Abstract

Stereo-digital image correlation (stereo-DIC) has been routinely used as a practical and powerful optical technique for surface 3D full-field shape and deformation measurements in various scenarios. However, it is challenging to perform accurate stereo-DIC measurements for submerged objects due to the significant refraction presented at the interfaces of air and water. In this paper, a novel underwater full-field 3D profile and deformation measurements method using the single camera stereo-DIC technique that combines single bilateral telecentric lens imaging and bi-prism-assisted pseudo stereovision is proposed. In using this technique, an immersed surface projects through the (semi-) submerged bi-prism and the bilateral telecentric lens, forming two virtual images on left and right parts of the camera sensor. Matching the virtual left and right images using DIC and substituting the matched image points into a set of newly derived linear equations, accurate 3D profiles and further 3D deformation fields can be readily obtained. The effectiveness and accuracy of the proposed method are successfully validated by a set of real experiments including underwater 3D shape reconstruction, in-plane and out-of-plane translation, and membrane inflation experiments. Because of the distinctive advantages of simple and compact optical configuration, without the need of stereo calibration, and strong robustness against water fluctuation and ambient light variation, the proposed method is expected to be a simple yet effective method for many underwater applications like in vitro biological tissues deformation measurements and submerged materials characterization.

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

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References

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  1. S. Tetlow and J. Spours, “Three-dimensional measurement of underwater work sites using structured laser light,” Meas. Sci. Technol. 10(12), 1162–1167 (1999).
    [Crossref]
  2. M. A. Sutton and C. McFadden, “Development of a methodology for non-contacting strain measurements in fluid environments using computer vision,” Opt. Lasers Eng. 32(4), 367–377 (1999).
    [Crossref]
  3. Y. H. Kwon and J. B. Casebolt, “Effects of light refraction on the accuracy of camera calibration and reconstruction in underwater motion analysis,” Sports Biomech. 5(2), 315–340 (2006).
    [Crossref] [PubMed]
  4. H. Schreier, J.-J. Orteu, and M. A. Sutton, Image Correlation for Shape, Motion and Deformation Measurements (Springer US, 2009).
  5. B. Pan, “Digital image correlation for surface deformation measurement: Historical developments, recent advances and future goals,” Meas. Sci. Technol. 29(8), 082001 (2018).
    [Crossref]
  6. B. Pan, L. P. Yu, and Q. B. Zhang, “Review of single-camera stereo-digital image correlation techniques for full-field 3D shape and deformation measurement,” Sci. China Technol. Sci. 61(1), 2–20 (2018).
    [Crossref]
  7. B. Pan and Q. Wang, “Single-camera microscopic stereo digital image correlation using a diffraction grating,” Opt. Express 21(21), 25056–25068 (2013).
    [Crossref] [PubMed]
  8. K. Genovese, L. Casaletto, J. A. Rayas, V. Flores, and A. Martinez, “Stereo-Digital Image Correlation (DIC) measurements with a single camera using a biprism,” Opt. Lasers Eng. 51(3), 278–285 (2013).
    [Crossref]
  9. A. Barta and G. Horváth, “Underwater binocular imaging of aerial objects versus the position of eyes relative to the flat water surface,” J. Opt. Soc. Am. A 20(12), 2370–2377 (2003).
    [Crossref] [PubMed]
  10. M. A. Haile and P. G. Ifju, “Application of elastic image registration and refraction correction for non-contact underwater strain measurement,” Strain 48(2), 136–142 (2012).
    [Crossref]
  11. S. Gupta, V. Parameswaran, M. A. Sutton, and A. Shukla, “Study of dynamic underwater implosion mechanics using digital image correlation,” Proc. R. Soc. A Math. Phys. Eng. Sci. 470(2172), (2014).
    [Crossref]
  12. X. Ke, M. A. Sutton, S. M. Lessner, and M. Yost, “Robust stereo vision and calibration methodology for accurate three-dimensional digital image correlation measurements on submerged objects,” J. Strain Anal. Eng. Des. 43(8), 689–704 (2008).
    [Crossref]
  13. F. Menna, E. Nocerino, F. Fassi, and F. Remondino, “Geometric and optic characterization of a hemispherical dome port for underwater photogrammetry,” Sensors (Basel) 16(1), 48 (2016).
    [Crossref] [PubMed]
  14. L. Wu, J. Zhu, and H. Xie, “Single-lens 3D digital image correlation system based on a bilateral telecentric lens and a bi-prism: validation and application,” Appl. Opt. 54(26), 7842–7850 (2015).
    [Crossref] [PubMed]
  15. L. F. Wu, J. G. Zhu, H. M. Xie, and Q. Zhang, “An Accurate Method for Shape Retrieval and Displacement Measurement Using Bi-Prism-Based Single Lens 3D Digital Image Correlation,” Exp. Mech. 56(9), 1611–1624 (2016).
    [Crossref]
  16. B. Pan, D. Wu, and Y. Xia, “An active imaging digital image correlation method for deformation measurement insensitive to ambient light,” Opt. Laser Technol. 44(1), 204–209 (2012).
    [Crossref]
  17. B. Pan, K. Qian, H. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: A review,” Meas. Sci. Technol. 20(6), 062001 (2009).
    [Crossref]
  18. B. Pan, K. Li, and W. Tong, “Fast, Robust and Accurate Digital Image Correlation Calculation Without Redundant Computations,” Exp. Mech. 53(7), 1277–1289 (2013).
    [Crossref]
  19. B. Pan, “Reliability-guided digital image correlation for image deformation measurement,” Appl. Opt. 48(8), 1535–1542 (2009).
    [Crossref] [PubMed]
  20. B. Pan, “Full-field strain measurement using a two-dimensional Savitzky-Golay digital differentiator in digital image correlation,” Opt. Eng. 46(3), 033601 (2007).
    [Crossref]
  21. B. Pan, W. Shi, and G. Lubineau, “Effect of camera temperature variations on stereo-digital image correlation measurements,” Appl. Opt. 54(34), 10089–10095 (2015).
    [Crossref] [PubMed]
  22. A. P. S. Selvadurai and M. Shi, “Fluid pressure loading of a hyperelastic membrane,” Int. J. Non-linear Mech. 47(2), 228–239 (2012).
    [Crossref]
  23. J. Y. Pan, P. Lin, F. Maseeh, and S. D. Senturia, “Verification of FEM analysis of load-deflection methods for measuring mechanical properties of thin films,” in IEEE 4th Technical Digest on Solid-State Sensor and Actuator Workshop (IEEE, 1990), pp. 70–73.
    [Crossref]
  24. W. K. Schomburg, “Membranes,” in Introduction to Microsystem Design (Springer, 2011), pp. 29–52.

