3 Data reduction

3.1 Bias and dark current

The basic image reduction was done using MIDAS.

The bias frames showed a fixed structure with an overall level that varied up to 20 counts during the course of each night. We corrected for this by using the overscan region of the detector, which mirrored the same variation. For each night, a median-filtered master bias was made from at least 20 individual bias images. An average bias level was determined for each image from its overscan region. The associated master bias was then scaled to each overscan mean and subtracted from each image, with the 0.5 count difference between the overscan and the bias average taken into account. No significant dark current was measured in the VLT test camera.

   
3.2 Creating the super sky flats

The greatest potential source of error in our final images is uncertainty in the flat-field. As many sky counts per pixel as possible are required to reduce the statistical error in the flat-field which, to avoid large systematic uncertainties, should be obtained using light with the same spectral energy distribution as the primary observation. This was done by creating a super flat-field made from careful combinations of the deep EIS and the HDF-S fields that were interleaved temporally with our observations of ESO 342-G017. The advantage of this method lies in the large total exposure of these deep fields, which are devoid of bright stars and were well-dithered between individual exposures. The HDF-S and EIS fields are located 26 $.\!\!^\circ$3 and 53 $.\!\!^\circ$8 away from ESO 342-G017, respectively.

Each candidate sky flat image was inspected visually; only those free of defects and temporally close to our observations of ESO 342-G017 were chosen. Observations of the HDF-S made on 28, 29, and 31 August 1998 were not used in our flat-field due to increasing sky levels from a waxing moon. The remaining 26 R-band and 31 V-band flat frames contained a total of 73560 and 39550 sky electrons per pixel, respectively. Considering only Poisson statistics of sky electrons, the flat-field formed from these frames should contribute a pixel-to-pixel error of 0.37% (R-band) and 0.50% (V-band). Of course, variations in the sky brightness across the image and remnant halos from inadequately removed bright stars, create large-scale errors above that expected from simple Poisson variations. We empirically determine the size of this dominant flat-field error below.

 

 

Table 3: RMS flatness of flat-fields.

Flat Correcting Flat	Filter	Rebinned size ( $^{\prime\prime}$)	Relevant scale	Measured rms	$\frac{{\rm Pixel-to-Pixel}~rms}{\sqrt{N_{\rm pixel}}}$
${\rm flatR1/flatR2}$	R	0 $.\!\!^{\prime\prime}$091	1 pixel	0.57%	-
${\rm flatV1/flatV2}$	V	0 $.\!\!^{\prime\prime}$091	1 pixel	0.78%	-
${\rm flatR1/flatR2}$	R	0 $.\!\!^{\prime\prime}$806	400pc ($\sim$ $h_{\rm disk}$)	0.11%	0.064%
${\rm flatV1/flatV2}$	V	0 $.\!\!^{\prime\prime}$806	400pc ($\sim$ $h_{\rm disk}$)	0.14%	0.088%
${\rm flatR1/flatR2}$	R	0 $.\!\!^{\prime\prime}$9	450pc (PSF FWHM in R)	0.16%	0.058%
${\rm flatV1/flatV2}$	V	1 $.\!\!^{\prime\prime}$1	550pc (PSF FWHM in V)	0.12%	0.065%
${\rm flatR1/flatR2}$	R	6 $.\!\!^{\prime\prime}$04	3kpc ($\sim$ $h_{\rm halo}$)	0.08%	0.0086%
${\rm flatV1/flatV2}$	V	6 $.\!\!^{\prime\prime}$04	3kpc ($\sim$ $h_{\rm halo}$)	0.11%	0.012%

The super flat-field was created for each filter separately as follows. Each individual flat-field sky frame was normalised to its modal value as determined in the central 3/5 of the image. The average value of pixel (i,j) was then determined from the stack of sky frames for the filter, accepting a pixel (i,j,k) from the kth frame in the computation of the average only if it passed two tests. First, its deviation from the mean pixel value in the stack at (i,j) must not exceed a given threshold measured in units of the noise at that pixel position (a $\kappa$-$\sigma$ clip). This criterion effectively removed cosmic-ray events and, since each image was dithered by at least 10 $^{\prime\prime}$ (110 pixels) in both $\alpha$ and $\delta$ between successive exposures, the bright cores of stars and galaxies as well. Second, a median-filtered frame was created over a 3$\times$3 pixel window from the average frame resulting from the first step. A $\kappa$-$\sigma$ clip was again applied to each pixel (i,j,k) based on the value of its local median. The second test was applied to remove any remnant faint extended wings of stars and galaxies, which would otherwise contaminate the resulting flat-field frame. Only pixels satisfying both these "filters'' entered the average for the flat-field frames. A normalization level was calculated from the median value in the central 3/5 of each flat-field frame, and each image was then flattened and renormalized.

In order to test the quality of the flat-fields, and to compute an empirical large scale flat-field error, we repeated the above procedure using only one-half of the available HDF-S and EIS images. In this way, flatR1 was made from HDF-S and EIS images from nights 17, 18, 22, and 23 August, while flatR2 was made from HDF-S and EIS images from nights 23 and 26 August. The two subflats R1 and R2 have approximately the same flux levels. Two V-band subflats were created in the same way. The flat-field frames flatR1 and flatV1 were then flattened using flatR2 and flatV2, respectively. Each was then examined visually for any remnant features, and then rebinned to a number of relevant scales and the rms variation across the frames measured. The cosmetic flaws inherent in the Test Camera CCD, particularly the "stain'' mentioned in Sect. 2.2, were removed effectively by our flat-field procedure. The results are summarized in Table 3, in which the measured rms is compared to that expected from photon statistics alone. The empirical values are used in our computation of flat-fielding errors.

