  ESO's two FOcal Reducer and low dispersion Spectrographs (FORS) are the
primary optical imaging instruments for the VLT. They are not direct-imaging
instruments, as there are several optical elements in the light path. In
particular, both instruments are attached to a field rotator. Obtaining truly
photometric data with such instruments present a significant challenge. In this
paper, we investigate in detail twilight flats taken with the FORS instruments.
We find that a large fraction of the structure seen in these flatfields rotates
with the field rotator.
  We discuss in detail the methods we use to determine the cause of this
effect. The effect was tracked down to be caused by the Linear Atmospheric
Dispersion Corrector (LADC). The results are thus of special interest for
designers of instruments with LADCs and developers of calibration plans and
pipelines for such instruments. The methods described here to find and correct
it, however, are of interest also for other instruments using a field rotator.
  If not properly corrected, this structure in the flatfield may degrade the
photometric accuracy of imaging observations taken with the FORS instruments by
adding a systematic error of up to 4% for broad band filters. We discuss
several strategies to obtain photometric images in the presence of rotating
flatfield pattern.