2018 (2)

B. Pan, “Digital image correlation for surface deformation measurement: Historical developments, recent advances and future goals,” Meas. Sci. Technol. 29(8), 082001 (2018).
[Crossref]

B. Pan, L. P. Yu, and Q. B. Zhang, “Review of single-camera stereo-digital image correlation techniques for full-field 3D shape and deformation measurement,” Sci. China Technol. Sci. 61(1), 2–20 (2018).
[Crossref]

2016 (2)

F. Menna, E. Nocerino, F. Fassi, and F. Remondino, “Geometric and optic characterization of a hemispherical dome port for underwater photogrammetry,” Sensors (Basel) 16(1), 48 (2016).
[Crossref] [PubMed]

L. F. Wu, J. G. Zhu, H. M. Xie, and Q. Zhang, “An Accurate Method for Shape Retrieval and Displacement Measurement Using Bi-Prism-Based Single Lens 3D Digital Image Correlation,” Exp. Mech. 56(9), 1611–1624 (2016).
[Crossref]

2015 (2)

2013 (3)

B. Pan, K. Li, and W. Tong, “Fast, Robust and Accurate Digital Image Correlation Calculation Without Redundant Computations,” Exp. Mech. 53(7), 1277–1289 (2013).
[Crossref]

B. Pan and Q. Wang, “Single-camera microscopic stereo digital image correlation using a diffraction grating,” Opt. Express 21(21), 25056–25068 (2013).
[Crossref] [PubMed]

K. Genovese, L. Casaletto, J. A. Rayas, V. Flores, and A. Martinez, “Stereo-Digital Image Correlation (DIC) measurements with a single camera using a biprism,” Opt. Lasers Eng. 51(3), 278–285 (2013).
[Crossref]

2012 (3)

M. A. Haile and P. G. Ifju, “Application of elastic image registration and refraction correction for non-contact underwater strain measurement,” Strain 48(2), 136–142 (2012).
[Crossref]

