Abstract

A wavelength scanning interferometry system is proposed that provides displacement fields inside the volume of semitransparent scattering materials with high spatial resolution and three-dimensional (3D) displacement sensitivity. This effectively extends digital speckle pattern interferometry into three dimensions. The sample is illuminated by three noncoplanar collimated beams around the observation direction. Sequences of two-dimensional interferograms are recorded while tuning the laser frequency at a constant rate. Different optical paths along each illumination direction ensure that the signals corresponding to each sensitivity vector do not overlap in the frequency domain. All the information required to reconstruct the location and the 3D displacement vector of scattering points within the material is thus recorded simultaneously. A controlled validation experiment is performed, which confirms the ability of the technique to provide 3D displacement distributions inside semitransparent scattering materials.

© 2012 Optical Society of America

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2011

M. Gates, J. Lambros, and M. T. Heath, “Towards high performance digital volume correlation,” Exp. Mech. 51, 491–507 (2011).
[CrossRef]

P. Li, A. Liu, L. Shi, X. Yin, S. Rugonyi, and R. K. Wang, “Assessment of strain and strain rate in embryonic chick heart in vivo using tissue Doppler optical coherence tomography,” Phys. Med. Biol. 56, 7081–7092 (2011).
[CrossRef]

P. Ruiz, J. Huntley, and J. Coupland, “Depth-resolved imaging and displacement measurement techniques viewed as linear filtering operations,” Exp. Mech. 51, 453–465 (2011).
[CrossRef]

2010

2009

I. Robinson and R. Harder, “Coherent x-ray diffraction imaging of strain at the nanoscale,” Nat. Mater. 8, 291–298 (2009).
[CrossRef]

F. Forsberg and C. R. Siviour, “3D deformation and strain analysis in compacted sugar using x-ray microtomography and digital volume correlation,” Meas. Sci. Technol. 20, 095703 (2009).
[CrossRef]

M. H. De la Torre-Ibarra, P. D. Ruiz, and J. M. Huntley, “Simultaneous measurement of in-plane and out-of-plane displacement fields in scattering media using phase-contrast spectral optical coherence tomography,” Opt. Lett. 34, 806–808 (2009).
[CrossRef]

2008

B. K. Bay, “Methods and applications of digital volume correlation,” J. Strain Anal. Eng. Des. 43, 745–760 (2008).
[CrossRef]

S. Avril, M. Bonnet, A. S. Bretelle, M. Grédiac, F. Hild, P. Ienny, F. Latourte, D. Lemosse, S. Pagano, E. Pagnacco, and F. Pierron, “Overview of identification methods of mechanical parameters based on full-field measurements,” Exp. Mech. 48, 381–402 (2008).
[CrossRef]

S. Avril, J. M. Huntley, F. Pierron, and D. D. Steele, “3D heterogeneous stiffness reconstruction using MRI and the virtual fields method,” Exp. Mech. 48, 479–494 (2008).
[CrossRef]

2007

R. K. Wang, S. Kirkpatrick, and M. Hinds, “Phase-sensitive optical coherence elastography for mapping tissue microstrains in real time,” Appl. Phys. Lett. 90, 164105 (2007).
[CrossRef]

A. Germaneau, P. Doumalin, and J. C. Dupre, “3D strain field measurement by correlation of volume images using scattered light: recording of images and choice of marks,” Strain 43, 207–218 (2007).
[CrossRef]

C. Franck, S. Hong, S. A. Maskarinec, D. A. Tirrell, and G. Ravichandran, “Three-dimensional full-field measurements of large deformations in soft materials using confocal microscopy and digital volume correlation,” Exp. Mech. 47, 427–438 (2007).
[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]

L. Liu and E. F. Morgan, “Accuracy and precision of digital volume correlation in quantifying displacements and strains in trabecular bone,” J. Biomech. 40, 3516–3520 (2007).
[CrossRef]

O. Marklund, J. M. Huntley, and R. Cusack, “Robust unwrapping algorithm for three-dimensional phase volumes of arbitrary shape containing knotted phase singularity loops,” Opt. Eng. 46, 085601 (2007).
[CrossRef]

2006

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. 462, 2481–2502 (2006).
[CrossRef]

M. F. Salfity, P. D. Ruiz, J. M. Huntley, M. J. Graves, R. Cusack, and D. A. Beauregard, “Branch cut surface placement for unwrapping of undersampled three-dimensional phase data: application to magnetic resonance imaging arterial flow mapping,” Appl. Opt. 45, 2711–2722 (2006).
[CrossRef]

M. H. De la Torre-Ibarra, P. D. Ruiz, and J. M. Huntley, “Double-shot depth-resolved displacement field measurement using phase-contrast spectral optical coherence tomography,” Opt. Express 14, 9643–9656 (2006).
[CrossRef]

G. E. Elsinga, F. Scarano, B. Wieneke, and B. W. van Oudheusden, “Tomographic particle image velocimetry,” Exp. Fluids 41, 933–947 (2006).
[CrossRef]

M. Grédiac, 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, F. Jumbo, A. Seaton, J. M. Huntley, I. A. Ashcroft, and G. M. Swallowe, “Numerical and experimental investigation of three-dimensional strains in adhesively bonded joints,” J. Strain Anal. Eng. Des. 41, 583–596 (2006).
[CrossRef]

2005

2004

C. L. Gilchrist, J. Q. Xia, L. A. Setton, and E. W. Hsu, “High-resolution determination of soft tissue deformation using MRI and first-order texture correlation,” IEEE Trans. Med. Imaging 23, 546–553 (2004).
[CrossRef]

P. D. Ruiz, Y. Zhou, J. M. Huntley, and R. D. Wildman, “Depth resolved whole field displacement measurement using wavelength scanning interferometry,” J. Opt. A 6, 679–683 (2004).
[CrossRef]

1998

1995

B. K. Bay, “Texture correlation: a method for the measurement of detailed strain distributions within trabecular bone,” J. Orthop. Res. 13, 258–267 (1995).
[CrossRef]

Ashcroft, I. A.

