Abstract

A phase-resolved heterodyne shearing interferometer concept is under development for high-rate, whole field observations of transient surface motion. The sensor utilizes frequency and polarization multiplexing with two temporal carrier frequencies to separate each segment of a shearing Mach-Zehnder interferometer. Post-processing routines have been developed to recombine the segments by extracting the scattered object phase from Doppler shifted intermediate carrier frequencies. The processing routines provide quantitative relative phase changes and information required to generate phase resolved shearographic fringe patterns without temporal or spatial phase shifting. Separation of each segment allows for adjustment of shearing distance and direction as well as simultaneous whole field Doppler velocity (LDV) measurements. This paper presents background theory and numerical model results leading to a sensor concept.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref]
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    [Crossref]
  7. S. Yoneyama and S. Arikawa, “Instantaneous phase-stepping interferometry based on a pixelated micro-polarizer array,” Theor. Appl. Mech. Lett. 6, 162–166 (2016).
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  13. G. L. Richoz and G. S. Schajer, “Simultaneous two-axis shearographic interferometer using multiple wavelengths and a color camera,” Opt. Lasers Eng. 77, 143–153 (2016).
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  15. T. W. Du Bosq and E. Repasi, “Detector integration time dependent atmospheric turbulence imaging simulation,” Proc. SPIE 9452, 94520B (2015).
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    [Crossref]
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  24. G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun. 282, 3693–3700 (2009).
    [Crossref]
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    [Crossref] [PubMed]
  28. H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).
    [Crossref]
  29. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company, 2007).
  30. S. Rothberg, “Numerical simulation of speckle noise in laser vibrometry,” Appl. Optics 45, 4523–4533 (2006).
    [Crossref]
  31. B.K. Park, O. Boric-Lubecke, and V. M. Lubecke, “Arctangent demodulation with dc offset compensation in quadrature doppler radar receiver systems,” IEEE T. Microw. Theory. 55(5), 1073–1079 (2007).
    [Crossref]
  32. A. Rogalski, Infrared Detectors (CRC, 2010).

2017 (2)

P. L. Reu, D. P. Rohe, and L. D. Jacobs, “Comparison of dic and ldv for practical vibration and modal measurements,” Mech. Syst. Signal Pr. 86, 2–16 (2017).
[Crossref]

X. Wang, Z. Gao, J. Qin, X. Zhang, and S. Yang, “Temporal heterodyne shearing speckle pattern interferometry,” Optics and Lasers in Engineering 93, 76–82 (2017).
[Crossref]

2016 (6)

G. L. Richoz and G. S. Schajer, “Simultaneous two-axis shearographic interferometer using multiple wavelengths and a color camera,” Opt. Lasers Eng. 77, 143–153 (2016).
[Crossref]

M. Khaleghi, J. T. Cheng, C. Furlong, and J. J. Rosowski, “In-plane and out-of-plane motions of the human tympanic membrane,” J. Acoust. Soc. Am. 139, 104–117 (2016).
[Crossref] [PubMed]

J. Perea and B. Libbey, “Development of a heterodyne speckle imager to measure 3 degrees of vibrational freedom,” Opt. Express 24, 8253–8265 (2016).
[Crossref] [PubMed]

F. Languy, J.-F. Vandenrijt, C. Thizy, J. Rochet, C. Loffet, D. Simon, and M. P. Georges, “Vibration mode shapes visualization in industrial environment by real-time time-averaged phase-stepped electronic speckle pattern interferometry at 10.6 μm and shearography at 532 nm,” Opt. Eng. 55, 121704 (2016).
[Crossref]

S. Yoneyama and S. Arikawa, “Instantaneous phase-stepping interferometry based on a pixelated micro-polarizer array,” Theor. Appl. Mech. Lett. 6, 162–166 (2016).
[Crossref]

X. Xie, C. P. Lee, J. Li, B. Zhang, and L. Yang, “Polarized digital shearography for simultaneous dual shearing directions measurements,” Rev. Sci. Instrum. 87, 083110 (2016).
[Crossref] [PubMed]

2015 (6)

C. Falldorf, R. Klattenhoff, and R. B. Bergmann, “Single shot lateral shear interferometer with variable shear,” Opt. Eng. 54, 054105 (2015).
[Crossref]

G. Rodríguez-Zurita, A. García-Arellano, N. Toto-Arellano, V. Flores-Muñoz, R. Pastrana-Sánchez, C. Robledo-Sánchez, O. Martínez-Bravo, N. Vásquez-Pasmiño, and C. Costa-Vera, “One–shot phase stepping with a pulsed laser and modulation of polarization: application to speckle interferometry,” Opt. Express 23, 23414–23427 (2015).
[Crossref]

J. G. Chen, R. W. Haupt, and O. Buyukozturk, “Operational and defect parameters concerning the acoustic-laser vibrometry method for frp-reinforced concrete,” NDTE Int. 71, 43–53 (2015).
[Crossref]

J. Bencteux, P. Pagnoux, T. Kostas, S. Bayat, and M. Atlan, “Holographic laser doppler imaging of pulsatile blood flow,” Biomed. Opt. 20, 066006 (2015).
[Crossref]

F. Tenner, D. Elz, Z. Zalevsky, and M. Schmidt, “Optical tremor analysis with the speckle imaging technique,” J. Imaging. Sci. Techn. 59, 104021 (2015).
[Crossref]

