Abstract

In this study, we propose a second-order moiré method by performing digital sampling at two stages to realize high-accuracy deformation measurement in a wide field of view, where a grid image is recorded at a low magnification. Simulations have verified that this method has high strain measurement accuracy when the grid pitch is close to or even smaller than two pixels for both parallel and oblique grids with random noise. As an application, the two-dimensional microscale strain distributions of a carbon fiber reinforced plastic specimen when the grid pitch was about 2.1 pixels were presented. Shear strain concentration was detected before an interlaminar crack emerged, and tensile strain concentration was found prior to the occurrence of a transverse crack. The proposed method makes the two-step phase-shifting technique achieved indirectly, not only enlarging the field of view, but also maintaining the measurement accuracy.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. T. Chu, W. Ranson, and M. A. Sutton, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25(3), 232–244 (1985).
    [Crossref]
  2. O. J. Løkberg and K. Høgmoen, “Vibration phase mapping using electronic speckle pattern interferometry,” Appl. Opt. 15(11), 2701–2704 (1976).
    [Crossref]
  3. M. Hÿch and L. Potez, “Geometric phase analysis of high-resolution electron microscopy images of antiphase domains: example Cu3Au,” Philos. Mag. A 76(6), 1119–1138 (1997).
    [Crossref]
  4. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72(1), 156–160 (1982).
    [Crossref]
  5. Q. Kemao, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43(13), 2695–2702 (2004).
    [Crossref]
  6. S. Avril, A. Vautrin, and Y. Surrel, “Grid method: application to the characterization of cracks,” Exp. Mech. 44(1), 37–43 (2004).
    [Crossref]
  7. C. Li, H. Xie, Z. Liu, S. Wang, and L. Li, “Experimental study on stress concentration of nickel-base superalloy at elevated temperatures with an in situ SEM system,” Mech. Mater. 103, 87–94 (2016).
    [Crossref]
  8. S. Kishimoto, M. Egashira, and N. Shinya, “Microcreep deformation measurements by a moiré method using electron beam lithography and electron beam scan,” Opt. Eng. 32(3), 522–526 (1993).
    [Crossref]
  9. H. Xie, H. Shang, F. Dai, B. Li, and Y. Xing, “Phase shifting SEM moiré method,” Opt. Laser Technol. 36(4), 291–297 (2004).
    [Crossref]
  10. M. Servin, M. Padilla, G. Garnica, and A. Gonzalez, “Profilometry of three-dimensional discontinuous solids by combining two-steps temporal phase unwrapping, co-phased profilometry and phase-shifting interferometry,” Opt. Laser. Eng. 87, 75–82 (2016).
    [Crossref]
  11. S. K. Debnath and Y. Park, “Real-time quantitative phase imaging with a spatial phase-shifting algorithm,” Opt. Lett. 36(23), 4677–4679 (2011).
    [Crossref]
  12. P. Ifju and B. Han, “Recent applications of moiré interferometry,” Exp. Mech. 50(8), 1129–1147 (2010).
    [Crossref]
  13. Q. Wang, S. Ri, H. Tsuda, and M. Koyama, “Optical full-field strain measurement method from wrapped sampling Moiré phase to minimize the influence of defects and its applications,” Opt. Laser. Eng. 110, 155–162 (2018).
    [Crossref]
  14. X. Chen and C.-C. Chang, “In-Plane Movement Measurement Technique Using Digital Sampling Moiré Method,” J. Bridge Eng. 24(4), 04019013 (2019).
    [Crossref]
  15. M. Fujigaki, A. Masaya, K. Shimo, and Y. Morimoto, “Dynamic shape and strain measurements of rotating tire using a sampling moiré method,” Opt. Eng. 50(10), 101506 (2011).
    [Crossref]
  16. Q. Wang and S. Kishimoto, “Simultaneous analysis of residual stress and stress intensity factor in a resist after UV-nanoimprint lithography based on electron moiré fringes,” J. Micromech. Microeng. 22(10), 105021 (2012).
    [Crossref]
  17. C. Li, Z. Liu, H. Xie, and D. Wu, “Novel 3D SEM Moiré method for micro height measurement,” Opt. Express 21(13), 15734–15746 (2013).
    [Crossref]
  18. H. Zhang, C. Wu, Z. Liu, and H. Xie, “A curved surface micro-moiré method and its application in evaluating curved surface residual stress,” Meas. Sci. Technol. 25(9), 095002 (2014).
    [Crossref]
  19. S. Yoneyama, P. G. Ifju, and S. E. Rohde, “Identifying through-thickness material properties of carbon-fiber-reinforced plastics using the virtual fields method combined with moiré interferometry,” Adv. Compos. Mater. 27(1), 1–17 (2018).
    [Crossref]
  20. J. Shao, Y. Ding, H. Tian, X. Li, X. Li, and H. Liu, “Digital moiré fringe measurement method for alignment in imprint lithography,” Opt. Laser Technol. 44(2), 446–451 (2012).
    [Crossref]
  21. Q. Wang, S. Kishimoto, X. Jiang, and Y. Yamauchi, “Formation of secondary Moiré patterns for characterization of nanoporous alumina structures in multiple domains with different orientations,” Nanoscale 5(6), 2285–2289 (2013).
    [Crossref]
  22. Q. Wang, S. Ri, and H. Tsuda, “Digital sampling Moiré as a substitute for microscope scanning Moiré for high-sensitivity and full-field deformation measurement at micron/nano scales,” Appl. Opt. 55(25), 6858–6865 (2016).
    [Crossref]
  23. F. Dai and Z. Wang, “Automatic fringe patterns analysis using digital processing tehniques: I fringe center method,” Acta Photonica Sin. 28, 700–706 (1999).
  24. M. Tang, H. Xie, Q. Wang, and J. Zhu, “Phase-shifting laser scanning confocal microscopy moiré method and its applications,” Meas. Sci. Technol. 21(5), 055110 (2010).
    [Crossref]
  25. E. Hack and J. Burke, “Invited review article: measurement uncertainty of linear phase-stepping algorithms,” Rev. Sci. Instrum. 82(6), 061101 (2011).
    [Crossref]
  26. C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Laser. Eng. 109, 23–59 (2018).
    [Crossref]
  27. J. Vargas, J. A. Quiroga, C. Sorzano, J. Estrada, and J. Carazo, “Two-step demodulation based on the Gram–Schmidt orthonormalization method,” Opt. Lett. 37(3), 443–445 (2012).
    [Crossref]
  28. W. Niu, L. Zhong, P. Sun, W. Zhang, and X. Lu, “Two-step phase retrieval algorithm based on the quotient of inner products of phase-shifting interferograms,” J. Opt. 17(8), 085703 (2015).
    [Crossref]
  29. S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50(4), 501–508 (2010).
    [Crossref]
  30. Q. Wang, S. Ri, H. Tsuda, M. Koyama, and K. Tsuzaki, “Two-dimensional Moire phase analysis for accurate strain distribution measurement and application in crack prediction,” Opt. Express 25(12), 13465–13480 (2017).
    [Crossref]
  31. Q. Zhang, H. Xie, Z. Liu, and W. Shi, “Sampling moiré method and its application to determine modulus of thermal barrier coatings under scanning electron microscope,” Opt. Laser. Eng. 107, 315–324 (2018).
    [Crossref]
  32. Q. Zhang, H. Xie, W. Shi, and B. Fan, “A novel sampling moiré method and its application for distortion calibration in scanning electron microscope,” Opt. Laser. Eng. 127, 105990 (2020).
    [Crossref]
  33. Z. Lei and Z. Wang, “Vibration testing parameters measured by sampling moire method,” Appl. Mech. Mater. 226-228, 1975–1980 (2012).
    [Crossref]
  34. S. Ri, Q. Wang, P. Xia, and H. Tsuda, “Spatiotemporal phase-shifting method for accurate phase analysis of fringe pattern,” J. Opt. 21(9), 095702 (2019).
    [Crossref]
  35. Y. Fukami, S. Ri, Q. Wang, H. Tsuda, R. Kitamura, and S. Ogihara, “Accuracy improvement of small strain distribution measurement based on the sampling moire method with multi-step filter processing,” in Asian Conference on Experimental Mechanics, 160195, 98–99 (2016).