P. D. Ruiz, F. Jumbo, A. Seaton, J. M. Huntley, I. A. Ashcroft, and G. M. Swallowe, “Numerical and experimental investigation of three-dimensional strains in adhesively bonded joints,” J. Strain Anal. Eng. Des. 41, 583–596 (2006).
[CrossRef]

Avril, S.

S. Avril, M. Bonnet, A. S. Bretelle, M. Grédiac, F. Hild, P. Ienny, F. Latourte, D. Lemosse, S. Pagano, E. Pagnacco, and F. Pierron, “Overview of identification methods of mechanical parameters based on full-field measurements,” Exp. Mech. 48, 381–402 (2008).
[CrossRef]

S. Avril, J. M. Huntley, F. Pierron, and D. D. Steele, “3D heterogeneous stiffness reconstruction using MRI and the virtual fields method,” Exp. Mech. 48, 479–494 (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. Grédiac, 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]

Baumann, B.

Bay, B. K.

B. K. Bay, “Methods and applications of digital volume correlation,” J. Strain Anal. Eng. Des. 43, 745–760 (2008).
[CrossRef]

B. K. Bay, “Texture correlation: a method for the measurement of detailed strain distributions within trabecular bone,” J. Orthop. Res. 13, 258–267 (1995).
[CrossRef]

Bayly, P. V.

A. K. Knutsen, Y. V. Chang, C. M. Grimm, L. Phan, L. A. Taber, and P. V. Bayly, “A new method to measure cortical growth in the developing brain,” J. Biomech. Eng. 132, 101004 (2010).
[CrossRef]

Beauregard, D. A.

Bonnet, M.

S. Avril, M. Bonnet, A. S. Bretelle, M. Grédiac, F. Hild, P. Ienny, F. Latourte, D. Lemosse, S. Pagano, E. Pagnacco, and F. Pierron, “Overview of identification methods of mechanical parameters based on full-field measurements,” Exp. Mech. 48, 381–402 (2008).
[CrossRef]

Bretelle, A. S.

S. Avril, M. Bonnet, A. S. Bretelle, M. Grédiac, F. Hild, P. Ienny, F. Latourte, D. Lemosse, S. Pagano, E. Pagnacco, and F. Pierron, “Overview of identification methods of mechanical parameters based on full-field measurements,” Exp. Mech. 48, 381–402 (2008).
[CrossRef]

Chang, Y. V.

A. K. Knutsen, Y. V. Chang, C. M. Grimm, L. Phan, L. A. Taber, and P. V. Bayly, “A new method to measure cortical growth in the developing brain,” J. Biomech. Eng. 132, 101004 (2010).
[CrossRef]

Coupland, J.

P. Ruiz, J. Huntley, and J. Coupland, “Depth-resolved imaging and displacement measurement techniques viewed as linear filtering operations,” Exp. Mech. 51, 453–465 (2011).
[CrossRef]

Cusack, R.

O. Marklund, J. M. Huntley, and R. Cusack, “Robust unwrapping algorithm for three-dimensional phase volumes of arbitrary shape containing knotted phase singularity loops,” Opt. Eng. 46, 085601 (2007).
[CrossRef]

M. F. Salfity, P. D. Ruiz, J. M. Huntley, M. J. Graves, R. Cusack, and D. A. Beauregard, “Branch cut surface placement for unwrapping of undersampled three-dimensional phase data: application to magnetic resonance imaging arterial flow mapping,” Appl. Opt. 45, 2711–2722 (2006).
[CrossRef]

De la Torre-Ibarra, M. H.

Doumalin, P.

A. Germaneau, P. Doumalin, and J. C. Dupre, “3D strain field measurement by correlation of volume images using scattered light: recording of images and choice of marks,” Strain 43, 207–218 (2007).
[CrossRef]

Dupre, J. C.

A. Germaneau, P. Doumalin, and J. C. Dupre, “3D strain field measurement by correlation of volume images using scattered light: recording of images and choice of marks,” Strain 43, 207–218 (2007).
[CrossRef]

Elsinga, G. E.

G. E. Elsinga, F. Scarano, B. Wieneke, and B. W. van Oudheusden, “Tomographic particle image velocimetry,” Exp. Fluids 41, 933–947 (2006).
[CrossRef]

Forsberg, F.

F. Forsberg and C. R. Siviour, “3D deformation and strain analysis in compacted sugar using x-ray microtomography and digital volume correlation,” Meas. Sci. Technol. 20, 095703 (2009).
[CrossRef]

Franck, C.

C. Franck, S. Hong, S. A. Maskarinec, D. A. Tirrell, and G. Ravichandran, “Three-dimensional full-field measurements of large deformations in soft materials using confocal microscopy and digital volume correlation,” Exp. Mech. 47, 427–438 (2007).
[CrossRef]

Gates, M.

M. Gates, J. Lambros, and M. T. Heath, “Towards high performance digital volume correlation,” Exp. Mech. 51, 491–507 (2011).
[CrossRef]

Germaneau, A.

