Geometric Calibration for a Small CCD Field of View

Natural satellites in our solar system are often observed for their positional measurements with a long focal length telescope. The advantages of using a long focal length telescope are obvious. For example, it can well expand some satellites in a CCD image near their primary planet because of its small scale factor. Besides, only a simple model is needed to reduce the observations since its perfect quality in both optics and astronomy. Many observations have shown that the posit ional accuracy of a natural satellite obtained with a long focal length telescope is usually better than that with a meridian circle. For instance, for some bright Saturnian satellites (S3~S6) an accuracy about ±0.08 ^1,3,5 could be reached, a better accuracy in the range of ±0.04~0.06 ^2,9 could be reached. But the best accuracy is only ±0.10 with a CCD meridian instrument ^4,6~8. However, we should pay attention to its geometric calibrat ion when a long focal length telescope is used to observe a natural satellite because we usually have no good position reference stars. Nowadays, a widely used calibration method is the/Bright Satellite Method0, i. e. the theoretical positions of some bright satellites, which usually have better theories than those for faint satellites, are used to determine the scale factor and orientation. Their research works of Harper et al.¹ and Shen et al.⁵ show that modern theories for Saturnian satellites can assure the utility and rationality of this/Bright Satellite Method0. In this paper, we give the formulae of solving the parameters of geometrical calibration for a small CCD field of view, and derive the formulae of their errors. Moreover, when more than two reference stars or satellites are available, these formulae show us how to design precisely an integrated reduction scheme. The scheme will be useful for the astrometric observation of some natural satellites and also for that of their optical counterparts of some extragalact ic radio sources when a small CCD field of view is used.