Abstract

Tilt scanning interferometry (TSI) is a novel experimental technique that allows the measurement of multicomponent displacement fields inside the volume of a sample. In this paper, we present a simulation model that allows for the evaluation of the speckle fields recorded in TSI when this technique is applied to the analysis of semitransparent scattering materials. The simulation is based on the convolution of the optical impulsive response of the optical system and the incident field amplitude. Different sections of the simulated imaging system are identified and the corresponding optical impulsive responses are determined. To evaluate the performance of the proposed model, a known internal displacement field as well as the illumination and detection strategies in a real TSI system are numerically simulated. Then, the corresponding depth-resolved out-of-plane and in-plane changes of phase are obtained by means of the data processing algorithm implemented in a TSI system.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. I. Friswell and J. E. Mottershead, Finite Model Updating in Structural Dynamics (Springer, 1995).
  2. M. Grediac, “Principe des travaux virtuels et identification,” C. R. Acad. Sci. Ser. II 309, 1-5 (1989).
  3. F. Pierron, S. Zhavoronok, and M. Grediac, “Identification of the through-thickness properties of thick laminated tubes using the virtual fields method,” Int. J. Solids Struct. 37, 4437-4453 (2000).
    [CrossRef]
  4. M. Grediac, F. Pierron, S. Avril, and E. Toussaint, “The virtual fields method for extracting constitutive parameters from full-field measurements: a review,” Strain 42, 233-253 (2006).
    [CrossRef]
  5. R. Jones and C. Wykes, Holographic and Speckle Interferometry (Cambridge University, 1989).
  6. P. K. Rastogi, Digital Speckle Pattern Interferometry and Related Techniques (Wiley, 2001).
  7. R. Rodriguez-Vera, D. Kerr, and F. Mendoza-Santoyo, “Electronic speckle contouring,” J. Opt. Soc. Am. A 9, 2000-2008(1992).
    [CrossRef]
  8. P. Jacquot, “Speckle interferometry: a review of the principal methods in use for experimental mechanics applications,” Strain 44, 57-69 (2008).
    [CrossRef]
  9. A. Giraudeau, B. Guo, and F. Pierron, “Stiffness and damping identification from full field measurements on vibrating plates,” Exp. Mech. 46, 777-787 (2006).
    [CrossRef]
  10. S. Avril and F. Pierron, “General framework for the identification of constitutive parameters from full-field measurements in linear elasticity,” Int. J. Solids Struct. 44, 4978-5002 (2007).
    [CrossRef]
  11. S. Avril, F. Pierron, M. A. Sutton, and J. H. Yan, “Identification of elasto-visco-plastic parameters and characterization of Luders behavior using digital image correlation and the virtual fields method,” Mech. Mater. 40, 729-742 (2008).
    [CrossRef]
  12. T. Abe, Y. Mitsunaga, and H. Koga, “Photoelastic computer-tomography--a novel measurement method for axial residual-stress profile in optical fibers,” J. Opt. Soc. Am. A 3, 133-138 (1986).
    [CrossRef]
  13. H. Aben, A. Errapart, L. Ainola, and J. Anton, “Photoelastic tomography for residual stress measurement in glass,” in Optical Metrology in Production Engineering, (SPIE, 2004) pp. 1-11.
  14. D. D. Steele, T. L. Chenevert, A. R. Skovoroda, and S. Y. Emelianov, “Three-dimensional static displacement stimulated echo NMR elasticity imaging,” Phys. Med. Biol. 45, 1633-1648 (2000).
    [CrossRef] [PubMed]
  15. M. T. Draney, R. J. Herfkens, T. J. R. Hughes, N. J. Pelc, K. L. Wedding, C. K. Zarins, and C. A. Taylor, “Quantification of vessel wall cyclic strain using cine phase contrast magnetic resonance imaging,” Ann. Biomed. Eng. 30, 1033-1045 (2002).
    [CrossRef] [PubMed]
  16. B. K. Bay, T. S. Smith, D. P. Fyhrie, and M. Saad, “Digital volume correlation: three-dimensional strain mapping using x-ray tomography,” Exp. Mech. 39, 217-226 (1999).
    [CrossRef]
  17. J. Schmitt, “OCT elastography: imaging microscopic deformation and strain of tissue,” Opt. Express 3, 199-211 (1998).
    [CrossRef] [PubMed]
  18. A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography--principles and applications,” Rep. Prog. Phys. 66, 239-303 (2003).
    [CrossRef]
  19. K. Gastinger, S. Winther, and K. D. Hinsch, “Low-coherence speckle interferometer (LCSI) for characterization of adhesion in adhesive-bonded joints,” Proc. SPIE 4933, 59-65 (2003).
    [CrossRef]
  20. G. Gülker, K. D. Hinsch, and A. Kraft, “Low-coherence ESPI in the investigation of ancient terracotta warriors,” Proc. SPIE 4933, 53-58 (2003).
    [CrossRef]
  21. P. D. Ruiz, J. M. Huntley, and A. Maranon, “Tilt scanning interferometry: a novel technique for mapping structure and three-dimensional displacement fields within optically scattering media,” Proc. R. Soc. A 462, 2481-2502 (2006).
    [CrossRef]
  22. J. M. Coupland and J. Lobera, “Holography, tomography and 3D microscopy as linear filtering operations,” Meas. Sci. Technol. 19, 074012 (2008).
    [CrossRef]
  23. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  24. S. Equis and P. Jacquot, “Simulation of speckle complex amplitude: advocating the linear model,” Proc. SPIE 6341, 634138.1-634138 (2006).
  25. A. Dávila, G. H. Kaufmann, and D. Kerr, “Digital processing of ESPI addition fringes,” in Fringe '93, W. Jüptner and W. Osten, eds. (Akademie Verlag, 1993), pp. 339-346.
  26. D. C. Ghiglia and M. D. Pritt, Two Dimensional Phase Unwrapping: Theory, Algorithms and Software (Wiley, 1998).
  27. P. D. Ruiz, G. H. Kaufmann, and G. E. Galizzi, “Unwrapping of digital speckle pattern interferometry phase maps by use of a minimum L0-norm algorithm,” Appl. Opt. 37, 7632-7644(1998).
    [CrossRef]

