A new calibration model for pointing a radio telescope that considers nonlinear errors in the azimuth axis

A new calibration model of a radio telescope that includes pointing error is presented, which considers nonlinear errors in the azimuth axis. For a large radio telescope, in particular for a telescope with a turntable, it is difficult to correct pointing errors using a traditional linear calibration model, because errors produced by the wheel-on-rail or center bearing structures are generally nonlinear. Fourier expansion is made for the oblique error and parameters describing the inclination direction along the azimuth axis based on the linear calibration model, and a new calibration model for pointing is derived. The new pointing model is applied to the 40 m radio telescope administered by Yunnan Observatories, which is a telescope that uses a turntable. The results show that this model can significantly reduce the residual systematic errors due to nonlinearity in the azimuth axis compared with the linear model.     

采用光学指向系统建立天马13m望远镜指向模型

描述了采用光学望远镜辅助天马13m射电望远镜进行指向测量以及建立指向误差修正模型的方法. 对于小口径望远镜, 指向校准目标源比较少, 用射电法建立指向模型难以覆盖全天区. 利用上海天文台天马13m射 电望远镜进行光学望远镜辅助射电望远镜指向测量研究, 在13m天线背架上安装一套光学指向系统, 获得了优 于3''的重复测量误差. 此外, 通过对影响天线指向因素的分析, 建立了包含8个误差项的指向误差修正模型以及 光轴和电轴偏差模型. 将指向模型代入天线伺服控制系统, 对校准目标射电源进行十字扫描, 得到指向样本残差约 为5''. 该研究可以为实现高精度指向建模提供一种参考方法.     

Correction Method of Antenna Pointing Error Caused by the Main Reflector Deformation

The pointing accuracy of a radio telescope is usually less than one-tenth of its antenna beam width. For large-aperture antennas at the short-centimeter band or millimeter-wave band, the pointing accuracy must be as high as several arc seconds. Therefore, for large-diameter and high-frequency reflector antennas, the pointing problem has become an important focal point to realize the antenna performance. Among many structural subsystem factors that affect the antenna pointing accuracy, there has been only less study on the factor of main reflector deformation. Based on the structural characteristics of the antenna, a reflector space coordinate system is established in this paper. And based on the space coordinates of the main reflector surface points after deformation, a non-linear least squares fitting method with 3 degrees of freedom is proposed to accurately predict the antenna pointing. Finally, the space geometric relationship is used to strictly derive the precise adjustments on the elevation and azimuth in order for correcting the antenna pointing error, and the indirect relationship between the main reflector deformation and the pointing error is constructed. This has certain guiding significance for improving the pointing accuracy of large radio antennas.     

低纬子午环的仪器误差

对低纬子午环的仪器误差作了分类，包括制造误差、安装误差、仪器重力变形和热变形的影响，还分别列出了各种误差测量设备的制造误差、安装误差、读数零点偏差及其漂移的影响。文中强调了在该仪器误差修正中，不建立和使用任何误差模型，而是采用实时测定值，并且特别注意消除系统误差的影响，在这基础上，才能通过重复采数来压缩随机误差的影响。     

Modeling and calibration of pointing errors with alt-az telescope

This paper presents a new model for improving the pointing accuracy of a telescope. The Denavit–Hartenberg (D–H) convention was used to perform an error analysis of the telescope's kinematics. A kinematic model was used to relate pointing errors to mechanical errors and the parameters of the kinematic model were estimated with a statistical model fit using data from two large astronomical telescopes. The model illustrates the geometric errors caused by imprecision in manufacturing and assembly processes and their effects on the pointing accuracy of the telescope. A kinematic model relates pointing error to axis position when certain geometric errors are assumed to be present in a telescope. In the parameter estimation portion, the semi-parametric regression model was introduced to compensate for remaining nonlinear errors. The experimental results indicate that the proposed semi-parametric regression model eliminates both geometric and nonlinear errors, and that the telescope's pointing accuracy significantly improves after this calibration.     

