Abstract

By combining dynamic mechanical testing with spectral-domain polarization-sensitive optical coherence tomography (SD-PS-OCT) performed at 1550 nm we are able to directly investigate for the first time changes within scattering technical materials during tensile and fracture tests. Spatially and temporally varying polarization patterns, due to defects and material inhomogeneities, were observed within bulk polymer samples and used to finally obtain – with the help of advanced image processing algorithms – quantitative maps of the evolving internal stress distribution. Furthermore, locally increased stress within fiber-reinforced composite materials was identified in situ with SD-PS-OCT to cause depolarizing sites of fiber-matrix debonding prior the onset of complete structural failure.

© 2010 OSA

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2010

B. Heise, K. Wiesauer, E. Götzinger, M. Pircher, C. K. Hitzenberger, R. Engelke, G. Ahrens, G. Grützner, and D. Stifter, “Spatially resolved stress measurements in materials with polarization-sensitive optical coherence tomography: image acquisition and processing aspects,” Strain 46, 61–68 (2010).
[CrossRef]

2009

Q. D. Liu, N. A. Fleck, J. E. Huber, and D. P. Chu, “Birefringence measurements of creep near an electrode tip in transparent PLZT,” J. Eur. Ceram. Soc. 29, 2289–2296 (2009).
[CrossRef]

S. J. Matcher, “A review of some recent developments in polarization-sensitive optical coherence tomography imaging techniques for the study of articular cartilage,” J. Appl. Phys . 105, 102041–1 - 102041–11 (2009).
[CrossRef]

J. S. Chen and Y. K. Huang, “Full-field mapping of stress-induced birefringence using a polarized low coherence interference microscope,” Proc. SPIE 7133, 7133I–1 (2009).

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(6), 806–808 (2009).
[CrossRef] [PubMed]

2008

E. Götzinger, M. Pircher, W. Geitzenauer, C. Ahlers, B. Baumann, S. Michels, U. Schmidt-Erfurth, and C. K. Hitzenberger, “Retinal pigment epithelium segmentation by polarization sensitive optical coherence tomography,” Opt. Express 16(21), 16410–16422 (2008).
[CrossRef] [PubMed]

P. Jacquot, “Speckle interferometry: a review of the principal methods in use for experimental mechanics applications,” Strain 44, 57–59 (2008).
[CrossRef]

2007

K. Wiesauer, M. Pircher, E. Götzinger, C. K. Hitzenberger, R. Oster, and D. Stifter, “Investigation of glass-fibre reinforced polymers by polarization-sensitive, ultra-high resolution optical coherence tomography: internal structures, defects and stress,” Compos. Sci. Technol. 67, 3051–3058 (2007).
[CrossRef]

D. Stifter, “Beyond biomedicine: a review of alternative applications and developments for optical coherence tomography,” Appl. Phys. B 88, 337–357 (2007).
[CrossRef]

2006

K. Wiesauer, M. Pircher, E. Goetzinger, C. K. Hitzenberger, R. Engelke, G. Ahrens, G. Gruetzner, and D. Stifter, “Transversal ultrahigh-resolution polarizationsensitive optical coherence tomography for strain mapping in materials,” Opt. Express 14(13), 5945–5953 (2006).
[CrossRef] [PubMed]

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(21), 9643–9656 (2006).
[CrossRef] [PubMed]

2005

E. Götzinger, M. Pircher, and C. K. Hitzenberger, “High speed spectral domain polarization sensitive optical coherence tomography of the human retina,” Opt. Express 13(25), 10217–10229 (2005).
[CrossRef] [PubMed]

B. H. Park, M. C. Pierce, B. Cense, S. H. Yun, M. Mujat, G. J. Tearney, B. E. Bouma, and J. F. de Boer, “Real-time fiber-based multi-functional spectral-domain optical coherence tomography at 1.3 microm,” Opt. Express 13(11), 3931–3944 (2005).
[CrossRef] [PubMed]

N. J. Kemp, H. N. Zaatari, J. Park, H. G. Rylander Iii, and T. E. Milner, “Depth-resolved optic axis orientation in multiple layered anisotropic tissues measured with enhanced polarization-sensitive optical coherence tomography (EPS-OCT),” Opt. Express 13(12), 4507–4518 (2005).
[CrossRef] [PubMed]

K. G. Larkin, “Uniform estimation of orientation using local and nonlocal 2-D energy operators,” Opt. Express 13(20), 8097–8121 (2005).
[CrossRef] [PubMed]

C. Damerval, S. Mignen, and V. Perrier, “A Fast Algorithm for Bidimensional EMD,” IEEE Signal Process. Lett. 12, 701–704 (2005).
[CrossRef]

K. Wiesauer, A. D. Sanchis Dufau, E. Götzinger, M. Pircher, C. K. Hitzenberger, and D. Stifter, “Non-destructive quantification of internal stress in polymer materials by polarisation sensitive optical coherence tomography,” Acta Mater. 53, 2785–2791 (2005).
[CrossRef]

2004

M. Todorović, S. Jiao, L. V. Wang, and G. Stoica, “Determination of local polarization properties of biological samples in the presence of diattenuation by use of Mueller optical coherence tomography,” Opt. Lett. 29(20), 2402–2404 (2004).
[CrossRef] [PubMed]

S. Guo, J. Zhang, L. Wang, J. S. Nelson, and Z. Chen, “Depth-resolved birefringence and differential optical axis orientation measurements with fiber-based polarization-sensitive optical coherence tomography,” Opt. Lett. 29(17), 2025–2027 (2004).
[CrossRef] [PubMed]

2003

R. Leitgeb, C. K. Hitzenberger, and A. F. Fercher, “Performance of fourier domain vs. time domain optical coherence tomography,” Opt. Express 11(8), 889–894 (2003).
[CrossRef] [PubMed]

J. F. de Boer, B. Cense, B. H. Park, M. C. Pierce, G. J. Tearney, and B. E. Bouma, “Improved signal-to-noise ratio in spectral-domain compared with time-domain optical coherence tomography,” Opt. Lett. 28(21), 2067–2069 (2003).
[CrossRef] [PubMed]

D. Stifter, P. Burgholzer, O. Höglinger, E. Götzinger, and C. K. Hitzenberger, “Polarisation-sensitive optical coherence tomography for material characterisation and strain-field mapping,” Appl. Phys., A Mater. Sci. Process. 76, 947–951 (2003).
[CrossRef]

J.-T. Oh and S.-W. Kim, “Polarization-sensitive optical coherence tomography for photoelasticity testing of glass/epoxy composites,” Opt. Express 11(14), 1669–1676 (2003).
[CrossRef] [PubMed]

2001

G. Gülker, K. D. Hinsch, and A. Kraft, “Deformation monitoring on ancient terracotta warriors by microscopic TV-holography,” Opt. Lasers Eng. 36, 501–512 (2001).
[CrossRef]

C. K. Hitzenberger, E. Goetzinger, M. Sticker, M. Pircher, and A. F. Fercher, “Measurement and imaging of birefringence and optic axis orientation by phase resolved polarization sensitive optical coherence tomography,” Opt. Express 9(13), 780–790 (2001).
[CrossRef] [PubMed]

K. G. Larkin, D. J. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform,” J. Opt. Soc. Am. A 18(8), 1862–1870 (2001).
[CrossRef]

M. Felsberg and G. Sommer, “The monogenic signal,” IEEE Trans. Signal Process. 49, 3136–3144 (2001).
[CrossRef]

2000

P. A. Tzaika, M. C. Boyce, and D. M. Parks, “Micromechanics of deformation in particle toughened Polyamides,” J. Mech. Phys. Solids 48, 1893–1929 (2000).
[CrossRef]