T. W. Du Bosq and E. Repasi, “Detector integration time dependent atmospheric turbulence imaging simulation,” Proc. SPIE 9452, 94520B (2015).
[Crossref]

2013 (1)

X. Xie, L. Yang, N. Xu, and X. Chen, “Michelson interferometer based spatial phase shift shearography,” Appl. Optics 52, 4063–4071 (2013).
[Crossref]

2012 (2)

D. I. Serrano-García, N. I. Toto-Arellano, A. Martínez-García, J. A. R. Álvarez, and G. R. Zurita, “Dynamic phase profile of phase objects based in the use of a quasi-common path interferometer,” Optik 123, 1742–1745 (2012).
[Crossref]

H. Y. Huang, L. Tian, Z. Zhang, Y. Liu, Z. Chen, and G. Barbastathis, “Path-independent phase unwrapping using phase gradient and total-variation (tv) denoising,” Opt. Express 20, 14075–14089 (2012).
[Crossref] [PubMed]

2010 (1)

D. Francis, R. Tatam, and R. Groves, “Shearography technology and applications: a review,” Meas. Sci. Technol. 21, 102001 (2010).
[Crossref]

2009 (1)

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun. 282, 3693–3700 (2009).
[Crossref]

2007 (1)

B.K. Park, O. Boric-Lubecke, and V. M. Lubecke, “Arctangent demodulation with dc offset compensation in quadrature doppler radar receiver systems,” IEEE T. Microw. Theory. 55(5), 1073–1079 (2007).
[Crossref]

2006 (1)

S. Rothberg, “Numerical simulation of speckle noise in laser vibrometry,” Appl. Optics 45, 4523–4533 (2006).
[Crossref]

2000 (1)

R. M. Groves, S. W. James, and R. P. Tatam, “Polarization-multiplexed and phase-stepped fibre optic shearography using laser wavelength modulation,” Meas. Sci. Technol. 11, 1389 (2000).
[Crossref]

1999 (1)

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).
[Crossref]

Aebischer, H. A.

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).
[Crossref]

Álvarez, J. A. R.

D. I. Serrano-García, N. I. Toto-Arellano, A. Martínez-García, J. A. R. Álvarez, and G. R. Zurita, “Dynamic phase profile of phase objects based in the use of a quasi-common path interferometer,” Optik 123, 1742–1745 (2012).
[Crossref]

Arikawa, S.

S. Yoneyama and S. Arikawa, “Instantaneous phase-stepping interferometry based on a pixelated micro-polarizer array,” Theor. Appl. Mech. Lett. 6, 162–166 (2016).
[Crossref]

Arizaga, R.

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun. 282, 3693–3700 (2009).
[Crossref]

Atlan, M.

J. Bencteux, P. Pagnoux, T. Kostas, S. Bayat, and M. Atlan, “Holographic laser doppler imaging of pulsatile blood flow,” Biomed. Opt. 20, 066006 (2015).
[Crossref]

Aylo, R.

G.T. Nehmetallah, R. Aylo, and L.A. Williams, Analog and Digital Holography with MATLAB (SPIE, 2015).
[Crossref]

Barbastathis, G.

Bayat, S.

J. Bencteux, P. Pagnoux, T. Kostas, S. Bayat, and M. Atlan, “Holographic laser doppler imaging of pulsatile blood flow,” Biomed. Opt. 20, 066006 (2015).
[Crossref]

Bencteux, J.

J. Bencteux, P. Pagnoux, T. Kostas, S. Bayat, and M. Atlan, “Holographic laser doppler imaging of pulsatile blood flow,” Biomed. Opt. 20, 066006 (2015).
[Crossref]

Bergmann, R. B.

C. Falldorf, R. Klattenhoff, and R. B. Bergmann, “Single shot lateral shear interferometer with variable shear,” Opt. Eng. 54, 054105 (2015).
[Crossref]

Bisle, W. J.

W. J. Bisle, D. Scherling, M. K. Kalms, and W. Osten, “Improved shearography for use on optical non cooperating surfaces under daylight conditions,” Proc. AIPB, 1928–1935 (2001).
[Crossref]

Boric-Lubecke, O.

B.K. Park, O. Boric-Lubecke, and V. M. Lubecke, “Arctangent demodulation with dc offset compensation in quadrature doppler radar receiver systems,” IEEE T. Microw. Theory. 55(5), 1073–1079 (2007).
[Crossref]

Buyukozturk, O.

J. G. Chen, R. W. Haupt, and O. Buyukozturk, “Operational and defect parameters concerning the acoustic-laser vibrometry method for frp-reinforced concrete,” NDTE Int. 71, 43–53 (2015).
[Crossref]

Chen, J. G.

J. G. Chen, R. W. Haupt, and O. Buyukozturk, “Operational and defect parameters concerning the acoustic-laser vibrometry method for frp-reinforced concrete,” NDTE Int. 71, 43–53 (2015).
[Crossref]

Chen, X.

X. Xie, L. Yang, N. Xu, and X. Chen, “Michelson interferometer based spatial phase shift shearography,” Appl. Optics 52, 4063–4071 (2013).
[Crossref]

Chen, Z.

Cheng, J. T.