A. P. S. Selvadurai and M. Shi, “Fluid pressure loading of a hyperelastic membrane,” Int. J. Non-linear Mech. 47(2), 228–239 (2012).
[Crossref]

B. Pan, D. Wu, and Y. Xia, “An active imaging digital image correlation method for deformation measurement insensitive to ambient light,” Opt. Laser Technol. 44(1), 204–209 (2012).
[Crossref]

2009 (2)

B. Pan, K. Qian, H. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: A review,” Meas. Sci. Technol. 20(6), 062001 (2009).
[Crossref]

B. Pan, “Reliability-guided digital image correlation for image deformation measurement,” Appl. Opt. 48(8), 1535–1542 (2009).
[Crossref] [PubMed]

2008 (1)

X. Ke, M. A. Sutton, S. M. Lessner, and M. Yost, “Robust stereo vision and calibration methodology for accurate three-dimensional digital image correlation measurements on submerged objects,” J. Strain Anal. Eng. Des. 43(8), 689–704 (2008).
[Crossref]

2007 (1)

B. Pan, “Full-field strain measurement using a two-dimensional Savitzky-Golay digital differentiator in digital image correlation,” Opt. Eng. 46(3), 033601 (2007).
[Crossref]

2006 (1)

Y. H. Kwon and J. B. Casebolt, “Effects of light refraction on the accuracy of camera calibration and reconstruction in underwater motion analysis,” Sports Biomech. 5(2), 315–340 (2006).
[Crossref] [PubMed]

2003 (1)

1999 (2)

S. Tetlow and J. Spours, “Three-dimensional measurement of underwater work sites using structured laser light,” Meas. Sci. Technol. 10(12), 1162–1167 (1999).
[Crossref]

M. A. Sutton and C. McFadden, “Development of a methodology for non-contacting strain measurements in fluid environments using computer vision,” Opt. Lasers Eng. 32(4), 367–377 (1999).
[Crossref]

Asundi, A.

B. Pan, K. Qian, H. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: A review,” Meas. Sci. Technol. 20(6), 062001 (2009).
[Crossref]

Barta, A.

Casaletto, L.

K. Genovese, L. Casaletto, J. A. Rayas, V. Flores, and A. Martinez, “Stereo-Digital Image Correlation (DIC) measurements with a single camera using a biprism,” Opt. Lasers Eng. 51(3), 278–285 (2013).
[Crossref]

Casebolt, J. B.

Y. H. Kwon and J. B. Casebolt, “Effects of light refraction on the accuracy of camera calibration and reconstruction in underwater motion analysis,” Sports Biomech. 5(2), 315–340 (2006).
[Crossref] [PubMed]

Fassi, F.

F. Menna, E. Nocerino, F. Fassi, and F. Remondino, “Geometric and optic characterization of a hemispherical dome port for underwater photogrammetry,” Sensors (Basel) 16(1), 48 (2016).
[Crossref] [PubMed]

Flores, V.

K. Genovese, L. Casaletto, J. A. Rayas, V. Flores, and A. Martinez, “Stereo-Digital Image Correlation (DIC) measurements with a single camera using a biprism,” Opt. Lasers Eng. 51(3), 278–285 (2013).
[Crossref]

Genovese, K.

K. Genovese, L. Casaletto, J. A. Rayas, V. Flores, and A. Martinez, “Stereo-Digital Image Correlation (DIC) measurements with a single camera using a biprism,” Opt. Lasers Eng. 51(3), 278–285 (2013).
[Crossref]

Haile, M. A.

M. A. Haile and P. G. Ifju, “Application of elastic image registration and refraction correction for non-contact underwater strain measurement,” Strain 48(2), 136–142 (2012).
[Crossref]

Horváth, G.

Ifju, P. G.

M. A. Haile and P. G. Ifju, “Application of elastic image registration and refraction correction for non-contact underwater strain measurement,” Strain 48(2), 136–142 (2012).
[Crossref]

Ke, X.

X. Ke, M. A. Sutton, S. M. Lessner, and M. Yost, “Robust stereo vision and calibration methodology for accurate three-dimensional digital image correlation measurements on submerged objects,” J. Strain Anal. Eng. Des. 43(8), 689–704 (2008).
[Crossref]

Kwon, Y. H.

Y. H. Kwon and J. B. Casebolt, “Effects of light refraction on the accuracy of camera calibration and reconstruction in underwater motion analysis,” Sports Biomech. 5(2), 315–340 (2006).
[Crossref] [PubMed]

Lessner, S. M.

