中文摘要：

摘要精确求解望远镜几何扭曲效应，有利于提高望远镜的天体测量定位精度，这对天文学的诸多学科具有十分重要的意义．为此，前人发展了一种针对密集星场抖动观测并针对观测底片迭代求解几何扭曲的自校准方法，取得了较好的效果．但是，先前的工作并未对星场的密集程度或抖动方式做进一步要求，而是经验地选择较为密集的星场和较多的抖动次数进行观测．这些经验的观测方式固然能够较好地给出几何扭曲，但有时会占用较多的望远镜观测时间导致效率较低．首先介绍了上述求解望远镜几何扭曲的一般方法；通过仿真模拟，对上述方法的有效性做评估，同时对该方法要求的星场密度和抖动次数等条件做进一步优化；最后，针对实际应用中几何扭曲改正后的定位精度与视场参考星数量的关系也做了进一步的仿真和分析．

英文摘要：

Measuring the geometric distortion is conducive to improve the astrometric accuracy of telescopes, which is meaningful for many disciplines of astronomy, such as stellar clusters, natural satellites, asteroids, comets, and the other celestial bodies in the solar system. For this reason, researchers have developed an iterative self-calibration method to measure the geometric distortion of telescopes by observing a dense star field in the dithering mode, and have achieved many good results. However, the pre- vious work did not constrain the density of star field or the dithering number in the observing mode, but chose relative good conditions to observe, which took up much observing time. In order to explore the validity of self-calibration method, and opti- mize its observing conditions, it is necessary to carry out the corresponding simulation. Firstly, we introduce the self-calibration method in detail in the present work. By the simulation method, the effectiveness of self-calibration method to give the geometric distortion is proved, and the observing conditions, such as the density of star field and dithering number, are optimized to give the geometric distortion with a high accuracy. Considering the practical application for correcting the geometric distortion, we also analyze the relation between the number of reference stars in the field of view and the astrometric accuracy by virtue of the simulation method.