Abstract

A real-time, dual-sensitive shearography system using a single-wavelength laser was developed for simultaneous and dynamic in-plane and out-of-plane strain measurements. The shearography system is capable of measuring crack-tip deformation fields quantitatively. A spatial multiplexing technique based on Fourier transform is employed for simultaneous and dynamic multi-component phase retrieval. Two slit spatial filters and a common-path shearing interferometer are used to obtain an improved phase quality for crack-tip deformation measurements. Mode-I fracture experiments under three-point bending were conducted to validate the feasibility and the capability of this method.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
  2. I. Yamaguchi, J.-i. Kato, and S. Ohta, “Surface shape measurement by phase-shifting digital holography,” Opt. Rev. 8, 85–89 (2001).
    [Crossref]
  3. U. P. Kumar, B. Bhaduri, M. P. Kothiyal, and N. K. Mohan, “Two-wavelength micro-interferometry for 3-D surface profiling,” Opt. Lasers Eng. 47, 223–229 (2009).
    [Crossref]
  4. L. Bilgeri, F. S. Bloise, M. Lu, S. Wang, M. Jakobi, and A. W. Koch, “Intensity distortions due to phase-only spatial light modulation: Characterization for applications in electronic speckle-pattern interferometry,” Rev. Sci. Instruments 89, 083701 (2018).
    [Crossref]
  5. N. Werth, F. S. Bloise, and A. W. Koch, “Influence of roughness in the phase-shifting speckle method: An experimental study with applications,” Rev. Sci. Instruments 85, 015114 (2014).
    [Crossref]
  6. J. Leendertz, “Interferometric displacement measurement on scattering surfaces utilizing speckle effect,” J. Phys. E: Sci. Instruments 3, 214–218 (1970).
    [Crossref]
  7. J. Butters and J. Leendertz, “Speckle pattern and holographic techniques in engineering metrology,” Opt. Lasers Eng. 3, 26–30 (1971).
    [Crossref]
  8. A. W. Koch, M. W. Ruprecht, O. Toedter, and G. Häusler, Optische messtechnik an technischen oberflächen (Expert-Verlag: Renningen-Malmsheim, Germany, 1998).
  9. J. Leendertz and J. Butters, “An image-shearing speckle-pattern interferometer for measuring bending moments,” J. Phys. E: Sci. Instruments 6, 1107–1110 (1973).
    [Crossref]
  10. Y. Hung and C. Liang, “Image-shearing camera for direct measurement of surface strains,” Appl. Opt. 18, 1046–1051 (1979).
    [Crossref] [PubMed]
  11. B. Bhaduri, M. Kothiyal, and N. K. Mohan, “Curvature measurement using three-aperture digital shearography and fast fourier transform,” Opt. Lasers Eng. 45, 1001–1004 (2007).
    [Crossref]
  12. M. Lu, S. Wang, L. Aulbach, and A. W. Koch, “Simultaneous displacement and slope measurement in electronic speckle pattern interferometry using adjustable aperture multiplexing,” Appl. Opt. 55, 5868–5875 (2016).
    [Crossref] [PubMed]
  13. M. Lu, S. Wang, L. Bilgeri, X. Song, M. Jakobi, and A. W. Koch, “Online 3D displacement measurement using speckle interferometer with a single illumination-detection path,” Sensors (Basel, Switzerland) 18, 1923 (2018).
    [Crossref]
  14. L. Yang, W. Steinchen, M. Schuth, and G. Kupfer, “Precision measurement and nondestructive testing by means of digital phase shifting speckle pattern and speckle pattern shearing interferometry,” Measurement 16, 149–160 (1995).
    [Crossref]
  15. B. Bhaduri, N. K. Mohan, and M. Kothiyal, “A dual-function espi system for the measurement of out-of-plane displacement and slope,” Opt. Lasers Eng. 44, 637–644 (2006).
    [Crossref]
  16. H. V. Tippur, “Simultaneous and real-time measurement of slope and curvature fringes in thin structures using shearing interferometery,” Opt. Eng. 43, 3014–3021 (2004).
    [Crossref]
  17. D. Sharma, R. Sirohi, and M. P. Kothiyal, “Simultaneous measurement of slope and curvature with a three-aperture speckle shearing interferometer,” Appl. Opt. 23, 1542–1546 (1984).
    [Crossref] [PubMed]
  18. K. Patorski and A. G. Olszak, “Digital in-plane electronic speckle pattern shearing interferometry,” Opt. Eng. 36, 2010–2016 (1997).
    [Crossref]
  19. G. Pedrini, Y.-L. Zou, and H. Tiziani, “Simultaneous quantitative evaluation of in-plane and out-of-plane deformations by use of a multidirectional spatial carrier,” Appl. Opt. 36, 786–792 (1997).
    [Crossref] [PubMed]
  20. P. Picart, E. Moisson, and D. Mounier, “Twin-sensitivity measurement by spatial multiplexing of digitally recorded holograms,” Appl. Opt. 42, 1947–1957 (2003).
    [Crossref] [PubMed]
  21. M. Mello, S. Hong, and A. Rosakis, “Extension of the coherent gradient sensor (cgs) to the combined measurement of in-plane and out-of-plane displacement field gradients,” Exp. Mech. 49, 277–289 (2009).
    [Crossref]
  22. M. Mello and A. J. Rosakis, “Surface characterization based on lateral shearing of diffracted wave fronts to measure in-plane and out-of-plane displacement gradient fields,” (2009). US Patent 7538891B1.
  23. D. Francis, S. James, and R. Tatam, “Surface strain measurement using multi-component shearography with coherent fibre-optic imaging bundles,” Meas. Sci. Technol. 18, 3583–3591 (2007).
    [Crossref]
  24. S. Wang, M. Lu, L. M. Bilgeri, M. Jakobi, F. S. Bloise, and A. W. Koch, “Temporal electronic speckle pattern interferometry for real-time in-plane rotation analysis,” Opt. Express 26, 8744–8755 (2018).
    [Crossref] [PubMed]
  25. M. Lu, S. Wang, L. Aulbach, M. Jakobi, and A. W. Koch, “Non-phase unwrapping interferometric approach for a real-time in-plane rotation measurement,” Opt. Lett. 42, 1986–1989 (2017).
    [Crossref] [PubMed]
  26. Y. Hung and J. Wang, “Dual-beam phase shift shearography for measurement of in-plane strains,” Opt. Lasers Eng. 24, 403–413 (1996).
    [Crossref]
  27. X. Xie, X. Chen, J. Li, Y. Wang, and L. Yang, “Measurement of in-plane strain with dual beam spatial phase-shift digital shearography,” Meas. Sci. Technol. 26, 115202 (2015).
    [Crossref]
  28. X. Gao, L. Yang, Y. Wang, B. Zhang, X. Dan, J. Li, and S. Wu, “Spatial phase-shift dual-beam speckle interferometry,” Appl. Opt. 57, 414–419 (2018).
    [Crossref] [PubMed]
  29. W. Steinchen, L. Yang, and M. Schuth, “TV-shearography for measuring 3D-strains,” Strain 32, 49–58 (1996).
    [Crossref]
  30. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” JOSA A 72, 156–160 (1982).
    [Crossref]
  31. H. Tada, P. C. Paris, and G. R. Irwin, “The stress analysis of cracks,” Handbook (Del Res. Corp., 1973).

