Abstract

In this Letter, an enhanced laser speckle optical sensor (LSOS) for nondestructive, noncontact, and high-accuracy strain measurement has been developed. Subsystems of laser beam shaping and telecentric imaging were incorporated into the LSOS to achieve optimized speckle patterns, and a field-of-view (FOV) separation was introduced to extend sensor gauge length. Validation tests confirmed that the LSOS achieved consistent results with resistive strain gauges in laboratory conditions with maximum RMS error (RMSE) of $ 9.44\;\unicode{x00B5} \unicode{x03B5} $. Sensing practicality was demonstrated in field tests. The results showed that the LSOS is capable of achieving accurate strain measurements in an external environment with maximum RMSE of $ 13.34\;\unicode{x00B5}\unicode{x03B5} $.

© 2020 Optical Society of America

Mechanical strain measured by changes in lengths is fundamentally significant in structural health monitoring. Available studies have shown that accurate strain sensing can be achieved by contact sensing devices: clip-on extensometers [1], resistive strain gauges [2], or fiber optic sensors [3]. However, the applications of clip-on extensometers are limited by specimen dimensions and travel distances. The installations of resistive strain gauges and fiber optic sensors require tedious specimen surface preparation and have no flexibility to adjust after their placement [4,5].

To address limitations of contact sensing techniques, a video extensometer based on digital image correlation (DIC) has been developed for noncontact and strain sensing in mechanical tests [6,7]. However, the accuracy of conventional DIC measurement is sensitive to out-of-plane movements and the quality of speckle patterns. Zhu et al. [8] introduced a dual-reflector-based DIC system to reduce the adverse effects of out-of-plane motions. However, the dual-reflector-based DIC system requires the access of both sides of the specimen, which is not always possible in practical applications. Su et al. [9] quantified the effects of speckle qualities on DIC accuracy and presented a few high-quality templates for speckle fabrication. However, the quality of speckle painting is easily affected by the air pressure, nozzle size, moisture, or paint viscosity [10] and is operator dependent. Novel speckle fabrication techniques such as water transfer printing and laser engraving have been introduced to improve the quality of speckle patterns [11,12]. Nevertheless, water transfer printing is not suitable for speckle fabrication on structures with complex features, and laser engraving may introduce excessive thermal stresses, which could damage the surface of the specimen [12]. Therefore, developing a noncontact and nondestructive optical system using an advanced speckle fabrication approach has profound implications for the structural health monitoring.

Laser speckle formed by illuminating an optically rough surface with coherent light is a nondestructive alternative to artificial speckles [13] and free of surface damage, spalling of paints, and speckle discolouration at elevated temperatures. Although the pioneering work done by Yamaguchi showed the technical feasibility in strain sensing [14], his study also revealed the difficulties of applying laser speckle to practical applications due to limited sensing ranges, short gauge lengths, and low robustness against out-of-plane motions. Thus, further improvements are required to address these challenges.

In this Letter, an enhanced laser speckle optical sensor (LSOS) has been developed as an alternative to commercialized contact strain sensors and artificial speckle-based DIC. This LSOS incorporates a laser beam shaping system, a dual field-of-view (FOV) design, and a telecentric imaging system to achieve optimized laser speckle patterns, adjustable gauge length, and high tolerance to out-of-plane motions, respectively. These enhancements enabled the LSOS to achieve accurate strain sensing in laboratory and field conditions.

 figure: Fig. 1.

Fig. 1. Optical configurations of dual-FOV laser speckle imaging system for sensing of strain.

