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3. Methods of calibration

In traditional photographic astrometry, the scale and orientation of the plate are determined by measuring the positions of several reference stars whose Right Ascensions and Declinations are known accurately. The much smaller field of view of a CCD prevents this from being a viable method for calibrating such a device, and it is therefore necessary to turn to other techniques.

Several methods have been suggested by previous authors. Jones et al. (1989) used the wide double star 61 Cygni to provide a target of known position angle and separation. Colas & Arlot (1991) proposed the use of globular clusters such as M15 as rich fields of stars for which astrometric catalogues exist (for example, Le Campion et al. 1992). They also suggested the classical technique of star trails. We have experimented with all of these methods, and some of our findings are reported in Beurle et al. (1993).

We expected that globular clusters would provide the most reliable method of calibration. On fitting individual images of M15 and M92 to astrometric catalogues of these fields, we obtained root-mean-square residuals of tex2html_wrap_inline1149 from samples of 40-60 stars. However, the scale and orientation derived from the M15 images was not consistent with those from images of M92. This is in accord with the findings of Colas & Arlot (1991) who were also unable to obtain reliable calibration parameters from their reduction of images of M15. They suggested that the main cause of the discrepancy is probably the flexure of the telescope as it was moved from one target to another.

We are currently working on a simplified empirical model which assumes the flexure to be a function of the target's position (Jones 1996). We have not made use of calibration parameters from globular cluster images whilst preparing our observations for publication in this paper.

Colas & Arlot (1991) describe several reductions of their observations of the Martian satellites in which the scale and orientation of the CCD device during each night are determined by calculating the values which minimise the observed-minus-computed (O-C) residuals of the inter-satellite positions when compared to the theories of Chapront-Touzé (1989). We have reported the use of a similar technique when analysing our 1991 observations (Beurle et al. 1993). In that paper, we calculated a correction to the scale factor which would optimise the O-C residuals when compared to the orbital models of Harper & Taylor (1993, 1994).

During the 1990 campaign, no usable calibration images were obtained. Moreover, it is not clear whether images of 61 Cygni, M15 and M92 obtained in later campaigns will prove to be of any value in providing consistent scale and orientation parameters. Consequently, we have adopted the technique described by Colas and Arlot.

Table 2: b. Number of satellites per CCD frame

In our implementation of this method, we took approximate values of the scale of the CCD from images of 61 Cygni or one of the globular clusters. In all years, we assumed initially that one axis of the CCD was parallel to the direction to the true North celestial pole. We then employed an iterative least-squares process to determine small corrections to the scale and orientation which optimised the goodness of fit between the observed positions of the major satellites and the corresponding positions predicted using the orbital models of Harper & Taylor (1993, 1994). Six such sets of corrections were calculated: one for each main campaign, with separate sets for the observations made during the periods 26 July to 3 August and 15 to 17 August 1990. The CCD was dismounted from the telescope between 4 and 14 August.

The observations were processed as inter-satellite measurements because the globe of the planet is saturated in all of the CCD images and its centre cannot reliably be determined. Such inter-satellite measurements are affected by differential parallax, aberration and refraction. The first two effects are small, but differential refraction can introduce changes of up to one part in tex2html_wrap_inline1153 in relative positions when the satellites are observed at elevations of less than tex2html_wrap_inline1155 above the horizon; this is equivalent to tex2html_wrap_inline1157 in extreme cases. All three effects were incorporated into the positions derived from the orbital models, and these positions could therefore be compared directly to the raw observed positions.

Only observations of Tethys, Dione, Rhea and Titan were used in calibrating the CCD, as these satellites have the most reliable orbital theories.

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