A geometric distortion solution specifically for historical observations and its implementation

Abstract: Geometric distortion (GD) critically constrains the precision of astrometry. Using well-established methods to correct GD requires calibration observations, which can only be obtained using a special dithering strategy during the observation period. Unfortunately, this special observation mode is not often used, especially for the historical observations before those GD correction methods presented. As a result, some telescopes have no GD calibration observations for a long period, making it impossible to accurately determine the GD effect. This limits the value of the telescope observations in certain astrometric scenarios, such as using historical observations of moving targets in the solar system to improve their orbits. We investigated a method for handling GD that does not rely on the calibration observations. With this advantage, it can be used to solve the GD models of telescopes which were intractable in the past. The method was implemented in Python and released on GitHub. It was then applied to solve GD in the observations taken with the 1-m and 2.4-m telescopes at Yunnan Observatory. The resulting GD models were compared with those obtained using well-established methods to demonstrate the accuracy. Furthermore, the method was applied in the reduction of observations for two targets, the moon of Jupiter (Himalia) and the binary GSC2038-0293, to show its effectiveness. After GD correction, the astrometric results for both targets show improvements. Notably, the mean residual between observed and computed position (O-C) for the binary GSC2038-0293 decreased from 36 mas to 5 mas.