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Tables Icon

Table 1. Specifications of Critical Optical Parts

Figure 1 shows the optical configuration of the enhanced LSOS with three subsystems, and Table 1 summarizes the specifications of critical components. A unique paired laser configuration was employed in the subsystem for profile shaping. A 630 nm visible laser was used to maintain the visibility for positioning and adjusting gauge length along with a 980 nm infrared laser, which produces speckle patterns for image correlation. Here, a 980 nm laser was chosen for speckle fabrication as it can produce 1.56 times larger speckle radius compared to that of a 630 nm laser (without using an excessively large numerical aperture). Thus, optimal speckle size and the present CCD frame rate can achieve a working distance up to 5 m. The 980 nm laser beam was in turn expanded, attenuated, and split using a expander, an apodizing filter, and a nonpolarizing splitter, respectively. The expander increased the diameter of the laser beam by 3 times, and the apodizing filter reshaped the Gaussian laser input into a constant-intensity and near-flattop beam profile. The iris was employed to control the beam size and clean the intensity noise close to the edge of the beam profile. A nonpolarizing splitter was employed to provide a 50:50 splitting. One of the sub-beams was absorbed by a block, and the other one was directed to the subsystem of FOV separation, which consists of a polarizing splitter (50:50 splitting), two half-blocks, and three mirrors. Here, half-blocks absorbed half of their respective beams after splitting to avoid the overlapping of reflected waves from the illuminated area; thus, speckle patterns at each FOVs can be simultaneously captured by a single CCD camera. Since the laser beams directed from mirror 1 and 3 are perpendicular to the specimen surface, adjustable gauge length can be achieved by changing the distance between these mirrors. The telecentric lens is beneficial in eliminating out-of-plane motions [15] and forms part of the subsystem of telecentric imaging with an extender ($ 3 \times $) and a bandpass filter. The extender makes the LSOS compact while tripling the existing focal length to between 15–300 mm, thus achieving a working distance of between 0.015–5 m. Moreover, the bandpass filter blocks the reflected waves of 630 nm but transmits the 980 nm waves to the CCD.

Unlike artificial speckle patterns, laser speckle as a light phenomenon exhibits tremendous flexibilities in adjusting speckle size to achieve optimal CCD sampling by controlling optical parameters, given by Ref. [16],

$${d_{\rm sp}} = 1.22\lambda {F_b}( {1 + M} ),$$
where $ {d_{\rm sp}} $, $ \lambda $, $ {F_b} $, and $ M $ denote the laser speckle radius, the laser wavelength, numerical aperture, and the magnification of the optical system, respectively. To determine the level of speckle sampling, zero-mean normalized cross-correlation (ZNCC) based autocorrelation in Eq. (2) was employed to estimate average speckle radius of laser speckle patterns, which is measured at the half-width of the half-maximum ZNCC intensity [9]
$${C} = \frac{{\sum \sum \left( {f\left[ {x,y} \right] - \bar f} \right)\left( {g\left[ {x,y} \right] - \bar g} \right)}}{{\sqrt {\sum \sum {{\left( {f\left[ {x,y} \right] - \bar f} \right)}^2}} \sqrt {\sum \sum {{\left( {g\left[ {x,y} \right] - \bar g} \right)}^2}} }},$$
where $ f[ {x,y} ] $, $ g[ {x,y} ] $ represent the intensity values for reference and target laser speckle patterns, respectively; $ \bar f $ and $ \bar g $ denote their corresponding mean intensity values, respectively.

Figures 2(a)2(c) show typical laser speckle patterns with inferior, optimal, and oversampling, respectively. All their corresponding 2D fast Fourier transform (FFT) power spectra show excellent nonperiodic and isotropy properties of laser speckles, which are desired for accurate displacement mapping [17]. Figure 2(d) shows that a fine speckle pattern exhibits a clear and sharp correlation peak when the pattern matches while the image correlation drops significantly when the speckles coarsen. In addition, the autocorrelation profiles in the $x$ direction coincide well with those in the $y$ direction [such as PA $x$-Direct and PA $y$-Direct in Fig. 2(d)], indicating that sizes of laser speckle estimated in both directions are consistent.

 figure: Fig. 2.

Fig. 2. (a)–(c) Laser speckle patterns with inferior, optimal, and oversampling, respectively, and their 2D-FFT (insets); (d) ZNNC-based autocorrelation of speckle patterns with inferior, optical, and oversampling; (e) the effects of laser speckle radii on pattern qualities.

