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Flatfielding spectroscopic data is not a straightforward procedure and it is recommended that observers experiment to find the optimum method that suits their data best. It should be noted that the optimum method will depend strongly on the nature of the detector, particularly if the CCD is subject to fringing.
It is important to distinguish between the different methods by which the detector is illuminated. For direct images through a filter, each part of the detector is illuminated with the same (limited) range of wavelength, whereas in spectroscopic observations, a particular point on the detector is illuminated by essentially monochromatic radiation whose wavelength depends in a complicated way on the position of the slit and on the grism used.
The point of flatfielding is to remove sensitivity variations in the detector (and/or optics) but these variations are likely to be wavelength dependent. If the detector is a dye-coated CCD or is thinned, there is the additional possibility of fringing effects caused by interference within the thin layer of the dye or depletion region. If such patterning is present, it may also be dependent on the slit width since increasing broadening the slit will increase the range of wavelength seen by a given pixel which may wash out the fringes. For this reason, it is strongly recommended that you take both types of flatfield described below.
(a) Direct flatfields
This is the same procedure as used for normal imaging data. Direct images are taken though the desired filters of a uniform source of illumination from (i) a calibration system which carefully mimics the telescope optical system, (ii) blank fields at dawn or dusk, when the signal level in the sky dominates the contribution from point sources. Experience suggests that the last method is best. If fringing is present, this may not flatfield out because the range of wavelengths present in the flatfield exposure does not match the wavelengths seen in real on-sky exposures, which is usually dominated by a few discrete night-sky emission lines. A possible solution here is to construct a `true' sky flatfield by median filtering a stack of your on-target observations to remove discrete sources.
The images are processed to produce a flatfield by subtracting the bias level (using the bias strip or a separate bias exposure if it is believed that the bias frame has structure) and dividing through by the mean signal level in the exposure to provide a flatfield with mean signal level of unity.
(b) Dispersed flatfields
Here it is important to simulate the conditions under which the exposure to be flatfielded is taken as closely as possible. A flatfield should be taken for each mask/filter/grism combination with a continuum light source. Ideally this should provide high signal level at all wavelengths of interest but few light sources do this.
It is normal to use the Tungsten lamp (with appropriate neutral density) in the calibration lamp system. It would be a good idea to experiment with the different colour filters provided in the calibration system to try and equalize the illumination level at all wavelengths. Nevertheless, it may be necessary to take two exposures for each combination, one which avoids saturating the CCD anywhere and gives a high signal level at the peak of the illumination (in the red) and another which either overexposes the level where the signal level is highest so as to produce acceptable signal in the faint areas or one in which a filter is used to block regions of the spectrum where the signal is high - the broadband B filter is well suited for this. The resultant exposures may be combined in some suitable way for further processing.
Twilight sky can also be used to obtain flat-field frames. These have the advantage that the light path is identical to that of the actual observations. However, it may be difficult to obtain flat-fields for every mask because the sky rapidly changes in brightness during twilight. This means there are only short periods of time when it is possible to obtain useful twilight flatfields: just after sunset and just before sunrise. Also absorption bands in the atmospheric spectrum make the signal to noise in the flatfields highly dependent on wavelength. Therefore, even if twilight skys are taken, Tungsten flats are also worth obtaining since they will have a more uniform signal to noise.
It should be noted that because of flexure of the instrument during the course of a long exposure, dispersed flatfields should strictly be taken after every long exposure or at least once during the course of the sequence of exposures rather than before the start of observing when the telescope is usually at the zenith. Whether you choose to do this depends on how carefully you want to do the flatfielding.