A. Baumgartner, S. Dichtl, C. K. Hitzenberger, H. Sattmann, B. Robl, A. Moritz, A. F. Fercher, and W. Sperr, “Polarization-sensitive optical coherence tomography of dental structures,” Caries Res. 34(1), 59–69 (2000).
[CrossRef]

1999

M. G. Ducros, J. F. de Boer, H. E. Huang, L. C. Chao, Z. P. Chen, J. S. Nelson, T. E. Milner, and H. G. Rylander, “Polarization sensitive optical coherence tomography of the rabbit eye,” IEEE J. Sel. Top. Quantum Electron. 5, 1159–1167 (1999).
[CrossRef]

J. Weickert, “Coherence-enhancing diffusion filtering,” Int. J. Comput. Vis. 31, 111–127 (1999).
[CrossRef]

1998

J. F. De Boer, S. Srinivas, A. Malekafzali, Z. Chen, and J. Nelson, “Imaging thermally damaged tissue by Polarization Sensitive Optical Coherence Tomography,” Opt. Express 3(6), 212–218 (1998).
[CrossRef] [PubMed]

J. M. Schmitt, “OCT elastography: imaging microscopic deformation and strain of tissue,” Opt. Express 3(6), 199–211 (1998).
[CrossRef] [PubMed]

1997

J. F. de Boer, T. E. Milner, M. J. C. van Gemert, and J. S. Nelson, “Two-dimensional birefringence imaging in biological tissue by polarization-sensitive optical coherence tomography,” Opt. Lett. 22(12), 934–936 (1997).
[CrossRef] [PubMed]

1992

R. Hee, D. Huang, and E. A. Swanson, “J. G. and Fujimoto, “Polarization-sensitive low-coherence reflectometer for birefringence characterization and ranging,” J. Opt. Soc. Am. B 9, 903–908 (1992).
[CrossRef]

1991

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

1985

S. Wu, “Phase structure and adhesion in polymer blends: A criterion for rubber toughening,” Polymer (Guildf.) 26, 1855–1863 (1985).
[CrossRef]

Ahlers, C.

E. Götzinger, M. Pircher, W. Geitzenauer, C. Ahlers, B. Baumann, S. Michels, U. Schmidt-Erfurth, and C. K. Hitzenberger, “Retinal pigment epithelium segmentation by polarization sensitive optical coherence tomography,” Opt. Express 16(21), 16410–16422 (2008).
[CrossRef] [PubMed]

Ahrens, G.

B. Heise, K. Wiesauer, E. Götzinger, M. Pircher, C. K. Hitzenberger, R. Engelke, G. Ahrens, G. Grützner, and D. Stifter, “Spatially resolved stress measurements in materials with polarization-sensitive optical coherence tomography: image acquisition and processing aspects,” Strain 46, 61–68 (2010).
[CrossRef]

K. Wiesauer, M. Pircher, E. Goetzinger, C. K. Hitzenberger, R. Engelke, G. Ahrens, G. Gruetzner, and D. Stifter, “Transversal ultrahigh-resolution polarizationsensitive optical coherence tomography for strain mapping in materials,” Opt. Express 14(13), 5945–5953 (2006).
[CrossRef] [PubMed]

Baumann, B.

E. Götzinger, M. Pircher, W. Geitzenauer, C. Ahlers, B. Baumann, S. Michels, U. Schmidt-Erfurth, and C. K. Hitzenberger, “Retinal pigment epithelium segmentation by polarization sensitive optical coherence tomography,” Opt. Express 16(21), 16410–16422 (2008).
[CrossRef] [PubMed]

Baumgartner, A.

A. Baumgartner, S. Dichtl, C. K. Hitzenberger, H. Sattmann, B. Robl, A. Moritz, A. F. Fercher, and W. Sperr, “Polarization-sensitive optical coherence tomography of dental structures,” Caries Res. 34(1), 59–69 (2000).
[CrossRef]

Bone, D. J.

K. G. Larkin, D. J. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform,” J. Opt. Soc. Am. A 18(8), 1862–1870 (2001).
[CrossRef]

Bouma, B. E.

B. H. Park, M. C. Pierce, B. Cense, S. H. Yun, M. Mujat, G. J. Tearney, B. E. Bouma, and J. F. de Boer, “Real-time fiber-based multi-functional spectral-domain optical coherence tomography at 1.3 microm,” Opt. Express 13(11), 3931–3944 (2005).
[CrossRef] [PubMed]

J. F. de Boer, B. Cense, B. H. Park, M. C. Pierce, G. J. Tearney, and B. E. Bouma, “Improved signal-to-noise ratio in spectral-domain compared with time-domain optical coherence tomography,” Opt. Lett. 28(21), 2067–2069 (2003).
[CrossRef] [PubMed]

Boyce, M. C.

P. A. Tzaika, M. C. Boyce, and D. M. Parks, “Micromechanics of deformation in particle toughened Polyamides,” J. Mech. Phys. Solids 48, 1893–1929 (2000).
[CrossRef]

Burgholzer, P.

D. Stifter, P. Burgholzer, O. Höglinger, E. Götzinger, and C. K. Hitzenberger, “Polarisation-sensitive optical coherence tomography for material characterisation and strain-field mapping,” Appl. Phys., A Mater. Sci. Process. 76, 947–951 (2003).
[CrossRef]

Cense, B.

B. H. Park, M. C. Pierce, B. Cense, S. H. Yun, M. Mujat, G. J. Tearney, B. E. Bouma, and J. F. de Boer, “Real-time fiber-based multi-functional spectral-domain optical coherence tomography at 1.3 microm,” Opt. Express 13(11), 3931–3944 (2005).
[CrossRef] [PubMed]

J. F. de Boer, B. Cense, B. H. Park, M. C. Pierce, G. J. Tearney, and B. E. Bouma, “Improved signal-to-noise ratio in spectral-domain compared with time-domain optical coherence tomography,” Opt. Lett. 28(21), 2067–2069 (2003).
[CrossRef] [PubMed]

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Chao, L. C.

M. G. Ducros, J. F. de Boer, H. E. Huang, L. C. Chao, Z. P. Chen, J. S. Nelson, T. E. Milner, and H. G. Rylander, “Polarization sensitive optical coherence tomography of the rabbit eye,” IEEE J. Sel. Top. Quantum Electron. 5, 1159–1167 (1999).
[CrossRef]

Chen, J. S.

J. S. Chen and Y. K. Huang, “Full-field mapping of stress-induced birefringence using a polarized low coherence interference microscope,” Proc. SPIE 7133, 7133I–1 (2009).

Chen, Z.

S. Guo, J. Zhang, L. Wang, J. S. Nelson, and Z. Chen, “Depth-resolved birefringence and differential optical axis orientation measurements with fiber-based polarization-sensitive optical coherence tomography,” Opt. Lett. 29(17), 2025–2027 (2004).
[CrossRef] [PubMed]

J. F. De Boer, S. Srinivas, A. Malekafzali, Z. Chen, and J. Nelson, “Imaging thermally damaged tissue by Polarization Sensitive Optical Coherence Tomography,” Opt. Express 3(6), 212–218 (1998).
[CrossRef] [PubMed]

Chen, Z. P.

M. G. Ducros, J. F. de Boer, H. E. Huang, L. C. Chao, Z. P. Chen, J. S. Nelson, T. E. Milner, and H. G. Rylander, “Polarization sensitive optical coherence tomography of the rabbit eye,” IEEE J. Sel. Top. Quantum Electron. 5, 1159–1167 (1999).
[CrossRef]

Chu, D. P.

Q. D. Liu, N. A. Fleck, J. E. Huber, and D. P. Chu, “Birefringence measurements of creep near an electrode tip in transparent PLZT,” J. Eur. Ceram. Soc. 29, 2289–2296 (2009).
[CrossRef]

Damerval, C.

