Precision CCD photometry over large fields-of-view and detection of faint and diffuse objects demand great care in the acquisition of flat-field frames. Variations in the illuminated field will introduce spatial variability in the flat field. Small angular displacements of the CCD, telescope, and instrument, with respect to the external light source yields a corresponding linear translation of the image on the CCD with respect to the true flat-field function, so that a functional equation relates the flat field to these shifted data sets. In two-dimensions an elliptic partial differential equation relating the offset CCD measurements to the flat- field function can be derived enabling relaxation solution techniques to be used. A simulation is presented and discussed.
Walter J. Wild,
"Reconstructing CCD flat fields using nonuniform background-illumination sources", Proc. SPIE 3355, Optical Astronomical Instrumentation, (9 July 1998); doi: 10.1117/12.316834; https://doi.org/10.1117/12.316834