2020 (1)

Q. Zhang, H. Xie, W. Shi, and B. Fan, “A novel sampling moiré method and its application for distortion calibration in scanning electron microscope,” Opt. Laser. Eng. 127, 105990 (2020).
[Crossref]

2019 (2)

X. Chen and C.-C. Chang, “In-Plane Movement Measurement Technique Using Digital Sampling Moiré Method,” J. Bridge Eng. 24(4), 04019013 (2019).
[Crossref]

S. Ri, Q. Wang, P. Xia, and H. Tsuda, “Spatiotemporal phase-shifting method for accurate phase analysis of fringe pattern,” J. Opt. 21(9), 095702 (2019).
[Crossref]

2018 (4)

Q. Wang, S. Ri, H. Tsuda, and M. Koyama, “Optical full-field strain measurement method from wrapped sampling Moiré phase to minimize the influence of defects and its applications,” Opt. Laser. Eng. 110, 155–162 (2018).
[Crossref]

Q. Zhang, H. Xie, Z. Liu, and W. Shi, “Sampling moiré method and its application to determine modulus of thermal barrier coatings under scanning electron microscope,” Opt. Laser. Eng. 107, 315–324 (2018).
[Crossref]

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Laser. Eng. 109, 23–59 (2018).
[Crossref]

S. Yoneyama, P. G. Ifju, and S. E. Rohde, “Identifying through-thickness material properties of carbon-fiber-reinforced plastics using the virtual fields method combined with moiré interferometry,” Adv. Compos. Mater. 27(1), 1–17 (2018).
[Crossref]

2017 (1)

2016 (3)

Q. Wang, S. Ri, and H. Tsuda, “Digital sampling Moiré as a substitute for microscope scanning Moiré for high-sensitivity and full-field deformation measurement at micron/nano scales,” Appl. Opt. 55(25), 6858–6865 (2016).
[Crossref]

M. Servin, M. Padilla, G. Garnica, and A. Gonzalez, “Profilometry of three-dimensional discontinuous solids by combining two-steps temporal phase unwrapping, co-phased profilometry and phase-shifting interferometry,” Opt. Laser. Eng. 87, 75–82 (2016).
[Crossref]

C. Li, H. Xie, Z. Liu, S. Wang, and L. Li, “Experimental study on stress concentration of nickel-base superalloy at elevated temperatures with an in situ SEM system,” Mech. Mater. 103, 87–94 (2016).
[Crossref]

2015 (1)

W. Niu, L. Zhong, P. Sun, W. Zhang, and X. Lu, “Two-step phase retrieval algorithm based on the quotient of inner products of phase-shifting interferograms,” J. Opt. 17(8), 085703 (2015).
[Crossref]

2014 (1)

H. Zhang, C. Wu, Z. Liu, and H. Xie, “A curved surface micro-moiré method and its application in evaluating curved surface residual stress,” Meas. Sci. Technol. 25(9), 095002 (2014).
[Crossref]

2013 (2)

Q. Wang, S. Kishimoto, X. Jiang, and Y. Yamauchi, “Formation of secondary Moiré patterns for characterization of nanoporous alumina structures in multiple domains with different orientations,” Nanoscale 5(6), 2285–2289 (2013).
[Crossref]

C. Li, Z. Liu, H. Xie, and D. Wu, “Novel 3D SEM Moiré method for micro height measurement,” Opt. Express 21(13), 15734–15746 (2013).
[Crossref]

2012 (4)

Q. Wang and S. Kishimoto, “Simultaneous analysis of residual stress and stress intensity factor in a resist after UV-nanoimprint lithography based on electron moiré fringes,” J. Micromech. Microeng. 22(10), 105021 (2012).
[Crossref]

J. Shao, Y. Ding, H. Tian, X. Li, X. Li, and H. Liu, “Digital moiré fringe measurement method for alignment in imprint lithography,” Opt. Laser Technol. 44(2), 446–451 (2012).
[Crossref]

J. Vargas, J. A. Quiroga, C. Sorzano, J. Estrada, and J. Carazo, “Two-step demodulation based on the Gram–Schmidt orthonormalization method,” Opt. Lett. 37(3), 443–445 (2012).
[Crossref]

Z. Lei and Z. Wang, “Vibration testing parameters measured by sampling moire method,” Appl. Mech. Mater. 226-228, 1975–1980 (2012).
[Crossref]

2011 (3)

E. Hack and J. Burke, “Invited review article: measurement uncertainty of linear phase-stepping algorithms,” Rev. Sci. Instrum. 82(6), 061101 (2011).
[Crossref]

M. Fujigaki, A. Masaya, K. Shimo, and Y. Morimoto, “Dynamic shape and strain measurements of rotating tire using a sampling moiré method,” Opt. Eng. 50(10), 101506 (2011).
[Crossref]

S. K. Debnath and Y. Park, “Real-time quantitative phase imaging with a spatial phase-shifting algorithm,” Opt. Lett. 36(23), 4677–4679 (2011).
[Crossref]

2010 (3)