2008 (3)

P. Jacquot, “Speckle interferometry: a review of the principal methods in use for experimental mechanics applications,” Strain 44, 57-69 (2008).
[CrossRef]

S. Avril, F. Pierron, M. A. Sutton, and J. H. Yan, “Identification of elasto-visco-plastic parameters and characterization of Luders behavior using digital image correlation and the virtual fields method,” Mech. Mater. 40, 729-742 (2008).
[CrossRef]

J. M. Coupland and J. Lobera, “Holography, tomography and 3D microscopy as linear filtering operations,” Meas. Sci. Technol. 19, 074012 (2008).
[CrossRef]

2007 (1)

S. Avril and F. Pierron, “General framework for the identification of constitutive parameters from full-field measurements in linear elasticity,” Int. J. Solids Struct. 44, 4978-5002 (2007).
[CrossRef]

2006 (4)

S. Equis and P. Jacquot, “Simulation of speckle complex amplitude: advocating the linear model,” Proc. SPIE 6341, 634138.1-634138 (2006).

A. Giraudeau, B. Guo, and F. Pierron, “Stiffness and damping identification from full field measurements on vibrating plates,” Exp. Mech. 46, 777-787 (2006).
[CrossRef]

M. Grediac, F. Pierron, S. Avril, and E. Toussaint, “The virtual fields method for extracting constitutive parameters from full-field measurements: a review,” Strain 42, 233-253 (2006).
[CrossRef]

P. D. Ruiz, J. M. Huntley, and A. Maranon, “Tilt scanning interferometry: a novel technique for mapping structure and three-dimensional displacement fields within optically scattering media,” Proc. R. Soc. A 462, 2481-2502 (2006).
[CrossRef]

2003 (3)

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography--principles and applications,” Rep. Prog. Phys. 66, 239-303 (2003).
[CrossRef]

K. Gastinger, S. Winther, and K. D. Hinsch, “Low-coherence speckle interferometer (LCSI) for characterization of adhesion in adhesive-bonded joints,” Proc. SPIE 4933, 59-65 (2003).
[CrossRef]

G. Gülker, K. D. Hinsch, and A. Kraft, “Low-coherence ESPI in the investigation of ancient terracotta warriors,” Proc. SPIE 4933, 53-58 (2003).
[CrossRef]

2002 (1)

M. T. Draney, R. J. Herfkens, T. J. R. Hughes, N. J. Pelc, K. L. Wedding, C. K. Zarins, and C. A. Taylor, “Quantification of vessel wall cyclic strain using cine phase contrast magnetic resonance imaging,” Ann. Biomed. Eng. 30, 1033-1045 (2002).
[CrossRef] [PubMed]

2000 (2)

D. D. Steele, T. L. Chenevert, A. R. Skovoroda, and S. Y. Emelianov, “Three-dimensional static displacement stimulated echo NMR elasticity imaging,” Phys. Med. Biol. 45, 1633-1648 (2000).
[CrossRef] [PubMed]

