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Next: Appendix B: limiting magnitudes Up: The Capodimonte Deep Field Previous: Conclusions

Appendix A: superflat and fringing correction

Several twilight sky exposures were used to create a mean nightly twilight-flat twiFlat; also, a nightly super-flat supFlat was created as the result of the median of all the science frames taken in the same filter. The nightly master-flat in each filter was created using as much information as possible from the twilight-flats and the super-flats: the supFlat / twiFlat ratio gives the information on the difference between the twilight-flats and the average science frame and hence, it provides the pattern due to large-scale non-uniform illumination which should be applied to flatten the science frames. However, this ratio is a low S/N image and must be smoothed in order to avoid the introduction of noise in the science frames. The master-flat, Flat, is then obtained by combining the mean twilight-flat with the super-flat as follows:

\begin{displaymath}
Flat = smooth \Big( \frac{supFlat}{twiFlat} \Big) \cdot twiFlat
\end{displaymath}

The dome-flats were not used for flat-fielding because, in the case of the ESO-WFI, they are not reproduceable and the corrections of the large-scale variation due to non-uniform illumination are worse than 5%.
For the fringing correction, a nightly fringing pattern frP was determined for each filter, first by flat-fielding the nightly fringed super-flat with the corresponding twilight-flat, and then by a subtraction of the background of the resulting flat-fielded super-flat, as follows:

\begin{displaymath}
frP = \frac {supFlat}{twiFlat} - backgr\_fit \Big(\frac {supFlat}{twiFlat} \Big)
\end{displaymath}

The background fit in the above expression gives us both the fringing pattern and the information for the non-uniform illumination correction from the fit itself[*]. In this case, the master-flat is determined using such fit instead of the smoothed ratio (see equation for Flat above). Once the raw images are de-biased, the flat-field and fringing correction are applied as follows:

\begin{displaymath}
PrI = \frac{Im}{Flat} - \eta \cdot frP
\end{displaymath}

where Im and PrI are the de-biased and reduced image respectively. The factor $\eta$ is a function of the sky background and the air-mass and varies from one scientific image to the other. It has been found that adopting $\eta_n$ = bckn / <bck>, where bckn is the mean background of the nth image and <bck> is the mean background of the supFlat, gives good results. Typical values of $\eta$ run from 0.8 to 1.2.


next up previous
Next: Appendix B: limiting magnitudes Up: The Capodimonte Deep Field Previous: Conclusions
Juan Alcala
2002-02-05