P. Ifju and B. Han, “Recent applications of moiré interferometry,” Exp. Mech. 50(8), 1129–1147 (2010).
[Crossref]

M. Tang, H. Xie, Q. Wang, and J. Zhu, “Phase-shifting laser scanning confocal microscopy moiré method and its applications,” Meas. Sci. Technol. 21(5), 055110 (2010).
[Crossref]

S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50(4), 501–508 (2010).
[Crossref]

2004 (3)

H. Xie, H. Shang, F. Dai, B. Li, and Y. Xing, “Phase shifting SEM moiré method,” Opt. Laser Technol. 36(4), 291–297 (2004).
[Crossref]

Q. Kemao, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43(13), 2695–2702 (2004).
[Crossref]

S. Avril, A. Vautrin, and Y. Surrel, “Grid method: application to the characterization of cracks,” Exp. Mech. 44(1), 37–43 (2004).
[Crossref]

1999 (1)

F. Dai and Z. Wang, “Automatic fringe patterns analysis using digital processing tehniques: I fringe center method,” Acta Photonica Sin. 28, 700–706 (1999).

1997 (1)

M. Hÿch and L. Potez, “Geometric phase analysis of high-resolution electron microscopy images of antiphase domains: example Cu3Au,” Philos. Mag. A 76(6), 1119–1138 (1997).
[Crossref]

1993 (1)

S. Kishimoto, M. Egashira, and N. Shinya, “Microcreep deformation measurements by a moiré method using electron beam lithography and electron beam scan,” Opt. Eng. 32(3), 522–526 (1993).
[Crossref]

1985 (1)

T. Chu, W. Ranson, and M. A. Sutton, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25(3), 232–244 (1985).
[Crossref]

1982 (1)

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72(1), 156–160 (1982).
[Crossref]

1976 (1)

Avril, S.

S. Avril, A. Vautrin, and Y. Surrel, “Grid method: application to the characterization of cracks,” Exp. Mech. 44(1), 37–43 (2004).
[Crossref]

Burke, J.

E. Hack and J. Burke, “Invited review article: measurement uncertainty of linear phase-stepping algorithms,” Rev. Sci. Instrum. 82(6), 061101 (2011).
[Crossref]

Carazo, J.

Chang, C.-C.

X. Chen and C.-C. Chang, “In-Plane Movement Measurement Technique Using Digital Sampling Moiré Method,” J. Bridge Eng. 24(4), 04019013 (2019).
[Crossref]

Chen, Q.

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Laser. Eng. 109, 23–59 (2018).
[Crossref]

Chen, X.

X. Chen and C.-C. Chang, “In-Plane Movement Measurement Technique Using Digital Sampling Moiré Method,” J. Bridge Eng. 24(4), 04019013 (2019).
[Crossref]

Chu, T.

T. Chu, W. Ranson, and M. A. Sutton, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25(3), 232–244 (1985).
[Crossref]

Dai, F.

H. Xie, H. Shang, F. Dai, B. Li, and Y. Xing, “Phase shifting SEM moiré method,” Opt. Laser Technol. 36(4), 291–297 (2004).
[Crossref]

F. Dai and Z. Wang, “Automatic fringe patterns analysis using digital processing tehniques: I fringe center method,” Acta Photonica Sin. 28, 700–706 (1999).

Debnath, S. K.

Ding, Y.

J. Shao, Y. Ding, H. Tian, X. Li, X. Li, and H. Liu, “Digital moiré fringe measurement method for alignment in imprint lithography,” Opt. Laser Technol. 44(2), 446–451 (2012).
[Crossref]

Egashira, M.

S. Kishimoto, M. Egashira, and N. Shinya, “Microcreep deformation measurements by a moiré method using electron beam lithography and electron beam scan,” Opt. Eng. 32(3), 522–526 (1993).
[Crossref]

Estrada, J.

Fan, B.

Q. Zhang, H. Xie, W. Shi, and B. Fan, “A novel sampling moiré method and its application for distortion calibration in scanning electron microscope,” Opt. Laser. Eng. 127, 105990 (2020).
[Crossref]

Feng, S.

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Laser. Eng. 109, 23–59 (2018).
[Crossref]

Fujigaki, M.

M. Fujigaki, A. Masaya, K. Shimo, and Y. Morimoto, “Dynamic shape and strain measurements of rotating tire using a sampling moiré method,” Opt. Eng. 50(10), 101506 (2011).
[Crossref]

S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50(4), 501–508 (2010).
[Crossref]

Fukami, Y.

Y. Fukami, S. Ri, Q. Wang, H. Tsuda, R. Kitamura, and S. Ogihara, “Accuracy improvement of small strain distribution measurement based on the sampling moire method with multi-step filter processing,” in Asian Conference on Experimental Mechanics, 160195, 98–99 (2016).

Garnica, G.

M. Servin, M. Padilla, G. Garnica, and A. Gonzalez, “Profilometry of three-dimensional discontinuous solids by combining two-steps temporal phase unwrapping, co-phased profilometry and phase-shifting interferometry,” Opt. Laser. Eng. 87, 75–82 (2016).
[Crossref]

Gonzalez, A.

M. Servin, M. Padilla, G. Garnica, and A. Gonzalez, “Profilometry of three-dimensional discontinuous solids by combining two-steps temporal phase unwrapping, co-phased profilometry and phase-shifting interferometry,” Opt. Laser. Eng. 87, 75–82 (2016).
[Crossref]

Hack, E.

E. Hack and J. Burke, “Invited review article: measurement uncertainty of linear phase-stepping algorithms,” Rev. Sci. Instrum. 82(6), 061101 (2011).
[Crossref]

Han, B.

P. Ifju and B. Han, “Recent applications of moiré interferometry,” Exp. Mech. 50(8), 1129–1147 (2010).
[Crossref]

Høgmoen, K.

Huang, L.

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Laser. Eng. 109, 23–59 (2018).
[Crossref]

Hÿch, M.

M. Hÿch and L. Potez, “Geometric phase analysis of high-resolution electron microscopy images of antiphase domains: example Cu3Au,” Philos. Mag. A 76(6), 1119–1138 (1997).
[Crossref]

Ifju, P.

P. Ifju and B. Han, “Recent applications of moiré interferometry,” Exp. Mech. 50(8), 1129–1147 (2010).
[Crossref]

Ifju, P. G.

S. Yoneyama, P. G. Ifju, and S. E. Rohde, “Identifying through-thickness material properties of carbon-fiber-reinforced plastics using the virtual fields method combined with moiré interferometry,” Adv. Compos. Mater. 27(1), 1–17 (2018).
[Crossref]

Ina, H.