M. Khaleghi, J. T. Cheng, C. Furlong, and J. J. Rosowski, “In-plane and out-of-plane motions of the human tympanic membrane,” J. Acoust. Soc. Am. 139, 104–117 (2016).
[Crossref] [PubMed]

Costa-Vera, C.

Du Bosq, T. W.

T. W. Du Bosq and E. Repasi, “Detector integration time dependent atmospheric turbulence imaging simulation,” Proc. SPIE 9452, 94520B (2015).
[Crossref]

Elz, D.

F. Tenner, D. Elz, Z. Zalevsky, and M. Schmidt, “Optical tremor analysis with the speckle imaging technique,” J. Imaging. Sci. Techn. 59, 104021 (2015).
[Crossref]

Falldorf, C.

C. Falldorf, R. Klattenhoff, and R. B. Bergmann, “Single shot lateral shear interferometer with variable shear,” Opt. Eng. 54, 054105 (2015).
[Crossref]

Flores-Muñoz, V.

Francis, D.

D. Francis, R. Tatam, and R. Groves, “Shearography technology and applications: a review,” Meas. Sci. Technol. 21, 102001 (2010).
[Crossref]

Furlong, C.

M. Khaleghi, J. T. Cheng, C. Furlong, and J. J. Rosowski, “In-plane and out-of-plane motions of the human tympanic membrane,” J. Acoust. Soc. Am. 139, 104–117 (2016).
[Crossref] [PubMed]

Gao, Z.

X. Wang, Z. Gao, J. Qin, X. Zhang, and S. Yang, “Temporal heterodyne shearing speckle pattern interferometry,” Optics and Lasers in Engineering 93, 76–82 (2017).
[Crossref]

García-Arellano, A.

Georges, M. P.

F. Languy, J.-F. Vandenrijt, C. Thizy, J. Rochet, C. Loffet, D. Simon, and M. P. Georges, “Vibration mode shapes visualization in industrial environment by real-time time-averaged phase-stepped electronic speckle pattern interferometry at 10.6 μm and shearography at 532 nm,” Opt. Eng. 55, 121704 (2016).
[Crossref]

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company, 2007).

J. W. Goodman, Introduction to Fourier optics (Roberts and Company, 2005).

Groves, R.

D. Francis, R. Tatam, and R. Groves, “Shearography technology and applications: a review,” Meas. Sci. Technol. 21, 102001 (2010).
[Crossref]

Groves, R. M.

R. M. Groves, S. W. James, and R. P. Tatam, “Polarization-multiplexed and phase-stepped fibre optic shearography using laser wavelength modulation,” Meas. Sci. Technol. 11, 1389 (2000).
[Crossref]

Hariharan, P.

P. Hariharan, Basics of Interferometry (Academic, 2010).

Haupt, R. W.

J. G. Chen, R. W. Haupt, and O. Buyukozturk, “Operational and defect parameters concerning the acoustic-laser vibrometry method for frp-reinforced concrete,” NDTE Int. 71, 43–53 (2015).
[Crossref]

Huang, H. Y.

Jacobs, L. D.

P. L. Reu, D. P. Rohe, and L. D. Jacobs, “Comparison of dic and ldv for practical vibration and modal measurements,” Mech. Syst. Signal Pr. 86, 2–16 (2017).
[Crossref]

James, S. W.

R. M. Groves, S. W. James, and R. P. Tatam, “Polarization-multiplexed and phase-stepped fibre optic shearography using laser wavelength modulation,” Meas. Sci. Technol. 11, 1389 (2000).
[Crossref]

Kalms, M. K.

W. J. Bisle, D. Scherling, M. K. Kalms, and W. Osten, “Improved shearography for use on optical non cooperating surfaces under daylight conditions,” Proc. AIPB, 1928–1935 (2001).
[Crossref]

Khaleghi, M.

M. Khaleghi, J. T. Cheng, C. Furlong, and J. J. Rosowski, “In-plane and out-of-plane motions of the human tympanic membrane,” J. Acoust. Soc. Am. 139, 104–117 (2016).
[Crossref] [PubMed]

Klattenhoff, R.

C. Falldorf, R. Klattenhoff, and R. B. Bergmann, “Single shot lateral shear interferometer with variable shear,” Opt. Eng. 54, 054105 (2015).
[Crossref]

Kong, J.A.

D.H. Staelin, A.W. Morgenthaler, and J.A. Kong, Electromagnetic waves (Prentice Hall, 1994).

Kostas, T.

J. Bencteux, P. Pagnoux, T. Kostas, S. Bayat, and M. Atlan, “Holographic laser doppler imaging of pulsatile blood flow,” Biomed. Opt. 20, 066006 (2015).
[Crossref]

Languy, F.

F. Languy, J.-F. Vandenrijt, C. Thizy, J. Rochet, C. Loffet, D. Simon, and M. P. Georges, “Vibration mode shapes visualization in industrial environment by real-time time-averaged phase-stepped electronic speckle pattern interferometry at 10.6 μm and shearography at 532 nm,” Opt. Eng. 55, 121704 (2016).
[Crossref]

Lee, C. P.

X. Xie, C. P. Lee, J. Li, B. Zhang, and L. Yang, “Polarized digital shearography for simultaneous dual shearing directions measurements,” Rev. Sci. Instrum. 87, 083110 (2016).
[Crossref] [PubMed]

Li, J.