2018 (4)

L. Bilgeri, F. S. Bloise, M. Lu, S. Wang, M. Jakobi, and A. W. Koch, “Intensity distortions due to phase-only spatial light modulation: Characterization for applications in electronic speckle-pattern interferometry,” Rev. Sci. Instruments 89, 083701 (2018).
[Crossref]

M. Lu, S. Wang, L. Bilgeri, X. Song, M. Jakobi, and A. W. Koch, “Online 3D displacement measurement using speckle interferometer with a single illumination-detection path,” Sensors (Basel, Switzerland) 18, 1923 (2018).
[Crossref]

X. Gao, L. Yang, Y. Wang, B. Zhang, X. Dan, J. Li, and S. Wu, “Spatial phase-shift dual-beam speckle interferometry,” Appl. Opt. 57, 414–419 (2018).
[Crossref] [PubMed]

S. Wang, M. Lu, L. M. Bilgeri, M. Jakobi, F. S. Bloise, and A. W. Koch, “Temporal electronic speckle pattern interferometry for real-time in-plane rotation analysis,” Opt. Express 26, 8744–8755 (2018).
[Crossref] [PubMed]

2017 (1)

2016 (1)

2015 (1)

X. Xie, X. Chen, J. Li, Y. Wang, and L. Yang, “Measurement of in-plane strain with dual beam spatial phase-shift digital shearography,” Meas. Sci. Technol. 26, 115202 (2015).
[Crossref]

2014 (1)

N. Werth, F. S. Bloise, and A. W. Koch, “Influence of roughness in the phase-shifting speckle method: An experimental study with applications,” Rev. Sci. Instruments 85, 015114 (2014).
[Crossref]

2009 (2)

U. P. Kumar, B. Bhaduri, M. P. Kothiyal, and N. K. Mohan, “Two-wavelength micro-interferometry for 3-D surface profiling,” Opt. Lasers Eng. 47, 223–229 (2009).
[Crossref]

M. Mello, S. Hong, and A. Rosakis, “Extension of the coherent gradient sensor (cgs) to the combined measurement of in-plane and out-of-plane displacement field gradients,” Exp. Mech. 49, 277–289 (2009).
[Crossref]

2007 (2)

D. Francis, S. James, and R. Tatam, “Surface strain measurement using multi-component shearography with coherent fibre-optic imaging bundles,” Meas. Sci. Technol. 18, 3583–3591 (2007).
[Crossref]

B. Bhaduri, M. Kothiyal, and N. K. Mohan, “Curvature measurement using three-aperture digital shearography and fast fourier transform,” Opt. Lasers Eng. 45, 1001–1004 (2007).
[Crossref]

2006 (1)

B. Bhaduri, N. K. Mohan, and M. Kothiyal, “A dual-function espi system for the measurement of out-of-plane displacement and slope,” Opt. Lasers Eng. 44, 637–644 (2006).
[Crossref]

2004 (1)

H. V. Tippur, “Simultaneous and real-time measurement of slope and curvature fringes in thin structures using shearing interferometery,” Opt. Eng. 43, 3014–3021 (2004).
[Crossref]

2003 (1)

2001 (1)

I. Yamaguchi, J.-i. Kato, and S. Ohta, “Surface shape measurement by phase-shifting digital holography,” Opt. Rev. 8, 85–89 (2001).
[Crossref]