基于光学辅助指向测量的太赫兹望远镜指向误差模型研究

针对太赫兹波段天文点源目标较少, 指向测量相对困难的特点, 研究了利用与太赫兹天线共轴的小型光学望远镜来辅助太赫兹望远镜指向测量以及建立指向误差修正模型的方法. 依托紫金山天文台1.2 m斜轴式太赫兹天线开展了光学辅助指向测量的实验研究, 利用一台安装在天线背架上的100mm口径折射式光学望远镜获得了优于2$''$的指向测量精度. 此外, 通过对斜轴天线的结构分析以及大气折射和本地恒星时(Local Sidereal Time, LST)偏差等误差来源的分析, 建立了包含23个误差项的斜轴式光学指向修正模型, 实现了约3$''$的拟合精度. 最后, 借助高精度数字摄影测量对光电轴一致性进行了标定, 并针对其对指向模型精度的影响进行了讨论. 研究成果将为南极5 m太赫兹望远镜(The 5m Dome A Terahertz Explorer, DATE5)及其他太赫兹望远镜提供指向测量和指向修正模型方面的技术参考.     

Study on the pointing model of a slant-axis terahertz antenna

This paper describes the establishment and verification of an accurate pointing model for a1.2 m aperture slant-axis terahertz antenna. A new analytical pointing model for the slant-axis antenna is presented based on an analogy to that of the alt-azimuth antennas. Furthermore, extra error terms are added to the pointing model based on the structure and mechanical analysis of the slant-axis antenna. To verify the pointing model experimentally, a pointing error measurement method based on photogrammetric techniques is proposed. Using this method, pointing behaviors of the antenna are accurately measured without the aid of astronomical observations, and major sources of the pointing errors are measured individually by photogrammetry and their respective coefficients are compared with those in the analytical pointing model.The results show that an extended pointing model consisting 21 error terms can significantly reduce the residual systematic errors compared with the traditional model, more details are given in the following sections.     

PSD法测量大型射电望远镜副面位姿

指向精度是大型射电望远镜天线具有挑战性的关键技术指标.在望远镜运行中,方位俯仰角的变化、重力以及日照等对副面撑杆的综合影响会引起望远镜的副面位姿改变从而引起指向误差的增加和天线效率的降低.基于天马65 m射电望远镜,使用位置传感器装置(PSD)法构建了副面位置偏移量测定系统,可以实时采集副面的3维位移数据,构建重力模型,将测试结果与射电法构建的现有副面模型进行对比,有较好的一致性.此外,该系统可以分析日照(引起撑腿局部温度效应)引起的副面位移情况,也可以监视风载和瞬时启停对副面位姿的影响.     

基于CCD提高射电望远镜极轴校准精度及修正

射电望远镜极轴的安装定位是否准确直接影响其指向精度和成像质量,通过运用光学CCD原理精确测量射电望远镜极轴偏差角度,用以安装校准极轴,达到提高射电望远镜指向精度和成像质量的效果,并且结合计算机可实现多极轴同时校准,提高工作效率。同时,基于CCD技术可以及时发现天线极轴出现的偏差并进行修正,提高了数据的质量。     

主反射面变形引起的天线指向误差修正方法

射电天线指向精度通常要求小于主波束宽度的1/10, 对于短厘米波段或毫米波段的大口径反射面天线, 指向精度要求高达几个角秒, 对于天线性能目标的实现是个巨大的挑战, 因此对于大口径高频段的反射面天线来说指向问题成为天线性能实现的重要关注焦点. 在众多影响天线指向精度的结构子系统因素中, 对主反射面变形因素的研究很少. 文章结合天线的结构特点建立了反射面空间坐标系统, 并基于变形后主面点的空间坐标值, 提出了3自由度下的非线性最小二乘吻合的方法去精准预测天线指向. 最后利用空间几何关系严格推导出了服务于天线指向误差修正的俯仰和方位的精确调整量, 从而构建了主面变形同指向误差之间的间接关系, 这对大型射电天线指向精度的提升具有一定的指导意义.     

