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基于四维协变量的光栅干涉系统频移理论研究

林子超 姚玉林 周通 薛栋柏 顾振杰 邓晓 程鑫彬 李同保

林子超,姚玉林,周通,等. 基于四维协变量的光栅干涉系统频移理论研究[J]. 计量科学与技术,2022, 66(11): 3-11, 26 doi: 10.12338/j.issn.2096-9015.2022.0248
引用本文: 林子超,姚玉林,周通,等. 基于四维协变量的光栅干涉系统频移理论研究[J]. 计量科学与技术,2022, 66(11): 3-11, 26 doi: 10.12338/j.issn.2096-9015.2022.0248
LIN Zichao, YAO Yulin, ZHOU Tong, XUE Dongbai, GU Zhenjie, DENG Xiao, CHENG Xinbin, LI Tongbao. Research on Frequency Shift Theory of Grating Interference Systems Based on 4D Covariates[J]. Metrology Science and Technology, 2022, 66(11): 3-11, 26. doi: 10.12338/j.issn.2096-9015.2022.0248
Citation: LIN Zichao, YAO Yulin, ZHOU Tong, XUE Dongbai, GU Zhenjie, DENG Xiao, CHENG Xinbin, LI Tongbao. Research on Frequency Shift Theory of Grating Interference Systems Based on 4D Covariates[J]. Metrology Science and Technology, 2022, 66(11): 3-11, 26. doi: 10.12338/j.issn.2096-9015.2022.0248

基于四维协变量的光栅干涉系统频移理论研究

doi: 10.12338/j.issn.2096-9015.2022.0248
基金项目: 国家重点研发计划(2022YFF0605502);国家自然科学基金面上项目(62075165);上海张江国家自主创新示范区专项发展资金重大项目(ZJ2021-ZD-008)。
详细信息
    作者简介:

    林子超(1998-),同济大学精密光学工程技术研究所在读博士生,研究方向:精密位移测量技术、原子光刻技术等,邮箱:zichao@tongji.edu.cn

    通讯作者:

    邓晓(1988-),同济大学精密光学工程技术研究所副教授,研究方向:纳米光栅标准物质、线宽标准物质、超精密测量及校准技术等,邮箱:18135@tongji.edu.cn

Research on Frequency Shift Theory of Grating Interference Systems Based on 4D Covariates

  • 摘要: 光栅干涉系统中的装配与角度调试误差是探测光发生几何错位、偏离探测器感光中心的直接原因。为厘清探测光综合姿态误差对干涉相位和位移测量结果的影响,本文基于狭义相对论波矢量的四维表达形式,将光频率和光波矢与光栅方程直接关联,构建了以任意角度入射、光栅沿任意方向运动的多普勒频移理论体系,论证了在不同光栅入射角度下,同级次衍射光频移关系具有一致性的物理特征。通过激光、光栅干涉系统之间物理图像的对比,阐明了即使系统光几何路径不随运动改变,也仍产生相位变化的原因是光栅表面的特殊波矢调制关系。结论表明,光栅干涉系统在探测光存在综合姿态误差情况下位移转化关系仍保持不变,光栅周期方向的偏转是系统几何测量误差的关键来源。最后,为初判某一系统的测量性能指标,文中给出了一种能够快速判断其位移测量原始分辨率的方法。由于本文的频移理论从物理底层逻辑出发,因此相关结论具有普适性,这不仅对所有光栅干涉系统的原理分析具有指导作用,同时还对各种先进系统中的几何测量误差分析具有重要参考价值。
  • 图  1  沿${x}''$运动的坐标旋转示意图

    Figure  1.  Schematic diagram of coordinate rotation along the $x''$ axis

    图  2  光栅与入射光源相对运动示意图

    Figure  2.  Schematic diagram of the relative motion between the grating and the incident light source

    图  3  光栅衍射过程的矢量分解示意图

    Figure  3.  Schematic diagram of vector decomposition of the grating diffraction process

    图  4  单频干涉位移系统测量原理的物理图像对比[15, 23]

    Figure  4.  Physical image comparison of measurement principle of single frequency interference displacement system

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出版历程
  • 网络出版日期:  2022-12-01
  • 刊出日期:  2023-01-17

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