A. Germaneau, P. Doumalin, and J. C. Dupre, “3D strain field measurement by correlation of volume images using scattered light: recording of images and choice of marks,” Strain 43, 207–218 (2007).
[CrossRef]

Gilchrist, C. L.

C. L. Gilchrist, J. Q. Xia, L. A. Setton, and E. W. Hsu, “High-resolution determination of soft tissue deformation using MRI and first-order texture correlation,” IEEE Trans. Med. Imaging 23, 546–553 (2004).
[CrossRef]

Götzinger, E.

Graves, M. J.

Grédiac, M.

S. Avril, M. Bonnet, A. S. Bretelle, M. Grédiac, F. Hild, P. Ienny, F. Latourte, D. Lemosse, S. Pagano, E. Pagnacco, and F. Pierron, “Overview of identification methods of mechanical parameters based on full-field measurements,” Exp. Mech. 48, 381–402 (2008).
[CrossRef]

M. Grédiac, 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]

Grimm, C. M.

A. K. Knutsen, Y. V. Chang, C. M. Grimm, L. Phan, L. A. Taber, and P. V. Bayly, “A new method to measure cortical growth in the developing brain,” J. Biomech. Eng. 132, 101004 (2010).
[CrossRef]

Han, Y.

Y. Han, B. Jhao, D. W. Kim, and H. J. Kwon, “Diagnosis of breast tumor using 2D and 3D ultrasound imaging,” presented at the ASME 2011 International Mechanical Engineering Congress & Exposition (IMECE2011), Denver, Colorado, USA, 11–17 November2011.

Harder, R.

I. Robinson and R. Harder, “Coherent x-ray diffraction imaging of strain at the nanoscale,” Nat. Mater. 8, 291–298 (2009).
[CrossRef]

Heath, M. T.

M. Gates, J. Lambros, and M. T. Heath, “Towards high performance digital volume correlation,” Exp. Mech. 51, 491–507 (2011).
[CrossRef]

Heise, B.

Hild, F.

S. Avril, M. Bonnet, A. S. Bretelle, M. Grédiac, F. Hild, P. Ienny, F. Latourte, D. Lemosse, S. Pagano, E. Pagnacco, and F. Pierron, “Overview of identification methods of mechanical parameters based on full-field measurements,” Exp. Mech. 48, 381–402 (2008).
[CrossRef]

Hinds, M.

R. K. Wang, S. Kirkpatrick, and M. Hinds, “Phase-sensitive optical coherence elastography for mapping tissue microstrains in real time,” Appl. Phys. Lett. 90, 164105 (2007).
[CrossRef]

Hitzenberger, C. K.

Hong, S.

C. Franck, S. Hong, S. A. Maskarinec, D. A. Tirrell, and G. Ravichandran, “Three-dimensional full-field measurements of large deformations in soft materials using confocal microscopy and digital volume correlation,” Exp. Mech. 47, 427–438 (2007).
[CrossRef]

Hsu, E. W.

C. L. Gilchrist, J. Q. Xia, L. A. Setton, and E. W. Hsu, “High-resolution determination of soft tissue deformation using MRI and first-order texture correlation,” IEEE Trans. Med. Imaging 23, 546–553 (2004).
[CrossRef]

Huntley, J.

P. Ruiz, J. Huntley, and J. Coupland, “Depth-resolved imaging and displacement measurement techniques viewed as linear filtering operations,” Exp. Mech. 51, 453–465 (2011).
[CrossRef]

Huntley, J. M.

M. H. De la Torre-Ibarra, P. D. Ruiz, and J. M. Huntley, “Simultaneous measurement of in-plane and out-of-plane displacement fields in scattering media using phase-contrast spectral optical coherence tomography,” Opt. Lett. 34, 806–808 (2009).
[CrossRef]

S. Avril, J. M. Huntley, F. Pierron, and D. D. Steele, “3D heterogeneous stiffness reconstruction using MRI and the virtual fields method,” Exp. Mech. 48, 479–494 (2008).
[CrossRef]

O. Marklund, J. M. Huntley, and R. Cusack, “Robust unwrapping algorithm for three-dimensional phase volumes of arbitrary shape containing knotted phase singularity loops,” Opt. Eng. 46, 085601 (2007).
[CrossRef]

M. F. Salfity, P. D. Ruiz, J. M. Huntley, M. J. Graves, R. Cusack, and D. A. Beauregard, “Branch cut surface placement for unwrapping of undersampled three-dimensional phase data: application to magnetic resonance imaging arterial flow mapping,” Appl. Opt. 45, 2711–2722 (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. 462, 2481–2502 (2006).
[CrossRef]

M. H. De la Torre-Ibarra, P. D. Ruiz, and J. M. Huntley, “Double-shot depth-resolved displacement field measurement using phase-contrast spectral optical coherence tomography,” Opt. Express 14, 9643–9656 (2006).
[CrossRef]

P. D. Ruiz, F. Jumbo, A. Seaton, J. M. Huntley, I. A. Ashcroft, and G. M. Swallowe, “Numerical and experimental investigation of three-dimensional strains in adhesively bonded joints,” J. Strain Anal. Eng. Des. 41, 583–596 (2006).
[CrossRef]

P. D. Ruiz, J. M. Huntley, and R. D. Wildman, “Depth-resolved whole-field displacement measurement by wavelength-scanning electronic speckle pattern interferometry,” Appl. Opt. 44, 3945–3953 (2005).
[CrossRef]

P. D. Ruiz, Y. Zhou, J. M. Huntley, and R. D. Wildman, “Depth resolved whole field displacement measurement using wavelength scanning interferometry,” J. Opt. A 6, 679–683 (2004).
[CrossRef]

J. M. Huntley and P. D. Ruiz, “Depth-resolved displacement field measurement,” in Advances in Speckle Metrology and Related Techniques, G. H. Kaufmann, ed. (Wiley-VCH, 2011), pp. 37–104.