F. Pierron, S. Zhavoronok, and M. Grediac, “Identification of the through-thickness properties of thick laminated tubes using the virtual fields method,” Int. J. Solids Struct. 37, 4437-4453 (2000).
[CrossRef]

1999 (1)

B. K. Bay, T. S. Smith, D. P. Fyhrie, and M. Saad, “Digital volume correlation: three-dimensional strain mapping using x-ray tomography,” Exp. Mech. 39, 217-226 (1999).
[CrossRef]

1998 (2)

1992 (1)

1989 (1)

M. Grediac, “Principe des travaux virtuels et identification,” C. R. Acad. Sci. Ser. II 309, 1-5 (1989).

1986 (1)

Abe, T.

Aben, H.

H. Aben, A. Errapart, L. Ainola, and J. Anton, “Photoelastic tomography for residual stress measurement in glass,” in Optical Metrology in Production Engineering, (SPIE, 2004) pp. 1-11.

Ainola, L.

H. Aben, A. Errapart, L. Ainola, and J. Anton, “Photoelastic tomography for residual stress measurement in glass,” in Optical Metrology in Production Engineering, (SPIE, 2004) pp. 1-11.

Anton, J.

H. Aben, A. Errapart, L. Ainola, and J. Anton, “Photoelastic tomography for residual stress measurement in glass,” in Optical Metrology in Production Engineering, (SPIE, 2004) pp. 1-11.

Avril, S.

S. Avril, F. Pierron, M. A. Sutton, and J. H. Yan, “Identification of elasto-visco-plastic parameters and characterization of Luders behavior using digital image correlation and the virtual fields method,” Mech. Mater. 40, 729-742 (2008).
[CrossRef]

S. Avril and F. Pierron, “General framework for the identification of constitutive parameters from full-field measurements in linear elasticity,” Int. J. Solids Struct. 44, 4978-5002 (2007).
[CrossRef]

M. Grediac, F. Pierron, S. Avril, and E. Toussaint, “The virtual fields method for extracting constitutive parameters from full-field measurements: a review,” Strain 42, 233-253 (2006).
[CrossRef]

Bay, B. K.

B. K. Bay, T. S. Smith, D. P. Fyhrie, and M. Saad, “Digital volume correlation: three-dimensional strain mapping using x-ray tomography,” Exp. Mech. 39, 217-226 (1999).
[CrossRef]

Chenevert, T. L.

D. D. Steele, T. L. Chenevert, A. R. Skovoroda, and S. Y. Emelianov, “Three-dimensional static displacement stimulated echo NMR elasticity imaging,” Phys. Med. Biol. 45, 1633-1648 (2000).
[CrossRef] [PubMed]

Coupland, J. M.

J. M. Coupland and J. Lobera, “Holography, tomography and 3D microscopy as linear filtering operations,” Meas. Sci. Technol. 19, 074012 (2008).
[CrossRef]

Dávila, A.

A. Dávila, G. H. Kaufmann, and D. Kerr, “Digital processing of ESPI addition fringes,” in Fringe '93, W. Jüptner and W. Osten, eds. (Akademie Verlag, 1993), pp. 339-346.

Draney, M. T.

M. T. Draney, R. J. Herfkens, T. J. R. Hughes, N. J. Pelc, K. L. Wedding, C. K. Zarins, and C. A. Taylor, “Quantification of vessel wall cyclic strain using cine phase contrast magnetic resonance imaging,” Ann. Biomed. Eng. 30, 1033-1045 (2002).
[CrossRef] [PubMed]

Drexler, W.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography--principles and applications,” Rep. Prog. Phys. 66, 239-303 (2003).
[CrossRef]

Emelianov, S. Y.

D. D. Steele, T. L. Chenevert, A. R. Skovoroda, and S. Y. Emelianov, “Three-dimensional static displacement stimulated echo NMR elasticity imaging,” Phys. Med. Biol. 45, 1633-1648 (2000).
[CrossRef] [PubMed]

Equis, S.

S. Equis and P. Jacquot, “Simulation of speckle complex amplitude: advocating the linear model,” Proc. SPIE 6341, 634138.1-634138 (2006).

Errapart, A.

H. Aben, A. Errapart, L. Ainola, and J. Anton, “Photoelastic tomography for residual stress measurement in glass,” in Optical Metrology in Production Engineering, (SPIE, 2004) pp. 1-11.