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Numerical experiments have been performed to further quantify the effects of laser speckle radii on measurement accuracy by creating a series of numerically translated patterns with additive Gaussian white noise (repetition of noise addition $ I = 500 $ times and standard deviation $ \sigma = 0.01 $). A series of laser speckle patterns ($ 512 \times 512\;{\rm pixels} $) with average speckle radii ranging from 1 to 5 pixels at an increment of 0.5 pixels was captured. Their average laser speckle sizes were controlled by adjusting the aperture size according to Eq. (1) and measured using ZNCC-based autocorrelation. Inverse compositional Gauss–Newton (IC–GN) algorithms [18] using the cubic B-spline interpolation [19], the zero-order shape function [20], and the sum of squared differences criterion [20] were employed to obtain their corresponding displacements of each numerically translated laser speckle patterns. The subset and step sizes for image registration were assigned to be 31 by 31 pixels and 15 pixels, respectively. The mean bias errors, standard deviation errors, and total errors in displacement measurement were computed using the methods in Ref. [19].

Figure 2(d) shows the effects of average laser speckle radii on maximum measurement errors of displacement. Relatively small speckle radii ($ {\leqslant}1.7 $pixels) were found to produce low standard deviation errors and large mean bias errors in displacement measurements, while relatively large speckle radii ($ {\geqslant}3.0 $pixels) will raise the standard deviation errors and reduce the mean bias errors in displacement measurements. These errors should be considered and become significant with short gauge length. The optimal laser speckle sizes with relatively low mean bias error and standard deviation error were found between 1.7 and 3 pixels. These findings are consistent with the work of Sutton et al. [21] based on artificial speckles and the theoretical estimation of Su et al. [19] based on synthetic speckles. Once the optimal speckle sampling was achieved, two displacement vectors ($ {u_a}(t) $ and $ {u_b}(t) $) of each laser speckle pattern under the illumination areas and sensor gauge length ($ L $) were employed to determine the axial strain using $ \unicode{x03B5} (t) = [ {{u_a}(t) - {u_b}(t)} ]/L $.

 figure: Fig. 3.

Fig. 3. Experimental setup of LSOS validation tests.

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 figure: Fig. 4.

Fig. 4. (a) and (c) Strain results under ramp and sine wave loads, respectively; (b) and (d) corresponding strain errors.

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Laboratory validation tests were conducted to demonstrate the sensing performance of LSOS. Figure 3 shows the experimental setup of the uniaxial tensile tests. Three resistive strain gauges (BF350-3AA $ 350\Omega $) were attached to the back of the aluminium specimen ($ 200\;{\rm mm} \times 18\;{\rm mm} \times 2\;{\rm mm} $) and recorded with a sampling frequency of 1 kHz using NI 9236 data acquisition (DAQ). The LSOS was mounded to a servohydraulic test system at a working distance of 40 mm from the specimen surface. The distance between two laser spots is defined as the gauge length (60 mm). The laser speckle pattern was focused using the telecentric lens and then optimized by adjusting its aperture, which resulted in a spatial resolution of 54.50 pixels/mm. The CCD frame rate was assigned to be 200 fps via ThorCam Graphical User Interface. To determine the displacement of laser spots, IC-GN algorithms were employed to process laser speckle patterns using a subset size of 35 by 35 pixels with a step size of 10 pixels. The strain data derived from displacements were spline interpolated to obtain sufficient data points for error calculations. At the start, the specimen was preloaded by 300 N to ensure the specimen was fully stretched. Then, the accuracy of the LSOS was evaluated by applying two different load signals: ramp and sine waves, respectively. The loading and unloading cycles were performed at various strain rates (from 8 to $ 32\;\unicode{x00B5} \unicode{x03B5} /{\rm s} $ with an increment of $ 8\;\unicode{x00B5} \unicode{x03B5} /{\rm s} $) using displacement control.

 figure: Fig. 5.

Fig. 5. (a) Setup of field tests for strain monitoring on a rail track; comparisons between strain gauges and LSOS measurement. (b) Test 1, train coach travels from left to right; (c) Test 2, train coach travels from right to left.

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Figures 4(a) and 4(c) show comparisons between LSOS and resistive strain gauge measurements under ramp and sine wave loads, respectively. Figures 4(b) and 4(d) show strain errors of LSOS measurements compared to those of resistive strain gauge data, in which good agreement was found in both loading profiles. In all tests, the strain errors fell within the range of $ \pm 30\;\unicode{x00B5} \unicode{x03B5} $, while slightly larger strain errors were observed at peaks of both ramp and sine wave signals, where the strain magnitudes were higher than $ 400\;\unicode{x00B5} \unicode{x03B5} $. The mean absolute error (MAE) and RMS error (RMSE) also increased slightly with the increase of strain magnitudes. This can be explained as the large deformation causing minor changes in surface features, which in turn changes the laser speckle distributions. The MAEs and RMSEs in validation tests were found in the range of $ 6.23 - 8.69\;\unicode{x00B5} \unicode{x03B5} $ and $ 6.82 - 9.44\;\unicode{x00B5} \unicode{x03B5} $, respectively. These errors are relatively low compared with the magnitudes of applied strain.

