Block Adjustment Of Overlapping CCD Frames

Because of the high quantum efficiency, high linear responsibility, and great convenience in real-time data processing of CCD, it has been applied extensively in astrometry since 1980s and gradually replaced photographic plate. But the size of CCD is usually 2~5cm and the field of view (FOV) is not larger than a few one-hundredth of a square degree in the case of long focal length telescope, and so within the FOV of CCD the number of reference stars is very limited with unevenly distribution. Because of the uncertainties of catalogue and measured coordinates of reference stars, the local reference frame (LRF) represented by these stars with limited number and sky coverage would be biased from the global reference frame (GRF) of the catalog in the form of translation, rotation and distortion, and which would result in undesirable effects on the precision and systematic consistency of the object positioning. The application of CCD with small FOV to the astrometric researches is accordingly restricted. In order to overcome this restriction, the block adjustment (BA) of overlapping CCD frames is proposed. In this method, the relation of model parameters of overlapping CCD frames is established by using common stars and then these overlapping CCDs will be processed in a combination way. The BA method is equivalent to the enlargement in FOV and so to increase the number of reference stars, which results in the improvement in the precision of LRF. Theoretical analysis shows that BA effectively combines the long focal length (small plate scale and high resolving power) with the large FOV (large number of reference stars), and so it is promising in principle in the improvement of precision of CCD astrometry. In this thesis the BA method is systematically analyzed and which is summarized as follows. (1) The history and application of BA in the reduction of overlapping photographic plates are reviewed. The reasons that the anticipated results have not been obtained by this method are analyzed. The theoretical advantage of BA of overlapping photographic plates was acknowledged even since the very beginning of the 20th century. However, because of the deficiency of photographic plates, it is difficult to guarantee the correction of plate models and the precision of estimated parameter. While the precision of BA depends on the completeness of the models of all photographic plates, and imperfect models would bring systematic influence into the reduction results. Therefore, though BA of overlapping photographic plates is of theoretical advantage, it does not bring out the anticipated results in practice. (2) The expression of the estimation of positioning precision in CCD astrometry is deduced. It is pointed out that for a given CCD, reference catalog and observation site, if the influence of abnormal atmosphere is neglected, then the approach of improving the precision of positioning in CCD astrometry is to extend the focal length (small plate scale and high resolving power) and to enlarge FOV (large number of reference stars). However, long focal length and large FOV compose a pair of inherent contradiction, and they cannot be satisfied simultaneously by the contemporary technology, which limits the positioning precision of CCD astrometry. Telescopes with long focal length and equipped with CCD are characterized by small plate scale. By taking overlapping CCD observations, establishing the relations between CCD frames, and performing BA, the result is equivalent to enlarge the FOV. Therefore, BA can effectively combine the long focal length and the large FOV and so is promising to improve the precision of CCD astrometry. (3) Based on the truth that there is only one mean position for a common star at the reference epoch, and in order to develop the computer program conveniently, we deduced the observation equations of BA in vectorial expression. With the constraints of common stars, all the overlapping CCD frames constitute a large CCD image, then the orientation of this image is determined by all the reference stars within the observed region, and finally the positions of objects are calculated based on the model parameters and the measured coordinates. Differing from other researchers'schemes, the unknowns in our BA are only the model parameters of CCD frames, but not including position parameters of a large number of field stars. Our scheme reduces the demand of computer resources and so benefits to the increasing in the reduction efficiency. (4) The characteristics of BA method are discussed and the measures to some key issues in the realization of BA are recommended as the following. (a) Our analysis shows that the BA reduction can be directly applied to process CCD frames with linear model, while for nonlinear model the nonlinear terms should be corrected before BA reduction in order to achieve high precision. (b) In the case of long focal length and small size of CCD, the plate model can be determined by the observations of astrometric standard regions and canbe applied to the BA reduction of overlapping CCD observations of objects. (c) In order to guarantee a simple and stable relationship between the standard and measured coordinates, the correction of atmosphere refraction and light aberration should be considered. Analysis and estimation show that though the coefficients of theoretical formula contain errors, their differential correction within a small FOV of CCD could be negligible. (d) When the observations are taken with relatively large epoch gaps the differential proper motions of common stars should be considered. If the high precision proper motions are unavailable, our recommendation is to use the proper motion information from some secondary catalogs. In this case, though the proper motions are not very precise, their uncertainties are usually one-order smaller in magnitude than the proper motions. It is advisable to use these data rather than neglect the proper motion. (e) The sparse characteristics of the coefficient matrix of normal equation of BA are analyzed. It is proposed that when large number observations are reduced with BA, the technology of sparse matrix should be referred in order to improve the reduction efficiency. (f) It is shown theoretically that because of the increase of the observation equations of common stars, the precision of estimated model parameters from BA is better compared with single CCD adjustment, and which benefits to the improvement of positioning precision of objects. (5) A FORTRAN version implementation of BA is developed. It includes three steps: (a) data preparation, (b) preprocessing and (c) BA reduction. Analysis of simulated data and CCD observations shows that the application of BA is equivalent to enlarge FOV and refer to all the reference stars in a combination way, and so the local reference frame can be effectively improved in the cases of sparse reference stars, non-uniformly distributed reference stars, some of the reference stars with significant position bias, and regional reference stars with some systematic position bias and so on. (6) BA is applied to the determination of optical positions of extragalactic radio sources. Two groups of observations from the 2.16m telescope in Xinglong Station of National Astronomical Observatories of China are reduced. The results show that the precision of optical positions from BA is improved compared with single CCD adjustment, and it is indicated that there is a possible regional systematic bias in the right ascension of some faint stars (Mag>16m) of UCAC2 nearby equator.