Fercher, A. F.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography--principles and applications,” Rep. Prog. Phys. 66, 239-303 (2003).
[CrossRef]

Friswell, M. I.

M. I. Friswell and J. E. Mottershead, Finite Model Updating in Structural Dynamics (Springer, 1995).

Fyhrie, D. P.

B. K. Bay, T. S. Smith, D. P. Fyhrie, and M. Saad, “Digital volume correlation: three-dimensional strain mapping using x-ray tomography,” Exp. Mech. 39, 217-226 (1999).
[CrossRef]

Galizzi, G. E.

Gastinger, K.

K. Gastinger, S. Winther, and K. D. Hinsch, “Low-coherence speckle interferometer (LCSI) for characterization of adhesion in adhesive-bonded joints,” Proc. SPIE 4933, 59-65 (2003).
[CrossRef]

Ghiglia, D. C.

D. C. Ghiglia and M. D. Pritt, Two Dimensional Phase Unwrapping: Theory, Algorithms and Software (Wiley, 1998).

Giraudeau, A.

A. Giraudeau, B. Guo, and F. Pierron, “Stiffness and damping identification from full field measurements on vibrating plates,” Exp. Mech. 46, 777-787 (2006).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Grediac, M.

M. Grediac, F. Pierron, S. Avril, and E. Toussaint, “The virtual fields method for extracting constitutive parameters from full-field measurements: a review,” Strain 42, 233-253 (2006).
[CrossRef]

F. Pierron, S. Zhavoronok, and M. Grediac, “Identification of the through-thickness properties of thick laminated tubes using the virtual fields method,” Int. J. Solids Struct. 37, 4437-4453 (2000).
[CrossRef]

M. Grediac, “Principe des travaux virtuels et identification,” C. R. Acad. Sci. Ser. II 309, 1-5 (1989).

Gülker, G.

G. Gülker, K. D. Hinsch, and A. Kraft, “Low-coherence ESPI in the investigation of ancient terracotta warriors,” Proc. SPIE 4933, 53-58 (2003).
[CrossRef]

Guo, B.

A. Giraudeau, B. Guo, and F. Pierron, “Stiffness and damping identification from full field measurements on vibrating plates,” Exp. Mech. 46, 777-787 (2006).
[CrossRef]

Herfkens, R. J.

M. T. Draney, R. J. Herfkens, T. J. R. Hughes, N. J. Pelc, K. L. Wedding, C. K. Zarins, and C. A. Taylor, “Quantification of vessel wall cyclic strain using cine phase contrast magnetic resonance imaging,” Ann. Biomed. Eng. 30, 1033-1045 (2002).
[CrossRef] [PubMed]

Hinsch, K. D.

G. Gülker, K. D. Hinsch, and A. Kraft, “Low-coherence ESPI in the investigation of ancient terracotta warriors,” Proc. SPIE 4933, 53-58 (2003).
[CrossRef]

K. Gastinger, S. Winther, and K. D. Hinsch, “Low-coherence speckle interferometer (LCSI) for characterization of adhesion in adhesive-bonded joints,” Proc. SPIE 4933, 59-65 (2003).
[CrossRef]

Hitzenberger, C. K.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography--principles and applications,” Rep. Prog. Phys. 66, 239-303 (2003).
[CrossRef]

Hughes, T. J. R.

M. T. Draney, R. J. Herfkens, T. J. R. Hughes, N. J. Pelc, K. L. Wedding, C. K. Zarins, and C. A. Taylor, “Quantification of vessel wall cyclic strain using cine phase contrast magnetic resonance imaging,” Ann. Biomed. Eng. 30, 1033-1045 (2002).
[CrossRef] [PubMed]

Huntley, J. M.

P. D. Ruiz, J. M. Huntley, and A. Maranon, “Tilt scanning interferometry: a novel technique for mapping structure and three-dimensional displacement fields within optically scattering media,” Proc. R. Soc. A 462, 2481-2502 (2006).
[CrossRef]

Jacquot, P.

P. Jacquot, “Speckle interferometry: a review of the principal methods in use for experimental mechanics applications,” Strain 44, 57-69 (2008).
[CrossRef]

S. Equis and P. Jacquot, “Simulation of speckle complex amplitude: advocating the linear model,” Proc. SPIE 6341, 634138.1-634138 (2006).

Jones, R.

R. Jones and C. Wykes, Holographic and Speckle Interferometry (Cambridge University, 1989).

Kaufmann, G. H.