X. Ke, M. A. Sutton, S. M. Lessner, and M. Yost, “Robust stereo vision and calibration methodology for accurate three-dimensional digital image correlation measurements on submerged objects,” J. Strain Anal. Eng. Des. 43(8), 689–704 (2008).
[Crossref]

Li, K.

B. Pan, K. Li, and W. Tong, “Fast, Robust and Accurate Digital Image Correlation Calculation Without Redundant Computations,” Exp. Mech. 53(7), 1277–1289 (2013).
[Crossref]

Lubineau, G.

Martinez, A.

K. Genovese, L. Casaletto, J. A. Rayas, V. Flores, and A. Martinez, “Stereo-Digital Image Correlation (DIC) measurements with a single camera using a biprism,” Opt. Lasers Eng. 51(3), 278–285 (2013).
[Crossref]

McFadden, C.

M. A. Sutton and C. McFadden, “Development of a methodology for non-contacting strain measurements in fluid environments using computer vision,” Opt. Lasers Eng. 32(4), 367–377 (1999).
[Crossref]

Menna, F.

F. Menna, E. Nocerino, F. Fassi, and F. Remondino, “Geometric and optic characterization of a hemispherical dome port for underwater photogrammetry,” Sensors (Basel) 16(1), 48 (2016).
[Crossref] [PubMed]

Nocerino, E.

F. Menna, E. Nocerino, F. Fassi, and F. Remondino, “Geometric and optic characterization of a hemispherical dome port for underwater photogrammetry,” Sensors (Basel) 16(1), 48 (2016).
[Crossref] [PubMed]

Pan, B.

B. Pan, “Digital image correlation for surface deformation measurement: Historical developments, recent advances and future goals,” Meas. Sci. Technol. 29(8), 082001 (2018).
[Crossref]

B. Pan, L. P. Yu, and Q. B. Zhang, “Review of single-camera stereo-digital image correlation techniques for full-field 3D shape and deformation measurement,” Sci. China Technol. Sci. 61(1), 2–20 (2018).
[Crossref]

B. Pan, W. Shi, and G. Lubineau, “Effect of camera temperature variations on stereo-digital image correlation measurements,” Appl. Opt. 54(34), 10089–10095 (2015).
[Crossref] [PubMed]

B. Pan and Q. Wang, “Single-camera microscopic stereo digital image correlation using a diffraction grating,” Opt. Express 21(21), 25056–25068 (2013).
[Crossref] [PubMed]

B. Pan, K. Li, and W. Tong, “Fast, Robust and Accurate Digital Image Correlation Calculation Without Redundant Computations,” Exp. Mech. 53(7), 1277–1289 (2013).
[Crossref]

B. Pan, D. Wu, and Y. Xia, “An active imaging digital image correlation method for deformation measurement insensitive to ambient light,” Opt. Laser Technol. 44(1), 204–209 (2012).
[Crossref]

B. Pan, K. Qian, H. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: A review,” Meas. Sci. Technol. 20(6), 062001 (2009).
[Crossref]

B. Pan, “Reliability-guided digital image correlation for image deformation measurement,” Appl. Opt. 48(8), 1535–1542 (2009).
[Crossref] [PubMed]

B. Pan, “Full-field strain measurement using a two-dimensional Savitzky-Golay digital differentiator in digital image correlation,” Opt. Eng. 46(3), 033601 (2007).
[Crossref]

Qian, K.

B. Pan, K. Qian, H. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: A review,” Meas. Sci. Technol. 20(6), 062001 (2009).
[Crossref]

Rayas, J. A.

K. Genovese, L. Casaletto, J. A. Rayas, V. Flores, and A. Martinez, “Stereo-Digital Image Correlation (DIC) measurements with a single camera using a biprism,” Opt. Lasers Eng. 51(3), 278–285 (2013).
[Crossref]

Remondino, F.

F. Menna, E. Nocerino, F. Fassi, and F. Remondino, “Geometric and optic characterization of a hemispherical dome port for underwater photogrammetry,” Sensors (Basel) 16(1), 48 (2016).
[Crossref] [PubMed]

Selvadurai, A. P. S.

A. P. S. Selvadurai and M. Shi, “Fluid pressure loading of a hyperelastic membrane,” Int. J. Non-linear Mech. 47(2), 228–239 (2012).
[Crossref]

Shi, M.