X. Xie, C. P. Lee, J. Li, B. Zhang, and L. Yang, “Polarized digital shearography for simultaneous dual shearing directions measurements,” Rev. Sci. Instrum. 87, 083110 (2016).
[Crossref] [PubMed]

Libbey, B.

Liu, Y.

Loffet, C.

F. Languy, J.-F. Vandenrijt, C. Thizy, J. Rochet, C. Loffet, D. Simon, and M. P. Georges, “Vibration mode shapes visualization in industrial environment by real-time time-averaged phase-stepped electronic speckle pattern interferometry at 10.6 μm and shearography at 532 nm,” Opt. Eng. 55, 121704 (2016).
[Crossref]

Lubecke, V. M.

B.K. Park, O. Boric-Lubecke, and V. M. Lubecke, “Arctangent demodulation with dc offset compensation in quadrature doppler radar receiver systems,” IEEE T. Microw. Theory. 55(5), 1073–1079 (2007).
[Crossref]

Martínez-Bravo, O.

Martínez-García, A.

D. I. Serrano-García, N. I. Toto-Arellano, A. Martínez-García, J. A. R. Álvarez, and G. R. Zurita, “Dynamic phase profile of phase objects based in the use of a quasi-common path interferometer,” Optik 123, 1742–1745 (2012).
[Crossref]

Morgenthaler, A.W.

D.H. Staelin, A.W. Morgenthaler, and J.A. Kong, Electromagnetic waves (Prentice Hall, 1994).

Nehmetallah, G.T.

G.T. Nehmetallah, R. Aylo, and L.A. Williams, Analog and Digital Holography with MATLAB (SPIE, 2015).
[Crossref]

Osten, W.

W. J. Bisle, D. Scherling, M. K. Kalms, and W. Osten, “Improved shearography for use on optical non cooperating surfaces under daylight conditions,” Proc. AIPB, 1928–1935 (2001).
[Crossref]

Pagnoux, P.

J. Bencteux, P. Pagnoux, T. Kostas, S. Bayat, and M. Atlan, “Holographic laser doppler imaging of pulsatile blood flow,” Biomed. Opt. 20, 066006 (2015).
[Crossref]

Park, B.K.

B.K. Park, O. Boric-Lubecke, and V. M. Lubecke, “Arctangent demodulation with dc offset compensation in quadrature doppler radar receiver systems,” IEEE T. Microw. Theory. 55(5), 1073–1079 (2007).
[Crossref]

Pastrana-Sánchez, R.

Perea, J.

Qin, J.

X. Wang, Z. Gao, J. Qin, X. Zhang, and S. Yang, “Temporal heterodyne shearing speckle pattern interferometry,” Optics and Lasers in Engineering 93, 76–82 (2017).
[Crossref]

Rabal, H.

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun. 282, 3693–3700 (2009).
[Crossref]

Repasi, E.

T. W. Du Bosq and E. Repasi, “Detector integration time dependent atmospheric turbulence imaging simulation,” Proc. SPIE 9452, 94520B (2015).
[Crossref]

Reu, P. L.

P. L. Reu, D. P. Rohe, and L. D. Jacobs, “Comparison of dic and ldv for practical vibration and modal measurements,” Mech. Syst. Signal Pr. 86, 2–16 (2017).
[Crossref]

Richoz, G. L.

G. L. Richoz and G. S. Schajer, “Simultaneous two-axis shearographic interferometer using multiple wavelengths and a color camera,” Opt. Lasers Eng. 77, 143–153 (2016).
[Crossref]

Robledo-Sánchez, C.

Rochet, J.

F. Languy, J.-F. Vandenrijt, C. Thizy, J. Rochet, C. Loffet, D. Simon, and M. P. Georges, “Vibration mode shapes visualization in industrial environment by real-time time-averaged phase-stepped electronic speckle pattern interferometry at 10.6 μm and shearography at 532 nm,” Opt. Eng. 55, 121704 (2016).
[Crossref]

Rodríguez-Zurita, G.

Rogalski, A.

A. Rogalski, Infrared Detectors (CRC, 2010).

Rohe, D. P.

P. L. Reu, D. P. Rohe, and L. D. Jacobs, “Comparison of dic and ldv for practical vibration and modal measurements,” Mech. Syst. Signal Pr. 86, 2–16 (2017).
[Crossref]

Rosowski, J. J.

M. Khaleghi, J. T. Cheng, C. Furlong, and J. J. Rosowski, “In-plane and out-of-plane motions of the human tympanic membrane,” J. Acoust. Soc. Am. 139, 104–117 (2016).
[Crossref] [PubMed]

Rothberg, S.

S. Rothberg, “Numerical simulation of speckle noise in laser vibrometry,” Appl. Optics 45, 4523–4533 (2006).
[Crossref]

Schajer, G. S.

G. L. Richoz and G. S. Schajer, “Simultaneous two-axis shearographic interferometer using multiple wavelengths and a color camera,” Opt. Lasers Eng. 77, 143–153 (2016).
[Crossref]

Scherling, D.

W. J. Bisle, D. Scherling, M. K. Kalms, and W. Osten, “Improved shearography for use on optical non cooperating surfaces under daylight conditions,” Proc. AIPB, 1928–1935 (2001).
[Crossref]

Schmidt, M.