2000 (1)

H. M. Shang, Y. Hung, W. Luo, and F. Chen, “Surface profiling using shearography,” Opt. Eng. 39, 23–32 (2000).
[Crossref]

1997 (2)

1996 (2)

Y. Hung and J. Wang, “Dual-beam phase shift shearography for measurement of in-plane strains,” Opt. Lasers Eng. 24, 403–413 (1996).
[Crossref]

W. Steinchen, L. Yang, and M. Schuth, “TV-shearography for measuring 3D-strains,” Strain 32, 49–58 (1996).
[Crossref]

1995 (1)

L. Yang, W. Steinchen, M. Schuth, and G. Kupfer, “Precision measurement and nondestructive testing by means of digital phase shifting speckle pattern and speckle pattern shearing interferometry,” Measurement 16, 149–160 (1995).
[Crossref]

1984 (1)

1982 (1)

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

1979 (1)

1973 (1)

J. Leendertz and J. Butters, “An image-shearing speckle-pattern interferometer for measuring bending moments,” J. Phys. E: Sci. Instruments 6, 1107–1110 (1973).
[Crossref]

1971 (1)

J. Butters and J. Leendertz, “Speckle pattern and holographic techniques in engineering metrology,” Opt. Lasers Eng. 3, 26–30 (1971).
[Crossref]

1970 (1)

J. Leendertz, “Interferometric displacement measurement on scattering surfaces utilizing speckle effect,” J. Phys. E: Sci. Instruments 3, 214–218 (1970).
[Crossref]

Aulbach, L.

Bhaduri, B.

U. P. Kumar, B. Bhaduri, M. P. Kothiyal, and N. K. Mohan, “Two-wavelength micro-interferometry for 3-D surface profiling,” Opt. Lasers Eng. 47, 223–229 (2009).
[Crossref]

B. Bhaduri, M. Kothiyal, and N. K. Mohan, “Curvature measurement using three-aperture digital shearography and fast fourier transform,” Opt. Lasers Eng. 45, 1001–1004 (2007).
[Crossref]

B. Bhaduri, N. K. Mohan, and M. Kothiyal, “A dual-function espi system for the measurement of out-of-plane displacement and slope,” Opt. Lasers Eng. 44, 637–644 (2006).
[Crossref]

Bilgeri, L.

L. Bilgeri, F. S. Bloise, M. Lu, S. Wang, M. Jakobi, and A. W. Koch, “Intensity distortions due to phase-only spatial light modulation: Characterization for applications in electronic speckle-pattern interferometry,” Rev. Sci. Instruments 89, 083701 (2018).
[Crossref]

M. Lu, S. Wang, L. Bilgeri, X. Song, M. Jakobi, and A. W. Koch, “Online 3D displacement measurement using speckle interferometer with a single illumination-detection path,” Sensors (Basel, Switzerland) 18, 1923 (2018).
[Crossref]

Bilgeri, L. M.

Bloise, F. S.

S. Wang, M. Lu, L. M. Bilgeri, M. Jakobi, F. S. Bloise, and A. W. Koch, “Temporal electronic speckle pattern interferometry for real-time in-plane rotation analysis,” Opt. Express 26, 8744–8755 (2018).
[Crossref] [PubMed]

L. Bilgeri, F. S. Bloise, M. Lu, S. Wang, M. Jakobi, and A. W. Koch, “Intensity distortions due to phase-only spatial light modulation: Characterization for applications in electronic speckle-pattern interferometry,” Rev. Sci. Instruments 89, 083701 (2018).
[Crossref]

N. Werth, F. S. Bloise, and A. W. Koch, “Influence of roughness in the phase-shifting speckle method: An experimental study with applications,” Rev. Sci. Instruments 85, 015114 (2014).
[Crossref]

Butters, J.

J. Leendertz and J. Butters, “An image-shearing speckle-pattern interferometer for measuring bending moments,” J. Phys. E: Sci. Instruments 6, 1107–1110 (1973).
[Crossref]

J. Butters and J. Leendertz, “Speckle pattern and holographic techniques in engineering metrology,” Opt. Lasers Eng. 3, 26–30 (1971).
[Crossref]

Chen, F.

H. M. Shang, Y. Hung, W. Luo, and F. Chen, “Surface profiling using shearography,” Opt. Eng. 39, 23–32 (2000).
[Crossref]

Chen, X.

X. Xie, X. Chen, J. Li, Y. Wang, and L. Yang, “Measurement of in-plane strain with dual beam spatial phase-shift digital shearography,” Meas. Sci. Technol. 26, 115202 (2015).
[Crossref]

Dan, X.

Francis, D.

D. Francis, S. James, and R. Tatam, “Surface strain measurement using multi-component shearography with coherent fibre-optic imaging bundles,” Meas. Sci. Technol. 18, 3583–3591 (2007).
[Crossref]

Gao, X.

Häusler, G.

A. W. Koch, M. W. Ruprecht, O. Toedter, and G. Häusler, Optische messtechnik an technischen oberflächen (Expert-Verlag: Renningen-Malmsheim, Germany, 1998).

Hong, S.

M. Mello, S. Hong, and A. Rosakis, “Extension of the coherent gradient sensor (cgs) to the combined measurement of in-plane and out-of-plane displacement field gradients,” Exp. Mech. 49, 277–289 (2009).
[Crossref]

Hung, Y.