A. P. S. Selvadurai and M. Shi, “Fluid pressure loading of a hyperelastic membrane,” Int. J. Non-linear Mech. 47(2), 228–239 (2012).
[Crossref]

Shi, W.

Spours, J.

S. Tetlow and J. Spours, “Three-dimensional measurement of underwater work sites using structured laser light,” Meas. Sci. Technol. 10(12), 1162–1167 (1999).
[Crossref]

Sutton, M. A.

X. Ke, M. A. Sutton, S. M. Lessner, and M. Yost, “Robust stereo vision and calibration methodology for accurate three-dimensional digital image correlation measurements on submerged objects,” J. Strain Anal. Eng. Des. 43(8), 689–704 (2008).
[Crossref]

M. A. Sutton and C. McFadden, “Development of a methodology for non-contacting strain measurements in fluid environments using computer vision,” Opt. Lasers Eng. 32(4), 367–377 (1999).
[Crossref]

Tetlow, S.

S. Tetlow and J. Spours, “Three-dimensional measurement of underwater work sites using structured laser light,” Meas. Sci. Technol. 10(12), 1162–1167 (1999).
[Crossref]

Tong, W.

B. Pan, K. Li, and W. Tong, “Fast, Robust and Accurate Digital Image Correlation Calculation Without Redundant Computations,” Exp. Mech. 53(7), 1277–1289 (2013).
[Crossref]

Wang, Q.

Wu, D.

B. Pan, D. Wu, and Y. Xia, “An active imaging digital image correlation method for deformation measurement insensitive to ambient light,” Opt. Laser Technol. 44(1), 204–209 (2012).
[Crossref]

Wu, L.

Wu, L. F.

L. F. Wu, J. G. Zhu, H. M. Xie, and Q. Zhang, “An Accurate Method for Shape Retrieval and Displacement Measurement Using Bi-Prism-Based Single Lens 3D Digital Image Correlation,” Exp. Mech. 56(9), 1611–1624 (2016).
[Crossref]

Xia, Y.

B. Pan, D. Wu, and Y. Xia, “An active imaging digital image correlation method for deformation measurement insensitive to ambient light,” Opt. Laser Technol. 44(1), 204–209 (2012).
[Crossref]

Xie, H.

L. Wu, J. Zhu, and H. Xie, “Single-lens 3D digital image correlation system based on a bilateral telecentric lens and a bi-prism: validation and application,” Appl. Opt. 54(26), 7842–7850 (2015).
[Crossref] [PubMed]

B. Pan, K. Qian, H. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: A review,” Meas. Sci. Technol. 20(6), 062001 (2009).
[Crossref]

Xie, H. M.

L. F. Wu, J. G. Zhu, H. M. Xie, and Q. Zhang, “An Accurate Method for Shape Retrieval and Displacement Measurement Using Bi-Prism-Based Single Lens 3D Digital Image Correlation,” Exp. Mech. 56(9), 1611–1624 (2016).
[Crossref]

Yost, M.

X. Ke, M. A. Sutton, S. M. Lessner, and M. Yost, “Robust stereo vision and calibration methodology for accurate three-dimensional digital image correlation measurements on submerged objects,” J. Strain Anal. Eng. Des. 43(8), 689–704 (2008).
[Crossref]

Yu, L. P.

B. Pan, L. P. Yu, and Q. B. Zhang, “Review of single-camera stereo-digital image correlation techniques for full-field 3D shape and deformation measurement,” Sci. China Technol. Sci. 61(1), 2–20 (2018).
[Crossref]

Zhang, Q.

L. F. Wu, J. G. Zhu, H. M. Xie, and Q. Zhang, “An Accurate Method for Shape Retrieval and Displacement Measurement Using Bi-Prism-Based Single Lens 3D Digital Image Correlation,” Exp. Mech. 56(9), 1611–1624 (2016).
[Crossref]

Zhang, Q. B.

B. Pan, L. P. Yu, and Q. B. Zhang, “Review of single-camera stereo-digital image correlation techniques for full-field 3D shape and deformation measurement,” Sci. China Technol. Sci. 61(1), 2–20 (2018).
[Crossref]

Zhu, J.

Zhu, J. G.