F. Tenner, D. Elz, Z. Zalevsky, and M. Schmidt, “Optical tremor analysis with the speckle imaging technique,” J. Imaging. Sci. Techn. 59, 104021 (2015).
[Crossref]

Sendra, G.

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun. 282, 3693–3700 (2009).
[Crossref]

Serrano-García, D. I.

D. I. Serrano-García, N. I. Toto-Arellano, A. Martínez-García, J. A. R. Álvarez, and G. R. Zurita, “Dynamic phase profile of phase objects based in the use of a quasi-common path interferometer,” Optik 123, 1742–1745 (2012).
[Crossref]

Simon, D.

F. Languy, J.-F. Vandenrijt, C. Thizy, J. Rochet, C. Loffet, D. Simon, and M. P. Georges, “Vibration mode shapes visualization in industrial environment by real-time time-averaged phase-stepped electronic speckle pattern interferometry at 10.6 μm and shearography at 532 nm,” Opt. Eng. 55, 121704 (2016).
[Crossref]

Staelin, D.H.

D.H. Staelin, A.W. Morgenthaler, and J.A. Kong, Electromagnetic waves (Prentice Hall, 1994).

Steinchen, W.

W. Steinchen and L. Yang, Digital Shearography: Theory and Application of Digital Speckle Pattern Shearing Interferometry (SPIE, 2003).

Tatam, R.

D. Francis, R. Tatam, and R. Groves, “Shearography technology and applications: a review,” Meas. Sci. Technol. 21, 102001 (2010).
[Crossref]

Tatam, R. P.

R. M. Groves, S. W. James, and R. P. Tatam, “Polarization-multiplexed and phase-stepped fibre optic shearography using laser wavelength modulation,” Meas. Sci. Technol. 11, 1389 (2000).
[Crossref]

Tenner, F.

F. Tenner, D. Elz, Z. Zalevsky, and M. Schmidt, “Optical tremor analysis with the speckle imaging technique,” J. Imaging. Sci. Techn. 59, 104021 (2015).
[Crossref]

Thizy, C.

F. Languy, J.-F. Vandenrijt, C. Thizy, J. Rochet, C. Loffet, D. Simon, and M. P. Georges, “Vibration mode shapes visualization in industrial environment by real-time time-averaged phase-stepped electronic speckle pattern interferometry at 10.6 μm and shearography at 532 nm,” Opt. Eng. 55, 121704 (2016).
[Crossref]

Tian, L.

Toto-Arellano, N.

Toto-Arellano, N. I.

D. I. Serrano-García, N. I. Toto-Arellano, A. Martínez-García, J. A. R. Álvarez, and G. R. Zurita, “Dynamic phase profile of phase objects based in the use of a quasi-common path interferometer,” Optik 123, 1742–1745 (2012).
[Crossref]

Trivi, M.

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun. 282, 3693–3700 (2009).
[Crossref]

Vandenrijt, J.-F.

F. Languy, J.-F. Vandenrijt, C. Thizy, J. Rochet, C. Loffet, D. Simon, and M. P. Georges, “Vibration mode shapes visualization in industrial environment by real-time time-averaged phase-stepped electronic speckle pattern interferometry at 10.6 μm and shearography at 532 nm,” Opt. Eng. 55, 121704 (2016).
[Crossref]

Vásquez-Pasmiño, N.

Waldner, S.

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).
[Crossref]

Wang, X.

X. Wang, Z. Gao, J. Qin, X. Zhang, and S. Yang, “Temporal heterodyne shearing speckle pattern interferometry,” Optics and Lasers in Engineering 93, 76–82 (2017).
[Crossref]

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G.T. Nehmetallah, R. Aylo, and L.A. Williams, Analog and Digital Holography with MATLAB (SPIE, 2015).
[Crossref]

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X. Xie, C. P. Lee, J. Li, B. Zhang, and L. Yang, “Polarized digital shearography for simultaneous dual shearing directions measurements,” Rev. Sci. Instrum. 87, 083110 (2016).
[Crossref] [PubMed]

X. Xie, L. Yang, N. Xu, and X. Chen, “Michelson interferometer based spatial phase shift shearography,” Appl. Optics 52, 4063–4071 (2013).
[Crossref]

L. Yang and X. Xie, Digital shearography: New Developments and Applications (SPIE, 2016).

Xu, N.

X. Xie, L. Yang, N. Xu, and X. Chen, “Michelson interferometer based spatial phase shift shearography,” Appl. Optics 52, 4063–4071 (2013).
[Crossref]

Yang, L.

X. Xie, C. P. Lee, J. Li, B. Zhang, and L. Yang, “Polarized digital shearography for simultaneous dual shearing directions measurements,” Rev. Sci. Instrum. 87, 083110 (2016).
[Crossref] [PubMed]

X. Xie, L. Yang, N. Xu, and X. Chen, “Michelson interferometer based spatial phase shift shearography,” Appl. Optics 52, 4063–4071 (2013).
[Crossref]

W. Steinchen and L. Yang, Digital Shearography: Theory and Application of Digital Speckle Pattern Shearing Interferometry (SPIE, 2003).

L. Yang and X. Xie, Digital shearography: New Developments and Applications (SPIE, 2016).

Yang, S.