C. Damerval, S. Mignen, and V. Perrier, “A Fast Algorithm for Bidimensional EMD,” IEEE Signal Process. Lett. 12, 701–704 (2005).
[CrossRef]

de Boer, J. F.

B. H. Park, M. C. Pierce, B. Cense, S. H. Yun, M. Mujat, G. J. Tearney, B. E. Bouma, and J. F. de Boer, “Real-time fiber-based multi-functional spectral-domain optical coherence tomography at 1.3 microm,” Opt. Express 13(11), 3931–3944 (2005).
[CrossRef] [PubMed]

J. F. de Boer, B. Cense, B. H. Park, M. C. Pierce, G. J. Tearney, and B. E. Bouma, “Improved signal-to-noise ratio in spectral-domain compared with time-domain optical coherence tomography,” Opt. Lett. 28(21), 2067–2069 (2003).
[CrossRef] [PubMed]

M. G. Ducros, J. F. de Boer, H. E. Huang, L. C. Chao, Z. P. Chen, J. S. Nelson, T. E. Milner, and H. G. Rylander, “Polarization sensitive optical coherence tomography of the rabbit eye,” IEEE J. Sel. Top. Quantum Electron. 5, 1159–1167 (1999).
[CrossRef]

J. F. De Boer, S. Srinivas, A. Malekafzali, Z. Chen, and J. Nelson, “Imaging thermally damaged tissue by Polarization Sensitive Optical Coherence Tomography,” Opt. Express 3(6), 212–218 (1998).
[CrossRef] [PubMed]

J. F. de Boer, T. E. Milner, M. J. C. van Gemert, and J. S. Nelson, “Two-dimensional birefringence imaging in biological tissue by polarization-sensitive optical coherence tomography,” Opt. Lett. 22(12), 934–936 (1997).
[CrossRef] [PubMed]

De la Torre Ibarra, M. H.

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(6), 806–808 (2009).
[CrossRef] [PubMed]

De la Torre-Ibarra, M. H.

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(21), 9643–9656 (2006).
[CrossRef] [PubMed]

Dichtl, S.

A. Baumgartner, S. Dichtl, C. K. Hitzenberger, H. Sattmann, B. Robl, A. Moritz, A. F. Fercher, and W. Sperr, “Polarization-sensitive optical coherence tomography of dental structures,” Caries Res. 34(1), 59–69 (2000).
[CrossRef]

Ducros, M. G.

M. G. Ducros, J. F. de Boer, H. E. Huang, L. C. Chao, Z. P. Chen, J. S. Nelson, T. E. Milner, and H. G. Rylander, “Polarization sensitive optical coherence tomography of the rabbit eye,” IEEE J. Sel. Top. Quantum Electron. 5, 1159–1167 (1999).
[CrossRef]

Engelke, R.

B. Heise, K. Wiesauer, E. Götzinger, M. Pircher, C. K. Hitzenberger, R. Engelke, G. Ahrens, G. Grützner, and D. Stifter, “Spatially resolved stress measurements in materials with polarization-sensitive optical coherence tomography: image acquisition and processing aspects,” Strain 46, 61–68 (2010).
[CrossRef]

K. Wiesauer, M. Pircher, E. Goetzinger, C. K. Hitzenberger, R. Engelke, G. Ahrens, G. Gruetzner, and D. Stifter, “Transversal ultrahigh-resolution polarizationsensitive optical coherence tomography for strain mapping in materials,” Opt. Express 14(13), 5945–5953 (2006).
[CrossRef] [PubMed]

Felsberg, M.

M. Felsberg and G. Sommer, “The monogenic signal,” IEEE Trans. Signal Process. 49, 3136–3144 (2001).
[CrossRef]

Fercher, A. F.

R. Leitgeb, C. K. Hitzenberger, and A. F. Fercher, “Performance of fourier domain vs. time domain optical coherence tomography,” Opt. Express 11(8), 889–894 (2003).
[CrossRef] [PubMed]

C. K. Hitzenberger, E. Goetzinger, M. Sticker, M. Pircher, and A. F. Fercher, “Measurement and imaging of birefringence and optic axis orientation by phase resolved polarization sensitive optical coherence tomography,” Opt. Express 9(13), 780–790 (2001).
[CrossRef] [PubMed]

A. Baumgartner, S. Dichtl, C. K. Hitzenberger, H. Sattmann, B. Robl, A. Moritz, A. F. Fercher, and W. Sperr, “Polarization-sensitive optical coherence tomography of dental structures,” Caries Res. 34(1), 59–69 (2000).
[CrossRef]

Fleck, N. A.

Q. D. Liu, N. A. Fleck, J. E. Huber, and D. P. Chu, “Birefringence measurements of creep near an electrode tip in transparent PLZT,” J. Eur. Ceram. Soc. 29, 2289–2296 (2009).
[CrossRef]

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Fujimoto, J. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Geitzenauer, W.

E. Götzinger, M. Pircher, W. Geitzenauer, C. Ahlers, B. Baumann, S. Michels, U. Schmidt-Erfurth, and C. K. Hitzenberger, “Retinal pigment epithelium segmentation by polarization sensitive optical coherence tomography,” Opt. Express 16(21), 16410–16422 (2008).
[CrossRef] [PubMed]

Goetzinger, E.

K. Wiesauer, M. Pircher, E. Goetzinger, C. K. Hitzenberger, R. Engelke, G. Ahrens, G. Gruetzner, and D. Stifter, “Transversal ultrahigh-resolution polarizationsensitive optical coherence tomography for strain mapping in materials,” Opt. Express 14(13), 5945–5953 (2006).
[CrossRef] [PubMed]

C. K. Hitzenberger, E. Goetzinger, M. Sticker, M. Pircher, and A. F. Fercher, “Measurement and imaging of birefringence and optic axis orientation by phase resolved polarization sensitive optical coherence tomography,” Opt. Express 9(13), 780–790 (2001).
[CrossRef] [PubMed]

Götzinger, E.

B. Heise, K. Wiesauer, E. Götzinger, M. Pircher, C. K. Hitzenberger, R. Engelke, G. Ahrens, G. Grützner, and D. Stifter, “Spatially resolved stress measurements in materials with polarization-sensitive optical coherence tomography: image acquisition and processing aspects,” Strain 46, 61–68 (2010).
[CrossRef]

E. Götzinger, M. Pircher, W. Geitzenauer, C. Ahlers, B. Baumann, S. Michels, U. Schmidt-Erfurth, and C. K. Hitzenberger, “Retinal pigment epithelium segmentation by polarization sensitive optical coherence tomography,” Opt. Express 16(21), 16410–16422 (2008).
[CrossRef] [PubMed]

K. Wiesauer, M. Pircher, E. Götzinger, C. K. Hitzenberger, R. Oster, and D. Stifter, “Investigation of glass-fibre reinforced polymers by polarization-sensitive, ultra-high resolution optical coherence tomography: internal structures, defects and stress,” Compos. Sci. Technol. 67, 3051–3058 (2007).
[CrossRef]

K. Wiesauer, A. D. Sanchis Dufau, E. Götzinger, M. Pircher, C. K. Hitzenberger, and D. Stifter, “Non-destructive quantification of internal stress in polymer materials by polarisation sensitive optical coherence tomography,” Acta Mater. 53, 2785–2791 (2005).
[CrossRef]

E. Götzinger, M. Pircher, and C. K. Hitzenberger, “High speed spectral domain polarization sensitive optical coherence tomography of the human retina,” Opt. Express 13(25), 10217–10229 (2005).
[CrossRef] [PubMed]

D. Stifter, P. Burgholzer, O. Höglinger, E. Götzinger, and C. K. Hitzenberger, “Polarisation-sensitive optical coherence tomography for material characterisation and strain-field mapping,” Appl. Phys., A Mater. Sci. Process. 76, 947–951 (2003).
[CrossRef]

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Gruetzner, G.