A Research on the Gravity Deformation of Delingha 13.7m Telescope

Based on digital photogrammetric measurements, the antenna panels of the Delingha 13.7m radio telescope are adjusted to make the main dish have an optimal paraboloidal surface at the elevation of 52°, thus the overall antenna efficiency is optimized for different observing elevations. Observations indicate that the aperture efficiency of the telescope has been improved approximately twice in comparison with the antenna panels adjusted on the basis of theodolite measurements. According to the results of the measurements at different elevations, the models of antenna gravity deformation are built, including the displacement and tilt angle of the subreflector, as well as the focal length and surface error of the main reflector, as functions of elevation angle. In the process of modeling the gravity deformation of the main dish, instead of the direct calculation method, the least square fitting on the measured surface errors at different elevation angles is adopted, in order to reduce the effect of measurement errors on the accuracy of the model.     

Subreflector model depending on elevation for the Tianma 65m Radio Telescope

A subreflector adjustment system for the Tianma 65 m radio telescope, administered by Shanghai Astronomical Observatory, has been installed to compensate for gravitational deformation of the main reflector and the structure supporting the subreflector. The position and attitude of the subreflector are variable in order to improve the efficiency at different elevations. The subreflector model has the goal of improving the antenna's performance. A new fitting formulation which is different from the traditional formulation is proposed to reduce the fitting error in the Y direction. The only difference in the subreflector models of the 65 m radio telescope is the bias of a constant term in the Z direction. We have investigated the effect of movements of the subreflector on the pointing of the antenna. The results of these performance measurements made by moving the antenna in elevation show that the subreflector model can effectively improve the efficiency of the 65 m radio telescope at each elevation. An antenna efficiency of about 60% at the K u band is reached in the whole angular range of elevation.     

基于自回归滑动平均模型的大口径天线风速预测方法

针对大口径、高性能射电望远镜天线受到的随机及时变风扰的问题, 利用自回归滑动平均模型预测望远镜周围风速, 提前计算风致结构变形量, 同时为望远镜伺服控制系统提供足够执行时间来降低风扰影响. 基于新疆奇台110m口径全向可动射电望远镜(QiTai Telescope, QTT)台址风场数据特征, 通过赤池信息准则和贝叶斯信息准则辨识模型阶次, 利用最大似然法估计模型参数, 分析模型残差特性以检验自回归滑动平均模型的有效性. 通过计算不同季度预测数据与测试数据偏差得到预测模型的精度, 夏季平均绝对误差为0.133mcdots^-1, 秋季平均绝对误差为0.162mcdots^-1, 冬季平均绝对误差为0.287mcdots^-1. 整体来看, 基于QTT台址不同季度风速数据建立的自回归滑动平均模型预测误差较小, 满足射电望远镜风扰控制系统的需求, 能为大口径射电望远镜风扰控制提供必要数据支撑.     

基于FS系统对乌鲁木齐VLBI射电望远镜进行天线测量

在天文观测中射电望远镜性能参数的好坏直接影响到观测数据质量,为了保证观测质量,提高观测效率,需要对天线性能进行测量.当前进行天线测量的方法有场地测量法和射电天文法,不同的方法应用范围和效果不同.对于大型天线而言采用射电天文法进行天线测量高效快捷.针对VLBI射电望远镜,介绍了使用终端FS系统对天线参数进行测量（基于射电天文法）的方法和过程,以乌鲁木齐南山25 m天线增益和指向精度测量作为范例,重点叙述了测量的方法和步骤,并对该方法进行了讨论.     