P. D. Ruiz, G. H. Kaufmann, and G. E. Galizzi, “Unwrapping of digital speckle pattern interferometry phase maps by use of a minimum L0-norm algorithm,” Appl. Opt. 37, 7632-7644(1998).
[CrossRef]

A. Dávila, G. H. Kaufmann, and D. Kerr, “Digital processing of ESPI addition fringes,” in Fringe '93, W. Jüptner and W. Osten, eds. (Akademie Verlag, 1993), pp. 339-346.

Kerr, D.

R. Rodriguez-Vera, D. Kerr, and F. Mendoza-Santoyo, “Electronic speckle contouring,” J. Opt. Soc. Am. A 9, 2000-2008(1992).
[CrossRef]

A. Dávila, G. H. Kaufmann, and D. Kerr, “Digital processing of ESPI addition fringes,” in Fringe '93, W. Jüptner and W. Osten, eds. (Akademie Verlag, 1993), pp. 339-346.

Koga, H.

Kraft, A.

G. Gülker, K. D. Hinsch, and A. Kraft, “Low-coherence ESPI in the investigation of ancient terracotta warriors,” Proc. SPIE 4933, 53-58 (2003).
[CrossRef]

Lasser, T.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography--principles and applications,” Rep. Prog. Phys. 66, 239-303 (2003).
[CrossRef]

Lobera, J.

J. M. Coupland and J. Lobera, “Holography, tomography and 3D microscopy as linear filtering operations,” Meas. Sci. Technol. 19, 074012 (2008).
[CrossRef]

Maranon, A.

P. D. Ruiz, J. M. Huntley, and A. Maranon, “Tilt scanning interferometry: a novel technique for mapping structure and three-dimensional displacement fields within optically scattering media,” Proc. R. Soc. A 462, 2481-2502 (2006).
[CrossRef]

Mendoza-Santoyo, F.

Mitsunaga, Y.

Mottershead, J. E.

M. I. Friswell and J. E. Mottershead, Finite Model Updating in Structural Dynamics (Springer, 1995).

Pelc, N. J.

M. T. Draney, R. J. Herfkens, T. J. R. Hughes, N. J. Pelc, K. L. Wedding, C. K. Zarins, and C. A. Taylor, “Quantification of vessel wall cyclic strain using cine phase contrast magnetic resonance imaging,” Ann. Biomed. Eng. 30, 1033-1045 (2002).
[CrossRef] [PubMed]

Pierron, F.

S. Avril, F. Pierron, M. A. Sutton, and J. H. Yan, “Identification of elasto-visco-plastic parameters and characterization of Luders behavior using digital image correlation and the virtual fields method,” Mech. Mater. 40, 729-742 (2008).
[CrossRef]

S. Avril and F. Pierron, “General framework for the identification of constitutive parameters from full-field measurements in linear elasticity,” Int. J. Solids Struct. 44, 4978-5002 (2007).
[CrossRef]

A. Giraudeau, B. Guo, and F. Pierron, “Stiffness and damping identification from full field measurements on vibrating plates,” Exp. Mech. 46, 777-787 (2006).
[CrossRef]

M. Grediac, F. Pierron, S. Avril, and E. Toussaint, “The virtual fields method for extracting constitutive parameters from full-field measurements: a review,” Strain 42, 233-253 (2006).
[CrossRef]

F. Pierron, S. Zhavoronok, and M. Grediac, “Identification of the through-thickness properties of thick laminated tubes using the virtual fields method,” Int. J. Solids Struct. 37, 4437-4453 (2000).
[CrossRef]

Pritt, M. D.

D. C. Ghiglia and M. D. Pritt, Two Dimensional Phase Unwrapping: Theory, Algorithms and Software (Wiley, 1998).

Rastogi, P. K.

P. K. Rastogi, Digital Speckle Pattern Interferometry and Related Techniques (Wiley, 2001).

Rodriguez-Vera, R.

Ruiz, P. D.

P. D. Ruiz, J. M. Huntley, and A. Maranon, “Tilt scanning interferometry: a novel technique for mapping structure and three-dimensional displacement fields within optically scattering media,” Proc. R. Soc. A 462, 2481-2502 (2006).
[CrossRef]

P. D. Ruiz, G. H. Kaufmann, and G. E. Galizzi, “Unwrapping of digital speckle pattern interferometry phase maps by use of a minimum L0-norm algorithm,” Appl. Opt. 37, 7632-7644(1998).
[CrossRef]

Saad, M.

B. K. Bay, T. S. Smith, D. P. Fyhrie, and M. Saad, “Digital volume correlation: three-dimensional strain mapping using x-ray tomography,” Exp. Mech. 39, 217-226 (1999).
[CrossRef]

Schmitt, J.

