奇台射电望远镜（QTT）的口径为110 m，计划成为世界上最大的全可动望远镜。理想情况下，望远镜的重复指向精度误差应小于2.5 角秒（arcsec）；因此，望远镜的结构必须满足超高精度的要求。为此，本文提出了一种轮轨表面的逆向设计方法，用以降低望远镜整体设计与制造的难度。首先，本文使用偏度系数和峰度系数方法验证了轮轨误差测试数据的分布特征。根据这些分布特征，采用了双尺度模型仿真分析了方位轮轨误差。在本文的实验中，长周期、小幅度的误差以大尺度为特征，采用三角函数描述，短周期、大幅度的误差以小尺度为特征，利用分形函数来模拟。本文首先基于双尺度模型，推导了误差对指向精度的影响机理；其次，推导了轮轨误差的均方根（RMS）与望远镜指向精度误差均方根之间的关系；最后，从容许的指向精度误差来推导出轮轨误差容许的RMS值。为了验证所提新方法的有效性，选择了两种典型的射电天文望远镜[绿岸望远镜（GBT）和大型毫米波望远镜（LMT）]作为实验实例。通过对比发现，望远镜指向精度的理论计算值与实测值基本一致，最大误差小于10%。

The Qi Tai Telescope (QTT), which has a 110 m aperture, is planned to be the largest scale steerable telescope in the world. Ideally, the telescope's repeated pointing accuracy error should be less than 2.5 arc seconds (arcsec); thus, the telescope structure must satisfy ultra-high precision requirements. In this pursuit, the present research envisages a reverse-design method for the track surface to reduce the difficulty of the telescope's design and manufacture. First, the distribution characteristics of the test data for the track error were verified using the skewness coefficient and kurtosis coefficient methods. According to the distribution characteristics, the azimuth track error was simulated by a two-scale model. The error of the long period and short amplitude was characterized as large-scale and described by a trigonometric function, while the short period and high amplitude error was characterized as small-scale and simulated by a fractal function. Based on the two-scale model, effect of the error on the pointing accuracy was deduced. Subsequently, the relationship between the root mean square (RMS) of the track error and the RMS of the pointing accuracy error of the telescope was deduced. Finally, the allowable RMS value of the track error was derived from the allowable pointing accuracy errors. To validate the effectiveness of the new design method, two typical radio telescopes (the Green Bank Telescope (GBT) and the Large Millimeter Telescope (LMT)) were selected as experimental examples. Through comparison, the theoretical calculated values of the pointing accuracy of the telescope were consistent with the measured values, with a maximum error of less than 10%.Graphical abstractQi Tai Telescope (QTT) with a 110 m caliber, it will become the largest scale steerable telescope in the world. Its repeated pointing accuracy error should be less than 2.5 arc seconds and the telescope structure must satisfy an ultra-high precision requirements. To reduce the difficulty of telescope's design and manufacture, a reverse design method of the track surface was proposed. Firstly, the distribution characteristics of the test data of track error were verified using the skewness coefficient and kurtosis coefficient methods. According to the distribution characteristics, the azimuth track error was simulated by a two scales model. The error of long-period-short-amplitude was defined as the large scale, which was described by the trigonometric function. The short-period-high-amplitude error was recognized as the small scale, and simulated by the fractal function. Based on the two scales model, effect of it on the pointing accuracy was deduced. And then the relationship between the RMS (Root Mean Square) of track error and the RMS value of the telescope's pointing accuracy errors was deduced. Finally, the allowable RMS value of track error was derived from the allowable pointing accuracy errors. To validate the effectiveness of the new design method, two typical radio telescopes (the Green Bank Telescope and the Large Millimeter Telescope) were selected as experimental examples. Through comparison, the theoretical calculated values of the telescope's pointing accuracy are in good agreement with the measured values, with a maximum error less than 10%.