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72(1), 156–160 (1982).
[Crossref]

Jiang, X.

Q. Wang, S. Kishimoto, X. Jiang, and Y. Yamauchi, “Formation of secondary Moiré patterns for characterization of nanoporous alumina structures in multiple domains with different orientations,” Nanoscale 5(6), 2285–2289 (2013).
[Crossref]

Kemao, Q.

Kishimoto, S.

Q. Wang, S. Kishimoto, X. Jiang, and Y. Yamauchi, “Formation of secondary Moiré patterns for characterization of nanoporous alumina structures in multiple domains with different orientations,” Nanoscale 5(6), 2285–2289 (2013).
[Crossref]

Q. Wang and S. Kishimoto, “Simultaneous analysis of residual stress and stress intensity factor in a resist after UV-nanoimprint lithography based on electron moiré fringes,” J. Micromech. Microeng. 22(10), 105021 (2012).
[Crossref]

S. Kishimoto, M. Egashira, and N. Shinya, “Microcreep deformation measurements by a moiré method using electron beam lithography and electron beam scan,” Opt. Eng. 32(3), 522–526 (1993).
[Crossref]

Kitamura, R.

Y. Fukami, S. Ri, Q. Wang, H. Tsuda, R. Kitamura, and S. Ogihara, “Accuracy improvement of small strain distribution measurement based on the sampling moire method with multi-step filter processing,” in Asian Conference on Experimental Mechanics, 160195, 98–99 (2016).

Kobayashi, S.

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72(1), 156–160 (1982).
[Crossref]

Koyama, M.

Q. Wang, S. Ri, H. Tsuda, and M. Koyama, “Optical full-field strain measurement method from wrapped sampling Moiré phase to minimize the influence of defects and its applications,” Opt. Laser. Eng. 110, 155–162 (2018).
[Crossref]

Q. Wang, S. Ri, H. Tsuda, M. Koyama, and K. Tsuzaki, “Two-dimensional Moire phase analysis for accurate strain distribution measurement and application in crack prediction,” Opt. Express 25(12), 13465–13480 (2017).
[Crossref]

Lei, Z.

Z. Lei and Z. Wang, “Vibration testing parameters measured by sampling moire method,” Appl. Mech. Mater. 226-228, 1975–1980 (2012).
[Crossref]

Li, B.

H. Xie, H. Shang, F. Dai, B. Li, and Y. Xing, “Phase shifting SEM moiré method,” Opt. Laser Technol. 36(4), 291–297 (2004).
[Crossref]

Li, C.

C. Li, H. Xie, Z. Liu, S. Wang, and L. Li, “Experimental study on stress concentration of nickel-base superalloy at elevated temperatures with an in situ SEM system,” Mech. Mater. 103, 87–94 (2016).
[Crossref]

C. Li, Z. Liu, H. Xie, and D. Wu, “Novel 3D SEM Moiré method for micro height measurement,” Opt. Express 21(13), 15734–15746 (2013).
[Crossref]

Li, L.

C. Li, H. Xie, Z. Liu, S. Wang, and L. Li, “Experimental study on stress concentration of nickel-base superalloy at elevated temperatures with an in situ SEM system,” Mech. Mater. 103, 87–94 (2016).
[Crossref]

Li, X.

J. Shao, Y. Ding, H. Tian, X. Li, X. Li, and H. Liu, “Digital moiré fringe measurement method for alignment in imprint lithography,” Opt. Laser Technol. 44(2), 446–451 (2012).
[Crossref]

J. Shao, Y. Ding, H. Tian, X. Li, X. Li, and H. Liu, “Digital moiré fringe measurement method for alignment in imprint lithography,” Opt. Laser Technol. 44(2), 446–451 (2012).
[Crossref]

Liu, H.

J. Shao, Y. Ding, H. Tian, X. Li, X. Li, and H. Liu, “Digital moiré fringe measurement method for alignment in imprint lithography,” Opt. Laser Technol. 44(2), 446–451 (2012).
[Crossref]

Liu, Z.

Q. Zhang, H. Xie, Z. Liu, and W. Shi, “Sampling moiré method and its application to determine modulus of thermal barrier coatings under scanning electron microscope,” Opt. Laser. Eng. 107, 315–324 (2018).
[Crossref]

C. Li, H. Xie, Z. Liu, S. Wang, and L. Li, “Experimental study on stress concentration of nickel-base superalloy at elevated temperatures with an in situ SEM system,” Mech. Mater. 103, 87–94 (2016).
[Crossref]

H. Zhang, C. Wu, Z. Liu, and H. Xie, “A curved surface micro-moiré method and its application in evaluating curved surface residual stress,” Meas. Sci. Technol. 25(9), 095002 (2014).
[Crossref]

C. Li, Z. Liu, H. Xie, and D. Wu, “Novel 3D SEM Moiré method for micro height measurement,” Opt. Express 21(13), 15734–15746 (2013).
[Crossref]

Løkberg, O. J.

Lu, X.

W. Niu, L. Zhong, P. Sun, W. Zhang, and X. Lu, “Two-step phase retrieval algorithm based on the quotient of inner products of phase-shifting interferograms,” J. Opt. 17(8), 085703 (2015).
[Crossref]

Masaya, A.

M. Fujigaki, A. Masaya, K. Shimo, and Y. Morimoto, “Dynamic shape and strain measurements of rotating tire using a sampling moiré method,” Opt. Eng. 50(10), 101506 (2011).
[Crossref]

Morimoto, Y.

M. Fujigaki, A. Masaya, K. Shimo, and Y. Morimoto, “Dynamic shape and strain measurements of rotating tire using a sampling moiré method,” Opt. Eng. 50(10), 101506 (2011).
[Crossref]

S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50(4), 501–508 (2010).
[Crossref]

Niu, W.

W. Niu, L. Zhong, P. Sun, W. Zhang, and X. Lu, “Two-step phase retrieval algorithm based on the quotient of inner products of phase-shifting interferograms,” J. Opt. 17(8), 085703 (2015).
[Crossref]

Ogihara, S.

Y. Fukami, S. Ri, Q. Wang, H. Tsuda, R. Kitamura, and S. Ogihara, “Accuracy improvement of small strain distribution measurement based on the sampling moire method with multi-step filter processing,” in Asian Conference on Experimental Mechanics, 160195, 98–99 (2016).

Padilla, M.

M. Servin, M. Padilla, G. Garnica, and A. Gonzalez, “Profilometry of three-dimensional discontinuous solids by combining two-steps temporal phase unwrapping, co-phased profilometry and phase-shifting interferometry,” Opt. Laser. Eng. 87, 75–82 (2016).
[Crossref]

Park, Y.