Ienny, P.

S. Avril, M. Bonnet, A. S. Bretelle, M. Grédiac, F. Hild, P. Ienny, F. Latourte, D. Lemosse, S. Pagano, E. Pagnacco, and F. Pierron, “Overview of identification methods of mechanical parameters based on full-field measurements,” Exp. Mech. 48, 381–402 (2008).
[CrossRef]

Jhao, B.

Y. Han, B. Jhao, D. W. Kim, and H. J. Kwon, “Diagnosis of breast tumor using 2D and 3D ultrasound imaging,” presented at the ASME 2011 International Mechanical Engineering Congress & Exposition (IMECE2011), Denver, Colorado, USA, 11–17 November2011.

Jumbo, F.

P. D. Ruiz, F. Jumbo, A. Seaton, J. M. Huntley, I. A. Ashcroft, and G. M. Swallowe, “Numerical and experimental investigation of three-dimensional strains in adhesively bonded joints,” J. Strain Anal. Eng. Des. 41, 583–596 (2006).
[CrossRef]

Kim, D. W.

Y. Han, B. Jhao, D. W. Kim, and H. J. Kwon, “Diagnosis of breast tumor using 2D and 3D ultrasound imaging,” presented at the ASME 2011 International Mechanical Engineering Congress & Exposition (IMECE2011), Denver, Colorado, USA, 11–17 November2011.

Kirkpatrick, S.

R. K. Wang, S. Kirkpatrick, and M. Hinds, “Phase-sensitive optical coherence elastography for mapping tissue microstrains in real time,” Appl. Phys. Lett. 90, 164105 (2007).
[CrossRef]

Knutsen, A. K.

A. K. Knutsen, Y. V. Chang, C. M. Grimm, L. Phan, L. A. Taber, and P. V. Bayly, “A new method to measure cortical growth in the developing brain,” J. Biomech. Eng. 132, 101004 (2010).
[CrossRef]

Kwon, H. J.

Y. Han, B. Jhao, D. W. Kim, and H. J. Kwon, “Diagnosis of breast tumor using 2D and 3D ultrasound imaging,” presented at the ASME 2011 International Mechanical Engineering Congress & Exposition (IMECE2011), Denver, Colorado, USA, 11–17 November2011.

Lambros, J.

M. Gates, J. Lambros, and M. T. Heath, “Towards high performance digital volume correlation,” Exp. Mech. 51, 491–507 (2011).
[CrossRef]

Latourte, F.

S. Avril, M. Bonnet, A. S. Bretelle, M. Grédiac, F. Hild, P. Ienny, F. Latourte, D. Lemosse, S. Pagano, E. Pagnacco, and F. Pierron, “Overview of identification methods of mechanical parameters based on full-field measurements,” Exp. Mech. 48, 381–402 (2008).
[CrossRef]

Leiss-Holzinger, E.

Lemosse, D.

S. Avril, M. Bonnet, A. S. Bretelle, M. Grédiac, F. Hild, P. Ienny, F. Latourte, D. Lemosse, S. Pagano, E. Pagnacco, and F. Pierron, “Overview of identification methods of mechanical parameters based on full-field measurements,” Exp. Mech. 48, 381–402 (2008).
[CrossRef]

Li, P.

P. Li, A. Liu, L. Shi, X. Yin, S. Rugonyi, and R. K. Wang, “Assessment of strain and strain rate in embryonic chick heart in vivo using tissue Doppler optical coherence tomography,” Phys. Med. Biol. 56, 7081–7092 (2011).
[CrossRef]

Lionheart, W. R. B.

D. Szotten, W. R. B. Lionheart, and R. A. Tomlinson, “Tomographic reconstruction of stress from photoelastic measurements using elastic regularization,” MIMS EPrint 2006.5 (Manchester Institute for Mathematical Sciences, University of Manchester, 2006).

Liu, A.

P. Li, A. Liu, L. Shi, X. Yin, S. Rugonyi, and R. K. Wang, “Assessment of strain and strain rate in embryonic chick heart in vivo using tissue Doppler optical coherence tomography,” Phys. Med. Biol. 56, 7081–7092 (2011).
[CrossRef]

Liu, L.

L. Liu and E. F. Morgan, “Accuracy and precision of digital volume correlation in quantifying displacements and strains in trabecular bone,” J. Biomech. 40, 3516–3520 (2007).
[CrossRef]

Major, Z.

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. 462, 2481–2502 (2006).
[CrossRef]

Marklund, O.

O. Marklund, J. M. Huntley, and R. Cusack, “Robust unwrapping algorithm for three-dimensional phase volumes of arbitrary shape containing knotted phase singularity loops,” Opt. Eng. 46, 085601 (2007).
[CrossRef]

Maskarinec, S. A.

C. Franck, S. Hong, S. A. Maskarinec, D. A. Tirrell, and G. Ravichandran, “Three-dimensional full-field measurements of large deformations in soft materials using confocal microscopy and digital volume correlation,” Exp. Mech. 47, 427–438 (2007).
[CrossRef]

Morgan, E. F.

