On middle frequency error distribution of large telescope based on structure function

Qi-Chang AN; Jing-xu ZHANG; Fei YANG; Hong-chao ZHAO

doi:10.3788/OPE.20172402.0433

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On middle frequency error distribution of large telescope based on structure function

Micro/Nano Technology and Fine Mechanics | 更新时间：2020-07-07

- On middle frequency error distribution of large telescope based on structure function
- Optics and Precision Engineering Vol. 25, Issue 2, Pages: 433-440(2017)
- 作者机构：
  
  1.中国科学院长春光学精密机械与物理研究所, 吉林长春 130033
  2.中国科学院大学, 北京 100039
- 作者简介：
- 基金信息：
- DOI：10.3788/OPE.20172402.0433
  CLC： TH751
- Received：20 July 2016，
  
  Accepted：25 August 2016，
  
  Published：25 February 2017
- 稿件说明：
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Qi-Chang AN, Jing-xu ZHANG, Fei YANG, et al. On middle frequency error distribution of large telescope based on structure function[J]. Optics and precision engineering, 2017, 25(2): 433-440.
DOI：

Qi-Chang AN, Jing-xu ZHANG, Fei YANG, et al. On middle frequency error distribution of large telescope based on structure function[J]. Optics and precision engineering, 2017, 25(2): 433-440. DOI： 10.3788/OPE.20172402.0433.

摘要

为了更好地对于大口径望远镜中频误差进行评价与分配，本文引入了结构函数来进行研究。本文首先对于结构函数的基本性质进行了推导，并与传统的误差均方根（RMS）进行比较，表明了其表征不同尺度误差的能力。之后分析了系统波前在不同的评价尺度下的统计特性差异，得出在较小尺度下，系统的误差分布可以较好的服从正态分布，而随着尺度的增加（如大于100mm）会逐渐偏离正态分布的结论。然后根据结构函数的基本性质，提出了一种可以同时考虑诸多误差源的大口径望远镜中频误差分配方法。结合美国三十米望远镜（TMT）团队所提出的标准化点源敏感性（normalized Point Source Sensitivity，PSSn），建立起了由结构函数到标准化点源敏感性的换算关系，通过此方法来进行误差分配指标间的交叉验证以及与其他单元技术之间的对接。最后，根据本文所提出的方法，对于某大口径望远镜的主镜系统进行了误差分配，得到在大尺度均方根为25nm，粗糙度为1nm，中频尺度为250mm，大气相干长度为0.4m（检测环境）的要求下，该系统的结构函数满足要求，同时由要求结构函数所计算得到的PSSn=0.999 6大于由镜面数据直接得到的PSSn=0.999 5，同样满足要求。

Abstract

To better evaluate and distribute the middle frequency errors of large telescope

structure function was put forward for such purposes in this paper. Firstly

we carried out a derivation in basic property of the structure function and compared it with traditional root mean square (RMS)

which indicates its capability of representing different-scale errors; secondly

conducted an analysis on the statistical property difference of system wavefront under different evaluation scales

which indicates that system error distribution can better follow the normalized distribution under small scale and tend to deviate from the normalized distribution with the scale increase (e.g.:a scale greater than 100 mm); then a method for middle frequency error distribution of large telescope that can simultaneously cover multiple error sources was put forward based on basic property of the structure function; established a conversion relation between the structure function and normalized point source sensitivity (PSSn) put forward by TMT team

and then completed the cross validation among the error distribution indexes and transfer of techniques; finally

carried out an error distribution in primary mirror system of a large telescope based on the method put forward in this paper

which indicates that structure function of the system can meet the requirements under the condition where large-scale RMS is 25nm

roughness is 1nm

middle frequency scale is 250 mm and atmospheric coherent length is 0.4 m (testing environment)

and that PSSn=0.9996 obtained from the structure function is greater than PSSn=0.999 5 directly obtained from mirror data can also meet the corresponding requirement.

关键词

Keywords

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