H. M. Shang, Y. Hung, W. Luo, and F. Chen, “Surface profiling using shearography,” Opt. Eng. 39, 23–32 (2000).
[Crossref]

Y. Hung and J. Wang, “Dual-beam phase shift shearography for measurement of in-plane strains,” Opt. Lasers Eng. 24, 403–413 (1996).
[Crossref]

Y. Hung and C. Liang, “Image-shearing camera for direct measurement of surface strains,” Appl. Opt. 18, 1046–1051 (1979).
[Crossref] [PubMed]

Ina, H.

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

Irwin, G. R.

H. Tada, P. C. Paris, and G. R. Irwin, “The stress analysis of cracks,” Handbook (Del Res. Corp., 1973).

Jakobi, M.

S. Wang, M. Lu, L. M. Bilgeri, M. Jakobi, F. S. Bloise, and A. W. Koch, “Temporal electronic speckle pattern interferometry for real-time in-plane rotation analysis,” Opt. Express 26, 8744–8755 (2018).
[Crossref] [PubMed]

L. Bilgeri, F. S. Bloise, M. Lu, S. Wang, M. Jakobi, and A. W. Koch, “Intensity distortions due to phase-only spatial light modulation: Characterization for applications in electronic speckle-pattern interferometry,” Rev. Sci. Instruments 89, 083701 (2018).
[Crossref]

M. Lu, S. Wang, L. Bilgeri, X. Song, M. Jakobi, and A. W. Koch, “Online 3D displacement measurement using speckle interferometer with a single illumination-detection path,” Sensors (Basel, Switzerland) 18, 1923 (2018).
[Crossref]

M. Lu, S. Wang, L. Aulbach, M. Jakobi, and A. W. Koch, “Non-phase unwrapping interferometric approach for a real-time in-plane rotation measurement,” Opt. Lett. 42, 1986–1989 (2017).
[Crossref] [PubMed]

James, S.

D. Francis, S. James, and R. Tatam, “Surface strain measurement using multi-component shearography with coherent fibre-optic imaging bundles,” Meas. Sci. Technol. 18, 3583–3591 (2007).
[Crossref]

Kato, J.-i.

I. Yamaguchi, J.-i. Kato, and S. Ohta, “Surface shape measurement by phase-shifting digital holography,” Opt. Rev. 8, 85–89 (2001).
[Crossref]

Kobayashi, S.

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

Koch, A. W.

L. Bilgeri, F. S. Bloise, M. Lu, S. Wang, M. Jakobi, and A. W. Koch, “Intensity distortions due to phase-only spatial light modulation: Characterization for applications in electronic speckle-pattern interferometry,” Rev. Sci. Instruments 89, 083701 (2018).
[Crossref]

M. Lu, S. Wang, L. Bilgeri, X. Song, M. Jakobi, and A. W. Koch, “Online 3D displacement measurement using speckle interferometer with a single illumination-detection path,” Sensors (Basel, Switzerland) 18, 1923 (2018).
[Crossref]

S. Wang, M. Lu, L. M. Bilgeri, M. Jakobi, F. S. Bloise, and A. W. Koch, “Temporal electronic speckle pattern interferometry for real-time in-plane rotation analysis,” Opt. Express 26, 8744–8755 (2018).
[Crossref] [PubMed]

M. Lu, S. Wang, L. Aulbach, M. Jakobi, and A. W. Koch, “Non-phase unwrapping interferometric approach for a real-time in-plane rotation measurement,” Opt. Lett. 42, 1986–1989 (2017).
[Crossref] [PubMed]

M. Lu, S. Wang, L. Aulbach, and A. W. Koch, “Simultaneous displacement and slope measurement in electronic speckle pattern interferometry using adjustable aperture multiplexing,” Appl. Opt. 55, 5868–5875 (2016).
[Crossref] [PubMed]

N. Werth, F. S. Bloise, and A. W. Koch, “Influence of roughness in the phase-shifting speckle method: An experimental study with applications,” Rev. Sci. Instruments 85, 015114 (2014).
[Crossref]

A. W. Koch, M. W. Ruprecht, O. Toedter, and G. Häusler, Optische messtechnik an technischen oberflächen (Expert-Verlag: Renningen-Malmsheim, Germany, 1998).

Kothiyal, M.

B. Bhaduri, M. Kothiyal, and N. K. Mohan, “Curvature measurement using three-aperture digital shearography and fast fourier transform,” Opt. Lasers Eng. 45, 1001–1004 (2007).
[Crossref]

B. Bhaduri, N. K. Mohan, and M. Kothiyal, “A dual-function espi system for the measurement of out-of-plane displacement and slope,” Opt. Lasers Eng. 44, 637–644 (2006).
[Crossref]

Kothiyal, M. P.

U. P. Kumar, B. Bhaduri, M. P. Kothiyal, and N. K. Mohan, “Two-wavelength micro-interferometry for 3-D surface profiling,” Opt. Lasers Eng. 47, 223–229 (2009).
[Crossref]

D. Sharma, R. Sirohi, and M. P. Kothiyal, “Simultaneous measurement of slope and curvature with a three-aperture speckle shearing interferometer,” Appl. Opt. 23, 1542–1546 (1984).
[Crossref] [PubMed]

Kumar, U. P.

