The purpose of this paper is to investigate a large radio telescope support point number effect on its pointing accuracy and provide a useful guideline for the large radio telescope design engineer. In a large radio telescope system, the azimuth track is used to support the whole telescope structure and the mounting error as well as the telescope wheel-track contact in a long term can cause unevenness on the azimuth track, which can further deteriorate the telescope pointing accuracy. Even though various compensation methods have been proposed to compensate for this pointing error, it remains as one of the challenges for the telescope pointing error reduction. In this paper, a general telescope pointing error estimation formula has been proposed to investigate different telescope support-point number designs on its pointing accuracy. In this approach, the azimuth track unevenness has been modelled as the Fourier function using the least square method after the raw track profile has been measured. Next, the elevation position matrix, azimuth position matrix, and the azimuth profile matrix can be constructed for different telescope support point numbers, and the telescope pointing error can then be obtained based on the proposed general formula. The telescope pointing error root mean square (RMS) value is used to quantify the effect of the telescope support point number on the pointing accuracy. Two interesting results can be observed in the numerical example. The first one is that the telescope pointing error curves have different dominant peaks during one azimuth track rotation, which is corresponding to the support point number. Another interesting finding is that the RMS value experienced a complex trend with the support point number change, and they are not a simple monotonous increasing or decreasing relationship with the support number. All the results in this paper can provide a useful guideline for reducing the telescope pointing error in the initial design stage.

中文翻译：

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大型射电望远镜支撑点数对其指向精度影响的概念研究

本文的目的是研究大型射电望远镜的支持点数对其指向精度的影响，并为大型射电望远镜的设计工程师提供有用的指导。在大型射电望远镜系统中，方位角轨道用于支撑整个望远镜的结构，并且安装误差以及望远镜轮轨的长期接触会导致方位角轨道上的不均匀性，从而进一步恶化望远镜的指向性准确性。即使已经提出了各种补偿方法来补偿该指向误差，但它仍然是减少望远镜指向误差的挑战之一。本文提出了一种通用的望远镜指向误差估计公式，以研究不同的望远镜支持点数设计的指向精度。在这种方法中，在测量原始轨迹轮廓之后，已使用最小二乘法将方位轨迹不均匀性建模为傅立叶函数。接下来，可以针对不同的望远镜支撑点编号构造仰角位置矩阵，方位角位置矩阵和方位角轮廓矩阵，然后根据所提出的通用公式获得望远镜指向误差。望远镜指向误差的均方根（RMS）值用于量化望远镜支撑点编号对指向精度的影响。在数值示例中可以观察到两个有趣的结果。第一个是望远镜指向误差曲线在一个方位角轨道旋转期间具有不同的主峰，这对应于支撑点数。另一个有趣的发现是，RMS值随着支撑点数量的变化而经历了复杂的趋势，并且它们并不是与支撑点数量简单的单调递增或递减关系。本文中的所有结果都可为在初始设计阶段减少望远镜指向误差提供有用的指导。