K. Wiesauer, M. Pircher, E. Goetzinger, C. K. Hitzenberger, R. Engelke, G. Ahrens, G. Gruetzner, and D. Stifter, “Transversal ultrahigh-resolution polarizationsensitive optical coherence tomography for strain mapping in materials,” Opt. Express 14(13), 5945–5953 (2006).
[CrossRef] [PubMed]

Grützner, G.

B. Heise, K. Wiesauer, E. Götzinger, M. Pircher, C. K. Hitzenberger, R. Engelke, G. Ahrens, G. Grützner, and D. Stifter, “Spatially resolved stress measurements in materials with polarization-sensitive optical coherence tomography: image acquisition and processing aspects,” Strain 46, 61–68 (2010).
[CrossRef]

Gülker, G.

G. Gülker, K. D. Hinsch, and A. Kraft, “Deformation monitoring on ancient terracotta warriors by microscopic TV-holography,” Opt. Lasers Eng. 36, 501–512 (2001).
[CrossRef]

Guo, S.

S. Guo, J. Zhang, L. Wang, J. S. Nelson, and Z. Chen, “Depth-resolved birefringence and differential optical axis orientation measurements with fiber-based polarization-sensitive optical coherence tomography,” Opt. Lett. 29(17), 2025–2027 (2004).
[CrossRef] [PubMed]

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Hee, R.

R. Hee, D. Huang, and E. A. Swanson, “J. G. and Fujimoto, “Polarization-sensitive low-coherence reflectometer for birefringence characterization and ranging,” J. Opt. Soc. Am. B 9, 903–908 (1992).
[CrossRef]

Heise, B.

B. Heise, K. Wiesauer, E. Götzinger, M. Pircher, C. K. Hitzenberger, R. Engelke, G. Ahrens, G. Grützner, and D. Stifter, “Spatially resolved stress measurements in materials with polarization-sensitive optical coherence tomography: image acquisition and processing aspects,” Strain 46, 61–68 (2010).
[CrossRef]

Hinsch, K. D.

G. Gülker, K. D. Hinsch, and A. Kraft, “Deformation monitoring on ancient terracotta warriors by microscopic TV-holography,” Opt. Lasers Eng. 36, 501–512 (2001).
[CrossRef]

Hitzenberger, C. K.

B. Heise, K. Wiesauer, E. Götzinger, M. Pircher, C. K. Hitzenberger, R. Engelke, G. Ahrens, G. Grützner, and D. Stifter, “Spatially resolved stress measurements in materials with polarization-sensitive optical coherence tomography: image acquisition and processing aspects,” Strain 46, 61–68 (2010).
[CrossRef]

E. Götzinger, M. Pircher, W. Geitzenauer, C. Ahlers, B. Baumann, S. Michels, U. Schmidt-Erfurth, and C. K. Hitzenberger, “Retinal pigment epithelium segmentation by polarization sensitive optical coherence tomography,” Opt. Express 16(21), 16410–16422 (2008).
[CrossRef] [PubMed]

K. Wiesauer, M. Pircher, E. Götzinger, C. K. Hitzenberger, R. Oster, and D. Stifter, “Investigation of glass-fibre reinforced polymers by polarization-sensitive, ultra-high resolution optical coherence tomography: internal structures, defects and stress,” Compos. Sci. Technol. 67, 3051–3058 (2007).
[CrossRef]

K. Wiesauer, M. Pircher, E. Goetzinger, C. K. Hitzenberger, R. Engelke, G. Ahrens, G. Gruetzner, and D. Stifter, “Transversal ultrahigh-resolution polarizationsensitive optical coherence tomography for strain mapping in materials,” Opt. Express 14(13), 5945–5953 (2006).
[CrossRef] [PubMed]

K. Wiesauer, A. D. Sanchis Dufau, E. Götzinger, M. Pircher, C. K. Hitzenberger, and D. Stifter, “Non-destructive quantification of internal stress in polymer materials by polarisation sensitive optical coherence tomography,” Acta Mater. 53, 2785–2791 (2005).
[CrossRef]

E. Götzinger, M. Pircher, and C. K. Hitzenberger, “High speed spectral domain polarization sensitive optical coherence tomography of the human retina,” Opt. Express 13(25), 10217–10229 (2005).
[CrossRef] [PubMed]

R. Leitgeb, C. K. Hitzenberger, and A. F. Fercher, “Performance of fourier domain vs. time domain optical coherence tomography,” Opt. Express 11(8), 889–894 (2003).
[CrossRef] [PubMed]

D. Stifter, P. Burgholzer, O. Höglinger, E. Götzinger, and C. K. Hitzenberger, “Polarisation-sensitive optical coherence tomography for material characterisation and strain-field mapping,” Appl. Phys., A Mater. Sci. Process. 76, 947–951 (2003).
[CrossRef]

C. K. Hitzenberger, E. Goetzinger, M. Sticker, M. Pircher, and A. F. Fercher, “Measurement and imaging of birefringence and optic axis orientation by phase resolved polarization sensitive optical coherence tomography,” Opt. Express 9(13), 780–790 (2001).
[CrossRef] [PubMed]

A. Baumgartner, S. Dichtl, C. K. Hitzenberger, H. Sattmann, B. Robl, A. Moritz, A. F. Fercher, and W. Sperr, “Polarization-sensitive optical coherence tomography of dental structures,” Caries Res. 34(1), 59–69 (2000).
[CrossRef]

Höglinger, O.

D. Stifter, P. Burgholzer, O. Höglinger, E. Götzinger, and C. K. Hitzenberger, “Polarisation-sensitive optical coherence tomography for material characterisation and strain-field mapping,” Appl. Phys., A Mater. Sci. Process. 76, 947–951 (2003).
[CrossRef]

Huang, D.

R. Hee, D. Huang, and E. A. Swanson, “J. G. and Fujimoto, “Polarization-sensitive low-coherence reflectometer for birefringence characterization and ranging,” J. Opt. Soc. Am. B 9, 903–908 (1992).
[CrossRef]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Huang, H. E.

M. G. Ducros, J. F. de Boer, H. E. Huang, L. C. Chao, Z. P. Chen, J. S. Nelson, T. E. Milner, and H. G. Rylander, “Polarization sensitive optical coherence tomography of the rabbit eye,” IEEE J. Sel. Top. Quantum Electron. 5, 1159–1167 (1999).
[CrossRef]

Huang, Y. K.

J. S. Chen and Y. K. Huang, “Full-field mapping of stress-induced birefringence using a polarized low coherence interference microscope,” Proc. SPIE 7133, 7133I–1 (2009).

Huber, J. E.

Q. D. Liu, N. A. Fleck, J. E. Huber, and D. P. Chu, “Birefringence measurements of creep near an electrode tip in transparent PLZT,” J. Eur. Ceram. Soc. 29, 2289–2296 (2009).
[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(6), 806–808 (2009).
[CrossRef] [PubMed]

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(21), 9643–9656 (2006).
[CrossRef] [PubMed]

Jacquot, P.

P. Jacquot, “Speckle interferometry: a review of the principal methods in use for experimental mechanics applications,” Strain 44, 57–59 (2008).
[CrossRef]

Jiao, S.

M. Todorović, S. Jiao, L. V. Wang, and G. Stoica, “Determination of local polarization properties of biological samples in the presence of diattenuation by use of Mueller optical coherence tomography,” Opt. Lett. 29(20), 2402–2404 (2004).
[CrossRef] [PubMed]

Kemp, N. J.