L. Liu and E. F. Morgan, “Accuracy and precision of digital volume correlation in quantifying displacements and strains in trabecular bone,” J. Biomech. 40, 3516–3520 (2007).
[CrossRef]

Orteu, J. J.

M. A. Sutton, J. J. Orteu, and H. W. Schreier, Image Correlation for Shape, Motion and Deformation Measurements—Basic Concepts, Theory and Applications (Springer, 2009).

Pagano, S.

S. Avril, M. Bonnet, A. S. Bretelle, M. Grédiac, F. Hild, P. Ienny, F. Latourte, D. Lemosse, S. Pagano, E. Pagnacco, and F. Pierron, “Overview of identification methods of mechanical parameters based on full-field measurements,” Exp. Mech. 48, 381–402 (2008).
[CrossRef]

Pagnacco, E.

S. Avril, M. Bonnet, A. S. Bretelle, M. Grédiac, F. Hild, P. Ienny, F. Latourte, D. Lemosse, S. Pagano, E. Pagnacco, and F. Pierron, “Overview of identification methods of mechanical parameters based on full-field measurements,” Exp. Mech. 48, 381–402 (2008).
[CrossRef]

Phan, L.

A. K. Knutsen, Y. V. Chang, C. M. Grimm, L. Phan, L. A. Taber, and P. V. Bayly, “A new method to measure cortical growth in the developing brain,” J. Biomech. Eng. 132, 101004 (2010).
[CrossRef]

Pierron, F.

S. Avril, J. M. Huntley, F. Pierron, and D. D. Steele, “3D heterogeneous stiffness reconstruction using MRI and the virtual fields method,” Exp. Mech. 48, 479–494 (2008).
[CrossRef]

S. Avril, M. Bonnet, A. S. Bretelle, M. Grédiac, F. Hild, P. Ienny, F. Latourte, D. Lemosse, S. Pagano, E. Pagnacco, and F. Pierron, “Overview of identification methods of mechanical parameters based on full-field measurements,” Exp. Mech. 48, 381–402 (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. Grédiac, 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]

Pircher, M.

Ravichandran, G.

C. Franck, S. Hong, S. A. Maskarinec, D. A. Tirrell, and G. Ravichandran, “Three-dimensional full-field measurements of large deformations in soft materials using confocal microscopy and digital volume correlation,” Exp. Mech. 47, 427–438 (2007).
[CrossRef]

Robinson, I.

I. Robinson and R. Harder, “Coherent x-ray diffraction imaging of strain at the nanoscale,” Nat. Mater. 8, 291–298 (2009).
[CrossRef]

Rugonyi, S.

P. Li, A. Liu, L. Shi, X. Yin, S. Rugonyi, and R. K. Wang, “Assessment of strain and strain rate in embryonic chick heart in vivo using tissue Doppler optical coherence tomography,” Phys. Med. Biol. 56, 7081–7092 (2011).
[CrossRef]

Ruiz, P.

P. Ruiz, J. Huntley, and J. Coupland, “Depth-resolved imaging and displacement measurement techniques viewed as linear filtering operations,” Exp. Mech. 51, 453–465 (2011).
[CrossRef]

Ruiz, P. D.

M. H. De la Torre-Ibarra, P. D. Ruiz, and J. M. Huntley, “Simultaneous measurement of in-plane and out-of-plane displacement fields in scattering media using phase-contrast spectral optical coherence tomography,” Opt. Lett. 34, 806–808 (2009).
[CrossRef]

M. H. De la Torre-Ibarra, P. D. Ruiz, and J. M. Huntley, “Double-shot depth-resolved displacement field measurement using phase-contrast spectral optical coherence tomography,” Opt. Express 14, 9643–9656 (2006).
[CrossRef]

M. F. Salfity, P. D. Ruiz, J. M. Huntley, M. J. Graves, R. Cusack, and D. A. Beauregard, “Branch cut surface placement for unwrapping of undersampled three-dimensional phase data: application to magnetic resonance imaging arterial flow mapping,” Appl. Opt. 45, 2711–2722 (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. 462, 2481–2502 (2006).
[CrossRef]

P. D. Ruiz, F. Jumbo, A. Seaton, J. M. Huntley, I. A. Ashcroft, and G. M. Swallowe, “Numerical and experimental investigation of three-dimensional strains in adhesively bonded joints,” J. Strain Anal. Eng. Des. 41, 583–596 (2006).
[CrossRef]

P. D. Ruiz, J. M. Huntley, and R. D. Wildman, “Depth-resolved whole-field displacement measurement by wavelength-scanning electronic speckle pattern interferometry,” Appl. Opt. 44, 3945–3953 (2005).
[CrossRef]

P. D. Ruiz, Y. Zhou, J. M. Huntley, and R. D. Wildman, “Depth resolved whole field displacement measurement using wavelength scanning interferometry,” J. Opt. A 6, 679–683 (2004).
[CrossRef]

J. M. Huntley and P. D. Ruiz, “Depth-resolved displacement field measurement,” in Advances in Speckle Metrology and Related Techniques, G. H. Kaufmann, ed. (Wiley-VCH, 2011), pp. 37–104.

Salfity, M. F.

Scarano, F.

G. E. Elsinga, F. Scarano, B. Wieneke, and B. W. van Oudheusden, “Tomographic particle image velocimetry,” Exp. Fluids 41, 933–947 (2006).
[CrossRef]

Schmitt, J. M.

Schreier, H. W.

