\sim$6%.

  
\begin{figure}
\resizebox {\columnwidth}{!}{\includegraphics{7652f20.eps}}\end{figure} Figure 20: Top panel: ratio of the number of objects found in a single-frame but not in the the coadded catalog of the reference field and total number of objects in the corresponding single-frame catalog. At $I \sim 22.5$there are 10% false objects and at $I \sim 23 $ there are 20% spurious detections. Bottom panel: total number counts in the single-frame catalog

5.7 Errors in magnitude and classification

A comparison between even and odd catalogs provides further useful information on the accuracy of the magnitudes and on the robustness of the classification as a function of magnitude. This comparison was done using a test region of 0.6 square degrees, with a median seeing of 0.95 arcsec. Using the same pairing procedure previously discussed, a catalog of paired objects in the test region was produced.

A lower limit estimate of the photometric errors can be obtained from the repeatability of the magnitudes of the paired objects. Figure 21 shows the magnitude difference of these objects as a function of magnitude. The standard deviation of the magnitude differences in the interval 16 < I < 20.5 ranges between 0.02 and 0.1, reaching 0.3 at $I \sim 23 $.

  
\begin{figure}
\resizebox {\columnwidth}{!}{\includegraphics[clip]{7652f21.eps}}\end{figure} Figure 21: The magnitude differences between detections in the even and odd catalogs as function of magnitude. At bright magnitudes the standard deviation varies between 0.03 mag and 0.1 mag, reaching 0.4 mag at $I \sim 23 $

Figure 22 shows a comparison between the errors determined from the magnitude difference shown above (divided by $\sqrt{2}$) and the SExtractor error estimates based on photon statistics. SExtractor provides reasonable error estimates over the interval of interest. At bright magnitudes photometric errors are dominated by effects such as flatfield errors, image quality, intrinsic stability of the MAG_AUTO estimator and relative photometry.

  
\begin{figure}
\includegraphics [width=7.5cm]{7652f22.eps}\end{figure} Figure 22: Comparison between the standard deviation of the EIS-magnitude differences (filled squares) and the magnitude errors estimated by SExtractor (open squares) as function of magnitude

For objects in the magnitude range 16 < I < 21 and adopting a stellarity index of 0.75 to separate stars and galaxies, about 5% of the objects have different classifications in the even and the odd catalogs. For magnitudes $I ~\rlap{$<$}{\lower 1.0ex\hbox{$\sim$}}\ 16$ most objects are saturated and may be classified as galaxies. However, they can be found as having the flag $f_{\rm w}=16$, which has been used to exclude them from subsequent analysis.


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