N. J. Kemp, H. N. Zaatari, J. Park, H. G. Rylander Iii, and T. E. Milner, “Depth-resolved optic axis orientation in multiple layered anisotropic tissues measured with enhanced polarization-sensitive optical coherence tomography (EPS-OCT),” Opt. Express 13(12), 4507–4518 (2005).
[CrossRef] [PubMed]

Kim, S.-W.

J.-T. Oh and S.-W. Kim, “Polarization-sensitive optical coherence tomography for photoelasticity testing of glass/epoxy composites,” Opt. Express 11(14), 1669–1676 (2003).
[CrossRef] [PubMed]

Kraft, A.

G. Gülker, K. D. Hinsch, and A. Kraft, “Deformation monitoring on ancient terracotta warriors by microscopic TV-holography,” Opt. Lasers Eng. 36, 501–512 (2001).
[CrossRef]

Larkin, K. G.

K. G. Larkin, “Uniform estimation of orientation using local and nonlocal 2-D energy operators,” Opt. Express 13(20), 8097–8121 (2005).
[CrossRef] [PubMed]

K. G. Larkin, D. J. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform,” J. Opt. Soc. Am. A 18(8), 1862–1870 (2001).
[CrossRef]

Leitgeb, R.

R. Leitgeb, C. K. Hitzenberger, and A. F. Fercher, “Performance of fourier domain vs. time domain optical coherence tomography,” Opt. Express 11(8), 889–894 (2003).
[CrossRef] [PubMed]

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Liu, Q. D.

Q. D. Liu, N. A. Fleck, J. E. Huber, and D. P. Chu, “Birefringence measurements of creep near an electrode tip in transparent PLZT,” J. Eur. Ceram. Soc. 29, 2289–2296 (2009).
[CrossRef]

Malekafzali, A.

J. F. De Boer, S. Srinivas, A. Malekafzali, Z. Chen, and J. Nelson, “Imaging thermally damaged tissue by Polarization Sensitive Optical Coherence Tomography,” Opt. Express 3(6), 212–218 (1998).
[CrossRef] [PubMed]

Matcher, S. J.

S. J. Matcher, “A review of some recent developments in polarization-sensitive optical coherence tomography imaging techniques for the study of articular cartilage,” J. Appl. Phys . 105, 102041–1 - 102041–11 (2009).
[CrossRef]

Michels, S.

E. Götzinger, M. Pircher, W. Geitzenauer, C. Ahlers, B. Baumann, S. Michels, U. Schmidt-Erfurth, and C. K. Hitzenberger, “Retinal pigment epithelium segmentation by polarization sensitive optical coherence tomography,” Opt. Express 16(21), 16410–16422 (2008).
[CrossRef] [PubMed]

Mignen, S.

C. Damerval, S. Mignen, and V. Perrier, “A Fast Algorithm for Bidimensional EMD,” IEEE Signal Process. Lett. 12, 701–704 (2005).
[CrossRef]

Milner, T. E.

N. J. Kemp, H. N. Zaatari, J. Park, H. G. Rylander Iii, and T. E. Milner, “Depth-resolved optic axis orientation in multiple layered anisotropic tissues measured with enhanced polarization-sensitive optical coherence tomography (EPS-OCT),” Opt. Express 13(12), 4507–4518 (2005).
[CrossRef] [PubMed]

M. G. Ducros, J. F. de Boer, H. E. Huang, L. C. Chao, Z. P. Chen, J. S. Nelson, T. E. Milner, and H. G. Rylander, “Polarization sensitive optical coherence tomography of the rabbit eye,” IEEE J. Sel. Top. Quantum Electron. 5, 1159–1167 (1999).
[CrossRef]

J. F. de Boer, T. E. Milner, M. J. C. van Gemert, and J. S. Nelson, “Two-dimensional birefringence imaging in biological tissue by polarization-sensitive optical coherence tomography,” Opt. Lett. 22(12), 934–936 (1997).
[CrossRef] [PubMed]

Moritz, A.

A. Baumgartner, S. Dichtl, C. K. Hitzenberger, H. Sattmann, B. Robl, A. Moritz, A. F. Fercher, and W. Sperr, “Polarization-sensitive optical coherence tomography of dental structures,” Caries Res. 34(1), 59–69 (2000).
[CrossRef]

Mujat, M.

B. H. Park, M. C. Pierce, B. Cense, S. H. Yun, M. Mujat, G. J. Tearney, B. E. Bouma, and J. F. de Boer, “Real-time fiber-based multi-functional spectral-domain optical coherence tomography at 1.3 microm,” Opt. Express 13(11), 3931–3944 (2005).
[CrossRef] [PubMed]

Nelson, J.

J. F. De Boer, S. Srinivas, A. Malekafzali, Z. Chen, and J. Nelson, “Imaging thermally damaged tissue by Polarization Sensitive Optical Coherence Tomography,” Opt. Express 3(6), 212–218 (1998).
[CrossRef] [PubMed]

Nelson, J. S.

S. Guo, J. Zhang, L. Wang, J. S. Nelson, and Z. Chen, “Depth-resolved birefringence and differential optical axis orientation measurements with fiber-based polarization-sensitive optical coherence tomography,” Opt. Lett. 29(17), 2025–2027 (2004).
[CrossRef] [PubMed]

M. G. Ducros, J. F. de Boer, H. E. Huang, L. C. Chao, Z. P. Chen, J. S. Nelson, T. E. Milner, and H. G. Rylander, “Polarization sensitive optical coherence tomography of the rabbit eye,” IEEE J. Sel. Top. Quantum Electron. 5, 1159–1167 (1999).
[CrossRef]

J. F. de Boer, T. E. Milner, M. J. C. van Gemert, and J. S. Nelson, “Two-dimensional birefringence imaging in biological tissue by polarization-sensitive optical coherence tomography,” Opt. Lett. 22(12), 934–936 (1997).
[CrossRef] [PubMed]

Oh, J.-T.

J.-T. Oh and S.-W. Kim, “Polarization-sensitive optical coherence tomography for photoelasticity testing of glass/epoxy composites,” Opt. Express 11(14), 1669–1676 (2003).
[CrossRef] [PubMed]

Oldfield, M. A.

K. G. Larkin, D. J. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform,” J. Opt. Soc. Am. A 18(8), 1862–1870 (2001).
[CrossRef]

Oster, R.

K. Wiesauer, M. Pircher, E. Götzinger, C. K. Hitzenberger, R. Oster, and D. Stifter, “Investigation of glass-fibre reinforced polymers by polarization-sensitive, ultra-high resolution optical coherence tomography: internal structures, defects and stress,” Compos. Sci. Technol. 67, 3051–3058 (2007).
[CrossRef]

Park, B. H.

B. H. Park, M. C. Pierce, B. Cense, S. H. Yun, M. Mujat, G. J. Tearney, B. E. Bouma, and J. F. de Boer, “Real-time fiber-based multi-functional spectral-domain optical coherence tomography at 1.3 microm,” Opt. Express 13(11), 3931–3944 (2005).
[CrossRef] [PubMed]

J. F. de Boer, B. Cense, B. H. Park, M. C. Pierce, G. J. Tearney, and B. E. Bouma, “Improved signal-to-noise ratio in spectral-domain compared with time-domain optical coherence tomography,” Opt. Lett. 28(21), 2067–2069 (2003).
[CrossRef] [PubMed]

Park, J.

N. J. Kemp, H. N. Zaatari, J. Park, H. G. Rylander Iii, and T. E. Milner, “Depth-resolved optic axis orientation in multiple layered anisotropic tissues measured with enhanced polarization-sensitive optical coherence tomography (EPS-OCT),” Opt. Express 13(12), 4507–4518 (2005).
[CrossRef] [PubMed]

Parks, D. M.

