Spatially separated heterodyne grating interferometer for in-plane displacement measurement

Xu XING; Di CHANG; Peng-cheng HU

doi:10.3788/OPE.20192708.1727

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Spatially separated heterodyne grating interferometer for in-plane displacement measurement

Modern Applied Optics | 更新时间：2020-08-13

- Spatially separated heterodyne grating interferometer for in-plane displacement measurement
- Optics and Precision Engineering Vol. 27, Issue 8, Pages: 1727-1736(2019)
- 作者机构：
  
  哈尔滨工业大学超精密光电仪器工程研究所 & 超精密仪器技术及智能化工业和信息化部重点实验室(哈尔滨工业大学)，黑龙江哈尔滨 150001
- 作者简介：
- 基金信息：
- DOI：10.3788/OPE.20192708.1727
  CLC： TP744.3;TH822
- Received：11 March 2019，
  
  Accepted：03 April 2019，
  
  Published：15 August 2019
- 稿件说明：
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Xu XING, Di CHANG, Peng-cheng HU. Spatially separated heterodyne grating interferometer for in-plane displacement measurement[J]. Optics and precision engineering, 2019, 27(8): 1727-1736.
DOI：

Xu XING, Di CHANG, Peng-cheng HU. Spatially separated heterodyne grating interferometer for in-plane displacement measurement[J]. Optics and precision engineering, 2019, 27(8): 1727-1736. DOI： 10.3788/OPE.20192708.1727.

摘要

为了实现平面二自由度位移测量，设计并搭建了空间分离式外差二自由度平面光栅干涉仪，并对所设计的光栅干涉仪的光学结构、测量原理、面内旋转安装误差补偿等进行了研究。基于平面光栅衍射特性和空间分离式外差光栅干涉结构设计并搭建了具有对称性的测头光路，结合实际光学器件的特点，利用琼斯矩阵分析了二自由度测量原理与显著降低周期非线性误差的特性。通过实验测定了光栅面内旋转安装误差以便于应用旋转矩阵对测量数据进行解耦。随后利用矩形和圆形轨迹分别验证了两测量轴在各自和同时运动的情况下，所设计的平面光栅干涉仪的测量能力。实验结果表明，在解耦补偿0.350°的光栅实际面内旋转安装误差的前提下，该空间分离式外差二自由度平面光栅干涉仪能够实现压电位移台30 μm内的位移测量，主要由机械振动等因素引起的误差不超过0.15 μm。本研究将空间分离式外差光栅干涉仪的测量维度拓展到了平面二自由度。

Abstract

To measure two Degree-Of-Freedom (DOF) in-plane displacement

a spatially separated heterodyne grating interferometer was designed and built. The optical configuration

measurement principle

and in-plane rotary assembling error of this instrument were investigated. Based on the diffraction of the planar grating and the spatially separated heterodyne grating interferometry

a symmetrical double-diffracted optical configuration was designed and analyzed. The measurement principle and the elimination of periodic nonlinear errors were modeled and studied using Jones matrices for the components. In-plane rotary assembling errors around the

-axis were measured to decouple the measurement results for the

-and

-axes using a two-dimensional rotation matrix. Then

the square and circular paths of the grating were driven to evaluate the functionality of the proposed interferometer. The experimental results indicate that the proposed interferometer is capable of measuring the in-plane displacements of a nanopositioning stage within the range of 30 μm after compensation for the 0.350° rotary assembling error. The error attributed to mechanical vibration is less than 0.15 μm. In this investigation

2-DOF in-plane measurement was demonstrated using a spatially separated heterodyne grating interferometer.

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references

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