Fringing
If you don't have a back-illuminated CCD and take images in red or very red filters, then you do not need to worry about fringing. I mention it here since it completes the picture of data reduction. Fringing is an interference effect of red/infrared light in the thinned substrate of back-illuminated CCDs, which become transparent to these wavelengths. In general, it looks like the wavy pattern in Fig. 9 below. You need a good SUPERFLAT to remove it. If you don't have any, then forget about it.
Fig. 4: Fringing in I-band with a back-illuminated CCD. The image was taken in a photometric
night, thus the fringing could easily be corrected (right). See text for details.
Image: WFI@2.2m MPG/ESO telescope, La Silla, Chile
The first step is to extract the fringing from the SUPERFLAT. This happens by smoothing the superflat with a large kernel (200-300 pixel width), and by subtracting the smoothed image from the unsmoothed SUPERFLAT. What remains is the fringing pattern and some pixel-to-pixel variations. In a photometric night (photometric means very clear and stable), the amplitude of the fringing pattern scales directly with the sky background in the individual images. One can then create an individual fringe correction image in the following way:
individual fringe correction = fringe model * <individual sky background> / <smoothed superflat>
Here the < > brackets denote the mean (or the mode or median, if you like).
In non-photometric or instable nights the assumption that the fringing amplitude scales with the sky background does not hold any more. The primary cause of the light causing fringing is OH recombination emission in the upper atmosphere, and the line ratios can change within a few minutes in time, and a few arcminutes on the sky. Therefore, the fringe scaling factor varies in a difficult manner across the CCD, which can make fringing uncorrectable.
When correcting for fringing one removes a systematic effect, but again the pixel-to-pixel noise in the fringing model is introduced into the image. If the fringing is very strong (for example 10% - 30% of the sky background in an I-band filter), then 5 images for the SUPERFLAT may be enough, since fringing clearly dominates the pixel-to-pixel variations. If it is on the few percent level (say in a wide R-band filter), then at least 20-30 images should be used.