# A Contactless Laser Doppler Strain Sensor for Fatigue Testing with Resonance-Testing Machine

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Optical Setup

## 3. Modeling

#### 3.1. Signal Power

#### 3.2. Noise Analysis and SNR

#### 3.3. Noise Limited Resolution

#### 3.4. Simulation for the Optimal Sensor Design

## 4. Experimental Setup and Results

## 5. Conclusions and Outlook

## 6. Patents

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Keil, S. Technology and Practical Use of Strain Gages with Particular Consideration of Stress Analysis Using Strain Gages; Ernst & Sohn: Berlin, Germany, 2017; pp. 17–108. [Google Scholar]
- Melle, S.; Alavie, A.; Karr, S.; Coroy, T.; Liu, K.; Measures, R. A Bragg grating-tuned fiber laser strain sensor system. IEEE Photon. Technol. Lett.
**1993**, 5, 263–266. [Google Scholar] [CrossRef] - Barot, D.; Wang, G.; Duan, L. High-Resolution Dynamic Strain Sensor Using a Polarization-Maintaining Fiber Bragg Grating. IEEE Photon. Technol. Lett.
**2019**, 31, 709–712. [Google Scholar] [CrossRef] - Pan, B.; Qian, K.; Xie, H.; Asundi, A. Two-dimensional digital image correlation for in-plane displacement and strain measurement: A review. Meas. Sci. Technol.
**2009**, 20, 20. [Google Scholar] [CrossRef] - Khoo, S.-W.; Karuppanan, S.; Tan, C.-S. A Review of Surface Deformation and Strain Measurement Using Two-Dimensional Digital Image Correlation. Metrol. Meas. Syst.
**2016**, 23, 461–480. [Google Scholar] [CrossRef] - Pan, B.; Tian, L. Advanced video extensometer for non-contact, real-time, high-accuracy strain measurement. Opt. Express
**2016**, 24, 19082–19093. [Google Scholar] [CrossRef] - Tian, L.; Yu, L.; Pan, B. Accuracy enhancement of a video extensometer by real-time error compensation. Opt. Lasers Eng.
**2018**, 110, 272–278. [Google Scholar] [CrossRef] - Pfeifer, T.; Mischo, H.K.; Ettemeyer, A.; Wang, Z.; Wegner, R. Strain/stress measurements using electronic speckle pattern interferometry. In Proceedings of the Three-Dimensional Imaging, Optical Metrology, and Inspection IV, Boston, MA, USA, 2–3 November 1998. [Google Scholar] [CrossRef]
- Zhu, Y.; Vaillant, J.; Montay, G.; François, M.; Hadjar, Y.; Bruyant, A. Simultaneous 2D in-plane deformation measurement using electronic speckle pattern interferometry with double phase modulations. Chin. Opt. Lett.
**2018**, 16, 071201. [Google Scholar] - Yamaguchi, I.; Takemori, T.; Kobayashi, K. Stabilized and accelerated speckle strain gauge. Opt. Eng.
**1993**, 32, 618–625. [Google Scholar] [CrossRef] - Pang, Y.; Chen, B.K.; Yu, S.F.; Lingamanaik, S.N. Enhanced laser speckle optical sensor for in situ strain sensing and structural health monitoring. Opt. Lett.
**2020**, 45, 2331–2334. [Google Scholar] [CrossRef] - Wang, W.; Xu, C.; Jin, H.; Meng, S.; Zhang, Y.; Xie, W. Measurement of high temperature full-field strain up to 2000 °C using digital image correlation. Meas. Sci. Technol.
**2017**, 28, 035007. [Google Scholar] [CrossRef] - Pan, Z.; Huang, S.; Su, Y.; Qiao, M.; Zhang, Q. Strain field measurements over 3000 °C using 3D-Digital image correlation. Opt. Lasers Eng.
**2020**, 127, 105942. [Google Scholar] [CrossRef] - Hung, Y.; Ho, H.P. Shearography: An optical measurement technique and applications. Mater. Sci. Eng. R Rep.
**2005**, 49, 61–87. [Google Scholar] [CrossRef] - Francis, D.; Tatam, R.P.; Groves, R.M. Shearography technology and applications: A review. Meas. Sci. Technol.
**2010**, 21, 21. [Google Scholar] [CrossRef] [Green Version] - Xie, X.; Chen, X.; Li, J.; Wang, Y.; Yang, L. Measurement of in-plane strain with dual beam spatial phase-shift digital shearography. Meas. Sci. Technol.
**2015**, 26, 115202. [Google Scholar] [CrossRef] - Cazzolato, B.; Wildy, S.; Codrington, J.; Kotousov, A.; Schuessler, M. Scanning Laser Vibrometer for Non-Contact Three-Dimensional Displacement and Strain Measurements. In Proceedings of the Australian Acoustical Society Conference, Geelong, Australia, 24–26 November 2008. [Google Scholar]
- Weisbecker, H.; Cazzolato, B.S.; Wildy, S.; Marburg, S.; Codrington, J.; Kotousov, A.; Kotousov, A. Surface Strain Measurements Using a 3D Scanning Laser Vibrometer. Exp. Mech.
