Volume 45 Issue 12
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Lin Cunbao, Yan Shuhua, You Fusheng, Du Zhiguang. Synthetical modeling and experimental study of fabrication and assembly errors of two-dimensional gratings[J]. Infrared and Laser Engineering, 2016, 45(12): 1217005-1217005(9). doi: 10.3788/IRLA201645.1217005
Citation: Lin Cunbao, Yan Shuhua, You Fusheng, Du Zhiguang. Synthetical modeling and experimental study of fabrication and assembly errors of two-dimensional gratings[J]. Infrared and Laser Engineering, 2016, 45(12): 1217005-1217005(9). doi: 10.3788/IRLA201645.1217005
shu

Synthetical modeling and experimental study of fabrication and assembly errors of two-dimensional gratings

doi: 10.3788/IRLA201645.1217005
  • 1.

    College of Mechatronic Engineering and Automation,National University of Defense Technology,Changsha 410073,China;

  • 2.

    Flight Training Base,Aviation University Air Force,Changchun 130062,China

  • Received Date: 2016-04-15
  • Rev Recd Date: 2016-05-23
  • Publish Date: 2016-12-25
  • The geometrical errors resulting from imperfection of the fabrication and assembly of two-dimensional(2D) grating were investigated. Based on the Doppler frequency shift theory and the coordinate transformation method, the general error model versus non-orthogonal and misalignment angles of 2D gratings was established. Then the effects of these error angles were quantitatively studied, and the cosine and the cross-talk errors of both directions were simulated and analyzed. The results illustrated that the geometrical errors were independent from the diffraction orders, diffraction times and the optical subdivision multiple, just determined by the error angles and the 2D displacement. Meanwhile, the cosine errors could be induced by all the error angles, but the cross-talk errors were mainly influenced by the non-orthogonal and raw angles. Besides, the cross-talk errors were more serious than the cosine errors, which is the dominant component of the geometrical errors. A planar displacement measurement system with 2D cross-grating was constructed, and the theoretical analyses and the numerical simulation were verified with the 10 mm square displacement measurement.
  • [1] Wu Jian, Yuan Bo, Wang Liqiang. New displacement measurement method based on digital Moir fringes formed by a single grating[J]. Infrared and Laser Engineering, 2014, 43(10):3404-3409. (in Chinese)伍剑, 袁波, 王立强. 单光栅数字莫尔位移测量法[J]. 红外与激光工程, 2014, 43(10):3404-3409.
    [2] Lin Cunbao, Yan Shuhua, Du Zhiguang, et al. Symmetrical short-period and high signal-to-noise ratio heterodyne grating interferometer[J]. Chinese Optics Letters, 2015, 13(10):100501.
    [3] Hsieh H, Pan S. Development of a grating-based interferometer for six-degree-of-freedom displacement and angle measurements[J]. Optics Express, 2015, 23(3):2451-2465.
    [4] Mi Xiaotao, Yu Hongzhu, Yu Haili, et al. Analysis and improvement of rod structures for large diffraction grating ruling engines[J]. Optics and Precision Engineering, 2015, 23(3):745-752. (in Chinese)糜小涛, 于宏柱, 于海利, 等. 大型衍射光栅刻划机拉杆结构的分析与改进[J]. 光学精密工程, 2015, 23(3):745-752.
    [5] Jiang Yanxiu, Bayan Heshig, Zhao Xulong, et al. Plane holographic varied-line-space grating for DCLS in EUV region[J]. Optics and Precision Engineering, 2015, 23(8):2117-2124. (in Chinese)姜岩秀, 巴音贺希格, 赵旭龙, 等. 自由电子激光器用极紫外波段平面变栅距光栅[J]. 光学精密工程, 2015, 23(8):2117-2124.
    [6] Liu Yongmeng, Yuan Maoqiang, Cao Jieru, et al. Use of two planar gratings to measure 3-DOF displacements of planar moving stage[J]. IEEE Transactions on Instrumentation Measurement, 2015, 64(1):163-169.
    [7] Wang Xuanze, Dong Xiaohua, Guo Jun, et al. Two-dimensional displacement sensing using a cross diffraction grating scheme[J]. Journal of Optics A:Pure and Applied Optics, 2004, 6(1):106-111.
    [8] Hsieh H, Chen J, Leronde G, et al. Two-dimensional displacement measurement by quasi-common-optical path heterodyne grating interferometer[J]. Optics Express, 2011, 19(10):9770-9782.
    [9] Xian Guang, Yan Changxiang. Analysis of attitude change impact on aerial push-broom imaging[J]. Infrared and Laser Engineering, 2015, 44(8):2178-2183. (in Chinese)贤光, 颜昌翔.态变化对航空推扫式成像的影响分析[J]. 红外与激光工程, 2015, 44(8):2178-2183.
    [10] Lin Cunbao, Yan Shuhua, Du Zhiguang, et al. High-efficiency gold-coated cross-grating for heterodyne grating interferometer with improved signal contrast and optical subdivision[J]. Optics Communications, 2015, 339(15):86-93.
    [11] Yang Dongxing, Yan Shuhua, Du Liebo, et al. Design of a miniature single-grating displacement measuring system with nanometer resolution[J]. Infrared and Laser Engineering, 2013, 42(4):1020-1025. (in Chinese)杨东兴, 颜树华, 杜列波, 等. 一种小型化纳米级单光栅位移测量系统的研制[J].红外与激光工程, 2013, 42(4):1020-1025.
    [12] Peng Lirong, Ma Zhanlong, Wang Gaowen, et al. Key technology of ultra-thin optical element precision manufacture[J]. Chinese Optics, 2015, 8(6):964-970. (in Chinese)彭利荣, 马占龙, 王高文, 等. 超薄光学元件精密加工关键技术[J]. 中国光学, 2015, 8(6):964-970.
    [13] Tao Xiaoping. Precise alignment method of online optical testing for large-aperture mirror fabrication[J]. Chinese Optics, 2015, 8(6):1027-1034. (in Chinese)陶小平. 大口径反射镜加工机床在线检测高精度对准方法[J]. 中国光学, 2015, 8(6):1027-1034.
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Synthetical modeling and experimental study of fabrication and assembly errors of two-dimensional gratings

doi: 10.3788/IRLA201645.1217005
  • 1. College of Mechatronic Engineering and Automation,National University of Defense Technology,Changsha 410073,China;
  • 2. Flight Training Base,Aviation University Air Force,Changchun 130062,China
  • Received Date: 2016-04-15
  • Rev Recd Date: 2016-05-23
  • Publish Date: 2016-12-25

Abstract: The geometrical errors resulting from imperfection of the fabrication and assembly of two-dimensional(2D) grating were investigated. Based on the Doppler frequency shift theory and the coordinate transformation method, the general error model versus non-orthogonal and misalignment angles of 2D gratings was established. Then the effects of these error angles were quantitatively studied, and the cosine and the cross-talk errors of both directions were simulated and analyzed. The results illustrated that the geometrical errors were independent from the diffraction orders, diffraction times and the optical subdivision multiple, just determined by the error angles and the 2D displacement. Meanwhile, the cosine errors could be induced by all the error angles, but the cross-talk errors were mainly influenced by the non-orthogonal and raw angles. Besides, the cross-talk errors were more serious than the cosine errors, which is the dominant component of the geometrical errors. A planar displacement measurement system with 2D cross-grating was constructed, and the theoretical analyses and the numerical simulation were verified with the 10 mm square displacement measurement.

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