U. P. Kumar, B. Bhaduri, M. P. Kothiyal, and N. K. Mohan, “Two-wavelength micro-interferometry for 3-D surface profiling,” Opt. Lasers Eng. 47, 223–229 (2009).
[Crossref]

Kupfer, G.

L. Yang, W. Steinchen, M. Schuth, and G. Kupfer, “Precision measurement and nondestructive testing by means of digital phase shifting speckle pattern and speckle pattern shearing interferometry,” Measurement 16, 149–160 (1995).
[Crossref]

Leendertz, J.

J. Leendertz and J. Butters, “An image-shearing speckle-pattern interferometer for measuring bending moments,” J. Phys. E: Sci. Instruments 6, 1107–1110 (1973).
[Crossref]

J. Butters and J. Leendertz, “Speckle pattern and holographic techniques in engineering metrology,” Opt. Lasers Eng. 3, 26–30 (1971).
[Crossref]

J. Leendertz, “Interferometric displacement measurement on scattering surfaces utilizing speckle effect,” J. Phys. E: Sci. Instruments 3, 214–218 (1970).
[Crossref]

Li, J.

X. Gao, L. Yang, Y. Wang, B. Zhang, X. Dan, J. Li, and S. Wu, “Spatial phase-shift dual-beam speckle interferometry,” Appl. Opt. 57, 414–419 (2018).
[Crossref] [PubMed]

X. Xie, X. Chen, J. Li, Y. Wang, and L. Yang, “Measurement of in-plane strain with dual beam spatial phase-shift digital shearography,” Meas. Sci. Technol. 26, 115202 (2015).
[Crossref]

Liang, C.

Lu, M.

M. Lu, S. Wang, L. Bilgeri, X. Song, M. Jakobi, and A. W. Koch, “Online 3D displacement measurement using speckle interferometer with a single illumination-detection path,” Sensors (Basel, Switzerland) 18, 1923 (2018).
[Crossref]

L. Bilgeri, F. S. Bloise, M. Lu, S. Wang, M. Jakobi, and A. W. Koch, “Intensity distortions due to phase-only spatial light modulation: Characterization for applications in electronic speckle-pattern interferometry,” Rev. Sci. Instruments 89, 083701 (2018).
[Crossref]

S. Wang, M. Lu, L. M. Bilgeri, M. Jakobi, F. S. Bloise, and A. W. Koch, “Temporal electronic speckle pattern interferometry for real-time in-plane rotation analysis,” Opt. Express 26, 8744–8755 (2018).
[Crossref] [PubMed]

M. Lu, S. Wang, L. Aulbach, M. Jakobi, and A. W. Koch, “Non-phase unwrapping interferometric approach for a real-time in-plane rotation measurement,” Opt. Lett. 42, 1986–1989 (2017).
[Crossref] [PubMed]

M. Lu, S. Wang, L. Aulbach, and A. W. Koch, “Simultaneous displacement and slope measurement in electronic speckle pattern interferometry using adjustable aperture multiplexing,” Appl. Opt. 55, 5868–5875 (2016).
[Crossref] [PubMed]

Luo, W.

H. M. Shang, Y. Hung, W. Luo, and F. Chen, “Surface profiling using shearography,” Opt. Eng. 39, 23–32 (2000).
[Crossref]

Mello, M.

M. Mello, S. Hong, and A. Rosakis, “Extension of the coherent gradient sensor (cgs) to the combined measurement of in-plane and out-of-plane displacement field gradients,” Exp. Mech. 49, 277–289 (2009).
[Crossref]

M. Mello and A. J. Rosakis, “Surface characterization based on lateral shearing of diffracted wave fronts to measure in-plane and out-of-plane displacement gradient fields,” (2009). US Patent 7538891B1.

Mohan, N. K.

U. P. Kumar, B. Bhaduri, M. P. Kothiyal, and N. K. Mohan, “Two-wavelength micro-interferometry for 3-D surface profiling,” Opt. Lasers Eng. 47, 223–229 (2009).
[Crossref]

B. Bhaduri, M. Kothiyal, and N. K. Mohan, “Curvature measurement using three-aperture digital shearography and fast fourier transform,” Opt. Lasers Eng. 45, 1001–1004 (2007).
[Crossref]

B. Bhaduri, N. K. Mohan, and M. Kothiyal, “A dual-function espi system for the measurement of out-of-plane displacement and slope,” Opt. Lasers Eng. 44, 637–644 (2006).
[Crossref]

Moisson, E.

Mounier, D.

Ohta, S.

I. Yamaguchi, J.-i. Kato, and S. Ohta, “Surface shape measurement by phase-shifting digital holography,” Opt. Rev. 8, 85–89 (2001).
[Crossref]

Olszak, A. G.

K. Patorski and A. G. Olszak, “Digital in-plane electronic speckle pattern shearing interferometry,” Opt. Eng. 36, 2010–2016 (1997).
[Crossref]

Paris, P. C.

H. Tada, P. C. Paris, and G. R. Irwin, “The stress analysis of cracks,” Handbook (Del Res. Corp., 1973).

Patorski, K.

K. Patorski and A. G. Olszak, “Digital in-plane electronic speckle pattern shearing interferometry,” Opt. Eng. 36, 2010–2016 (1997).
[Crossref]

Pedrini, G.