P. A. Tzaika, M. C. Boyce, and D. M. Parks, “Micromechanics of deformation in particle toughened Polyamides,” J. Mech. Phys. Solids 48, 1893–1929 (2000).
[CrossRef]

Perrier, V.

C. Damerval, S. Mignen, and V. Perrier, “A Fast Algorithm for Bidimensional EMD,” IEEE Signal Process. Lett. 12, 701–704 (2005).
[CrossRef]

Pierce, M. C.

B. H. Park, M. C. Pierce, B. Cense, S. H. Yun, M. Mujat, G. J. Tearney, B. E. Bouma, and J. F. de Boer, “Real-time fiber-based multi-functional spectral-domain optical coherence tomography at 1.3 microm,” Opt. Express 13(11), 3931–3944 (2005).
[CrossRef] [PubMed]

J. F. de Boer, B. Cense, B. H. Park, M. C. Pierce, G. J. Tearney, and B. E. Bouma, “Improved signal-to-noise ratio in spectral-domain compared with time-domain optical coherence tomography,” Opt. Lett. 28(21), 2067–2069 (2003).
[CrossRef] [PubMed]

Pircher, M.

B. Heise, K. Wiesauer, E. Götzinger, M. Pircher, C. K. Hitzenberger, R. Engelke, G. Ahrens, G. Grützner, and D. Stifter, “Spatially resolved stress measurements in materials with polarization-sensitive optical coherence tomography: image acquisition and processing aspects,” Strain 46, 61–68 (2010).
[CrossRef]

E. Götzinger, M. Pircher, W. Geitzenauer, C. Ahlers, B. Baumann, S. Michels, U. Schmidt-Erfurth, and C. K. Hitzenberger, “Retinal pigment epithelium segmentation by polarization sensitive optical coherence tomography,” Opt. Express 16(21), 16410–16422 (2008).
[CrossRef] [PubMed]

K. Wiesauer, M. Pircher, E. Götzinger, C. K. Hitzenberger, R. Oster, and D. Stifter, “Investigation of glass-fibre reinforced polymers by polarization-sensitive, ultra-high resolution optical coherence tomography: internal structures, defects and stress,” Compos. Sci. Technol. 67, 3051–3058 (2007).
[CrossRef]

K. Wiesauer, M. Pircher, E. Goetzinger, C. K. Hitzenberger, R. Engelke, G. Ahrens, G. Gruetzner, and D. Stifter, “Transversal ultrahigh-resolution polarizationsensitive optical coherence tomography for strain mapping in materials,” Opt. Express 14(13), 5945–5953 (2006).
[CrossRef] [PubMed]

K. Wiesauer, A. D. Sanchis Dufau, E. Götzinger, M. Pircher, C. K. Hitzenberger, and D. Stifter, “Non-destructive quantification of internal stress in polymer materials by polarisation sensitive optical coherence tomography,” Acta Mater. 53, 2785–2791 (2005).
[CrossRef]

E. Götzinger, M. Pircher, and C. K. Hitzenberger, “High speed spectral domain polarization sensitive optical coherence tomography of the human retina,” Opt. Express 13(25), 10217–10229 (2005).
[CrossRef] [PubMed]

C. K. Hitzenberger, E. Goetzinger, M. Sticker, M. Pircher, and A. F. Fercher, “Measurement and imaging of birefringence and optic axis orientation by phase resolved polarization sensitive optical coherence tomography,” Opt. Express 9(13), 780–790 (2001).
[CrossRef] [PubMed]

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Robl, B.

A. Baumgartner, S. Dichtl, C. K. Hitzenberger, H. Sattmann, B. Robl, A. Moritz, A. F. Fercher, and W. Sperr, “Polarization-sensitive optical coherence tomography of dental structures,” Caries Res. 34(1), 59–69 (2000).
[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(6), 806–808 (2009).
[CrossRef] [PubMed]

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(21), 9643–9656 (2006).
[CrossRef] [PubMed]

Rylander, H. G.

M. G. Ducros, J. F. de Boer, H. E. Huang, L. C. Chao, Z. P. Chen, J. S. Nelson, T. E. Milner, and H. G. Rylander, “Polarization sensitive optical coherence tomography of the rabbit eye,” IEEE J. Sel. Top. Quantum Electron. 5, 1159–1167 (1999).
[CrossRef]

Rylander Iii, H. G.

N. J. Kemp, H. N. Zaatari, J. Park, H. G. Rylander Iii, and T. E. Milner, “Depth-resolved optic axis orientation in multiple layered anisotropic tissues measured with enhanced polarization-sensitive optical coherence tomography (EPS-OCT),” Opt. Express 13(12), 4507–4518 (2005).
[CrossRef] [PubMed]

Sanchis Dufau, A. D.

K. Wiesauer, A. D. Sanchis Dufau, E. Götzinger, M. Pircher, C. K. Hitzenberger, and D. Stifter, “Non-destructive quantification of internal stress in polymer materials by polarisation sensitive optical coherence tomography,” Acta Mater. 53, 2785–2791 (2005).
[CrossRef]

Sattmann, H.

A. Baumgartner, S. Dichtl, C. K. Hitzenberger, H. Sattmann, B. Robl, A. Moritz, A. F. Fercher, and W. Sperr, “Polarization-sensitive optical coherence tomography of dental structures,” Caries Res. 34(1), 59–69 (2000).
[CrossRef]

Schmidt-Erfurth, U.

E. Götzinger, M. Pircher, W. Geitzenauer, C. Ahlers, B. Baumann, S. Michels, U. Schmidt-Erfurth, and C. K. Hitzenberger, “Retinal pigment epithelium segmentation by polarization sensitive optical coherence tomography,” Opt. Express 16(21), 16410–16422 (2008).
[CrossRef] [PubMed]

Schmitt, J. M.

J. M. Schmitt, “OCT elastography: imaging microscopic deformation and strain of tissue,” Opt. Express 3(6), 199–211 (1998).
[CrossRef] [PubMed]

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Sommer, G.

M. Felsberg and G. Sommer, “The monogenic signal,” IEEE Trans. Signal Process. 49, 3136–3144 (2001).
[CrossRef]

Sperr, W.

A. Baumgartner, S. Dichtl, C. K. Hitzenberger, H. Sattmann, B. Robl, A. Moritz, A. F. Fercher, and W. Sperr, “Polarization-sensitive optical coherence tomography of dental structures,” Caries Res. 34(1), 59–69 (2000).
[CrossRef]

Srinivas, S.

J. F. De Boer, S. Srinivas, A. Malekafzali, Z. Chen, and J. Nelson, “Imaging thermally damaged tissue by Polarization Sensitive Optical Coherence Tomography,” Opt. Express 3(6), 212–218 (1998).
[CrossRef] [PubMed]

Sticker, M.

C. K. Hitzenberger, E. Goetzinger, M. Sticker, M. Pircher, and A. F. Fercher, “Measurement and imaging of birefringence and optic axis orientation by phase resolved polarization sensitive optical coherence tomography,” Opt. Express 9(13), 780–790 (2001).
[CrossRef] [PubMed]

Stifter, D.

