Solution To Geometric Distortions For A CCD Frame

It is crucial to solve accurately the geometric distortion (GD) of a field of viewfor high precision astrometry. In order to improve the measurement accuracy of longfocal length ground-based telescopes, a convenient approach is proposed in this paperusing the reference for the solution of equivalent to the Hubble Space Telescope(HST). This paper has studied the geometric distortion under different circumstances,with a hope that it can be applied to the measurement of the natural satellite, or othermoving objects.By reference to the method of solving GD for HST, we observe the same sky withsmall dithers, so that the same stars in different images can map at different CCD chippositions. Then we calculate the theoretical position based on the variousastronomical effects and the observed position for each star.The residuals of position (O-C)(Observed minus Computed) include three parts:measured error of the star, the distortion error of the point that the star falls in the chipand the catalog theoretical error. Since the catalog theoretical error can be thought asconstant within a certain amount of time, it will be cancelled by subtracting theresiduals of position from the same stars but imaged in other different areas of theCCD chips. Therefore, the remaining residuals of the star are almost the distortionerror and measured error. The measured errors can be compressed by averaging theremaining of a large number of stars that imaged in the same small area, and then theaverage residuals will be the indicative of the distortion error at that chip location.The proposed method is applied to two groups of observations which wereobtained at Kunming and Lijiang observational sites of Yunnan Observatory. It isshown that there exist obvious geometric distortions for both telescopes. Themaximum distortion of the field of view for the1m telescope is about0.8pixels(~160mas) and1.8pixels (~500mas) for the2.4m telescope. In addition, it was foundthat different filters are corresponding to different distributions, and the GD is quiteobvious even without filter for the1-m telescope. Further more, it is shown from ourdata analysis that the precision of stellar positions is significantly improved aftercorrecting the distortion.