面向指向精度的奇台射电望远镜轮轨误差逆向设计方法
A Reverse-Design Strategy for the Track Error of the Qi Tai Telescope Based on Pointing Accuracy
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%.
| RMS | Pointing error | ||
|---|---|---|---|
| Calculated values (arcsec) | Measured values (arcsec) | Relative errors (%) | |
| 0.2591 | 0.2382 | 8.77 | |
| 0.2589 | 0.2407 | 7.56 | |
| 0.3663 | 0.3386 | 8.18 | |
| RMS | Pointing error | ||
|---|---|---|---|
| Calculated values (arcsec) | Measured values (arcsec) | Relative errors (%) | |
| 1.2399 | 1.3022 | 4.78 | |
| 1.2368 | 1.3228 | 6.50 | |
| 1.7513 | 1.8562 | 5.65 | |
| [1] |
Kärcher HJ. Experience with the design and construction of huge telescope pedestals. In: Proceedings of Second Backaslog Workshop on Extremely Large Telescopes; 2003 Sep 9‒11; Backaskog, Sweden. SPIE; 2003. p. 233‒44. |
| [2] |
Chu TS, Turrin R. Depolarization properties of offset reflector antennas. IEEE Trans Antennas Propaga 1973;21(3):339‒45. |
| [3] |
Bolli P, Orlati A, Stringhetti L, Orfei A, Righini S, Ambrosini R, et al. Sardinia radio telescope: general description, technical commissioning and first light. J Astron Instru 2015;4(3‒4):1550008. |
| [4] |
Antebi J, Kan FW. Precision continuous high-strength azimuth track for large telescopes. In: AngelJRP, GilmozziR, editors. Proceedings of Future Giant Telescopes; 2002 Aug 26‒28; Waikoloa, New Zealand. SPIE; 2002. p. 612‒23. |
| [5] |
Schloerb FP. The large millimeter telescope. In: Proceedings of Ground-Based and Airborne Telescopes II; 2008 Jun 23‒28; Marseille, France. SPIE; 2008 p.626701. |
| [6] |
Kaercher HJ, Baars JWM. Design of the large millimeter telescope/gran telescopio millimetrico (LMT/GTM). In: Butcher HR, editor. Proceedings of Astronomical Telescopes and Instrumentation; 2000 Mar 27‒Apr 1; Munich, Germany. SPIE; 2000. p. 155‒68. |
| [7] |
Zhang XZ, Zhu XY, Kong DQ, Zheng L, Yao C, Zhang HB, et al. Measurements of electronic properties of the Miyun 50 m radio telescope. Res Astron Astrophys 2009;9(3):367‒76. |
| [8] |
Guiar CN, Lansing FL, Riggs R. Antenna pointing systematic error model derivations. Telecommun Acquis Prog Rep 1986;42(88):36‒46. |
| [9] |
Keitzer S, Kimbrell JE, Greenwald D. Deterministic errors in pointing and tracking system I: identification and correction of static errors. In: Proceedings of Acquisition, Tracking, and Pointing V; 1991 Aug 1; Orlando, FL, USA. SPIE; 1991. p. 406‒14. |
| [10] |
Juneja G, Kan FW, Antebi J. Update on slip and wear in multi-layer azimuth track systems. In: Proceedings of Optomechanical Technologies for Astronomy; 2006 May 26‒31; Orlando, FL, USA. SPIE; 2006. p. 6273. |
| [11] |
Deng D, Kiyoshima S. Numerical simulation of welding temperature field, residual stress and deformation induced by electro slag welding. Comp Mater Sci 2012;62(5):23‒34. |
| [12] |
Zong Y, Hu N, Duan B, Yang G, Cao H, Xu W. Manufacturing error sensitivity analysis and optimal design method of cable-network antenna structures. Acta Astronaut 2016;120:182‒91. |
| [13] |
Antebi J, Kan FW. Precision continuous high-strength azimuth track for large telescopes. In: Proceedings of Future Giant Telescopes; 2002 Aug 22‒28; Waikoloa, HI, USA. SPIE; 2002. p. 612‒23. |
| [14] |
Gawronski W, Baher F, Quintero O. Azimuth-track level compensation to reduce blind-pointing errors of the Deep Space Network antennas. IEEE Antenn Propag Mag 2000;42(2):28‒38. |