Field tests were conducted to evaluate the performance of LSOS for monitoring the strain response of rail track subjected to wheel loads from a 10 m long train coach weighing 20 tons, as shown in Fig. 5(a). Three resistive strain gauges were attached to the railhead at 15 mm below the top surface of the rail with a 10 mm horizontal separation between them. The strain responses from three strain gauges were sampled for a period of 10 s at 5 kHz and then averaged to provide a comparison with LSOS measurements. The LSOS was placed 1.5 m away from the rail surface. A gradienter was employed to ensure the LSOS is placed horizontally on the ground. The gauge length of our LSOS was adjusted to be 60 mm, which corresponds to the location where the resistive strain gauges measure. The CCD frame rate was configured at 200 fps, and the telecentric lens was adjusted to achieve optimal laser speckle pattern with a spatial resolution of 23.42 pixels/mm. The subset size and step size used for in situ tests were the same as those used in validation tests. The strains measured by LSOS were spline interpolated for error calculations.

Figures 5(b) and 5(c) show the comparison between resistive strain gauges and LSOS measurements in field tests. Both strain gauges and LSOS data showed four peak signals in two tests corresponding to four wheels traveling to-and-fro over the testing site. During the measurement, the railhead mainly experienced compressive strain up to ${-}280\;\unicode{x00B5} \unicode{x03B5} $ at peak signals. Slight tensile strains up to $ 70\;\unicode{x00B5} \unicode{x03B5} $ were also observed at the railhead, which were introduced by the wheel loads applied to the track interval preceding the measurement site. A small number of instantaneously abnormal strain responses was found in resistive strain gauge signals, which could be associated with impact loads due to wheel irregularities or rail imperfections. The MAEs of strain results in field test 1 and 2 were $ 9.93\;\unicode{x00B5} \unicode{x03B5} $ and $ 11.29\;\unicode{x00B5} \unicode{x03B5} $, respectively, and the RMSEs in both tests were found to be $ 11.83\;\unicode{x00B5} \unicode{x03B5} $ and $ 13.34\;\unicode{x00B5} \unicode{x03B5} $, respectively. Slightly larger discrepancies were observed at peaks of strain signals [enlarged view in Figs. 5(b) and 5(c)] with maximum strain errors up to $ \pm 50\;\unicode{x00B5} \unicode{x03B5} $, which could be attributed to the limited frame rate of the CCD camera. The baseline strain error in both field tests was found to be approximately $ \pm 25\;\unicode{x00B5} \unicode{x03B5} $, which can be further reduced via the elimination of ambient vibration by placing the LSOS on vibration suppression pads.

In conclusion, an enhanced LSOS has been developed for nondestructive, noncontact, and highly accurate strain sensing. Field tests have confirmed that LSOS can replace conventional resistive strain gauges with advantages being noncontact and having flexible target positioning, adjustable gauge length, and good accuracy. This enhanced LSOS can be further applied to assess the structural integrity of other engineering structures. However, it may not be suitable to work on mirror surfaces, light absorption surfaces, or transparency materials.

Funding

Rail Manufacturing CRC (R3.7.7); National Natural Science Foundation of China (61775187).

Disclosures

The authors declare no conflicts of interest.