Picart, P.

Rosakis, A.

M. Mello, S. Hong, and A. Rosakis, “Extension of the coherent gradient sensor (cgs) to the combined measurement of in-plane and out-of-plane displacement field gradients,” Exp. Mech. 49, 277–289 (2009).
[Crossref]

Rosakis, A. J.

M. Mello and A. J. Rosakis, “Surface characterization based on lateral shearing of diffracted wave fronts to measure in-plane and out-of-plane displacement gradient fields,” (2009). US Patent 7538891B1.

Ruprecht, M. W.

A. W. Koch, M. W. Ruprecht, O. Toedter, and G. Häusler, Optische messtechnik an technischen oberflächen (Expert-Verlag: Renningen-Malmsheim, Germany, 1998).

Schuth, M.

W. Steinchen, L. Yang, and M. Schuth, “TV-shearography for measuring 3D-strains,” Strain 32, 49–58 (1996).
[Crossref]

L. Yang, W. Steinchen, M. Schuth, and G. Kupfer, “Precision measurement and nondestructive testing by means of digital phase shifting speckle pattern and speckle pattern shearing interferometry,” Measurement 16, 149–160 (1995).
[Crossref]

Shang, H. M.

H. M. Shang, Y. Hung, W. Luo, and F. Chen, “Surface profiling using shearography,” Opt. Eng. 39, 23–32 (2000).
[Crossref]

Sharma, D.

Sirohi, R.

Song, X.

M. Lu, S. Wang, L. Bilgeri, X. Song, M. Jakobi, and A. W. Koch, “Online 3D displacement measurement using speckle interferometer with a single illumination-detection path,” Sensors (Basel, Switzerland) 18, 1923 (2018).
[Crossref]

Steinchen, W.

W. Steinchen, L. Yang, and M. Schuth, “TV-shearography for measuring 3D-strains,” Strain 32, 49–58 (1996).
[Crossref]

L. Yang, W. Steinchen, M. Schuth, and G. Kupfer, “Precision measurement and nondestructive testing by means of digital phase shifting speckle pattern and speckle pattern shearing interferometry,” Measurement 16, 149–160 (1995).
[Crossref]

Tada, H.

H. Tada, P. C. Paris, and G. R. Irwin, “The stress analysis of cracks,” Handbook (Del Res. Corp., 1973).

Takeda, M.

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

Tatam, R.

D. Francis, S. James, and R. Tatam, “Surface strain measurement using multi-component shearography with coherent fibre-optic imaging bundles,” Meas. Sci. Technol. 18, 3583–3591 (2007).
[Crossref]

Tippur, H. V.

H. V. Tippur, “Simultaneous and real-time measurement of slope and curvature fringes in thin structures using shearing interferometery,” Opt. Eng. 43, 3014–3021 (2004).
[Crossref]

Tiziani, H.

Toedter, O.

A. W. Koch, M. W. Ruprecht, O. Toedter, and G. Häusler, Optische messtechnik an technischen oberflächen (Expert-Verlag: Renningen-Malmsheim, Germany, 1998).

Wang, J.

Y. Hung and J. Wang, “Dual-beam phase shift shearography for measurement of in-plane strains,” Opt. Lasers Eng. 24, 403–413 (1996).
[Crossref]

Wang, S.

M. Lu, S. Wang, L. Bilgeri, X. Song, M. Jakobi, and A. W. Koch, “Online 3D displacement measurement using speckle interferometer with a single illumination-detection path,” Sensors (Basel, Switzerland) 18, 1923 (2018).
[Crossref]

L. Bilgeri, F. S. Bloise, M. Lu, S. Wang, M. Jakobi, and A. W. Koch, “Intensity distortions due to phase-only spatial light modulation: Characterization for applications in electronic speckle-pattern interferometry,” Rev. Sci. Instruments 89, 083701 (2018).
[Crossref]

S. Wang, M. Lu, L. M. Bilgeri, M. Jakobi, F. S. Bloise, and A. W. Koch, “Temporal electronic speckle pattern interferometry for real-time in-plane rotation analysis,” Opt. Express 26, 8744–8755 (2018).
[Crossref] [PubMed]

M. Lu, S. Wang, L. Aulbach, M. Jakobi, and A. W. Koch, “Non-phase unwrapping interferometric approach for a real-time in-plane rotation measurement,” Opt. Lett. 42, 1986–1989 (2017).
[Crossref] [PubMed]

M. Lu, S. Wang, L. Aulbach, and A. W. Koch, “Simultaneous displacement and slope measurement in electronic speckle pattern interferometry using adjustable aperture multiplexing,” Appl. Opt. 55, 5868–5875 (2016).
[Crossref] [PubMed]

Wang, Y.

X. Gao, L. Yang, Y. Wang, B. Zhang, X. Dan, J. Li, and S. Wu, “Spatial phase-shift dual-beam speckle interferometry,” Appl. Opt. 57, 414–419 (2018).
[Crossref] [PubMed]

X. Xie, X. Chen, J. Li, Y. Wang, and L. Yang, “Measurement of in-plane strain with dual beam spatial phase-shift digital shearography,” Meas. Sci. Technol. 26, 115202 (2015).
[Crossref]

Werth, N.