| [15] |
Pisanu T, Buffa F, Morsiani M, Pernechele C, Poppi S. Thermal behavior of the Medicina 32-meter radio telescope. In: Proceedings of Modern Technologies in Space- and Ground-based Telescopes and Instrumentation; 2010 Jun 27‒Jul 2; San Diego, CA, USA. SPIE; 2010. p. 35‒44. |
| [16] |
Kong DQ, Wang SG, Wang JQ, Wang M, Zhang HB. A new calibration model for pointing a radio telescope that considers nonlinear errors in the azimuth axis. Res Astron Astrophys 2014;14(6):733‒40. |
| [17] |
Belov Y, Naumov A, Chernikova S, Poperchenko B, Sapozhnikov B. The application of correlation analysis in the process of pointing calibration of 64-m Bear Lakes radio telescope. IEEE Antennas Propag Soc Int Symp 1997;1(1):568‒71. |
| [18] |
Alvarez ML, Torres CT, Rios EH, Santos DC, Cuevas LC, Leon-Huerta A, et al. Metrology and surface adjustment of primary reflector panels on the LMT. In:Proceedings of Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation; 2014 Jun 22‒27; Montréal, QC, Canada. SPIE; 2014. p. 3‒11. |
| [19] |
Doane DP, Seward LE. Measuring skewness: a forgotten statistic? J Stat Educ 2011;19(2):1‒18. |
| [20] |
Joanes DN, Gill CA. Comparing measures of sample skewness and kurtosis. J Roy Stat Soc 1998;47(1):183‒9. |
| [21] |
Deng D, Murakawa H. Prediction of welding distortion and residual stress in a thin plate butt-welded joint. Comp Mater Sci 2008;43(2):353‒65. |
| [22] |
Majumdar A, Bhushan B. Role of fractal geometry in roughness characterization and contact mechanics of surfaces. J Tribol 1990;112(2):205‒16. |
| [23] |
Hu YZ, Tonder K. Simulation of 3-D random rough surface by 2-D digital filter and Fourier analysis. Int J Mach Tools Manufact 1992;32(1‒2):83‒90. |
| [24] |
Qiao B, Liu S. Error assessment in modeling with fractal Brownian motions. Fract 2013;21(3‒4):1‒8. |
| [25] |
Wielebinski R, Junkes N, Grahl BH. The effelsberg 100-m radio telescope: construction and forty years of radio astronomy. J Astron Hist Herit 2011;14(1):3‒21. |
| [26] |
Gawronski W, Baher F, Quintero O. Azimuth-track level compensation to reduce blind-pointing errors of the deep space network antennas. IEEE Antennas Propag Mag 2000;42(2):28‒38. |
| [27] |
Matsuzawa A, Saito M, Iguchi S, Nakanishi K, Saito H. Development of highaccuracy pointing verification for ALMA antenna. In: Proceedings of Groundbased and Airborne Telescopes V; 2014 Jun 22‒27; Montréal, QC, Canada. SPIE; 2014. p. 1‒7. |
| [28] |
Prestage RM, Constantikes KT, Hunter TR, King LJ, Lacasse RJ, Lockman FJ, et al. The green bank telescope. Proc IEEE 2009;97(8):1382‒90. |
| [29] |
Symmes A, Anderson R, Egan D. Improving the service life of the 100-meter green bank telescope azimuth track. In: Proceedings of Ground-Based and Airborne Telescope II; 2008 Jun 23‒28; Marseille, France. SPIE; 2008. p.1‒12. |
| [30] |
Hughes DH, Correa JJ, Schloerb FP, Erickson N, Romero JG, Heyer M, et al. The large millimeter telescope. In: Proceedings of Ground-Based and Airborne Telescopes III; 2010 Jun 27‒Jul 2; San Diego, CA, USA. SPIE; 2010.p. 1‒13. |
| [31] |
Okubo H, Kawai E, Kondo T, Osaki H, Nakajima J, Ishizuka K. Inclinometer measurement of Kashima 34 m antenna. Technol Dev Cent News 2001;11(19):13‒4. |
()
/
| 〈 |
|
〉 |
PDF
(1882KB)