REFERENCES

1. J. Tabin and M. Prącik, Measurement 63, 176 (2015). [CrossRef]  

2. M. R. Viotti, A. A. Gonçalves Jr., and W. A. Kapp, Appl. Opt. 50, 1014 (2011). [CrossRef]  

3. Z. Liu, C. Wu, M.-L. V. Tse, C. Lu, and H.-Y. Tam, Opt. Lett. 38, 1385 (2013). [CrossRef]  

4. L. J. Butler, J. Xu, P. He, N. Gibbons, S. Dirar, C. R. Middleton, and M. Z. Elshafie, Struct. Health Monit. 17, 635 (2018). [CrossRef]  

5. J. R. Edwards, Z. Gao, H. E. Wolf, M. S. Dersch, and Y. Qian, Measurement 111, 197 (2017). [CrossRef]  

6. L. Tian, L. Yu, and B. Pan, Opt. Laser Eng. 110, 272 (2018). [CrossRef]  

7. B. Dong, C. Li, and B. Pan, Opt. Lett. 44, 4499 (2019). [CrossRef]  

8. F. Zhu, P. Bai, Y. Gong, D. Lei, and X. He, Measurement 119, 18 (2018). [CrossRef]  

9. Y. Su, Q. Zhang, Z. Fang, Y. Wang, Y. Liu, and S. Wu, Opt. Laser Eng. 114, 60 (2019). [CrossRef]  

10. G. Lionello and L. Cristofolini, Meas. Sci. Technol. 25, 107001 (2014). [CrossRef]  

11. Z. Chen, C. Quan, F. Zhu, and X. He, Meas. Sci. Technol. 26, 095201 (2015). [CrossRef]  

12. Y. Hu, F. Liu, W. Zhu, and J. Zhu, Mech. Mater. 121, 10 (2018). [CrossRef]  

13. J. C. Dainty, Laser Speckle and Related Phenomena (Springer, 2013), Vol. 9.

14. I. Yamaguchi, J. Phys. E 14, 1270 (1981). [CrossRef]  

15. B. Pan, L. Yu, and D. Wu, Exp. Mech. 53, 1719 (2013). [CrossRef]  

16. P. Rastogi, Digital Optical Measurement Techniques and Applications (Artech House, 2015).

17. Y. Dong and B. Pan, Exp. Mech. 57, 1161 (2017). [CrossRef]  

18. S. Baker and I. Matthews, Int. J. Comput. Vis. 56, 221 (2004). [CrossRef]  

19. Y. Su, Q. Zhang, X. Xu, and Z. Gao, Opt. Laser Eng. 86, 132 (2016). [CrossRef]  

20. B. Pan, H. Xie, Z. Wang, K. Qian, and Z. Wang, Opt. Express 16, 7037 (2008). [CrossRef]  

21. M. A. Sutton, J. J. Orteu, and H. Schreier, Image Correlation for Shape, Motion and Deformation Measurements: Basic Concepts, Theory and Applications (Springer, 2009).

References

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  1. J. Tabin and M. Prącik, Measurement 63, 176 (2015).
    [Crossref]
  2. M. R. Viotti, A. A. Gonçalves Jr., and W. A. Kapp, Appl. Opt. 50, 1014 (2011).
    [Crossref]
  3. Z. Liu, C. Wu, M.-L. V. Tse, C. Lu, and H.-Y. Tam, Opt. Lett. 38, 1385 (2013).
    [Crossref]
  4. L. J. Butler, J. Xu, P. He, N. Gibbons, S. Dirar, C. R. Middleton, and M. Z. Elshafie, Struct. Health Monit. 17, 635 (2018).
    [Crossref]
  5. J. R. Edwards, Z. Gao, H. E. Wolf, M. S. Dersch, and Y. Qian, Measurement 111, 197 (2017).
    [Crossref]
  6. L. Tian, L. Yu, and B. Pan, Opt. Laser Eng. 110, 272 (2018).
    [Crossref]
  7. B. Dong, C. Li, and B. Pan, Opt. Lett. 44, 4499 (2019).
    [Crossref]
  8. F. Zhu, P. Bai, Y. Gong, D. Lei, and X. He, Measurement 119, 18 (2018).
    [Crossref]
  9. Y. Su, Q. Zhang, Z. Fang, Y. Wang, Y. Liu, and S. Wu, Opt. Laser Eng. 114, 60 (2019).
    [Crossref]
  10. G. Lionello and L. Cristofolini, Meas. Sci. Technol. 25, 107001 (2014).
    [Crossref]
  11. Z. Chen, C. Quan, F. Zhu, and X. He, Meas. Sci. Technol. 26, 095201 (2015).
    [Crossref]
  12. Y. Hu, F. Liu, W. Zhu, and J. Zhu, Mech. Mater. 121, 10 (2018).
    [Crossref]
  13. J. C. Dainty, Laser Speckle and Related Phenomena (Springer, 2013), Vol. 9.
  14. I. Yamaguchi, J. Phys. E 14, 1270 (1981).
    [Crossref]
  15. B. Pan, L. Yu, and D. Wu, Exp. Mech. 53, 1719 (2013).
    [Crossref]
  16. P. Rastogi, Digital Optical Measurement Techniques and Applications (Artech House, 2015).
  17. Y. Dong and B. Pan, Exp. Mech. 57, 1161 (2017).
    [Crossref]
  18. S. Baker and I. Matthews, Int. J. Comput. Vis. 56, 221 (2004).
    [Crossref]
  19. Y. Su, Q. Zhang, X. Xu, and Z. Gao, Opt. Laser Eng. 86, 132 (2016).
    [Crossref]
  20. B. Pan, H. Xie, Z. Wang, K. Qian, and Z. Wang, Opt. Express 16, 7037 (2008).
    [Crossref]
  21. M. A. Sutton, J. J. Orteu, and H. Schreier, Image Correlation for Shape, Motion and Deformation Measurements: Basic Concepts, Theory and Applications (Springer, 2009).