X. Wang, Z. Gao, J. Qin, X. Zhang, and S. Yang, “Temporal heterodyne shearing speckle pattern interferometry,” Optics and Lasers in Engineering 93, 76–82 (2017).
[Crossref]

Yoneyama, S.

S. Yoneyama and S. Arikawa, “Instantaneous phase-stepping interferometry based on a pixelated micro-polarizer array,” Theor. Appl. Mech. Lett. 6, 162–166 (2016).
[Crossref]

Zalevsky, Z.

F. Tenner, D. Elz, Z. Zalevsky, and M. Schmidt, “Optical tremor analysis with the speckle imaging technique,” J. Imaging. Sci. Techn. 59, 104021 (2015).
[Crossref]

Zhang, B.

X. Xie, C. P. Lee, J. Li, B. Zhang, and L. Yang, “Polarized digital shearography for simultaneous dual shearing directions measurements,” Rev. Sci. Instrum. 87, 083110 (2016).
[Crossref] [PubMed]

Zhang, X.

X. Wang, Z. Gao, J. Qin, X. Zhang, and S. Yang, “Temporal heterodyne shearing speckle pattern interferometry,” Optics and Lasers in Engineering 93, 76–82 (2017).
[Crossref]

Zhang, Z.

Zurita, G. R.

D. I. Serrano-García, N. I. Toto-Arellano, A. Martínez-García, J. A. R. Álvarez, and G. R. Zurita, “Dynamic phase profile of phase objects based in the use of a quasi-common path interferometer,” Optik 123, 1742–1745 (2012).
[Crossref]

Appl. Optics (2)

X. Xie, L. Yang, N. Xu, and X. Chen, “Michelson interferometer based spatial phase shift shearography,” Appl. Optics 52, 4063–4071 (2013).
[Crossref]

S. Rothberg, “Numerical simulation of speckle noise in laser vibrometry,” Appl. Optics 45, 4523–4533 (2006).
[Crossref]

Biomed. Opt. (1)

J. Bencteux, P. Pagnoux, T. Kostas, S. Bayat, and M. Atlan, “Holographic laser doppler imaging of pulsatile blood flow,” Biomed. Opt. 20, 066006 (2015).
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B.K. Park, O. Boric-Lubecke, and V. M. Lubecke, “Arctangent demodulation with dc offset compensation in quadrature doppler radar receiver systems,” IEEE T. Microw. Theory. 55(5), 1073–1079 (2007).
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J. Acoust. Soc. Am. (1)

M. Khaleghi, J. T. Cheng, C. Furlong, and J. J. Rosowski, “In-plane and out-of-plane motions of the human tympanic membrane,” J. Acoust. Soc. Am. 139, 104–117 (2016).
[Crossref] [PubMed]

J. Imaging. Sci. Techn. (1)

F. Tenner, D. Elz, Z. Zalevsky, and M. Schmidt, “Optical tremor analysis with the speckle imaging technique,” J. Imaging. Sci. Techn. 59, 104021 (2015).
[Crossref]

Meas. Sci. Technol. (2)

R. M. Groves, S. W. James, and R. P. Tatam, “Polarization-multiplexed and phase-stepped fibre optic shearography using laser wavelength modulation,” Meas. Sci. Technol. 11, 1389 (2000).
[Crossref]

D. Francis, R. Tatam, and R. Groves, “Shearography technology and applications: a review,” Meas. Sci. Technol. 21, 102001 (2010).
[Crossref]

Mech. Syst. Signal Pr. (1)

P. L. Reu, D. P. Rohe, and L. D. Jacobs, “Comparison of dic and ldv for practical vibration and modal measurements,” Mech. Syst. Signal Pr. 86, 2–16 (2017).
[Crossref]

NDTE Int. (1)

J. G. Chen, R. W. Haupt, and O. Buyukozturk, “Operational and defect parameters concerning the acoustic-laser vibrometry method for frp-reinforced concrete,” NDTE Int. 71, 43–53 (2015).
[Crossref]

Opt. Commun. (2)

G. Sendra, H. Rabal, M. Trivi, and R. Arizaga, “Numerical model for simulation of dynamic speckle reference patterns,” Opt. Commun. 282, 3693–3700 (2009).
[Crossref]

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).
[Crossref]

Opt. Eng. (2)

C. Falldorf, R. Klattenhoff, and R. B. Bergmann, “Single shot lateral shear interferometer with variable shear,” Opt. Eng. 54, 054105 (2015).
[Crossref]

F. Languy, J.-F. Vandenrijt, C. Thizy, J. Rochet, C. Loffet, D. Simon, and M. P. Georges, “Vibration mode shapes visualization in industrial environment by real-time time-averaged phase-stepped electronic speckle pattern interferometry at 10.6 μm and shearography at 532 nm,” Opt. Eng. 55, 121704 (2016).
[Crossref]

Opt. Express (3)

Opt. Lasers Eng. (1)

G. L. Richoz and G. S. Schajer, “Simultaneous two-axis shearographic interferometer using multiple wavelengths and a color camera,” Opt. Lasers Eng. 77, 143–153 (2016).
[Crossref]

Optics and Lasers in Engineering (1)

