3-DOF measurement method for non-diffracting Moiré fringes based on CGH

Lv Qinghua; Cheng Zhuang; Zhai Zhongsheng; Wang Xuanze; Cui Jiachen; Lv Hui

doi:10.12086/oee.2020.190331

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Lv Q H, Cheng Z, Zhai Z S, et al. 3-DOF measurement method for non-diffracting Moiré fringes based on CGH[J]. Opto-Electron Eng, 2020, 47(2): 190331. doi: 10.12086/oee.2020.190331

Citation:

Lv Q H, Cheng Z, Zhai Z S, et al. 3-DOF measurement method for non-diffracting Moiré fringes based on CGH[J]. Opto-Electron Eng, 2020, 47(2): 190331. doi: 10.12086/oee.2020.190331

3-DOF measurement method for non-diffracting Moiré fringes based on CGH

1.
Hubei Collaborative Innovation Center for High-efficient Utilization of Solar Energy, Wuhan, Hubei 430068, China
2.
School of Science, Hubei University of Technology, Wuhan, Hubei 430068, China
3.
Hubei Key Laboratory of Modern Manufacturing Quantity Engineering, School of Mechanical Engineering, Hubei University of Technology, Wuhan, Hubei 430068, China

Fund Project: Supported by National Natural Science Foundation of China (51575164), the Science and Technology Research Project of Department of Education of Hubei Province (D20161406), and Hubei Collaborative Innovation Center for High-efficient Utilization of Solar Energy (HBSKFZD2014007)

More Information

^*Corresponding author: Zhai Zhongsheng, E-mail:zs.zhai@mail.hbut.edu.cn

Received Date 14 June 2019

Revised Date 04 November 2019

Published Date 01 February 2020

Abstract

Abstract

Aiming at the motion errors of the linear stage, a measurement method for the determination of three-degree-of-freedom (3-DOF) error motions is proposed based on non-diffracting Moiré fringes produced by computer-generated holograms (CGHs). A liquid crystal spatial light modulator (SLM) is used to generate non-diffracting beams, and two non-diffracting beams form Moiré fringes. A 3-DOF measuring optical path of non-diffracting Moiré fringes is designed. Meanwhile, a 3-DOF mathematical model of motion errors is established, and three kinds of motion errors (yaw angle, roll angle and pitch angle) are separated by geometric analysis method. A rotary table is used to simulate the 3-DOF motion errors on different conditions. The NDB and non-diffracting Moiré fringe patterns are obtained by CCD1 and CCD2 respectively. Experimental results show that the motion errors calculated by the positions of the central points agree well with the theoretical value with the error less than 0.0104°, which can verify the feasibility and correctness of the 3-DOF measurement system for non-diffracting Moiré fringes.
- 3-DOF measurement /
- non-diffracting beam /
- Moiré fringes /
- SLM

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References

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Overview

Overview

Overview: Error motions of a linear stage directly influence the performance of the precision positioning system in which the stage is used. Therefore, it is a critical task to measure the error motions. A measurement method for the determination of three-degree-of-freedom (3-DOF) error motions based on non-diffracting Moiré fringes is proposed.

A semi-transparent mirror (STM), a beam splitter and a mirror are adopted as the measurement head, which is fixed on the moving stage in order to sense 3-DOF angular errors. Two CCDs are used to capture the non-diffracting beams patterns that are carrying the errors. Computer generated holograms (CGHs) are loaded into a liquid crystal spatial light modulator (SLM) to produce non-diffracting beams. A beam splitter prism (BS1), placed after the SLM, splits the non-diffracting beam into two beams, the transmitted beam and the reflection beam. The reflected non-diffracting beam, after reflection by mirror 2, traveling through BS3, is reflected by the STM, and reaches CCD1. The image of the non-diffracting beams is captured by CCD1. The other beam transmits from BS3 to CCD2 after travelling through STM and BS2. The transmitted non-diffracting beam exiting BS1 passes through an attenuator, and then is reflected by mirror 1, from where it meets the beam from the moving unit. These two non-diffracting beams generate non-diffracting Moiré fringes, which are captured by CCD2.

When the stage moves, the position of the central points of the non-diffracting beams (as received by CCD 1) and the forms of Moiré fringes (obtained by CCD 2) will change in relation to different errors. It can measure the 3-DOF errors, which are yaw, pitch, and roll. By analyzing the geometric position of these center points, mathematical models for 3-DOF motion errors are established. Obviously, one of central points in CCD2 will be unchanged while the other one will changes according to different motion errors of stage.

A rotary table is used to simulate the 3-DOF motion errors and demonstrate the theoretical analysis. The measurement head is fixed on the table, which rotates different small angles (0°, 0.125°, 0.25°, 0.375°, 0.5°). The on-diffracting beam and non-diffracting Moiré fringe patterns are obtained by CCD1 and CCD2, respectively. The actual angular displacement is calculated by the offset of the center of the spot with the mathematical models. Compared with the theoretical value, the angular displacement error is less than 0.0104°, which verifies the feasibility and correctness of the 3-DOF measurement system for non-diffracting Moiré fringes.