L. F. Wu, J. G. Zhu, H. M. Xie, and Q. Zhang, “An Accurate Method for Shape Retrieval and Displacement Measurement Using Bi-Prism-Based Single Lens 3D Digital Image Correlation,” Exp. Mech. 56(9), 1611–1624 (2016).
[Crossref]

Appl. Opt. (3)

Exp. Mech. (2)

L. F. Wu, J. G. Zhu, H. M. Xie, and Q. Zhang, “An Accurate Method for Shape Retrieval and Displacement Measurement Using Bi-Prism-Based Single Lens 3D Digital Image Correlation,” Exp. Mech. 56(9), 1611–1624 (2016).
[Crossref]

B. Pan, K. Li, and W. Tong, “Fast, Robust and Accurate Digital Image Correlation Calculation Without Redundant Computations,” Exp. Mech. 53(7), 1277–1289 (2013).
[Crossref]

Int. J. Non-linear Mech. (1)

A. P. S. Selvadurai and M. Shi, “Fluid pressure loading of a hyperelastic membrane,” Int. J. Non-linear Mech. 47(2), 228–239 (2012).
[Crossref]

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

J. Strain Anal. Eng. Des. (1)

X. Ke, M. A. Sutton, S. M. Lessner, and M. Yost, “Robust stereo vision and calibration methodology for accurate three-dimensional digital image correlation measurements on submerged objects,” J. Strain Anal. Eng. Des. 43(8), 689–704 (2008).
[Crossref]

Meas. Sci. Technol. (3)

B. Pan, K. Qian, H. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: A review,” Meas. Sci. Technol. 20(6), 062001 (2009).
[Crossref]

S. Tetlow and J. Spours, “Three-dimensional measurement of underwater work sites using structured laser light,” Meas. Sci. Technol. 10(12), 1162–1167 (1999).
[Crossref]

B. Pan, “Digital image correlation for surface deformation measurement: Historical developments, recent advances and future goals,” Meas. Sci. Technol. 29(8), 082001 (2018).
[Crossref]

Opt. Eng. (1)

B. Pan, “Full-field strain measurement using a two-dimensional Savitzky-Golay digital differentiator in digital image correlation,” Opt. Eng. 46(3), 033601 (2007).
[Crossref]

Opt. Express (1)

Opt. Laser Technol. (1)

B. Pan, D. Wu, and Y. Xia, “An active imaging digital image correlation method for deformation measurement insensitive to ambient light,” Opt. Laser Technol. 44(1), 204–209 (2012).
[Crossref]

Opt. Lasers Eng. (2)

K. Genovese, L. Casaletto, J. A. Rayas, V. Flores, and A. Martinez, “Stereo-Digital Image Correlation (DIC) measurements with a single camera using a biprism,” Opt. Lasers Eng. 51(3), 278–285 (2013).
[Crossref]

M. A. Sutton and C. McFadden, “Development of a methodology for non-contacting strain measurements in fluid environments using computer vision,” Opt. Lasers Eng. 32(4), 367–377 (1999).
[Crossref]

Sci. China Technol. Sci. (1)

B. Pan, L. P. Yu, and Q. B. Zhang, “Review of single-camera stereo-digital image correlation techniques for full-field 3D shape and deformation measurement,” Sci. China Technol. Sci. 61(1), 2–20 (2018).
[Crossref]

Sensors (Basel) (1)

F. Menna, E. Nocerino, F. Fassi, and F. Remondino, “Geometric and optic characterization of a hemispherical dome port for underwater photogrammetry,” Sensors (Basel) 16(1), 48 (2016).
[Crossref] [PubMed]

Sports Biomech. (1)

Y. H. Kwon and J. B. Casebolt, “Effects of light refraction on the accuracy of camera calibration and reconstruction in underwater motion analysis,” Sports Biomech. 5(2), 315–340 (2006).
[Crossref] [PubMed]

Strain (1)

M. A. Haile and P. G. Ifju, “Application of elastic image registration and refraction correction for non-contact underwater strain measurement,” Strain 48(2), 136–142 (2012).
[Crossref]

Other (4)

S. Gupta, V. Parameswaran, M. A. Sutton, and A. Shukla, “Study of dynamic underwater implosion mechanics using digital image correlation,” Proc. R. Soc. A Math. Phys. Eng. Sci. 470(2172), (2014).
[Crossref]

H. Schreier, J.-J. Orteu, and M. A. Sutton, Image Correlation for Shape, Motion and Deformation Measurements (Springer US, 2009).