Potez, L.

M. Hÿch and L. Potez, “Geometric phase analysis of high-resolution electron microscopy images of antiphase domains: example Cu3Au,” Philos. Mag. A 76(6), 1119–1138 (1997).
[Crossref]

Quiroga, J. A.

Ranson, W.

T. Chu, W. Ranson, and M. A. Sutton, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25(3), 232–244 (1985).
[Crossref]

Ri, S.

S. Ri, Q. Wang, P. Xia, and H. Tsuda, “Spatiotemporal phase-shifting method for accurate phase analysis of fringe pattern,” J. Opt. 21(9), 095702 (2019).
[Crossref]

Q. Wang, S. Ri, H. Tsuda, and M. Koyama, “Optical full-field strain measurement method from wrapped sampling Moiré phase to minimize the influence of defects and its applications,” Opt. Laser. Eng. 110, 155–162 (2018).
[Crossref]

Q. Wang, S. Ri, H. Tsuda, M. Koyama, and K. Tsuzaki, “Two-dimensional Moire phase analysis for accurate strain distribution measurement and application in crack prediction,” Opt. Express 25(12), 13465–13480 (2017).
[Crossref]

Q. Wang, S. Ri, and H. Tsuda, “Digital sampling Moiré as a substitute for microscope scanning Moiré for high-sensitivity and full-field deformation measurement at micron/nano scales,” Appl. Opt. 55(25), 6858–6865 (2016).
[Crossref]

S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50(4), 501–508 (2010).
[Crossref]

Y. Fukami, S. Ri, Q. Wang, H. Tsuda, R. Kitamura, and S. Ogihara, “Accuracy improvement of small strain distribution measurement based on the sampling moire method with multi-step filter processing,” in Asian Conference on Experimental Mechanics, 160195, 98–99 (2016).

Rohde, S. E.

S. Yoneyama, P. G. Ifju, and S. E. Rohde, “Identifying through-thickness material properties of carbon-fiber-reinforced plastics using the virtual fields method combined with moiré interferometry,” Adv. Compos. Mater. 27(1), 1–17 (2018).
[Crossref]

Servin, M.

M. Servin, M. Padilla, G. Garnica, and A. Gonzalez, “Profilometry of three-dimensional discontinuous solids by combining two-steps temporal phase unwrapping, co-phased profilometry and phase-shifting interferometry,” Opt. Laser. Eng. 87, 75–82 (2016).
[Crossref]

Shang, H.

H. Xie, H. Shang, F. Dai, B. Li, and Y. Xing, “Phase shifting SEM moiré method,” Opt. Laser Technol. 36(4), 291–297 (2004).
[Crossref]

Shao, J.

J. Shao, Y. Ding, H. Tian, X. Li, X. Li, and H. Liu, “Digital moiré fringe measurement method for alignment in imprint lithography,” Opt. Laser Technol. 44(2), 446–451 (2012).
[Crossref]

Shi, W.

Q. Zhang, H. Xie, W. Shi, and B. Fan, “A novel sampling moiré method and its application for distortion calibration in scanning electron microscope,” Opt. Laser. Eng. 127, 105990 (2020).
[Crossref]

Q. Zhang, H. Xie, Z. Liu, and W. Shi, “Sampling moiré method and its application to determine modulus of thermal barrier coatings under scanning electron microscope,” Opt. Laser. Eng. 107, 315–324 (2018).
[Crossref]

Shimo, K.

M. Fujigaki, A. Masaya, K. Shimo, and Y. Morimoto, “Dynamic shape and strain measurements of rotating tire using a sampling moiré method,” Opt. Eng. 50(10), 101506 (2011).
[Crossref]

Shinya, N.

S. Kishimoto, M. Egashira, and N. Shinya, “Microcreep deformation measurements by a moiré method using electron beam lithography and electron beam scan,” Opt. Eng. 32(3), 522–526 (1993).
[Crossref]

Sorzano, C.

Sun, P.

W. Niu, L. Zhong, P. Sun, W. Zhang, and X. Lu, “Two-step phase retrieval algorithm based on the quotient of inner products of phase-shifting interferograms,” J. Opt. 17(8), 085703 (2015).
[Crossref]

Surrel, Y.

S. Avril, A. Vautrin, and Y. Surrel, “Grid method: application to the characterization of cracks,” Exp. Mech. 44(1), 37–43 (2004).
[Crossref]

Sutton, M. A.

T. Chu, W. Ranson, and M. A. Sutton, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25(3), 232–244 (1985).
[Crossref]

Takeda, M.

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72(1), 156–160 (1982).
[Crossref]

Tang, M.

M. Tang, H. Xie, Q. Wang, and J. Zhu, “Phase-shifting laser scanning confocal microscopy moiré method and its applications,” Meas. Sci. Technol. 21(5), 055110 (2010).
[Crossref]

Tao, T.

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Laser. Eng. 109, 23–59 (2018).
[Crossref]

Tian, H.

J. Shao, Y. Ding, H. Tian, X. Li, X. Li, and H. Liu, “Digital moiré fringe measurement method for alignment in imprint lithography,” Opt. Laser Technol. 44(2), 446–451 (2012).
[Crossref]

Tsuda, H.

S. Ri, Q. Wang, P. Xia, and H. Tsuda, “Spatiotemporal phase-shifting method for accurate phase analysis of fringe pattern,” J. Opt. 21(9), 095702 (2019).
[Crossref]

Q. Wang, S. Ri, H. Tsuda, and M. Koyama, “Optical full-field strain measurement method from wrapped sampling Moiré phase to minimize the influence of defects and its applications,” Opt. Laser. Eng. 110, 155–162 (2018).
[Crossref]

Q. Wang, S. Ri, H. Tsuda, M. Koyama, and K. Tsuzaki, “Two-dimensional Moire phase analysis for accurate strain distribution measurement and application in crack prediction,” Opt. Express 25(12), 13465–13480 (2017).
[Crossref]

Q. Wang, S. Ri, and H. Tsuda, “Digital sampling Moiré as a substitute for microscope scanning Moiré for high-sensitivity and full-field deformation measurement at micron/nano scales,” Appl. Opt. 55(25), 6858–6865 (2016).
[Crossref]

Y. Fukami, S. Ri, Q. Wang, H. Tsuda, R. Kitamura, and S. Ogihara, “Accuracy improvement of small strain distribution measurement based on the sampling moire method with multi-step filter processing,” in Asian Conference on Experimental Mechanics, 160195, 98–99 (2016).

Tsuzaki, K.

Vargas, J.

Vautrin, A.