2019 (2)

B. Dong, C. Li, and B. Pan, Opt. Lett. 44, 4499 (2019).
[Crossref]

Y. Su, Q. Zhang, Z. Fang, Y. Wang, Y. Liu, and S. Wu, Opt. Laser Eng. 114, 60 (2019).
[Crossref]

2018 (4)

Y. Hu, F. Liu, W. Zhu, and J. Zhu, Mech. Mater. 121, 10 (2018).
[Crossref]

F. Zhu, P. Bai, Y. Gong, D. Lei, and X. He, Measurement 119, 18 (2018).
[Crossref]

L. Tian, L. Yu, and B. Pan, Opt. Laser Eng. 110, 272 (2018).
[Crossref]

L. J. Butler, J. Xu, P. He, N. Gibbons, S. Dirar, C. R. Middleton, and M. Z. Elshafie, Struct. Health Monit. 17, 635 (2018).
[Crossref]

2017 (2)

J. R. Edwards, Z. Gao, H. E. Wolf, M. S. Dersch, and Y. Qian, Measurement 111, 197 (2017).
[Crossref]

Y. Dong and B. Pan, Exp. Mech. 57, 1161 (2017).
[Crossref]

2016 (1)

Y. Su, Q. Zhang, X. Xu, and Z. Gao, Opt. Laser Eng. 86, 132 (2016).
[Crossref]

2015 (2)

Z. Chen, C. Quan, F. Zhu, and X. He, Meas. Sci. Technol. 26, 095201 (2015).
[Crossref]

J. Tabin and M. Prącik, Measurement 63, 176 (2015).
[Crossref]

2014 (1)

G. Lionello and L. Cristofolini, Meas. Sci. Technol. 25, 107001 (2014).
[Crossref]

2013 (2)

2011 (1)

2008 (1)

2004 (1)

S. Baker and I. Matthews, Int. J. Comput. Vis. 56, 221 (2004).
[Crossref]

1981 (1)

I. Yamaguchi, J. Phys. E 14, 1270 (1981).
[Crossref]

Bai, P.

F. Zhu, P. Bai, Y. Gong, D. Lei, and X. He, Measurement 119, 18 (2018).
[Crossref]

Baker, S.

S. Baker and I. Matthews, Int. J. Comput. Vis. 56, 221 (2004).
[Crossref]

Butler, L. J.

L. J. Butler, J. Xu, P. He, N. Gibbons, S. Dirar, C. R. Middleton, and M. Z. Elshafie, Struct. Health Monit. 17, 635 (2018).
[Crossref]

Chen, Z.

Z. Chen, C. Quan, F. Zhu, and X. He, Meas. Sci. Technol. 26, 095201 (2015).
[Crossref]

Cristofolini, L.

G. Lionello and L. Cristofolini, Meas. Sci. Technol. 25, 107001 (2014).
[Crossref]

Dainty, J. C.