J. Y. Pan, P. Lin, F. Maseeh, and S. D. Senturia, “Verification of FEM analysis of load-deflection methods for measuring mechanical properties of thin films,” in IEEE 4th Technical Digest on Solid-State Sensor and Actuator Workshop (IEEE, 1990), pp. 70–73.
[Crossref]

W. K. Schomburg, “Membranes,” in Introduction to Microsystem Design (Springer, 2011), pp. 29–52.

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Figures (10)

Fig. 1
Fig. 1 Optical arrangement of the proposed technique using a bilateral telecentric imaging system and a semi-submerged bi-prism.
Fig. 2
Fig. 2 Imaging model of the BTL-stereo-DIC with (a) semi-submerged and (b) submerged bi-prisms.
Fig. 3
Fig. 3 Procedures of underwater 3D profile and deformation measurements.
Fig. 4
Fig. 4 Pictures of (a) in-plane and out-of-plane translation and (b) membrane inflation tests; (c) schematic experimental details of the membrane inflation experiment.
Fig. 5
Fig. 5 Contour of the reconstructed ball profile.
Fig. 6
Fig. 6 (a) Mean U-displacement for in-plane and mean W-displacement for out-of-plane translation tests versus the imposed displacements; (b) mean error and standard deviation of the measured displacements for both in-plane and out-of-plane tests.
Fig. 7
Fig. 7 Images captured by the camera at initial (a) and deformed (b) state; (c) Measured 3D profiles and central deflection of the membrane versus the applied fluid pressure.
Fig. 8
Fig. 8 (a) Displacement and (b) strain fields of the membrane at the final states of the test.
Fig. 9
Fig. 9 (a) The imposed and predicted fluid pressure versus measured central deflection; (b) the measured and predict central deflection versus the applied fluid pressure.
Fig. 10
Fig. 10 Stress fields in (a) X-direction and (b) Y-direction; (c) shear stress (d) von Mises stress fields.

Equations (23)

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( X L1 Y L1 )=s( x 1 c x y 1 c y ),
( X L2 Y L2 )=s( x 2 c x y 2 c y ),
Y= 1 2 ( Y L1 + Y L2 )+ΔY.
( X A Z A )=( X L1 +ΔX 0 ),
( X B Z B )=( X L2 +ΔX 0 ).
C=( X C Z C )=( X A t 0 X A tan(α) ),
D=( X D Z D )=( X B t 0 + X B tan(α) ).
β= sin 1 ( n 1 n 2 sin( α ) ),
cp = ( sin( βα ),cos( βα ) ) T ,
dp = ( sin( βα ),cos( βα ) ) T .
P 1 =C+ λ 1 cp ,
P 2 =D+ λ 2 dp ,
P 1 =( X A λ 1 sin( βα ), t 0 X A tan( α )+ λ 1 cos( βα ) ),
P 2 =( X B + λ 2 sin( βα ), t 0 + X B tan( α )+ λ 2 cos( βα ) ).
P 1 = P 2 .
λ 1 = 1 2 { [ tan(α) cos(βα) 1 sin(βα) ] X B +[ 1 sin(βα) + tan(α) cos(βα) ] X A },
λ 2 = 1 2 { [ 1 sin(βα) + tan(α) cos(βα) ] X B +[ 1 sin(βα) tan(α) cos(βα) ] X A }.
( X Y Z )= s 2 ( [ 1tan( α )tan( βα ) ]( x 1 + x 2 ) y 1 + y 2 [ cot( βα )tan( α ) ]( x 1 x 2 ) )+( [ 1tan( α )tan( βα ) ]( ΔXs c x ) ΔYs c y t 0 ).
( X Y Z )= s 2 ( [ 1tan( α )tan( βα ) ]( x 1 + x 2 ) y 1 + y 2 [ cot( βα )tan( α ) ]( x 1 x 2 ) ).
C ZNSSD ( p )= i=M M j=M M [ f( x 1 i , y 1 j ) f ¯ i=M M j=M M [ f( x 1 i , y 1 j ) f ¯ ] g( x 2 i , y 2 j ) g ¯ i=M M j=M M [ g( x 2 i , y 2 j ) g ¯ ] ] 2 ,
Δp= 4 w 0 d M R M 2 ( σ 0 + 2 w 0 2 3 R M 2 E M 1.0260.793 v M 0.233 v M 2 ).
Δp=a w 0 3 +b w 0 .
a= 8 d M E M 3 R M 4 ( 1.0260.793 v M 0.233 v M 2 ) .

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