S. Avril, A. Vautrin, and Y. Surrel, “Grid method: application to the characterization of cracks,” Exp. Mech. 44(1), 37–43 (2004).
[Crossref]

Wang, Q.

S. Ri, Q. Wang, P. Xia, and H. Tsuda, “Spatiotemporal phase-shifting method for accurate phase analysis of fringe pattern,” J. Opt. 21(9), 095702 (2019).
[Crossref]

Q. Wang, S. Ri, H. Tsuda, and M. Koyama, “Optical full-field strain measurement method from wrapped sampling Moiré phase to minimize the influence of defects and its applications,” Opt. Laser. Eng. 110, 155–162 (2018).
[Crossref]

Q. Wang, S. Ri, H. Tsuda, M. Koyama, and K. Tsuzaki, “Two-dimensional Moire phase analysis for accurate strain distribution measurement and application in crack prediction,” Opt. Express 25(12), 13465–13480 (2017).
[Crossref]

Q. Wang, S. Ri, and H. Tsuda, “Digital sampling Moiré as a substitute for microscope scanning Moiré for high-sensitivity and full-field deformation measurement at micron/nano scales,” Appl. Opt. 55(25), 6858–6865 (2016).
[Crossref]

Q. Wang, S. Kishimoto, X. Jiang, and Y. Yamauchi, “Formation of secondary Moiré patterns for characterization of nanoporous alumina structures in multiple domains with different orientations,” Nanoscale 5(6), 2285–2289 (2013).
[Crossref]

Q. Wang and S. Kishimoto, “Simultaneous analysis of residual stress and stress intensity factor in a resist after UV-nanoimprint lithography based on electron moiré fringes,” J. Micromech. Microeng. 22(10), 105021 (2012).
[Crossref]

M. Tang, H. Xie, Q. Wang, and J. Zhu, “Phase-shifting laser scanning confocal microscopy moiré method and its applications,” Meas. Sci. Technol. 21(5), 055110 (2010).
[Crossref]

Y. Fukami, S. Ri, Q. Wang, H. Tsuda, R. Kitamura, and S. Ogihara, “Accuracy improvement of small strain distribution measurement based on the sampling moire method with multi-step filter processing,” in Asian Conference on Experimental Mechanics, 160195, 98–99 (2016).

Wang, S.

C. Li, H. Xie, Z. Liu, S. Wang, and L. Li, “Experimental study on stress concentration of nickel-base superalloy at elevated temperatures with an in situ SEM system,” Mech. Mater. 103, 87–94 (2016).
[Crossref]

Wang, Z.

Z. Lei and Z. Wang, “Vibration testing parameters measured by sampling moire method,” Appl. Mech. Mater. 226-228, 1975–1980 (2012).
[Crossref]

F. Dai and Z. Wang, “Automatic fringe patterns analysis using digital processing tehniques: I fringe center method,” Acta Photonica Sin. 28, 700–706 (1999).

Wu, C.

H. Zhang, C. Wu, Z. Liu, and H. Xie, “A curved surface micro-moiré method and its application in evaluating curved surface residual stress,” Meas. Sci. Technol. 25(9), 095002 (2014).
[Crossref]

Wu, D.

Xia, P.

S. Ri, Q. Wang, P. Xia, and H. Tsuda, “Spatiotemporal phase-shifting method for accurate phase analysis of fringe pattern,” J. Opt. 21(9), 095702 (2019).
[Crossref]

Xie, H.

Q. Zhang, H. Xie, W. Shi, and B. Fan, “A novel sampling moiré method and its application for distortion calibration in scanning electron microscope,” Opt. Laser. Eng. 127, 105990 (2020).
[Crossref]

Q. Zhang, H. Xie, Z. Liu, and W. Shi, “Sampling moiré method and its application to determine modulus of thermal barrier coatings under scanning electron microscope,” Opt. Laser. Eng. 107, 315–324 (2018).
[Crossref]

C. Li, H. Xie, Z. Liu, S. Wang, and L. Li, “Experimental study on stress concentration of nickel-base superalloy at elevated temperatures with an in situ SEM system,” Mech. Mater. 103, 87–94 (2016).
[Crossref]

H. Zhang, C. Wu, Z. Liu, and H. Xie, “A curved surface micro-moiré method and its application in evaluating curved surface residual stress,” Meas. Sci. Technol. 25(9), 095002 (2014).
[Crossref]

C. Li, Z. Liu, H. Xie, and D. Wu, “Novel 3D SEM Moiré method for micro height measurement,” Opt. Express 21(13), 15734–15746 (2013).
[Crossref]

M. Tang, H. Xie, Q. Wang, and J. Zhu, “Phase-shifting laser scanning confocal microscopy moiré method and its applications,” Meas. Sci. Technol. 21(5), 055110 (2010).
[Crossref]

H. Xie, H. Shang, F. Dai, B. Li, and Y. Xing, “Phase shifting SEM moiré method,” Opt. Laser Technol. 36(4), 291–297 (2004).
[Crossref]

Xing, Y.

H. Xie, H. Shang, F. Dai, B. Li, and Y. Xing, “Phase shifting SEM moiré method,” Opt. Laser Technol. 36(4), 291–297 (2004).
[Crossref]

Yamauchi, Y.

Q. Wang, S. Kishimoto, X. Jiang, and Y. Yamauchi, “Formation of secondary Moiré patterns for characterization of nanoporous alumina structures in multiple domains with different orientations,” Nanoscale 5(6), 2285–2289 (2013).
[Crossref]

Yin, W.

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Laser. Eng. 109, 23–59 (2018).
[Crossref]

Yoneyama, S.

S. Yoneyama, P. G. Ifju, and S. E. Rohde, “Identifying through-thickness material properties of carbon-fiber-reinforced plastics using the virtual fields method combined with moiré interferometry,” Adv. Compos. Mater. 27(1), 1–17 (2018).
[Crossref]

Zhang, H.

H. Zhang, C. Wu, Z. Liu, and H. Xie, “A curved surface micro-moiré method and its application in evaluating curved surface residual stress,” Meas. Sci. Technol. 25(9), 095002 (2014).
[Crossref]

Zhang, Q.

Q. Zhang, H. Xie, W. Shi, and B. Fan, “A novel sampling moiré method and its application for distortion calibration in scanning electron microscope,” Opt. Laser. Eng. 127, 105990 (2020).
[Crossref]

Q. Zhang, H. Xie, Z. Liu, and W. Shi, “Sampling moiré method and its application to determine modulus of thermal barrier coatings under scanning electron microscope,” Opt. Laser. Eng. 107, 315–324 (2018).
[Crossref]

Zhang, W.