Skovoroda, A. R.

D. D. Steele, T. L. Chenevert, A. R. Skovoroda, and S. Y. Emelianov, “Three-dimensional static displacement stimulated echo NMR elasticity imaging,” Phys. Med. Biol. 45, 1633-1648 (2000).
[CrossRef] [PubMed]

Smith, T. S.

B. K. Bay, T. S. Smith, D. P. Fyhrie, and M. Saad, “Digital volume correlation: three-dimensional strain mapping using x-ray tomography,” Exp. Mech. 39, 217-226 (1999).
[CrossRef]

Steele, D. D.

D. D. Steele, T. L. Chenevert, A. R. Skovoroda, and S. Y. Emelianov, “Three-dimensional static displacement stimulated echo NMR elasticity imaging,” Phys. Med. Biol. 45, 1633-1648 (2000).
[CrossRef] [PubMed]

Sutton, M. A.

S. Avril, F. Pierron, M. A. Sutton, and J. H. Yan, “Identification of elasto-visco-plastic parameters and characterization of Luders behavior using digital image correlation and the virtual fields method,” Mech. Mater. 40, 729-742 (2008).
[CrossRef]

Taylor, C. A.

M. T. Draney, R. J. Herfkens, T. J. R. Hughes, N. J. Pelc, K. L. Wedding, C. K. Zarins, and C. A. Taylor, “Quantification of vessel wall cyclic strain using cine phase contrast magnetic resonance imaging,” Ann. Biomed. Eng. 30, 1033-1045 (2002).
[CrossRef] [PubMed]

Toussaint, E.

M. Grediac, F. Pierron, S. Avril, and E. Toussaint, “The virtual fields method for extracting constitutive parameters from full-field measurements: a review,” Strain 42, 233-253 (2006).
[CrossRef]

Wedding, K. L.

M. T. Draney, R. J. Herfkens, T. J. R. Hughes, N. J. Pelc, K. L. Wedding, C. K. Zarins, and C. A. Taylor, “Quantification of vessel wall cyclic strain using cine phase contrast magnetic resonance imaging,” Ann. Biomed. Eng. 30, 1033-1045 (2002).
[CrossRef] [PubMed]

Winther, S.

K. Gastinger, S. Winther, and K. D. Hinsch, “Low-coherence speckle interferometer (LCSI) for characterization of adhesion in adhesive-bonded joints,” Proc. SPIE 4933, 59-65 (2003).
[CrossRef]

Wykes, C.

R. Jones and C. Wykes, Holographic and Speckle Interferometry (Cambridge University, 1989).

Yan, J. H.

S. Avril, F. Pierron, M. A. Sutton, and J. H. Yan, “Identification of elasto-visco-plastic parameters and characterization of Luders behavior using digital image correlation and the virtual fields method,” Mech. Mater. 40, 729-742 (2008).
[CrossRef]

Zarins, C. K.

M. T. Draney, R. J. Herfkens, T. J. R. Hughes, N. J. Pelc, K. L. Wedding, C. K. Zarins, and C. A. Taylor, “Quantification of vessel wall cyclic strain using cine phase contrast magnetic resonance imaging,” Ann. Biomed. Eng. 30, 1033-1045 (2002).
[CrossRef] [PubMed]

Zhavoronok, S.

F. Pierron, S. Zhavoronok, and M. Grediac, “Identification of the through-thickness properties of thick laminated tubes using the virtual fields method,” Int. J. Solids Struct. 37, 4437-4453 (2000).
[CrossRef]

Ann. Biomed. Eng. (1)

M. T. Draney, R. J. Herfkens, T. J. R. Hughes, N. J. Pelc, K. L. Wedding, C. K. Zarins, and C. A. Taylor, “Quantification of vessel wall cyclic strain using cine phase contrast magnetic resonance imaging,” Ann. Biomed. Eng. 30, 1033-1045 (2002).
[CrossRef] [PubMed]

Appl. Opt. (1)

C. R. Acad. Sci. Ser. II (1)

M. Grediac, “Principe des travaux virtuels et identification,” C. R. Acad. Sci. Ser. II 309, 1-5 (1989).

Exp. Mech. (2)

A. Giraudeau, B. Guo, and F. Pierron, “Stiffness and damping identification from full field measurements on vibrating plates,” Exp. Mech. 46, 777-787 (2006).
[CrossRef]

B. K. Bay, T. S. Smith, D. P. Fyhrie, and M. Saad, “Digital volume correlation: three-dimensional strain mapping using x-ray tomography,” Exp. Mech. 39, 217-226 (1999).
[CrossRef]

