3. Data reduction
3.1. Image processing
Because of the very faint limiting magnitudes we want to reach for our distant comet observing programs, special care was taken to obtain very high quality ancillary calibration frames; the image processing techniques have also been carefully optimized for the minimization of the noise. All the image processing was performed using MIDAS ("Munich Image and Data Analysis System," an interactive package developped and maintained by ESO, which allows the user to write procedure in a special language, possibly calling some FORTRAN or C programs). A template bias frame was created by taking the 2-dimensional median of a collection of many zero second exposures obtained at the beginning and end of each night. This composite bias was subtracted frame by frame from all the raw data. Additional variations of the global bias level were corrected by using the mean of the overscan region of each frame. The dark current was estimated using long, dark exposures; in all cases, it was found small enough to be neglected. Special care was taken to generate excellent detector sensitivity maps, or flat-fields, that correct all the sensitivity variations without introducing any significant amount of noise. Ideally, for each night, a series of dome flat-fields and sky twilight flat-fields were obtained. They were bias subtracted, then normalized to a mean level of 1, and median averaged to form a template dome flat-field and a template twilight flat-field. The long scientific exposures are themselves very valuable as flat-fields, as the sky color and detector illumination are exactly those prevailing during the observations, while the twilight and especially the dome flats are obtained with a different color of light and type of illumination. In order to use the science images as flat-fields, it is important to dither the telescope between each of the exposures, so that a given object always falls on a different part of the detector. Tables of random offsets are generated in advance for that purpose. The scientific images are normalized so that their mean sky level is equal to 1, the brightest stars and objects of each frames are marked, and all the frames are median averaged (rejecting the marked regions, if necessary), forming a template science flat-field.
Each of the three template flat-fields has its advantages and problems: the dome flat has an excellent signal-to-noise ratio, but very poorly represents the large scale variations of sensitivity; the twilight flat has also a good signal-to-noise ratio, and better represents the large scale variations of the flat-field. These variations are perfectly measured by the science frame flat, but this flat has a very poor signal-to-noise ratio (being the average of only a few frames, each one having only a few hundred to thousand counts), and is therefore useless for small scale sensitivity variations. If only one of the three templates can be used, the twilight flat is a very good compromise. When possible, however, full advantage of each of the templates can be utilized (Hainaut et al., 1994). To do this, we separated each of template flats into a series of frames, each containing the information from the sensitivity map for a range of spatial frequencies (pixel-to-pixel variations, small scale variations, small scale gradients to finally large scale gradients). This separation is performed using a wavelet decomposition package implemented in MIDAS. The final flat-field template is obtained by combining the frames corresponding to the frequencies that each of the templates sample the best. While the actual combination varies from situation to situation, a typical example would be
where is the final flat field, D is the dome flat, T is the twilight flat, and S is the science flat.
3.2. Photometric calibration
The images presented in this paper were obtained over a long time period, using different detectors and telescopes; moreover, some of the observing runs were not photometric. Therefore, we preferred to re-calibrate all the data in order to achieve a better uniformity. During the June 1997 run, all the fields were re-imaged using the UH2.2m telescope, through the Kron-Cousins R and I filters (R: Å, = 1245Å; I: Å, = 1888Å). During this run, we also obtained images of a large number of photometric standard fields (Landolt, 1992) at a wide range of airmasses, ensuring a complete calibration of the system used, including the atmospheric extinction and the color terms of the photometric transformation. The magnitude of the comet (or the limiting magnitudes) during the other runs was determined from relative photometry using all the stars visible in the original and June 1997 images. The magnitude of the comet was obtained using a color R-I = 0.35 for the color transformation; this color was selected as the mean of a well measured sample of cometary nuclei (Meech, 1998). Note that the change introduced by the use of another value would be much smaller than the other errors.
3.3. Astrometric calibration
The position of the comet was calibrated using the position of field stars as measured on the Digital Sky Survey. At least 5 or 6 stars were used in the transformations; the RMS residuals of the transformation are 0.1- depending on several factors, including the number and brightness of the stars, and their trailing in the original images. All the frames were registered with respect to each other using several stars visible in each image. The registered frames were then calibrated astrometrically, and the expected position of the comet was obtained using its equatorial position computed for the epoch of the mid-exposure and the astrometric transformation. The frames were also co-added after registration on the expected position of the comet. The resulting composites show the stars as long trails, and the comet (whenever visible) as a point source. It should be noted that the trails are not necessarily straight lines, since the ephemerides used for the dithering took into account the variations of the comet's proper motion caused by the earth's rotation (daily parallax). The astrometry for 55P/Tempel-Tuttle is shown in Table 2, with the observatory code indicated (568=Mauna Kea; 809=La Silla).
© European Southern Observatory (ESO) 1998
Online publication: April 20, 1998