M. A. Sutton, J. J. Orteu, and H. W. Schreier, Image Correlation for Shape, Motion and Deformation Measurements—Basic Concepts, Theory and Applications (Springer, 2009).

Seaton, A.

P. D. Ruiz, F. Jumbo, A. Seaton, J. M. Huntley, I. A. Ashcroft, and G. M. Swallowe, “Numerical and experimental investigation of three-dimensional strains in adhesively bonded joints,” J. Strain Anal. Eng. Des. 41, 583–596 (2006).
[CrossRef]

Setton, L. A.

C. L. Gilchrist, J. Q. Xia, L. A. Setton, and E. W. Hsu, “High-resolution determination of soft tissue deformation using MRI and first-order texture correlation,” IEEE Trans. Med. Imaging 23, 546–553 (2004).
[CrossRef]

Shi, L.

P. Li, A. Liu, L. Shi, X. Yin, S. Rugonyi, and R. K. Wang, “Assessment of strain and strain rate in embryonic chick heart in vivo using tissue Doppler optical coherence tomography,” Phys. Med. Biol. 56, 7081–7092 (2011).
[CrossRef]

Siviour, C. R.

F. Forsberg and C. R. Siviour, “3D deformation and strain analysis in compacted sugar using x-ray microtomography and digital volume correlation,” Meas. Sci. Technol. 20, 095703 (2009).
[CrossRef]

Steele, D. D.

S. Avril, J. M. Huntley, F. Pierron, and D. D. Steele, “3D heterogeneous stiffness reconstruction using MRI and the virtual fields method,” Exp. Mech. 48, 479–494 (2008).
[CrossRef]

Stifter, D.

Sutton, M. A.

M. A. Sutton, J. J. Orteu, and H. W. Schreier, Image Correlation for Shape, Motion and Deformation Measurements—Basic Concepts, Theory and Applications (Springer, 2009).

Swallowe, G. M.

P. D. Ruiz, F. Jumbo, A. Seaton, J. M. Huntley, I. A. Ashcroft, and G. M. Swallowe, “Numerical and experimental investigation of three-dimensional strains in adhesively bonded joints,” J. Strain Anal. Eng. Des. 41, 583–596 (2006).
[CrossRef]

Szotten, D.

D. Szotten, W. R. B. Lionheart, and R. A. Tomlinson, “Tomographic reconstruction of stress from photoelastic measurements using elastic regularization,” MIMS EPrint 2006.5 (Manchester Institute for Mathematical Sciences, University of Manchester, 2006).

Taber, L. A.

A. K. Knutsen, Y. V. Chang, C. M. Grimm, L. Phan, L. A. Taber, and P. V. Bayly, “A new method to measure cortical growth in the developing brain,” J. Biomech. Eng. 132, 101004 (2010).
[CrossRef]

Tirrell, D. A.

C. Franck, S. Hong, S. A. Maskarinec, D. A. Tirrell, and G. Ravichandran, “Three-dimensional full-field measurements of large deformations in soft materials using confocal microscopy and digital volume correlation,” Exp. Mech. 47, 427–438 (2007).
[CrossRef]

Tomlinson, R. A.

D. Szotten, W. R. B. Lionheart, and R. A. Tomlinson, “Tomographic reconstruction of stress from photoelastic measurements using elastic regularization,” MIMS EPrint 2006.5 (Manchester Institute for Mathematical Sciences, University of Manchester, 2006).

Toussaint, E.

M. Grédiac, 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]

van Oudheusden, B. W.

G. E. Elsinga, F. Scarano, B. Wieneke, and B. W. van Oudheusden, “Tomographic particle image velocimetry,” Exp. Fluids 41, 933–947 (2006).
[CrossRef]

Wang, R. K.

P. Li, A. Liu, L. Shi, X. Yin, S. Rugonyi, and R. K. Wang, “Assessment of strain and strain rate in embryonic chick heart in vivo using tissue Doppler optical coherence tomography,” Phys. Med. Biol. 56, 7081–7092 (2011).
[CrossRef]

R. K. Wang, S. Kirkpatrick, and M. Hinds, “Phase-sensitive optical coherence elastography for mapping tissue microstrains in real time,” Appl. Phys. Lett. 90, 164105 (2007).
[CrossRef]

Wieneke, B.

G. E. Elsinga, F. Scarano, B. Wieneke, and B. W. van Oudheusden, “Tomographic particle image velocimetry,” Exp. Fluids 41, 933–947 (2006).
[CrossRef]

Wildman, R. D.

P. D. Ruiz, J. M. Huntley, and R. D. Wildman, “Depth-resolved whole-field displacement measurement by wavelength-scanning electronic speckle pattern interferometry,” Appl. Opt. 44, 3945–3953 (2005).
[CrossRef]

P. D. Ruiz, Y. Zhou, J. M. Huntley, and R. D. Wildman, “Depth resolved whole field displacement measurement using wavelength scanning interferometry,” J. Opt. A 6, 679–683 (2004).
[CrossRef]

Xia, J. Q.

C. L. Gilchrist, J. Q. Xia, L. A. Setton, and E. W. Hsu, “High-resolution determination of soft tissue deformation using MRI and first-order texture correlation,” IEEE Trans. Med. Imaging 23, 546–553 (2004).
[CrossRef]

Yin, X.

P. Li, A. Liu, L. Shi, X. Yin, S. Rugonyi, and R. K. Wang, “Assessment of strain and strain rate in embryonic chick heart in vivo using tissue Doppler optical coherence tomography,” Phys. Med. Biol. 56, 7081–7092 (2011).
[CrossRef]

Zhou, Y.