N. Werth, F. S. Bloise, and A. W. Koch, “Influence of roughness in the phase-shifting speckle method: An experimental study with applications,” Rev. Sci. Instruments 85, 015114 (2014).
[Crossref]

Wu, S.

Xie, X.

X. Xie, X. Chen, J. Li, Y. Wang, and L. Yang, “Measurement of in-plane strain with dual beam spatial phase-shift digital shearography,” Meas. Sci. Technol. 26, 115202 (2015).
[Crossref]

Yamaguchi, I.

I. Yamaguchi, J.-i. Kato, and S. Ohta, “Surface shape measurement by phase-shifting digital holography,” Opt. Rev. 8, 85–89 (2001).
[Crossref]

Yang, L.

X. Gao, L. Yang, Y. Wang, B. Zhang, X. Dan, J. Li, and S. Wu, “Spatial phase-shift dual-beam speckle interferometry,” Appl. Opt. 57, 414–419 (2018).
[Crossref] [PubMed]

X. Xie, X. Chen, J. Li, Y. Wang, and L. Yang, “Measurement of in-plane strain with dual beam spatial phase-shift digital shearography,” Meas. Sci. Technol. 26, 115202 (2015).
[Crossref]

W. Steinchen, L. Yang, and M. Schuth, “TV-shearography for measuring 3D-strains,” Strain 32, 49–58 (1996).
[Crossref]

L. Yang, W. Steinchen, M. Schuth, and G. Kupfer, “Precision measurement and nondestructive testing by means of digital phase shifting speckle pattern and speckle pattern shearing interferometry,” Measurement 16, 149–160 (1995).
[Crossref]

Zhang, B.

Zou, Y.-L.

Appl. Opt. (6)

Exp. Mech. (1)

M. Mello, S. Hong, and A. Rosakis, “Extension of the coherent gradient sensor (cgs) to the combined measurement of in-plane and out-of-plane displacement field gradients,” Exp. Mech. 49, 277–289 (2009).
[Crossref]

J. Phys. E: Sci. Instruments (2)

J. Leendertz and J. Butters, “An image-shearing speckle-pattern interferometer for measuring bending moments,” J. Phys. E: Sci. Instruments 6, 1107–1110 (1973).
[Crossref]

J. Leendertz, “Interferometric displacement measurement on scattering surfaces utilizing speckle effect,” J. Phys. E: Sci. Instruments 3, 214–218 (1970).
[Crossref]

JOSA A (1)

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

Meas. Sci. Technol. (2)

D. Francis, S. James, and R. Tatam, “Surface strain measurement using multi-component shearography with coherent fibre-optic imaging bundles,” Meas. Sci. Technol. 18, 3583–3591 (2007).
[Crossref]

X. Xie, X. Chen, J. Li, Y. Wang, and L. Yang, “Measurement of in-plane strain with dual beam spatial phase-shift digital shearography,” Meas. Sci. Technol. 26, 115202 (2015).
[Crossref]

Measurement (1)

L. Yang, W. Steinchen, M. Schuth, and G. Kupfer, “Precision measurement and nondestructive testing by means of digital phase shifting speckle pattern and speckle pattern shearing interferometry,” Measurement 16, 149–160 (1995).
[Crossref]

Opt. Eng. (3)

H. V. Tippur, “Simultaneous and real-time measurement of slope and curvature fringes in thin structures using shearing interferometery,” Opt. Eng. 43, 3014–3021 (2004).
[Crossref]

K. Patorski and A. G. Olszak, “Digital in-plane electronic speckle pattern shearing interferometry,” Opt. Eng. 36, 2010–2016 (1997).
[Crossref]

H. M. Shang, Y. Hung, W. Luo, and F. Chen, “Surface profiling using shearography,” Opt. Eng. 39, 23–32 (2000).
[Crossref]

Opt. Express (1)

Opt. Lasers Eng. (5)

Y. Hung and J. Wang, “Dual-beam phase shift shearography for measurement of in-plane strains,” Opt. Lasers Eng. 24, 403–413 (1996).
[Crossref]

U. P. Kumar, B. Bhaduri, M. P. Kothiyal, and N. K. Mohan, “Two-wavelength micro-interferometry for 3-D surface profiling,” Opt. Lasers Eng. 47, 223–229 (2009).
[Crossref]

J. Butters and J. Leendertz, “Speckle pattern and holographic techniques in engineering metrology,” Opt. Lasers Eng. 3, 26–30 (1971).
[Crossref]

B. Bhaduri, M. Kothiyal, and N. K. Mohan, “Curvature measurement using three-aperture digital shearography and fast fourier transform,” Opt. Lasers Eng. 45, 1001–1004 (2007).
[Crossref]

B. Bhaduri, N. K. Mohan, and M. Kothiyal, “A dual-function espi system for the measurement of out-of-plane displacement and slope,” Opt. Lasers Eng. 44, 637–644 (2006).
[Crossref]

Opt. Lett. (1)

Opt. Rev. (1)

I. Yamaguchi, J.-i. Kato, and S. Ohta, “Surface shape measurement by phase-shifting digital holography,” Opt. Rev. 8, 85–89 (2001).
[Crossref]

Rev. Sci. Instruments (2)

L. Bilgeri, F. S. Bloise, M. Lu, S. Wang, M. Jakobi, and A. W. Koch, “Intensity distortions due to phase-only spatial light modulation: Characterization for applications in electronic speckle-pattern interferometry,” Rev. Sci. Instruments 89, 083701 (2018).
[Crossref]