X. Wang, Z. Gao, J. Qin, X. Zhang, and S. Yang, “Temporal heterodyne shearing speckle pattern interferometry,” Optics and Lasers in Engineering 93, 76–82 (2017).
[Crossref]

Optik (1)

D. I. Serrano-García, N. I. Toto-Arellano, A. Martínez-García, J. A. R. Álvarez, and G. R. Zurita, “Dynamic phase profile of phase objects based in the use of a quasi-common path interferometer,” Optik 123, 1742–1745 (2012).
[Crossref]

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T. W. Du Bosq and E. Repasi, “Detector integration time dependent atmospheric turbulence imaging simulation,” Proc. SPIE 9452, 94520B (2015).
[Crossref]

Rev. Sci. Instrum. (1)

X. Xie, C. P. Lee, J. Li, B. Zhang, and L. Yang, “Polarized digital shearography for simultaneous dual shearing directions measurements,” Rev. Sci. Instrum. 87, 083110 (2016).
[Crossref] [PubMed]

Theor. Appl. Mech. Lett. (1)

S. Yoneyama and S. Arikawa, “Instantaneous phase-stepping interferometry based on a pixelated micro-polarizer array,” Theor. Appl. Mech. Lett. 6, 162–166 (2016).
[Crossref]

Other (9)

W. J. Bisle, D. Scherling, M. K. Kalms, and W. Osten, “Improved shearography for use on optical non cooperating surfaces under daylight conditions,” Proc. AIPB, 1928–1935 (2001).
[Crossref]

W. Steinchen and L. Yang, Digital Shearography: Theory and Application of Digital Speckle Pattern Shearing Interferometry (SPIE, 2003).

L. Yang and X. Xie, Digital shearography: New Developments and Applications (SPIE, 2016).

G.T. Nehmetallah, R. Aylo, and L.A. Williams, Analog and Digital Holography with MATLAB (SPIE, 2015).
[Crossref]

P. Hariharan, Basics of Interferometry (Academic, 2010).

J. W. Goodman, Introduction to Fourier optics (Roberts and Company, 2005).

D.H. Staelin, A.W. Morgenthaler, and J.A. Kong, Electromagnetic waves (Prentice Hall, 1994).

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company, 2007).

A. Rogalski, Infrared Detectors (CRC, 2010).

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Figures (9)

Fig. 1
Fig. 1 Comparison of surface displacement and the gradient of displacement, ∂w/∂x in the x-direction.
Fig. 2
Fig. 2 Schematic of heterodyne shearographic vibrometer with a dynamic diffuse-scatterer for the target. Lenses have been omitted for clarity. Laser, 200mW SLM 532nm; BS1, non-polarizing beam splitter to generate reference and measurement legs; AOM 1, upshift acousto-optic modulator; BS2, BS3, non-polarizing beam splitter to separate segments for polarization multiplexing; AOM 2, downshift acousto-optic modulator, creating first kHz frequency carrier; ur1, electric field for reference leg 1; AOM 3, downshift acousto-optic modulator, creating second kHz frequency carrier; ur2, electric field for reference leg 2; λ/2, half-wave plate to rotate the polarization by 90°; PBS1, PBS2, polarizing beam splitters recombine components with orthogonal polarization states; PF, polarizing filter; um1, electric field for measurement leg 1; um2, electric field for measurement leg 2; BS4, non-polarizing beam splitter combines measurement and reference legs; FPA, high rate focal plane array.
Fig. 3
Fig. 3 Gaussian surface displacement.
Fig. 4
Fig. 4 Non-phase resolved shearographic fringe pattern produced by numerical model.
Fig. 5
Fig. 5 Constraints on carrier frequency selection due to finite bandwidth limitations.
Fig. 6
Fig. 6 (a) Numerically modeled phase resolved shearographic fringe pattern, Δ, generated by extracting phase from two Doppler shifted frequency carriers and applying Eq. (49), (b) Sine-cosine filtered, phase resolved shearographic fringe pattern. Δ was generated by applying Eq. (50).
Fig. 7
Fig. 7 (a) Iterative sine-cosine smoothing filtered, phase resolved shearographic fringe pattern and (b) Post-processing adjustment to shearing amount and direction
Fig. 8
Fig. 8 Unwrapped shearogram generated by extracting phase from two Doppler shifted frequency carriers.
Fig. 9
Fig. 9 Doppler velocity extracted from one carrier frequency, spatially filtered to remove speckle noise.

Equations (51)