Int. J. Solids Struct. (2)

S. Avril and F. Pierron, “General framework for the identification of constitutive parameters from full-field measurements in linear elasticity,” Int. J. Solids Struct. 44, 4978-5002 (2007).
[CrossRef]

F. Pierron, S. Zhavoronok, and M. Grediac, “Identification of the through-thickness properties of thick laminated tubes using the virtual fields method,” Int. J. Solids Struct. 37, 4437-4453 (2000).
[CrossRef]

J. Opt. Soc. Am. A (2)

Meas. Sci. Technol. (1)

J. M. Coupland and J. Lobera, “Holography, tomography and 3D microscopy as linear filtering operations,” Meas. Sci. Technol. 19, 074012 (2008).
[CrossRef]

Mech. Mater. (1)

S. Avril, F. Pierron, M. A. Sutton, and J. H. Yan, “Identification of elasto-visco-plastic parameters and characterization of Luders behavior using digital image correlation and the virtual fields method,” Mech. Mater. 40, 729-742 (2008).
[CrossRef]

Opt. Express (1)

Phys. Med. Biol. (1)

D. D. Steele, T. L. Chenevert, A. R. Skovoroda, and S. Y. Emelianov, “Three-dimensional static displacement stimulated echo NMR elasticity imaging,” Phys. Med. Biol. 45, 1633-1648 (2000).
[CrossRef] [PubMed]

Proc. R. Soc. A (1)

P. D. Ruiz, J. M. Huntley, and A. Maranon, “Tilt scanning interferometry: a novel technique for mapping structure and three-dimensional displacement fields within optically scattering media,” Proc. R. Soc. A 462, 2481-2502 (2006).
[CrossRef]

Proc. SPIE (3)

S. Equis and P. Jacquot, “Simulation of speckle complex amplitude: advocating the linear model,” Proc. SPIE 6341, 634138.1-634138 (2006).

K. Gastinger, S. Winther, and K. D. Hinsch, “Low-coherence speckle interferometer (LCSI) for characterization of adhesion in adhesive-bonded joints,” Proc. SPIE 4933, 59-65 (2003).
[CrossRef]

G. Gülker, K. D. Hinsch, and A. Kraft, “Low-coherence ESPI in the investigation of ancient terracotta warriors,” Proc. SPIE 4933, 53-58 (2003).
[CrossRef]

Rep. Prog. Phys. (1)

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography--principles and applications,” Rep. Prog. Phys. 66, 239-303 (2003).
[CrossRef]

Strain (2)

P. Jacquot, “Speckle interferometry: a review of the principal methods in use for experimental mechanics applications,” Strain 44, 57-69 (2008).
[CrossRef]

M. Grediac, F. Pierron, S. Avril, and E. Toussaint, “The virtual fields method for extracting constitutive parameters from full-field measurements: a review,” Strain 42, 233-253 (2006).
[CrossRef]

Other (7)

R. Jones and C. Wykes, Holographic and Speckle Interferometry (Cambridge University, 1989).

P. K. Rastogi, Digital Speckle Pattern Interferometry and Related Techniques (Wiley, 2001).

M. I. Friswell and J. E. Mottershead, Finite Model Updating in Structural Dynamics (Springer, 1995).

H. Aben, A. Errapart, L. Ainola, and J. Anton, “Photoelastic tomography for residual stress measurement in glass,” in Optical Metrology in Production Engineering, (SPIE, 2004) pp. 1-11.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

A. Dávila, G. H. Kaufmann, and D. Kerr, “Digital processing of ESPI addition fringes,” in Fringe '93, W. Jüptner and W. Osten, eds. (Akademie Verlag, 1993), pp. 339-346.

D. C. Ghiglia and M. D. Pritt, Two Dimensional Phase Unwrapping: Theory, Algorithms and Software (Wiley, 1998).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Imaging system and sample geometry used to simulate the speckle fields used in TSI to measure depth-resolved displacements inside semitransparent scattering materials: L i and L o form a 4 f system; D, detector array; A, aperture of the imaging system; BS, beam splitter; R, reference surface; M, material sample with refractive index n M .

Fig. 2
Fig. 2

Schematic diagram of the TSI system: R, reference surface placed at z = 0 and y 0 ; M, material sample with refractive index n M ; Q, internal point within the sample; LS, lens system used to image M and R; BS, beam splitter; D, detector array.

