Flat-fielding is worthy of some extra discussion, since it can be complicated by the presence of the polarimeter in the light path. The purpose of flat-fielding is to ensure that there are no spatial variations in the sensitivity of the detector. This is normally achieved by taking images of a photometrically flat surface such as the inside of the observatory dome, or the twilight sky3. Since the brightness of this surface is constant, any variations in the recorded image (the ``flat-field'' image) must be due to variations in the sensitivity of the detector. These variations can then be removed from the target observation by dividing every pixel value in the target image by the corresponding pixel value in the flat-field image.
Introducing a polarimeter into the light path can complicate this if the flat-field is taken in polarized light (such as is produced by reflective surfaces in the dome, or by light scattering in the atmosphere). In this case the intensity of the light reaching the detector will not be constant across the field, but will depend on the polarization.
If the polarization of the flat-field is non-zero and spatially constant, then the and ray flat-field images will have different mean values (visible as sharply defined dark and light areas in the flat field). If such a flat-field is used to correct the target exposures, then the different mean values in the flat-field will result in an apparent difference in sensitivity between the two channels of the polarimeter (known as the ``F-factor''). Such a difference in sensitivity can be corrected for when calculating the polarization if the additional target exposures and are available.
Note, the same flat-field should be used to flat-field all target exposures, irrespective of half-wave plate position.
A mathematical description of the flat-fielding and F-factor corrections is given here.