W. Niu, L. Zhong, P. Sun, W. Zhang, and X. Lu, “Two-step phase retrieval algorithm based on the quotient of inner products of phase-shifting interferograms,” J. Opt. 17(8), 085703 (2015).
[Crossref]

Zhong, L.

W. Niu, L. Zhong, P. Sun, W. Zhang, and X. Lu, “Two-step phase retrieval algorithm based on the quotient of inner products of phase-shifting interferograms,” J. Opt. 17(8), 085703 (2015).
[Crossref]

Zhu, J.

M. Tang, H. Xie, Q. Wang, and J. Zhu, “Phase-shifting laser scanning confocal microscopy moiré method and its applications,” Meas. Sci. Technol. 21(5), 055110 (2010).
[Crossref]

Zuo, C.

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Laser. Eng. 109, 23–59 (2018).
[Crossref]

Acta Photonica Sin. (1)

F. Dai and Z. Wang, “Automatic fringe patterns analysis using digital processing tehniques: I fringe center method,” Acta Photonica Sin. 28, 700–706 (1999).

Adv. Compos. Mater. (1)

S. Yoneyama, P. G. Ifju, and S. E. Rohde, “Identifying through-thickness material properties of carbon-fiber-reinforced plastics using the virtual fields method combined with moiré interferometry,” Adv. Compos. Mater. 27(1), 1–17 (2018).
[Crossref]

Appl. Mech. Mater. (1)

Z. Lei and Z. Wang, “Vibration testing parameters measured by sampling moire method,” Appl. Mech. Mater. 226-228, 1975–1980 (2012).
[Crossref]

Appl. Opt. (3)

Exp. Mech. (4)

S. Avril, A. Vautrin, and Y. Surrel, “Grid method: application to the characterization of cracks,” Exp. Mech. 44(1), 37–43 (2004).
[Crossref]

T. Chu, W. Ranson, and M. A. Sutton, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25(3), 232–244 (1985).
[Crossref]

P. Ifju and B. Han, “Recent applications of moiré interferometry,” Exp. Mech. 50(8), 1129–1147 (2010).
[Crossref]

S. Ri, M. Fujigaki, and Y. Morimoto, “Sampling moiré method for accurate small deformation distribution measurement,” Exp. Mech. 50(4), 501–508 (2010).
[Crossref]

J. Bridge Eng. (1)

X. Chen and C.-C. Chang, “In-Plane Movement Measurement Technique Using Digital Sampling Moiré Method,” J. Bridge Eng. 24(4), 04019013 (2019).
[Crossref]

J. Micromech. Microeng. (1)

Q. Wang and S. Kishimoto, “Simultaneous analysis of residual stress and stress intensity factor in a resist after UV-nanoimprint lithography based on electron moiré fringes,” J. Micromech. Microeng. 22(10), 105021 (2012).
[Crossref]

J. Opt. (2)

S. Ri, Q. Wang, P. Xia, and H. Tsuda, “Spatiotemporal phase-shifting method for accurate phase analysis of fringe pattern,” J. Opt. 21(9), 095702 (2019).
[Crossref]

W. Niu, L. Zhong, P. Sun, W. Zhang, and X. Lu, “Two-step phase retrieval algorithm based on the quotient of inner products of phase-shifting interferograms,” J. Opt. 17(8), 085703 (2015).
[Crossref]

J. Opt. Soc. Am. A (1)

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72(1), 156–160 (1982).
[Crossref]

Meas. Sci. Technol. (2)

M. Tang, H. Xie, Q. Wang, and J. Zhu, “Phase-shifting laser scanning confocal microscopy moiré method and its applications,” Meas. Sci. Technol. 21(5), 055110 (2010).
[Crossref]

H. Zhang, C. Wu, Z. Liu, and H. Xie, “A curved surface micro-moiré method and its application in evaluating curved surface residual stress,” Meas. Sci. Technol. 25(9), 095002 (2014).
[Crossref]

Mech. Mater. (1)

C. Li, H. Xie, Z. Liu, S. Wang, and L. Li, “Experimental study on stress concentration of nickel-base superalloy at elevated temperatures with an in situ SEM system,” Mech. Mater. 103, 87–94 (2016).
[Crossref]

Nanoscale (1)

Q. Wang, S. Kishimoto, X. Jiang, and Y. Yamauchi, “Formation of secondary Moiré patterns for characterization of nanoporous alumina structures in multiple domains with different orientations,” Nanoscale 5(6), 2285–2289 (2013).
[Crossref]

Opt. Eng. (2)

S. Kishimoto, M. Egashira, and N. Shinya, “Microcreep deformation measurements by a moiré method using electron beam lithography and electron beam scan,” Opt. Eng. 32(3), 522–526 (1993).
[Crossref]

M. Fujigaki, A. Masaya, K. Shimo, and Y. Morimoto, “Dynamic shape and strain measurements of rotating tire using a sampling moiré method,” Opt. Eng. 50(10), 101506 (2011).
[Crossref]

Opt. Express (2)

Opt. Laser Technol. (2)

J. Shao, Y. Ding, H. Tian, X. Li, X. Li, and H. Liu, “Digital moiré fringe measurement method for alignment in imprint lithography,” Opt. Laser Technol. 44(2), 446–451 (2012).
[Crossref]

H. Xie, H. Shang, F. Dai, B. Li, and Y. Xing, “Phase shifting SEM moiré method,” Opt. Laser Technol. 36(4), 291–297 (2004).
[Crossref]

Opt. Laser. Eng. (5)

M. Servin, M. Padilla, G. Garnica, and A. Gonzalez, “Profilometry of three-dimensional discontinuous solids by combining two-steps temporal phase unwrapping, co-phased profilometry and phase-shifting interferometry,” Opt. Laser. Eng. 87, 75–82 (2016).
[Crossref]

Q. Wang, S. Ri, H. Tsuda, and M. Koyama, “Optical full-field strain measurement method from wrapped sampling Moiré phase to minimize the influence of defects and its applications,” Opt. Laser. Eng. 110, 155–162 (2018).
[Crossref]

Q. Zhang, H. Xie, Z. Liu, and W. Shi, “Sampling moiré method and its application to determine modulus of thermal barrier coatings under scanning electron microscope,” Opt. Laser. Eng. 107, 315–324 (2018).
[Crossref]

Q. Zhang, H. Xie, W. Shi, and B. Fan, “A novel sampling moiré method and its application for distortion calibration in scanning electron microscope,” Opt. Laser. Eng. 127, 105990 (2020).
[Crossref]

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Laser. Eng. 109, 23–59 (2018).
[Crossref]

Opt. Lett. (2)

Philos. Mag. A (1)

M. Hÿch and L. Potez, “Geometric phase analysis of high-resolution electron microscopy images of antiphase domains: example Cu3Au,” Philos. Mag. A 76(6), 1119–1138 (1997).
[Crossref]

Rev. Sci. Instrum. (1)

E. Hack and J. Burke, “Invited review article: measurement uncertainty of linear phase-stepping algorithms,” Rev. Sci. Instrum. 82(6), 061101 (2011).
[Crossref]

Other (1)

Y. Fukami, S. Ri, Q. Wang, H. Tsuda, R. Kitamura, and S. Ogihara, “Accuracy improvement of small strain distribution measurement based on the sampling moire method with multi-step filter processing,” in Asian Conference on Experimental Mechanics, 160195, 98–99 (2016).