B. Heise, K. Wiesauer, E. Götzinger, M. Pircher, C. K. Hitzenberger, R. Engelke, G. Ahrens, G. Grützner, and D. Stifter, “Spatially resolved stress measurements in materials with polarization-sensitive optical coherence tomography: image acquisition and processing aspects,” Strain 46, 61–68 (2010).
[CrossRef]

D. Stifter, “Beyond biomedicine: a review of alternative applications and developments for optical coherence tomography,” Appl. Phys. B 88, 337–357 (2007).
[CrossRef]

K. Wiesauer, M. Pircher, E. Götzinger, C. K. Hitzenberger, R. Oster, and D. Stifter, “Investigation of glass-fibre reinforced polymers by polarization-sensitive, ultra-high resolution optical coherence tomography: internal structures, defects and stress,” Compos. Sci. Technol. 67, 3051–3058 (2007).
[CrossRef]

K. Wiesauer, M. Pircher, E. Goetzinger, C. K. Hitzenberger, R. Engelke, G. Ahrens, G. Gruetzner, and D. Stifter, “Transversal ultrahigh-resolution polarizationsensitive optical coherence tomography for strain mapping in materials,” Opt. Express 14(13), 5945–5953 (2006).
[CrossRef] [PubMed]

K. Wiesauer, A. D. Sanchis Dufau, E. Götzinger, M. Pircher, C. K. Hitzenberger, and D. Stifter, “Non-destructive quantification of internal stress in polymer materials by polarisation sensitive optical coherence tomography,” Acta Mater. 53, 2785–2791 (2005).
[CrossRef]

D. Stifter, P. Burgholzer, O. Höglinger, E. Götzinger, and C. K. Hitzenberger, “Polarisation-sensitive optical coherence tomography for material characterisation and strain-field mapping,” Appl. Phys., A Mater. Sci. Process. 76, 947–951 (2003).
[CrossRef]

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Stoica, G.

M. Todorović, S. Jiao, L. V. Wang, and G. Stoica, “Determination of local polarization properties of biological samples in the presence of diattenuation by use of Mueller optical coherence tomography,” Opt. Lett. 29(20), 2402–2404 (2004).
[CrossRef] [PubMed]

Swanson, E. A.

R. Hee, D. Huang, and E. A. Swanson, “J. G. and Fujimoto, “Polarization-sensitive low-coherence reflectometer for birefringence characterization and ranging,” J. Opt. Soc. Am. B 9, 903–908 (1992).
[CrossRef]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Tearney, G. J.

B. H. Park, M. C. Pierce, B. Cense, S. H. Yun, M. Mujat, G. J. Tearney, B. E. Bouma, and J. F. de Boer, “Real-time fiber-based multi-functional spectral-domain optical coherence tomography at 1.3 microm,” Opt. Express 13(11), 3931–3944 (2005).
[CrossRef] [PubMed]

J. F. de Boer, B. Cense, B. H. Park, M. C. Pierce, G. J. Tearney, and B. E. Bouma, “Improved signal-to-noise ratio in spectral-domain compared with time-domain optical coherence tomography,” Opt. Lett. 28(21), 2067–2069 (2003).
[CrossRef] [PubMed]

Todorovic, M.

M. Todorović, S. Jiao, L. V. Wang, and G. Stoica, “Determination of local polarization properties of biological samples in the presence of diattenuation by use of Mueller optical coherence tomography,” Opt. Lett. 29(20), 2402–2404 (2004).
[CrossRef] [PubMed]

Tzaika, P. A.

P. A. Tzaika, M. C. Boyce, and D. M. Parks, “Micromechanics of deformation in particle toughened Polyamides,” J. Mech. Phys. Solids 48, 1893–1929 (2000).
[CrossRef]

van Gemert, M. J. C.

J. F. de Boer, T. E. Milner, M. J. C. van Gemert, and J. S. Nelson, “Two-dimensional birefringence imaging in biological tissue by polarization-sensitive optical coherence tomography,” Opt. Lett. 22(12), 934–936 (1997).
[CrossRef] [PubMed]

Wang, L.

S. Guo, J. Zhang, L. Wang, J. S. Nelson, and Z. Chen, “Depth-resolved birefringence and differential optical axis orientation measurements with fiber-based polarization-sensitive optical coherence tomography,” Opt. Lett. 29(17), 2025–2027 (2004).
[CrossRef] [PubMed]

Wang, L. V.

M. Todorović, S. Jiao, L. V. Wang, and G. Stoica, “Determination of local polarization properties of biological samples in the presence of diattenuation by use of Mueller optical coherence tomography,” Opt. Lett. 29(20), 2402–2404 (2004).
[CrossRef] [PubMed]

Weickert, J.

J. Weickert, “Coherence-enhancing diffusion filtering,” Int. J. Comput. Vis. 31, 111–127 (1999).
[CrossRef]

Wiesauer, K.

B. Heise, K. Wiesauer, E. Götzinger, M. Pircher, C. K. Hitzenberger, R. Engelke, G. Ahrens, G. Grützner, and D. Stifter, “Spatially resolved stress measurements in materials with polarization-sensitive optical coherence tomography: image acquisition and processing aspects,” Strain 46, 61–68 (2010).
[CrossRef]

K. Wiesauer, M. Pircher, E. Götzinger, C. K. Hitzenberger, R. Oster, and D. Stifter, “Investigation of glass-fibre reinforced polymers by polarization-sensitive, ultra-high resolution optical coherence tomography: internal structures, defects and stress,” Compos. Sci. Technol. 67, 3051–3058 (2007).
[CrossRef]

K. Wiesauer, M. Pircher, E. Goetzinger, C. K. Hitzenberger, R. Engelke, G. Ahrens, G. Gruetzner, and D. Stifter, “Transversal ultrahigh-resolution polarizationsensitive optical coherence tomography for strain mapping in materials,” Opt. Express 14(13), 5945–5953 (2006).
[CrossRef] [PubMed]

K. Wiesauer, A. D. Sanchis Dufau, E. Götzinger, M. Pircher, C. K. Hitzenberger, and D. Stifter, “Non-destructive quantification of internal stress in polymer materials by polarisation sensitive optical coherence tomography,” Acta Mater. 53, 2785–2791 (2005).
[CrossRef]

Wu, S.

S. Wu, “Phase structure and adhesion in polymer blends: A criterion for rubber toughening,” Polymer (Guildf.) 26, 1855–1863 (1985).
[CrossRef]

Yun, S. H.

B. H. Park, M. C. Pierce, B. Cense, S. H. Yun, M. Mujat, G. J. Tearney, B. E. Bouma, and J. F. de Boer, “Real-time fiber-based multi-functional spectral-domain optical coherence tomography at 1.3 microm,” Opt. Express 13(11), 3931–3944 (2005).
[CrossRef] [PubMed]

Zaatari, H. N.

N. J. Kemp, H. N. Zaatari, J. Park, H. G. Rylander Iii, and T. E. Milner, “Depth-resolved optic axis orientation in multiple layered anisotropic tissues measured with enhanced polarization-sensitive optical coherence tomography (EPS-OCT),” Opt. Express 13(12), 4507–4518 (2005).
[CrossRef] [PubMed]

Zhang, J.

S. Guo, J. Zhang, L. Wang, J. S. Nelson, and Z. Chen, “Depth-resolved birefringence and differential optical axis orientation measurements with fiber-based polarization-sensitive optical coherence tomography,” Opt. Lett. 29(17), 2025–2027 (2004).
[CrossRef] [PubMed]

Acta Mater.

K. Wiesauer, A. D. Sanchis Dufau, E. Götzinger, M. Pircher, C. K. Hitzenberger, and D. Stifter, “Non-destructive quantification of internal stress in polymer materials by polarisation sensitive optical coherence tomography,” Acta Mater. 53, 2785–2791 (2005).
[CrossRef]

Appl. Phys. B

D. Stifter, “Beyond biomedicine: a review of alternative applications and developments for optical coherence tomography,” Appl. Phys. B 88, 337–357 (2007).
[CrossRef]

Appl. Phys., A Mater. Sci. Process.

D. Stifter, P. Burgholzer, O. Höglinger, E. Götzinger, and C. K. Hitzenberger, “Polarisation-sensitive optical coherence tomography for material characterisation and strain-field mapping,” Appl. Phys., A Mater. Sci. Process. 76, 947–951 (2003).
[CrossRef]

Caries Res.