P. D. Ruiz, Y. Zhou, J. M. Huntley, and R. D. Wildman, “Depth resolved whole field displacement measurement using wavelength scanning interferometry,” J. Opt. A 6, 679–683 (2004).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

R. K. Wang, S. Kirkpatrick, and M. Hinds, “Phase-sensitive optical coherence elastography for mapping tissue microstrains in real time,” Appl. Phys. Lett. 90, 164105 (2007).
[CrossRef]

Exp. Fluids

G. E. Elsinga, F. Scarano, B. Wieneke, and B. W. van Oudheusden, “Tomographic particle image velocimetry,” Exp. Fluids 41, 933–947 (2006).
[CrossRef]

Exp. Mech.

M. Gates, J. Lambros, and M. T. Heath, “Towards high performance digital volume correlation,” Exp. Mech. 51, 491–507 (2011).
[CrossRef]

S. Avril, M. Bonnet, A. S. Bretelle, M. Grédiac, F. Hild, P. Ienny, F. Latourte, D. Lemosse, S. Pagano, E. Pagnacco, and F. Pierron, “Overview of identification methods of mechanical parameters based on full-field measurements,” Exp. Mech. 48, 381–402 (2008).
[CrossRef]

S. Avril, J. M. Huntley, F. Pierron, and D. D. Steele, “3D heterogeneous stiffness reconstruction using MRI and the virtual fields method,” Exp. Mech. 48, 479–494 (2008).
[CrossRef]

C. Franck, S. Hong, S. A. Maskarinec, D. A. Tirrell, and G. Ravichandran, “Three-dimensional full-field measurements of large deformations in soft materials using confocal microscopy and digital volume correlation,” Exp. Mech. 47, 427–438 (2007).
[CrossRef]

P. Ruiz, J. Huntley, and J. Coupland, “Depth-resolved imaging and displacement measurement techniques viewed as linear filtering operations,” Exp. Mech. 51, 453–465 (2011).
[CrossRef]

IEEE Trans. Med. Imaging

C. L. Gilchrist, J. Q. Xia, L. A. Setton, and E. W. Hsu, “High-resolution determination of soft tissue deformation using MRI and first-order texture correlation,” IEEE Trans. Med. Imaging 23, 546–553 (2004).
[CrossRef]

Int. J. Solids Struct.

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]

J. Biomech.

L. Liu and E. F. Morgan, “Accuracy and precision of digital volume correlation in quantifying displacements and strains in trabecular bone,” J. Biomech. 40, 3516–3520 (2007).
[CrossRef]

J. Biomech. Eng.

A. K. Knutsen, Y. V. Chang, C. M. Grimm, L. Phan, L. A. Taber, and P. V. Bayly, “A new method to measure cortical growth in the developing brain,” J. Biomech. Eng. 132, 101004 (2010).
[CrossRef]

J. Opt. A

P. D. Ruiz, Y. Zhou, J. M. Huntley, and R. D. Wildman, “Depth resolved whole field displacement measurement using wavelength scanning interferometry,” J. Opt. A 6, 679–683 (2004).
[CrossRef]

J. Orthop. Res.

B. K. Bay, “Texture correlation: a method for the measurement of detailed strain distributions within trabecular bone,” J. Orthop. Res. 13, 258–267 (1995).
[CrossRef]

J. Strain Anal. Eng. Des.

P. D. Ruiz, F. Jumbo, A. Seaton, J. M. Huntley, I. A. Ashcroft, and G. M. Swallowe, “Numerical and experimental investigation of three-dimensional strains in adhesively bonded joints,” J. Strain Anal. Eng. Des. 41, 583–596 (2006).
[CrossRef]

B. K. Bay, “Methods and applications of digital volume correlation,” J. Strain Anal. Eng. Des. 43, 745–760 (2008).
[CrossRef]

Meas. Sci. Technol.

F. Forsberg and C. R. Siviour, “3D deformation and strain analysis in compacted sugar using x-ray microtomography and digital volume correlation,” Meas. Sci. Technol. 20, 095703 (2009).
[CrossRef]

Nat. Mater.

I. Robinson and R. Harder, “Coherent x-ray diffraction imaging of strain at the nanoscale,” Nat. Mater. 8, 291–298 (2009).
[CrossRef]

Opt. Eng.

O. Marklund, J. M. Huntley, and R. Cusack, “Robust unwrapping algorithm for three-dimensional phase volumes of arbitrary shape containing knotted phase singularity loops,” Opt. Eng. 46, 085601 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Med. Biol.

P. Li, A. Liu, L. Shi, X. Yin, S. Rugonyi, and R. K. Wang, “Assessment of strain and strain rate in embryonic chick heart in vivo using tissue Doppler optical coherence tomography,” Phys. Med. Biol. 56, 7081–7092 (2011).
[CrossRef]

Proc. R. Soc.

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. 462, 2481–2502 (2006).
[CrossRef]

Strain

M. Grédiac, 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]

A. Germaneau, P. Doumalin, and J. C. Dupre, “3D strain field measurement by correlation of volume images using scattered light: recording of images and choice of marks,” Strain 43, 207–218 (2007).
[CrossRef]

Other

Y. Han, B. Jhao, D. W. Kim, and H. J. Kwon, “Diagnosis of breast tumor using 2D and 3D ultrasound imaging,” presented at the ASME 2011 International Mechanical Engineering Congress & Exposition (IMECE2011), Denver, Colorado, USA, 11–17 November2011.