Fig. 3
Fig. 3

Mean value of the spectrum of the interference signal | I D | 2 evaluated along the y axis for (a) a horizontal position and (b) over the ( x , f ) plane. The peak identified as P R corresponds to the reference surface and the band P M is associated with the semitransparent sample.

Fig. 4
Fig. 4

Mean value of the spectrum of the interference signal evaluated along the y axis on the ( x , f ) plane. The peaks identified as P R , P 0 , and P l correspond to the reference surface R, the object surface S 0 , and the inner scattering layer S l , respectively.

Fig. 5
Fig. 5

Out-of-plane phase change obtained by a numerical simulation of a TSI system due to a rigid body tilt of the sample about the y axis. The wrapped phase maps correspond to (a) the front surface and (b) the slice within the material at a distance d l from the front surface.

Fig. 6
Fig. 6

In-plane phase change obtained by a numerical simulation of a TSI system due to a linear horizontal displacement applied to the sample along the x axis. The wrapped phase maps correspond to (a) the front surface and (b) the slice within the material at a distance d l from the front surface.

Fig. 7
Fig. 7

Comparison between the original out-of-plane displacement component w (line a) and the displacement obtained at the internal layer S l (line b). An offset of 0.4 μm was added to the original displacement (line a) for the sake of clarity.

Fig. 8
Fig. 8

Comparison between the original in-plane displacement component u (line a) and the displacement obtained at the internal layer S l (line b). An offset of 0.4 μm was added to the original displacement (line a) for the sake of clarity.

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

u o = h u i ,
U o = H U i ,
u i = exp [ j ( φ d + φ s ) ] ,
U o = FT ( u o ) = H FT { exp [ j ( φ d + φ s ) ] } ,
H f s = exp ( j k d f s ) exp [ j π λ d f s ( f x 2 + f y 2 ) ] ,
H 4 f = { 1 if ( f x 2 + f y 2 ) 1 2 Ω c 0 otherwise ,
Ω c = D A 4 λ f ,
U o M = H 4 f H f s 0 ( U i S 0 + l H f s l U i S l ) ,
H f s 0 = exp ( j k d r ) exp [ j π λ d r ( f x 2 + f y 2 ) ] , H f s l = exp ( j k n M d l ) exp [ j π λ n M d l ( f x 2 + f y 2 ) ] ,
U o R = H 4 f U i R ,
ϕ ( x , y , z ) = 2 π λ [ n 0 x sin θ + n 0 d r ( 1 + cos θ ) + n M ( z d r ) ( 1 + cos θ r ) ] .
θ ( t ) = θ c + Δ θ T t ,
1 2 π ϕ t = f ( x , y , z ) = n 0 Δ θ λ T [ x cos θ d r sin θ ( z d r ) ξ ] = f x ( x , y ) + f d r ( y , d r ) + f z ( y , z d r ) ,
ξ = θ r θ sin θ = χ cos θ sin θ ( 1 χ 2 sin 2 θ ) 1 / 2 ,
i D ( x , y , t ) = i r ( x , y ) + 2 d r z max [ i r ( x , y ) i ( x , y , z ) ] 1 / 2 cos [ 2 π f ( x , y , z ) t ] d z + 2 d r z max d r z max [ i ( x , y , z ) i ( x , y , z ) ] 1 / 2 × cos { 2 π [ f ( x , y , z ) f ( x , y , z ) ] t } d z d z .
z ( x , y ) = d r λ T f z ( y , z d r ) ξ n 0 Δ θ ,
Δ f = n 0 | ξ | Δ θ λ T Δ z .
Δ ϕ R ( x , y , z ) = 2 π λ { u ( x , y , z ) n 0 sin θ R + w ( x , y , d r ) n 0 ( 1 + cos θ R ) + [ w ( x , y , z ) w ( x , y , d r ) ] n M ( 1 + cos θ R r ) } , Δ ϕ L ( x , y , z ) = 2 π λ { u ( x , y , z ) n 0 sin θ L + w ( x , y , d r ) n 0 ( 1 + cos θ L ) + [ w ( x , y , z ) w ( x , y , d r ) ] n M ( 1 + cos θ L r ) } ,
u ( x , y , z ) = λ Δ ϕ x ( x , y , z ) 4 π n 0 sin θ , w ( x , y , z ) = λ Δ ϕ z ( x , y , z ) 4 π n M ( 1 + cos θ r ) λ Δ ϕ z ( x , y , d r ) 4 π [ 1 n M ( 1 + cos θ r ) 1 n 0 ( 1 + cos θ r ) ] .
δ z = λ γ n 0 | ξ | Δ θ ,

Metrics