上海天马望远镜光程差的计算方法研究∗

摘要

Based on the Shanghai Tian Ma Telescope (TM), an optical path difference calculation method of the shaped Cassegrain antenna is presented in the paper. Firstly, the mathematical model of the TM optics is established based on the antenna reciprocity theorem. Secondly, the TM sub-reflector and main reflector are fitted by the Non-Uniform Rational B-Splines (NURBS). Finally, the method of optical path difference calculation is implemented, and the expanding application of the Ruze optical path difference formulas in the TM is researched. The method can be used to calculate the optical path difference distributions across the aperture field of the TM due to misalignment like the axial and lateral displacements of the feed and sub-reflector, or the tilt of the sub-reflector. When the misalignment quantity is small, the expanding Ruze optical path difference formulas can be used to calculate the optical path difference quickly. The paper supports the real-time measurement and adjustment of the TM structure. The research has universality, and can provide reference for the optical path difference calculation of other radio telescopes with shaped surfaces.%基于上海天马望远镜(Shanghai Tian Ma Telescope,简称TM),提出一种赋形卡塞格伦天线光程差的计算方法。首先,基于天线互易定理,建立天马望远镜光路的数学模型；其次,采用非均匀有理B样条拟合天马望远镜的主面和副面；最终,实现光程差的计算方法,并对鲁兹光程差公式在天马望远镜上的扩展应用进行研究。采用此方法可计算馈源、副面的轴向偏移和横向偏移以及副面旋转等非准直情况下的光程差,同时在非准直量较小时,可采用扩展鲁兹光程差公式快速计算光程差。为天马望远镜结构的实时测量和调整提供支持,同时相关研究也具有通用性,可为其他具有赋形面型的射电望远镜光程差的计算提供参考。