**2011**, 52, 805–815. [Google Scholar] [CrossRef] - Reyes, J.M.; Avitabile, P. Use of 3D Scanning Laser Vibrometer for Full Field Strain Measurements. In Experimental Techniques, Rotating Machinery, and Acoustics; The Society for Experimental Mechanics Series; Springer: Cham, Switzerland, 2015; Volume 8, pp. 197–209. [Google Scholar] [CrossRef]
- Jakobsen, M.L.; Hanson, S.G. Lenticular array for spatial filtering velocimetry of laser speckles from solid surfaces. Appl. Opt.
**2004**, 43, 4643–4651. [Google Scholar] [CrossRef] - Jakobsen, M.L.; Larsen, H.E.; Hanson, S.G. Optical spatial filtering velocimetry sensor for sub-micron, in-plane vibration measurements. J. Opt. A Pure Appl. Opt.
**2005**, 7, S303–S307. [Google Scholar] [CrossRef] - Aizu, Y.; Asakura, T. Spatial Filtering Velocimetry; Springer Science and Business Media LLC: Cham, Switzerland, 2005; pp. 139–170. [Google Scholar] [CrossRef] [Green Version]
- Albrecht, H.-E.; Borys, I.M.; Damaschke, D.-I.N.; Tropea, I.C. Basic Measurement Principles. In Laser Doppler and Phase Doppler Measurement Techniques; Springer Science and Business Media LLC: Cham, Switzerland, 2003; pp. 9–26. [Google Scholar] [CrossRef]
- Hercher, M.; Wyntjes, G.; Deweerd, H. Non-Contact Laser Extensometer. In Proceedings of the Industrial Laser Interferometry, Los Angeles, CA, USA, 10 September 1987; Volume 746, pp. 185–193. [Google Scholar] [CrossRef]
- Bin, L.; Jing-Wen, L.; Chun-Yong, Y. Study on the measurement of in-plane displacement of solid surfaces by laser Doppler velocimetry. Opt. Laser Technol.
**1995**, 27, 89–93. [Google Scholar] [CrossRef] - Gasparetti, M.; Revel, G.M. The influence of operating conditions on the accuracy of in-plane laser Doppler velocimetry measurements. Measurement
**1999**, 26, 207–220. [Google Scholar] [CrossRef] - Zhong, Y.; Zhang, G.; Leng, C.; Zhang, T. A differential laser Doppler system for one-dimensional in-plane motion measurement of MEMS. Measurement
**2007**, 40, 623–627. [Google Scholar] [CrossRef] - Agusanto, K.; Lau, G.-K.; Wu, K.; Liu, T.; Zhu, C.; Yuan, L. Directional-sensitive differential laser Doppler vibrometry for in-plane motion measurement of specular surface. In Proceedings of the International Conference on Experimental Mechanics 2014, Singapore, 15–17 November 2014. [Google Scholar] [CrossRef]
- Wang, F.; Scholz, A.; Hug, J.; Rembe, C. Laser-Doppler-Dehnungssensor / Laser-Doppler strain gauge. TM Tech. Mess.
**2019**, 86, 82–86. [Google Scholar] [CrossRef] [Green Version] - Rembe, C.; Siegmund, G.; Steger, H.; Wörtge, M. Measuring MEMS in Motion by Laser Doppler Vibrometry. In Optical Science and Engineering; Informa UK Limited: London, UK, 2006; pp. 245–292. [Google Scholar] [CrossRef]
- Dräbenstedt, A. Diversity combining in laser Doppler vibrometry for improved signal reliability. In Proceedings of the 11th International Conference on Vibration Measurements by Laser and Noncontact Techniques–Aivela 2014: Advances and Applications, Ancona, Italy, 25–27 June 2014. [Google Scholar] [CrossRef]
- Rembe, C.; Dräbenstedt, A. D1.1—Speckle-Insensitive Laser-Doppler Vibrometry with Adaptive Optics and Signal Diversity. In Proceedings SENSOR 2015; AMA Service GmbH: Wunstorf, Germany, 2015; pp. 505–510. [Google Scholar] [CrossRef]