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Figures (12)

Fig. 1.
Fig. 1. Measurement principle: (a) Generation process of 2-pixel sampling moiré fringes, and (b) measurement principle of the second-order moiré method where the grating pitch is greater than 1.5 pixels.
Fig. 2.
Fig. 2. Geometry of an oblique 2D grid including gratings X and Y, and deformation measurement process of the second-order moiré method from a 2D grid with a pitch of about 2 pixels.
Fig. 3.
Fig. 3. Comparation of RMS errors in strain in the range of (a) 0-0.1 and (b) 0-0.0025 measured by Fourier transform, the sampling moiré method and the second-order method versus the theoretical strain of a 1D grating with a pitch of 2.1 pixels.
Fig. 4.
Fig. 4. Comparation of RMS errors in strain measured by Fourier transform, the sampling moiré method and the second-order method versus the grating pitch of (a) a parallel grating and (b) an oblique grating when the grating is inclined by 2°, where the noise level is σ=10%.
Fig. 5.
Fig. 5. Simulation results of RMS errors in strains obtained by the second-order moiré method: (a) Diagram of a 2D grid with a pitch of 2.1 pixels, and RMS errors in strains in the (b) x and (c) y directions versus the theoretical strains, where examples of the strain distributions in 300×300 pixels are shown when the theoretical strains are -0.005 in the x direction and 0.05 in the y direction, respectively.
Fig. 6.
Fig. 6. Relative errors in strain (a) in the x direction along the horizontal line AA’ when the theoretical strain is ɛxx=-0.005, and (b) in the y directions along the vertical line BB’ when the theoretical strain is ɛyy=0.05, where the noise level is σ=10%, and AA’ and BB’ are marked in Figs. 5(b) and 5(c), respectively.
Fig. 7.
Fig. 7. Loading configuration and CFRP specimen appearance: (a) Diagram of three-point bending test, (b) laminate structure and laser microscope image of the specimen surface with a 3-µm-pitch grid, and (c) enlarged image of the fabricated grid.
Fig. 8.
Fig. 8. Photograph of the three-point bending device under a laser microscope.
Fig. 9.
Fig. 9. Grid images with a pitch of about 2.1 pixels in the 45° direction in the analysis area on CFRP under different three-point bending loads.
Fig. 10.
Fig. 10. Phase distributions of the second-order moiré fringes at 0 MPa and 197 MPa as well as the phase differences in the x and y directions in the analysis area on CFRP.
Fig. 11.
Fig. 11. Distributions of (a) strain x, (b) strain y, (c) shear strain, (d) maximum principal strain measured by the second-order moiré method in the analysis area on CFRP under different three-point bending loads.
Fig. 12.
Fig. 12. Damage location prediction: (a) evaluation of interlaminar crack occurrence from shear strain distributions, and (b) evaluation of transverse crack occurrence from strain distributions in the x direction, where crack A and crack B are marked in Fig. 9.

Equations (16)

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I ( x , y ) = a ( x , y ) cos [ 2 π y P y + φ 0 ] + b ( x , y )
I m ( x , y ; t ) = A ( x , y ) cos [ 2 π y ( 1 P y 1 T ) + φ 0 + 2 π t T ] + B ( x , y )   ( t = 0 ,   1 ,   ,   T 1 )
T ( 2 ) = round ( 1 / | 1 P y 1 T | ) = round ( P y T | P y T | )
I m ( 2 ) ( x , y ; t , k ) = A ( 2 ) ( x , y ) cos [ 2 π y ( 1 P y 1 T 1 T ( 2 ) ) + φ 0 + 2 π t T + 2 π k T ( 2 ) ] + B ( 2 ) ( x , y )   ( t = 0 ,   1 ,   ,   T 1 ;   k = 0 ,   1 ,   ,   T ( 2 ) 1 )
φ m ( 2 ) ( y ) = 2 π y ( 1 P y 1 T 1 T ( 2 ) ) + φ 0  = arg { k = 0 T ( 2 ) 1 t = 0 T 1 [ I m ( 2 ) ( x , y ; t , k ) ] W T t W T ( 2 ) k }  
W N n  = exp (  -  j 2 π n N )  ,  ( n = 0 ,   1 ,   ,   N 1 )
φ m ( y ) = φ m ( 2 ) ( y ) + 2 π y T ( 2 )
φ s ( y ) = φ m ( y ) + 2 π y T = φ m ( 2 ) ( y ) + 2 π y T ( 2 ) + 2 π y T
Δ φ s ( y ) = Δ φ m ( y ) = Δ φ m ( 2 ) ( y )
Δ φ s ( y ) = 2 π y ( 1 P y 1 P y )
u y = p y 2 π Δ φ s ( y )  =  p y 2 π Δ φ m ( 2 ) ( y )
u x = p x 2 π Δ φ s ( x )  =  p x 2 π Δ φ m ( 2 ) ( x )
ε x x = u x x = p x 2 π Δ φ m ( 2 ) ( x ) x ε y y = u y y = p y 2 π Δ φ m ( 2 ) ( y ) y γ x y = u x y + u y x = p x 2 π Δ φ m ( 2 ) ( x ) y p y 2 π Δ φ m ( 2 ) ( y ) x
( u x u y ) = 1 2 π ( 1 / p X x 1 / p X y 1 / p Y x 1 / p Y y ) 1 ( Δ φ m ( 2 ) ( X ) Δ φ m ( 2 ) ( Y ) ) = M 2 π ( Δ φ m ( 2 ) ( X ) Δ φ m ( 2 ) ( Y ) )
( ε x x ε x y ε y x ε y y ) = M 2 π ( Δ φ m ( 2 ) ( X ) x Δ φ m ( 2 ) ( X ) y Δ φ m ( 2 ) ( Y ) x Δ φ m ( 2 ) ( Y ) y ) γ x y = ε x y + ε y x
M = p ( cos θ sin θ sin θ   cos θ ) 1

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