J. C. Dainty, Laser Speckle and Related Phenomena (Springer, 2013), Vol. 9.

Dersch, M. S.

J. R. Edwards, Z. Gao, H. E. Wolf, M. S. Dersch, and Y. Qian, Measurement 111, 197 (2017).
[Crossref]

Dirar, S.

L. J. Butler, J. Xu, P. He, N. Gibbons, S. Dirar, C. R. Middleton, and M. Z. Elshafie, Struct. Health Monit. 17, 635 (2018).
[Crossref]

Dong, B.

Dong, Y.

Y. Dong and B. Pan, Exp. Mech. 57, 1161 (2017).
[Crossref]

Edwards, J. R.

J. R. Edwards, Z. Gao, H. E. Wolf, M. S. Dersch, and Y. Qian, Measurement 111, 197 (2017).
[Crossref]

Elshafie, M. Z.

L. J. Butler, J. Xu, P. He, N. Gibbons, S. Dirar, C. R. Middleton, and M. Z. Elshafie, Struct. Health Monit. 17, 635 (2018).
[Crossref]

Fang, Z.

Y. Su, Q. Zhang, Z. Fang, Y. Wang, Y. Liu, and S. Wu, Opt. Laser Eng. 114, 60 (2019).
[Crossref]

Gao, Z.

J. R. Edwards, Z. Gao, H. E. Wolf, M. S. Dersch, and Y. Qian, Measurement 111, 197 (2017).
[Crossref]

Y. Su, Q. Zhang, X. Xu, and Z. Gao, Opt. Laser Eng. 86, 132 (2016).
[Crossref]

Gibbons, N.

L. J. Butler, J. Xu, P. He, N. Gibbons, S. Dirar, C. R. Middleton, and M. Z. Elshafie, Struct. Health Monit. 17, 635 (2018).
[Crossref]

Gonçalves Jr., A. A.

Gong, Y.

F. Zhu, P. Bai, Y. Gong, D. Lei, and X. He, Measurement 119, 18 (2018).
[Crossref]

He, P.

L. J. Butler, J. Xu, P. He, N. Gibbons, S. Dirar, C. R. Middleton, and M. Z. Elshafie, Struct. Health Monit. 17, 635 (2018).
[Crossref]

He, X.

F. Zhu, P. Bai, Y. Gong, D. Lei, and X. He, Measurement 119, 18 (2018).
[Crossref]

Z. Chen, C. Quan, F. Zhu, and X. He, Meas. Sci. Technol. 26, 095201 (2015).
[Crossref]

Hu, Y.

Y. Hu, F. Liu, W. Zhu, and J. Zhu, Mech. Mater. 121, 10 (2018).
[Crossref]

Kapp, W. A.

Lei, D.

F. Zhu, P. Bai, Y. Gong, D. Lei, and X. He, Measurement 119, 18 (2018).
[Crossref]

Li, C.

Lionello, G.

G. Lionello and L. Cristofolini, Meas. Sci. Technol. 25, 107001 (2014).
[Crossref]

Liu, F.

Y. Hu, F. Liu, W. Zhu, and J. Zhu, Mech. Mater. 121, 10 (2018).
[Crossref]

Liu, Y.

Y. Su, Q. Zhang, Z. Fang, Y. Wang, Y. Liu, and S. Wu, Opt. Laser Eng. 114, 60 (2019).
[Crossref]

Liu, Z.

Lu, C.

Matthews, I.

S. Baker and I. Matthews, Int. J. Comput. Vis. 56, 221 (2004).
[Crossref]

Middleton, C. R.

L. J. Butler, J. Xu, P. He, N. Gibbons, S. Dirar, C. R. Middleton, and M. Z. Elshafie, Struct. Health Monit. 17, 635 (2018).
[Crossref]

Orteu, J. J.

M. A. Sutton, J. J. Orteu, and H. Schreier, Image Correlation for Shape, Motion and Deformation Measurements: Basic Concepts, Theory and Applications (Springer, 2009).

Pan, B.