**Figure 3.**(

**a**) The velocities of both endpoints of the test specimen; (

**b**) The velocities measured by the laser Doppler strain sensor.

**Figure 6.**(

**a**) The noise-limited minimum detectable strain in $1/\sqrt{\mathrm{H}\mathrm{z}}$ in relation to the crossing angle $\theta $; (

**b**) The noise-limited minimum detectable strain in relation to the Bandwidth $\mathit{B}$.

**Figure 9.**(

**a**) Measurement results from the optical sensor and a traditional strain gauge. Both results are presented with a bandwidth of 2.5 kHz and a resolution bandwidth of 2.37 Hz. (

**b**) The spectrum of the results from both sensors. (

**c**) The sinusoidal force produced by the resonance-testing machine. (

**d**) Strain deviation, the difference between results from both sensors.

**Figure 10.**(

**a**) Measurement results from the optical sensor with bad speckle and the strain gauge. Both results are presented with a bandwidth of 2.5 kHz and a resolution bandwidth of 2.37 Hz. (

**b**) The spectrum of the results from both sensors.

Parameter | Value | Parameter | Value | Parameter | Value |
---|---|---|---|---|---|

$\lambda $ | $1550\text{}\mathrm{n}\mathrm{m}$ | ${\mathit{E}}_{in}$ | $3183\text{}\mathrm{W}/{\mathrm{m}}^{2}$ | ${\mathit{R}}_{f}$ | $3.5\text{}\mathrm{k}\mathsf{\Omega}$ |

${\mathit{A}}_{0}$ | $5.63\xb7{10}^{-3}{\text{}\mathrm{m}\mathrm{m}}^{2}$ | $\mathit{K}$ | $1.03\text{}\mathrm{A}/\mathrm{W}$ | $\mathit{l}$ | $6\text{}\mathrm{m}\mathrm{m}$ |

$\phi $ | $14.9\xb0$ | ${\delta}_{s}$ | $0.5$ | $\eta $ | $0.5$ |

$\mathit{T}$ | $293\text{}\mathrm{K}$ | ${\mathit{e}}_{n}$ | $6\mathrm{n}\mathrm{V}/\sqrt{\mathrm{H}\mathrm{z}}$ | ${\mathit{i}}_{n}$ | $1\mathrm{p}\mathrm{A}/\sqrt{\mathrm{H}\mathrm{z}}$ |

${\mathit{G}}_{n}$ | $9.6\text{}\mathrm{d}\mathrm{B}$ |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wang, F.; Krause, S.; Hug, J.; Rembe, C.
A Contactless Laser Doppler Strain Sensor for Fatigue Testing with Resonance-Testing Machine. *Sensors* **2021**, *21*, 319.
https://doi.org/10.3390/s21010319

**AMA Style**

Wang F, Krause S, Hug J, Rembe C.
A Contactless Laser Doppler Strain Sensor for Fatigue Testing with Resonance-Testing Machine. *Sensors*. 2021; 21(1):319.
https://doi.org/10.3390/s21010319

**Chicago/Turabian Style**

Wang, Fangjian, Steffen Krause, Joachim Hug, and Christian Rembe.
2021. "A Contactless Laser Doppler Strain Sensor for Fatigue Testing with Resonance-Testing Machine" *Sensors* 21, no. 1: 319.
https://doi.org/10.3390/s21010319