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u 1 = | M 1 | exp [ j ( ω o t + θ 1 ) ]
u 2 = | M 2 | exp [ j ( ω o t + θ 2 ) ] ,
I = | M 1 | 2 + | M 2 | 2 + 2 | M 1 | | M 2 | cos ( θ 1 θ 2 ) .
θ 2 ( x ) = θ 1 ( x + δ x ) ,
I = | M 1 | 2 + | M 2 | 2 + 2 | M 1 | | M 2 | cos ( ϕ ) ,
I = | M 1 | 2 + | M 2 | 2 + 2 | M 1 | | M 2 | cos ( ϕ ) ,
ϕ = Δ + ϕ .
Δ I = | I I | = 2 | M 1 | | M 2 | [ cos ( ϕ ) cos ( ϕ ) ] .
Δ I = 4 | M 1 | | M 2 | [ sin ( ϕ + ϕ 2 ) sin ( ϕ ϕ 2 ) ] .
Δ I = 4 | M 1 | | M 2 | [ sin ( ϕ + Δ 2 ) sin ( Δ 2 ) ] .
Δ = 4 π λ δ x w z x ,
u m 1 = x ^ | M 1 | exp [ j ( ω o t β z + ψ 1 ) ]
u m 2 = y ^ | M 2 | exp [ j ( ω o t β z + ψ 2 + π ) ] ,
ψ 1 , 2 = ϕ dop + θ 1 , 2 .
u r 1 = x ^ R 1 exp { j [ ( ω o + ω 1 ) t β z ] }
u r 2 = y ^ R 2 exp { j [ ( ω o + ω 2 ) t β z + π ] } ,
u t = u r 1 + u r 2 + u m 1 + u m 2 .
I = u t u t * = ( u r 1 + u r 2 + u m 1 + u m 2 ) ( u r 1 * + u r 2 * + u m 1 * + u m 2 * ) .
u r 1 u m 1 * + u r 1 * u m 1 = 2 R 1 | M 1 | cos ( ω 1 t + ψ 1 ) ,
u r 2 u m 2 * + u r 2 * u m 2 = 2 R 2 | M 2 | cos ( ω 2 t + ψ 2 ) .
I = R 1 2 + R 2 2 + | M 1 | 2 + | M 2 | 2 + 2 R 1 | M 1 | cos ( ω 1 t + ψ 1 ) + 2 R 2 | M 2 | cos ( ω 2 t + ψ 2 ) .
I = R 1 2 + R 2 2 + | M 1 | 2 + | M 2 | 2 + 2 R 1 | M 1 | cos ( ω 1 t + ψ 1 ) + 2 R 2 | M 2 | cos ( ω 2 t + ψ 2 ) .
ψ 1 = Demod [ I ] ω 1 = ϕ dop + θ 1
ψ 2 = Demod [ I ] ω 2 = ϕ dop + θ 2 .
ψ 2 ψ 1 = θ 2 θ 1 = ϕ .
ψ 1 = ϕ dop + θ 1 ,
ψ 2 = ϕ dop + θ 2 ,
ψ 2 ψ 1 = θ 2 θ 1 = ϕ .
( ψ 2 ψ 1 ) ( ψ 2 ψ 1 ) = ϕ ϕ = Δ .
w z ( ξ , η , t ) = Asin ( 2 π f obj t ) exp { [ ( ξ 2 ξ o ) 2 + ( η 2 η o ) 2 2 σ 2 ] } ,
Δ p ( ξ , η , t ) = exp [ j 4 π λ w z ( ξ , η , t ) ] .
u o ( ξ , η , t ) = A o ( ξ , η ) exp { j [ θ ( ξ , η ) + Δ p ( ξ , η , t ) ] } ,
u l ( x , y , t ) = κ FFT [ u o ( ξ , η , t ) exp [ j π λ z ( ξ 2 + η 2 ) ] ] x , y
κ = exp ( j k z ) j λ z exp [ j k 2 z ( x 2 + y 2 ) ] .
TL = exp [ j π λ f ( x 2 + y 2 ) ] ,
u 1 ( x , y , t ) = | M 1 | ( x , y , t ) exp [ j θ 1 ( x , y , t ) ] .
u m 1 ( x , y , t ) = | u 1 | exp { j [ ω o t + ( u 1 ( x , y , t ) ) ] }
u m 2 ( x , y , t ) = | u 2 | exp { j [ ω o t + ( u 2 ( x , y , t ) ) ] }
u r 1 ( x , y , t ) = | u ref | exp { j [ ( ω o + ω 1 ) t + ( u ref ( x , y , t ) ) ] }
u r 2 ( x , y , t ) = | u ref | exp { j [ ( ω o + ω 2 ) t + ( u ref ( x , y , t ) ) ] } .
I sig 1 = ( u m 1 + u r 1 ) ( u m 1 * + u r 1 * )
I sig 2 = ( u m 2 + u r 2 ) ( u m 2 * + u r 2 * ) ,
I = I sig 1 + I sig 2 .
Δ ω = d d t ( 4 π λ v ( t ) 2 π f obj ) ,
w z ( t ) = v ( t ) 2 π f obj .
w z , peak = ( ω 2 ω 1 ) 2 λ 4 π ω obj .
Q 1 , 2 ( t ) = lowpass [ highpass [ I ( t ) ] sin ( ω 1 , 2 t ) ] I 1 , 2 ( t ) = lowpass [ highpass [ I ( t ) ] cos ( ω 1 , 2 t ) ] .
ψ 1 , 2 = unwrap [ tan 1 ( Q 1 , 2 ( t ) I 1 , 2 ( t ) ) ] .
Δ = { ( ψ 2 ψ 1 ) ( ψ 2 ψ 1 ) for ( ψ 2 ψ 1 ) ( ψ 2 ψ 1 ) ( ψ 2 ψ 1 ) ( ψ 2 ψ 1 ) + 2 π , for ( ψ 2 ψ 1 ) < ( ψ 2 ψ 1 ) .
Δ = atan 2 [ sin ( Δ , cos ( Δ ) ) ]
v ( x , y , t ) = d d t { ( λ 4 π ) unwrap [ ψ ( x , y , t ) ] } .

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