B. Dong, C. Li, and B. Pan, Opt. Lett. 44, 4499 (2019).
[Crossref]

L. Tian, L. Yu, and B. Pan, Opt. Laser Eng. 110, 272 (2018).
[Crossref]

Y. Dong and B. Pan, Exp. Mech. 57, 1161 (2017).
[Crossref]

B. Pan, L. Yu, and D. Wu, Exp. Mech. 53, 1719 (2013).
[Crossref]

B. Pan, H. Xie, Z. Wang, K. Qian, and Z. Wang, Opt. Express 16, 7037 (2008).
[Crossref]

Pracik, M.

J. Tabin and M. Prącik, Measurement 63, 176 (2015).
[Crossref]

Qian, K.

Qian, Y.

J. R. Edwards, Z. Gao, H. E. Wolf, M. S. Dersch, and Y. Qian, Measurement 111, 197 (2017).
[Crossref]

Quan, C.

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Appl. Opt. (1)

Exp. Mech. (2)

B. Pan, L. Yu, and D. Wu, Exp. Mech. 53, 1719 (2013).
[Crossref]

Y. Dong and B. Pan, Exp. Mech. 57, 1161 (2017).
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[Crossref]

J. Phys. E (1)

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[Crossref]

Meas. Sci. Technol. (2)

G. Lionello and L. Cristofolini, Meas. Sci. Technol. 25, 107001 (2014).
[Crossref]

Z. Chen, C. Quan, F. Zhu, and X. He, Meas. Sci. Technol. 26, 095201 (2015).
[Crossref]

Measurement (3)

J. R. Edwards, Z. Gao, H. E. Wolf, M. S. Dersch, and Y. Qian, Measurement 111, 197 (2017).
[Crossref]

J. Tabin and M. Prącik, Measurement 63, 176 (2015).
[Crossref]

F. Zhu, P. Bai, Y. Gong, D. Lei, and X. He, Measurement 119, 18 (2018).
[Crossref]

Mech. Mater. (1)

Y. Hu, F. Liu, W. Zhu, and J. Zhu, Mech. Mater. 121, 10 (2018).
[Crossref]

Opt. Express (1)

Opt. Laser Eng. (3)

L. Tian, L. Yu, and B. Pan, Opt. Laser Eng. 110, 272 (2018).
[Crossref]

Y. Su, Q. Zhang, Z. Fang, Y. Wang, Y. Liu, and S. Wu, Opt. Laser Eng. 114, 60 (2019).
[Crossref]

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[Crossref]

Opt. Lett. (2)

Struct. Health Monit. (1)

L. J. Butler, J. Xu, P. He, N. Gibbons, S. Dirar, C. R. Middleton, and M. Z. Elshafie, Struct. Health Monit. 17, 635 (2018).
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Other (3)

J. C. Dainty, Laser Speckle and Related Phenomena (Springer, 2013), Vol. 9.

P. Rastogi, Digital Optical Measurement Techniques and Applications (Artech House, 2015).

M. A. Sutton, J. J. Orteu, and H. Schreier, Image Correlation for Shape, Motion and Deformation Measurements: Basic Concepts, Theory and Applications (Springer, 2009).

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Figures (5)

Fig. 1.
Fig. 1. Optical configurations of dual-FOV laser speckle imaging system for sensing of strain.
Fig. 2.
Fig. 2. (a)–(c) Laser speckle patterns with inferior, optimal, and oversampling, respectively, and their 2D-FFT (insets); (d) ZNNC-based autocorrelation of speckle patterns with inferior, optical, and oversampling; (e) the effects of laser speckle radii on pattern qualities.
Fig. 3.
Fig. 3. Experimental setup of LSOS validation tests.
Fig. 4.
Fig. 4. (a) and (c) Strain results under ramp and sine wave loads, respectively; (b) and (d) corresponding strain errors.
Fig. 5.
Fig. 5. (a) Setup of field tests for strain monitoring on a rail track; comparisons between strain gauges and LSOS measurement. (b) Test 1, train coach travels from left to right; (c) Test 2, train coach travels from right to left.

Tables (1)

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Table 1. Specifications of Critical Optical Parts

Equations (2)

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d s p = 1.22 λ F b ( 1 + M ) ,
C = ( f [ x , y ] f ¯ ) ( g [ x , y ] g ¯ ) ( f [ x , y ] f ¯ ) 2 ( g [ x , y ] g ¯ ) 2 ,

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