   
3.3 Mosaicing and masking the galaxy frames

Figure 2: Histogram of the number of objects in our R-band image detected by the SeXtractor program, as a function of the object's classification. The dividing line between a stellar and an extended detection is approximately 0.8; the VLT field surrounding ESO 342-G017 is clearly dominated by background galaxies.

A region of sky 2 $.\mkern-4mu^\prime$8$\times$2 $.\mkern-4mu^\prime$2 (R) and 2 $.\mkern-4mu^\prime$2$\times$2 $.\mkern-4mu^\prime$0 (V) around ESO 342-G017 was tiled with VLT test camera exposures and then combined into a final mosaic. Centroids of a number of stars and galaxies (usually 6 to 10) were measured in each individual image to compute their positional offsets within the mosaic. In order to remove cosmic ray events, images were divided into groups of four closely overlapping frames. Using the computed offsets, each group was combined into a temporary median-filtered image. Each input images was compared to its group median and all pixels deviating by more than 3.5$\sigma$ were replaced by the median value. Since cosmic ray events are often surrounded by lower brightness halos or tails, a second iteration was done at each position at which a cosmic ray was detected. In this second pass, a lower pixel correction criteria of 2.0$\sigma$ was applied.

The 14 (R-band) and 11 (V-band) frames with the best seeing were then combined, using integer pixel shifts, into R- and V-band mosaic frames. Given the small pixel size and large over-sampling, this did not limit the resolution of our resulting image. Since different regions of the mosaic are constructed from different numbers of images, it is necessary to renormalize. To do this an identical set of frames was created having the same sizes and offsets, but containing only the modal value of the source-free sky background. These were also combined into a mosaic and used to renormalize the R- and V-band mosaic frames. A subsection of the R-band image resulting from this procedure is shown in Fig. 1.

Figure 3: Final R-band (top) and V-band masked images of ESO 342-G017. Objects detected with SeXtractor in either band have been masked in both frames. Levels $-3.5\sigma _{\rm sky}$ to 10 $\sigma _{\rm sky}$ around the frame median are shown, where $\sigma _{\rm sky}$ is the background rms/pixel of the frame.

In order to be able detect faint light associated with ESO 342-G017 in our deep mosaic, foreground stars and background galaxies must be masked out. Since ESO 342-G017 was explicitly chosen for its paucity of foreground stars, most of the objects contaminating its background are galaxies (see Fig. 2), and simple profile fitting cannot be used to model and subtract contaminants.

Instead, we used the SeXtractor detection algorithm (Bertin & Arnouts 1996) to find sources not associated with ESO 342-G017. A source was defined to consist of at least five connected pixels at a level of 1.5$\sigma$ above the local background, which was computed over a $32\times32$ pixel mesh. The so-called OBJECTS output of SeXtractor, essentially a frame of all detected objects separated by null pixels, proved valuable in creating a mask for objects beyond the outermost contours of ESO 342-G017. The initial output masks still retained a faint halo of emission around brighter sources. For this reason, the masks were grown in size iteratively until a histogram of the unmasked background pixels no longer changed shape, indicating that the local background level had been reached.

A crucial step in the data reduction process is the determination of an accurate value for the background sky level. A large central section of both masked mosaics was extracted so that its area contained the largest possible number of overlapping individual images ($\ge$11 for the R-band and $\ge$8 for the V-band). In order to prevent any emission from ESO 342-G017 contributing to the sky signal, the galaxy was liberally masked out to 20 $.\!\!^{\prime\prime}$1 (10kpc) above and below the central plane of its disk, and along its major axis to the outermost edges of the images. The mask sizes of the brightest field stars were also liberally increased for this procedure.

   
3.4 Determination of sky level

Figure 4: Histogram of sky pixels from the completely masked R-band (left panel) and V-band (right panel). A Gaussian fit to the histograms ( ${\rm exp}(-(x-x_0)^2/2\sigma ^2)$ with x0(R)=16651.5 e-1pix-1, $\sigma (R)=120.2$ e-1pix-1 and x0(V)=2950.2 e-1pix-1, $\sigma (V)=39.7$ e-1pix-1) is shown as a dotted line.

Figure 5: The positions of the profile extractions shown on the mosaiced, masked, R-band image. The V-band image was extracted at the identical positions, but since it is smaller (see Fig. 3), the V profiles only reach number 52. The vertical profiles averaged together to create Figs. 7 and 8 are labelled at the top.

The distribution of sky values are shown in the histograms of Fig. 4, which were used to compute the true background value of the unmasked pixels in each image, and the associated error in its mean. These sky values are ${\cal S}_{R} = {\rm 16651.5 \pm 0.4~e^{-}~pix^{-1}}$ and ${\cal S}_{V} = {\rm 2950.2 \pm 0.2~e^{-}~pix^{-1}}$in the R and V bands, respectively. Using the calibration described in the next section, these values correspond to $m_{\rm sky}({R}) = 20.98$ mag/sqarcsec and $m_{\rm sky}(V) = 21.60$ mag/sqarcsec, with a systematic uncertainty dominated by calibration errors of $\sim$5%. The systematic deviation from Gaussian behaviour seen at extreme pixel values in Fig. 4 is slight and very much smaller, in its integrated effect on the average sky value, than the uncertainties $\delta {\cal S}$ based on Gaussian statistics reported above.

   
3.5 Calibration to standard system

Our photometric calibration was based on results supplied by the SV team together with the distribution of our data. A photometric solution was available only for the observations of ESO 342-G017 on 22 and 15 August, as these were the two photometric nights. Typically, four standard fields were observed several times during each of these nights, with an average of about 10 Landolt standard stars being used to compute the photometric solutions. The standards chosen spanned a significant range of colours in order to adequately measure the colour term.