一种偏振定标单元方位角误差的约束非线性最小化优化定标方法

偏振定标单元(Polarization Calibration Unit, PCU)对于定标由偏振系统和天文望远镜产生的仪器偏振至关重要, 然而偏振定标单元 中偏振元件光轴的方位角误差是限制定标精度的主要因素之一. 为解决该问题, 提出了一种基于约束非线性最 小化优化的方位角误差定标方法, 该方法具有定标精度高、定标速度快的优点. 首先将偏振定标单元中的线性 偏振片和四分之一波片的光轴方位角误差设置为两个待优化的自由变量, 然后利用产生和测量的Stokes参数 以及偏振定标获得的响应矩阵定义优化目标函数, 最终使用约束非线性最小化优化方法来确定 两个偏振元件的方位角误差. 分别从理论模拟和实际测量两个方面对优化方法进行了验证, 实验结果表明, 该 优化方法能够成功获得上述两个方位角误差, 精度分别优于2.79$''$和2.72$''$. 此外, 从理论上 计算分析了不同方位角误差对各Stokes分量的影响情况. 该优化方法有望应用到我国太阳望远镜中偏振定标 装置的误差定标及研制之中.     

Active sub-reflector research for a large radio telescope

This paper proposes an active sub-reflector suitable for large radio telescopes, which can compensate both of the deformation of the main reflector and sub-reflector position offsets. The mathematical formula of the main reflector deformation compensated by the sub-reflector is deduced based on Cassegrain and Gregory antenna structures. The position of the sub-reflector is adjustable to compensate for defocusing errors on high and low elevations, which are mainly caused by the deformation of the sub-reflector supporting legs. In this paper, the method of obtaining the optimum position of the sub-reflector from the aperture phase by the interferometric method is introduced. The actual measurement is verified on the Tianma 65 m radio telescope, which provides a new way to diagnose the position error of the sub-reflector.     

65 cm水平式望远镜静态指向模型

由于传统的静态指向模型对于水平式装置存在法方程条件差的困难,针对紫金山天文台盱眙站65 cm水平式空间碎片望远镜,基于真实的可能产生误差的来源建立了独特的静态指向模型,使模型参数具有明确的物理意义,从而基本剔除了望远镜的系统误差,大大提高了该望远镜的指向精度,达到了4”．     

一种测定望远镜极轴偏差的方法

利用望远镜的恒动跟踪，对两颗恒星进行无斗星曝光０．５小时，扣除蒙气差影响，用球面三角方法计算出望远镜极轴指向的偏差在赤经和赤纬方向上的分量，据此对望远镜极轴进行调整，就可以方便地把望远镜极轴指向调整到较高精度。     

Research on Wind Tower Position Optimization Method of Radio Telescope Site Based on Numerical Simulation

Wind field is a critical issue for radio telescope antenna structure design and observation. As the telescope performance requirements are getting higher and higher, the antenna structure design becomes more and more complicated, and the influence of wind load on antenna pointing in the observation is also serious. How to ensure the stiffness and strength of the structure during the design and to improve the effective observation time during the observation all need accurate wind field data. Due to the traditional wind tower setup method cannot quantitatively evaluate the reliability of the setting point position, so a method based on numerical simulation to optimize the position of the wind tower is proposed. The boundary conditions of numerical simulation are set based on specification parameters, the overall trend is consistent with the measured data, and therefore the simulation accuracy could meet the requirement. Four wind tower positions were set at the test site. According to the simulation results, the root-mean-square error (RMSE) of wind speed between point P2 and the antenna position is the smallest. So, the measured data in P2 could better represent the wind field characteristics of the antenna area.     

Pointing of HAGAR telescope mirrors

An array of seven atmospheric Cherenkov telescopes was commissioned at a high altitude site in Hanle in the Ladakh region of the Himalayas. The array called HAGAR has been designed to observe celestial γ-rays of energy >100 GeV. Each telescope is altitude-azimuth mounted and carries seven parabolic mirrors whose optic axes are co-aligned with the telescope axis. The telescopes point and track a celestial source using a PC-based drive control system. Two important issues in positioning of each HAGAR telescope are pointing accuracy of telescope axis and co-alignment of mirrors’ optic axes with the telescope axis. We have adopted a three pronged strategy to address these issues, namely use of pointing models to improve pointing accuracy of the telescopes, RA-DEC scan technique to measure the pointing offsets of the mirrors and mechanical fine-tuning of off-axis mirrors by sighting a distant stationary light source. This paper discusses our efforts in this regard as well as the current status of pointing and monitoring of HAGAR telescopes.