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Figure 27 shows a bias- and dark-corrected sky-flat. There is a huge dynamic range between the well-exposed region of the chip (where the bright sky lines fall) and the red and blue ends. There is also a great deal of vertical structure caused by the non-uniform slit illumination. That vertical structure is what we are trying to measure with these frames. We need to process the sky-flats to extract information on the vertical structure without the detailed spectral information getting in the way. As discussed in Section 4.1.3, the full field of the detector is not exposed to the sky when using the spectrograph. This is what leads to the underexposed areas at the bottom and the top of the frame in Fig. 27. Inspection of Fig. 27 indicates that the "useful field of view" as reported in the SBIG manual is inaccurate. The actual useful field, as demonstrated by sky observations, is about 640 rows, beginning at row 21. Thus the frames discussed from here on have been cropped accordingly. Figure 28 shows the cropped version of the image presented in Fig. 27.
Once the sky-flats have been cropped, the next step is to combine the sequence to improve the overall signal-to-noise ratio. However, a given series of sky-flats have been obtained with very different exposure times, and very different mean signal levels. To demonstrate this, I find the highest exposure level on the chip, to measure the peak count-rate as a function of time relative to local sunset. This is plotted for the narrow and wide slits in Figure 29. To account for this, one must normalize the individual frames by their mean values. This results in a set of median-combined sky-flats, with average pixel values of 1. Figure 30 shows an example of such a combined flat. In order to extract only the large-scale variation due to the slit illumination, it is necessary to filter out all the large-scale structure. That is, we need to pass the image through a low-pass filter.
There is a specialized method for constructing such a low-pass filtered image for astronomical spectroscopy. It involves selecting bins of the image in the dispersion direction, and fitting a smooth function to the spatial variation in the data for each bin of pixels. The obvious tilt in the dispersion axis of our spectrograph, as well as the clear variation in illumination with wavelength argues that several such bins are needed for our spectrograph. I have experimented with various strategies, and concluded that the bins shown in Table 3 appear to work fairly well. The actual generation of the slit-illumination frame from the medianed sky-flat is done with the illumination task in IRAF. The task generates an image of the slit illumination by fitting functions across the slit at however many points are requested, and interpolating between the dispersion points. Figure 31 shows the slit-illumination frame generated from the sky-flat shown in Fig. 30, using the dispersion bins given in Table 3.
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