M. A. Sutton, J. J. Orteu, and H. W. Schreier, Image Correlation for Shape, Motion and Deformation Measurements—Basic Concepts, Theory and Applications (Springer, 2009).

D. Szotten, W. R. B. Lionheart, and R. A. Tomlinson, “Tomographic reconstruction of stress from photoelastic measurements using elastic regularization,” MIMS EPrint 2006.5 (Manchester Institute for Mathematical Sciences, University of Manchester, 2006).

J. M. Huntley and P. D. Ruiz, “Depth-resolved displacement field measurement,” in Advances in Speckle Metrology and Related Techniques, G. H. Kaufmann, ed. (Wiley-VCH, 2011), pp. 37–104.

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Figures (9)

Fig. 1.
Fig. 1.

WSI setup showing the tunable laser (TL), 2×4 PLC splitter, InGaAs detector, pellicle beamsplitter (PBS), absorber plate (AP), pinhole (PH), aperture stop (AS), sample (S), lenses (L1L7), optical fibers (OF1, OF2, OF3, OFR), and personal computer (PC).

Fig. 2.
Fig. 2.

Generalized optical path diagram for WSI with multiple illumination directions for a (a) scattering material and an (b) opaque surface.

Fig. 3.
Fig. 3.

(a) Intensity signal recorded at 1 pixel during a WSI scan, when an opaque flat surface is imaged under three-beam illumination; (b) its corresponding Fourier transform, showing cross correlation terms “01,” “02,” and “03” and autocorrelation terms “12,” “13,” and “23”; (c) peak 01 in more detail.

Fig. 4.
Fig. 4.

yΛ cross section of the magnitude of the Fourier transform volume obtained when a flat opaque surface is reconstructed, shown in reverse contrast for clarity. Lines corresponding to the auto correlation terms “12,” “23,” and “13” and the cross-correlation terms “01,” “02,” and “03” are clearly visible. Their tilt is a consequence of the oblique illumination.

Fig. 5.
Fig. 5.

(a) Planes of best fit obtained for reconstructions “01,” “02,” and “03” for a reference flat surface; (b) plane of best fit for reconstruction “01” showing its normal vector; and (c) sensitivity and observation vectors, as evaluated from the reference surface reconstructions using Eqs. (16)–(22).

Fig. 6.
Fig. 6.

Schematic diagram of the data processing for the reference surface and a volume sample.

Fig. 7.
Fig. 7.

Cross sections of magnitude and the wrapped phase volumes of a scattering sample that has undergone simultaneous in-plane rotation and out-of-plane tilt (phase values between π and π).

Fig. 8.
Fig. 8.

Cross sections of the measured 3D displacement field corresponding to a sample under in-plane rotation and out-of-plane tilt. The rows indicate the displacement components u, v, and w along the x, y, and z axes, respectively. The columns show sections of the data volume on planes yΛ, xΛ, and xy. Displacements units in meters.

Fig. 9.
Fig. 9.

“Measured” (bold line) and “reference” (dotted line) average displacement profiles obtained for simultaneous in-plane rotation and out-of-plane tilt of the sample.

Equations (25)

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

Λp(x,y,z)=n0[ep·(r0rp)+ep·(rer0)]+n1[ep·(rre)+eo·(rsr)]+n0eo·rs,
|rsre|=|rrs|tan(θp)
n0(N×ep)=n1(N×ep),
I(m,n,t)=|A0(m,n,t)+p=13j=1NsApj(m,n,t)exp[iϕpj(m,n,t)]|2.
I(m,n,t)=A02+p=13j=1NsApj2+2p=12q=p+13j=1Ns1k=j+1NsApjAqkcos(ϕpjϕqk)+2A0p=13j=1NsApjcosϕpj.
ϕpj(m,n,t)=ϕsj(m,n)+k(t)Λpj(m,n),
k(t)=kc+δkt,
ϕpj(m,n,t)=ϕsj(m,n)+kcΛpj(m,n)+δkΛpj(m,n)t.
fΛpj(m,n)=δkΛpj(m,n)/2π,
f^Λpj(m,n)=fΛpjNt=ΔkΛpj(m,n)/2π.
I˜(f^)=W˜(f^)*{(I0+p=13j=1NsIpj)δ(f^)+p=13j=1NsI0Ipjexp(±iϕ0pj)δ(f^f^Λpj)+p=12q=p+13j=1Ns1k=j+1NsIpjIqkexp[±i(ϕ0pjϕ0qk)]δ[f^(f^Λpjf^Λqk)]},
ΛM=πδk.
δΛ=γ2πNtδk,
δΛ=γπn1cos(θp/2)Ntδk,
Λp(x,y,z)=n0[ep·(r0rp)+ep·(rr0)+eo·r],
np=(sinαpcosβp,sinαpsinβp,cosαp),
αp=cos1(k^·np),
βp=tan1(j^·npi^·np),
tanαp=|rr0|sinθp|rr0|=sinθp.
ξp=βp+π.
ep=(sinθpcosξp,sinθpsinξp,cosθp).
Sp=2πλc(epeo)=2πλc(sinθpcosξp,sinθpsinξp,1+cosθp),
S=2πλc(sinθ1cosξ1sinθ1sinξ11+cosθ1sinθ2cosξ2sinθ2sinξ21+cosθ2sinθ3cosξ3sinθ3sinξ31+cosθ3).
Φ=SΔr,
Δr=S1Φ.

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