N. Werth, F. S. Bloise, and A. W. Koch, “Influence of roughness in the phase-shifting speckle method: An experimental study with applications,” Rev. Sci. Instruments 85, 015114 (2014).
[Crossref]

Sensors (Basel, Switzerland) (1)

M. Lu, S. Wang, L. Bilgeri, X. Song, M. Jakobi, and A. W. Koch, “Online 3D displacement measurement using speckle interferometer with a single illumination-detection path,” Sensors (Basel, Switzerland) 18, 1923 (2018).
[Crossref]

Strain (1)

W. Steinchen, L. Yang, and M. Schuth, “TV-shearography for measuring 3D-strains,” Strain 32, 49–58 (1996).
[Crossref]

Other (3)

H. Tada, P. C. Paris, and G. R. Irwin, “The stress analysis of cracks,” Handbook (Del Res. Corp., 1973).

M. Mello and A. J. Rosakis, “Surface characterization based on lateral shearing of diffracted wave fronts to measure in-plane and out-of-plane displacement gradient fields,” (2009). US Patent 7538891B1.

A. W. Koch, M. W. Ruprecht, O. Toedter, and G. Häusler, Optische messtechnik an technischen oberflächen (Expert-Verlag: Renningen-Malmsheim, Germany, 1998).

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Figures (5)

Fig. 1
Fig. 1 Symmetric dual-sensitive shearography. (a) Schematic of the optical shearography setup. (b) Shearograms obtained using the shearography system. (c) Spatial-carrier frequency generated by the common-path shearing device.
Fig. 2
Fig. 2 Experimental setup. The spectrum maps acquired from the left (a) and right (b) channels of the interferometer and the resulting spectrum (c).
Fig. 3
Fig. 3 The three-point bending fracture test setup and the PMMA specimen (105×40×10mm3).
Fig. 4
Fig. 4 Out-of-plane and in-plane coupled phase maps relating to the left (a) and right (b) sensitivity vectors, respectively.
Fig. 5
Fig. 5 Measured phase maps relating to the out-of-plane crack-tip strain component (a) Δlzy, and the in-plane crack-tip strain component (c) Δlxy. Analytical solutions (b) Δlzy and (d) Δlxy by linear elastic fracture mechanics.

Equations (16)

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k 1 = 2 π λ ( w 0 ) ,
k 21 = 2 π λ ( sin θ u 0 + cos θ w 0 ) ,
k 22 = 2 π λ ( sin θ u 0 + cos θ w 0 ) ,
Δ ϕ l = k l ( u , v , w ) Δ l ( x , y ) = [ ( k 1 k 21 ) | ( x , y ) ( k 1 k 21 ) | ( x , y + Δ y ) ] ( Δ l x u 0 + Δ l y y 0 + Δ l z w 0 ) = 2 π λ [ sin θ Δ l x Δ y ( 1 + cos θ ) Δ l z Δ y ] Δ y ,
Δ ϕ r = k r ( u , v , w ) Δ l ( x , y ) = [ ( k 1 k 22 ) | ( x , y ) ( k 1 k 22 ) | ( x , y + Δ y ) ] ( Δ l x u 0 + Δ l y y 0 + Δ l z w 0 ) = 2 π λ [ sin θ Δ l x Δ y ( 1 + cos θ ) Δ l z Δ y ] Δ y ,
Δ ϕ l + Δ ϕ r = 4 π λ [ ( 1 + cos θ ) Δ l z Δ y ] Δ y .
Δ ϕ l Δ ϕ r = 4 π λ [ ( sin θ ) Δ l x Δ y ] Δ y .
u 11 ( x , y ) = | u 11 ( x , y ) | e [ i ϕ ( x , y ) + i 2 π y f l y ] ,
u 12 ( x , y + Δ y ) = | u 12 ( x , y + Δ y ) | e [ i ϕ ( x , y + Δ y ) i 2 π y f l y ] ,
I l ( x , y ) = [ u 11 ( x , y ) + u 12 ( x , y ) + Δ y ] [ u 11 ( x , y ) + u 12 ( x , y + Δ y ) ] * = u 11 ( x , y ) u 11 * ( x , y ) + u 12 ( x , y ) u 12 * ( x , y ) + u 11 ( x , y ) u 12 * ( x , y ) + u 12 ( x , y ) u 11 * ( x , y ) ,
FT ( I l ) = DC + U 11 ( f x , f y ) U 12 * ( f x , f y + f 0 ) + U 12 ( f x , f y + f 0 ) U 11 * ( f x , f y ) ,
Δ ϕ l ( x , y + Δ y ) = Δ tan 1 Im [ u 11 u 12 * ] Re [ u 11 u 12 * ] .
Δ ϕ r ( x , y + Δ y ) = Δ tan 1 Im [ u 21 u 22 * ] Re [ u 21 u 22 * ] .
U = ( 1 + ν ) K 1 2 E r 2 π [ ( 2 k + 1 ) sin θ 2 sin 3 θ 2 ] ,
V = ( 1 + ν ) K 1 2 E r 2 π [ ( 2 k 1 ) cos θ 2 cos 3 θ 2 ] ,
W = ν h K 1 E 1 2 π r cos θ 2 ,

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