As explained in the previous section on sky subtraction, flat field information is not required in staring mode when the correction for sky polarization need not be extremely accurate and an average instrumental gain correction suffices. In most applications this will be the case.
Flat-field information is needed in at least 2 applications. The most common is when one does not want to assume constant gain in correcting for sky polarization obtained from a different set of pixels than was used for the star. The other is in compressing a spectrum of finite width into a 1-dimensional array of numbers. The average gain of a row of pixels drops out in the course of polarimetric reduction, but if the star image did not expose exactly the same pixels in the 2 exposures for the 2 halfwave plate positions (e.g. no autoguiding), ``average'' does not refer to the same collection of pixels and one should refer the recorded intensities to one and the same standard pixel in both exposures. It is therefore advisable always to take flat fields, with the rotating halfwave plate in the beam.
Something to remember is not to change any sensitivity parameters of the system between programme exposure and calibration. This applies particularly to gratings, grating settings, and filters. The CCD frame contains a set of monochromatic images of the slit, for a range of wavelengths. Each monochromatic slit image in the CCD frame is a separate entity. Spectrophotometry tries to relate the intensities in separate slit images to each other, but spectro polarimetry does not bother; we are only determining the state of polarization at each wavelength separately (by a proper observing schedule including standard stars one could use the same frame for spectrophotometry, but that does not concern us here). So the term ``flat field'' in the present context relates only to the relative system gains along a monochromatic image of the strip of sky isolated by the slit. As long as the grating remains put, pixel is synonymous with wavelength. When the relation is disturbed by moving the grating, we must realise that we are aiming to calibrate the pixel system gain, for light of a certain wavelength; since ``system gain'' includes the spectrograph optics, it will not always be true to say that a pixel calibration at one wavelength will be correct for a neighbouring wavelength; likewise, as long as CCDs are not very nearly uniform, a calibration for a certain wavelength at one pixel location will not necessarily be correct for a neighbouring pixel at the same wavelength. For the best spectropolarimetry it is a must to flat-field (whether explicitly or implicitly) at precisely the same grating setting as for the programme exposure; if the proper flat field has not been obtained, it is probably best, for the foreseeable future, to use the data for corresponding pixels, even if the calibration is at a slightly different wavelength (just beware of Wood's anomalies, which could now show up as false polarization; see ING La Palma Technical Note no 76).
To obtain a genuinely unpolarized field, we employ the waveplates as depolarizers. Generally, only the halfwave is likely to be needed; it reverses any circular polarization that may be present, which will then be divided 50/50 by the calcite plate (as will unpolarized light). If you do wish to depolarize any circular polarization present, you could insert the quarterwave, behind the halfwave, rotating in the opposite direction at some other rate; focal-plane field is reduced in this case. Depolarization is only complete if the exposure contains an integral number of quarter-revolutions of the halfwave plate; it is safest to use exposure times long enough for any non-integral part of a revolution not to cause an unacceptable error: if flat-field source polarization = x %, desired error level y %, rotation rate z Hz, exposure time t seconds, then
If one is only interested in flat-fielding the pixels one is using in programme observations, one uses the same Dekker. However, one could employ one of the comb-type Dekkers and flat-field a larger part of the CCD in one exposure; one just has to make sure that the comb Dekker includes the pixels of the Dekker one is interested in.
We have found that a convenient way to get a well-exposed flat-field frame quickly is to use blue sky when the Sun has an altitude of between 10 and 30 degrees. Experiment with slit width and ND filters to obtain a satisfactory signal level (close to CCD saturation). Since the rotating halfwave plate is a linear depolarizer, pre-slit filters are permitted even if they modify the polarization. We used exposures of 30 seconds or more, according to the formula above, the halfwave rotating at 1 Hz.
A completely different alternative would be to expose the entire CCD without any Dekker and with the halfwave out of the beam, but first through one of the A&G polaroid calibrators oriented to provide exactly the polarization of one of the 2 beams from the calcite plate, then through the other. Given a truly flat field of unpolarized illumination, this would yield 2 maps of the system gain, each for one polarization, both on the same scale. In practice one could probably obtain a truly flat field (see discussion above), but the light will be polarized to some extent (minor if one uses sky close to the Moon) and the scale for the 2 maps will not be the same. At any one wavelength, the relative intensities in each frame map the relative gains correctly; what is lacking is the relation between the 2 frames. This relation one may obtain by an exposure of the same field through the rotating halfwave plate, without the calibration polarizer, and with a comb-type Dekker; such an exposure yields relative system gains in 2 polarizations for the apertures in the comb Dekker. These data can be used to bring the 2 earlier single-polarization maps on to a common scale.
We stress that these procedures have not yet been tried extensively. Since much of what will be done with ISIS will not need explicit flat-fielding, such tests are not urgent. From the discussion it should be clear in which direction to experiment.