A. Baumgartner, S. Dichtl, C. K. Hitzenberger, H. Sattmann, B. Robl, A. Moritz, A. F. Fercher, and W. Sperr, “Polarization-sensitive optical coherence tomography of dental structures,” Caries Res. 34(1), 59–69 (2000).
[CrossRef]

Compos. Sci. Technol.

K. Wiesauer, M. Pircher, E. Götzinger, C. K. Hitzenberger, R. Oster, and D. Stifter, “Investigation of glass-fibre reinforced polymers by polarization-sensitive, ultra-high resolution optical coherence tomography: internal structures, defects and stress,” Compos. Sci. Technol. 67, 3051–3058 (2007).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

M. G. Ducros, J. F. de Boer, H. E. Huang, L. C. Chao, Z. P. Chen, J. S. Nelson, T. E. Milner, and H. G. Rylander, “Polarization sensitive optical coherence tomography of the rabbit eye,” IEEE J. Sel. Top. Quantum Electron. 5, 1159–1167 (1999).
[CrossRef]

IEEE Signal Process. Lett.

C. Damerval, S. Mignen, and V. Perrier, “A Fast Algorithm for Bidimensional EMD,” IEEE Signal Process. Lett. 12, 701–704 (2005).
[CrossRef]

IEEE Trans. Signal Process.

M. Felsberg and G. Sommer, “The monogenic signal,” IEEE Trans. Signal Process. 49, 3136–3144 (2001).
[CrossRef]

Int. J. Comput. Vis.

J. Weickert, “Coherence-enhancing diffusion filtering,” Int. J. Comput. Vis. 31, 111–127 (1999).
[CrossRef]

J. Appl. Phys

S. J. Matcher, “A review of some recent developments in polarization-sensitive optical coherence tomography imaging techniques for the study of articular cartilage,” J. Appl. Phys . 105, 102041–1 - 102041–11 (2009).
[CrossRef]

J. Eur. Ceram. Soc.

Q. D. Liu, N. A. Fleck, J. E. Huber, and D. P. Chu, “Birefringence measurements of creep near an electrode tip in transparent PLZT,” J. Eur. Ceram. Soc. 29, 2289–2296 (2009).
[CrossRef]

J. Mech. Phys. Solids

P. A. Tzaika, M. C. Boyce, and D. M. Parks, “Micromechanics of deformation in particle toughened Polyamides,” J. Mech. Phys. Solids 48, 1893–1929 (2000).
[CrossRef]

J. Opt. Soc. Am. A

K. G. Larkin, D. J. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform,” J. Opt. Soc. Am. A 18(8), 1862–1870 (2001).
[CrossRef]

J. Opt. Soc. Am. B

R. Hee, D. Huang, and E. A. Swanson, “J. G. and Fujimoto, “Polarization-sensitive low-coherence reflectometer for birefringence characterization and ranging,” J. Opt. Soc. Am. B 9, 903–908 (1992).
[CrossRef]

Opt. Express

J. F. De Boer, S. Srinivas, A. Malekafzali, Z. Chen, and J. Nelson, “Imaging thermally damaged tissue by Polarization Sensitive Optical Coherence Tomography,” Opt. Express 3(6), 212–218 (1998).
[CrossRef] [PubMed]

J.-T. Oh and S.-W. Kim, “Polarization-sensitive optical coherence tomography for photoelasticity testing of glass/epoxy composites,” Opt. Express 11(14), 1669–1676 (2003).
[CrossRef] [PubMed]

K. Wiesauer, M. Pircher, E. Goetzinger, C. K. Hitzenberger, R. Engelke, G. Ahrens, G. Gruetzner, and D. Stifter, “Transversal ultrahigh-resolution polarizationsensitive optical coherence tomography for strain mapping in materials,” Opt. Express 14(13), 5945–5953 (2006).
[CrossRef] [PubMed]

E. Götzinger, M. Pircher, and C. K. Hitzenberger, “High speed spectral domain polarization sensitive optical coherence tomography of the human retina,” Opt. Express 13(25), 10217–10229 (2005).
[CrossRef] [PubMed]

B. H. Park, M. C. Pierce, B. Cense, S. H. Yun, M. Mujat, G. J. Tearney, B. E. Bouma, and J. F. de Boer, “Real-time fiber-based multi-functional spectral-domain optical coherence tomography at 1.3 microm,” Opt. Express 13(11), 3931–3944 (2005).
[CrossRef] [PubMed]

C. K. Hitzenberger, E. Goetzinger, M. Sticker, M. Pircher, and A. F. Fercher, “Measurement and imaging of birefringence and optic axis orientation by phase resolved polarization sensitive optical coherence tomography,” Opt. Express 9(13), 780–790 (2001).
[CrossRef] [PubMed]

J. M. Schmitt, “OCT elastography: imaging microscopic deformation and strain of tissue,” Opt. Express 3(6), 199–211 (1998).
[CrossRef] [PubMed]

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(21), 9643–9656 (2006).
[CrossRef] [PubMed]

R. Leitgeb, C. K. Hitzenberger, and A. F. Fercher, “Performance of fourier domain vs. time domain optical coherence tomography,” Opt. Express 11(8), 889–894 (2003).
[CrossRef] [PubMed]

E. Götzinger, M. Pircher, W. Geitzenauer, C. Ahlers, B. Baumann, S. Michels, U. Schmidt-Erfurth, and C. K. Hitzenberger, “Retinal pigment epithelium segmentation by polarization sensitive optical coherence tomography,” Opt. Express 16(21), 16410–16422 (2008).
[CrossRef] [PubMed]

K. G. Larkin, “Uniform estimation of orientation using local and nonlocal 2-D energy operators,” Opt. Express 13(20), 8097–8121 (2005).
[CrossRef] [PubMed]

N. J. Kemp, H. N. Zaatari, J. Park, H. G. Rylander Iii, and T. E. Milner, “Depth-resolved optic axis orientation in multiple layered anisotropic tissues measured with enhanced polarization-sensitive optical coherence tomography (EPS-OCT),” Opt. Express 13(12), 4507–4518 (2005).
[CrossRef] [PubMed]

Opt. Lasers Eng.

G. Gülker, K. D. Hinsch, and A. Kraft, “Deformation monitoring on ancient terracotta warriors by microscopic TV-holography,” Opt. Lasers Eng. 36, 501–512 (2001).
[CrossRef]

Opt. Lett.

J. F. de Boer, B. Cense, B. H. Park, M. C. Pierce, G. J. Tearney, and B. E. Bouma, “Improved signal-to-noise ratio in spectral-domain compared with time-domain optical coherence tomography,” Opt. Lett. 28(21), 2067–2069 (2003).
[CrossRef] [PubMed]

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(6), 806–808 (2009).
[CrossRef] [PubMed]

J. F. de Boer, T. E. Milner, M. J. C. van Gemert, and J. S. Nelson, “Two-dimensional birefringence imaging in biological tissue by polarization-sensitive optical coherence tomography,” Opt. Lett. 22(12), 934–936 (1997).
[CrossRef] [PubMed]

M. Todorović, S. Jiao, L. V. Wang, and G. Stoica, “Determination of local polarization properties of biological samples in the presence of diattenuation by use of Mueller optical coherence tomography,” Opt. Lett. 29(20), 2402–2404 (2004).
[CrossRef] [PubMed]

S. Guo, J. Zhang, L. Wang, J. S. Nelson, and Z. Chen, “Depth-resolved birefringence and differential optical axis orientation measurements with fiber-based polarization-sensitive optical coherence tomography,” Opt. Lett. 29(17), 2025–2027 (2004).
[CrossRef] [PubMed]

Polymer (Guildf.)

S. Wu, “Phase structure and adhesion in polymer blends: A criterion for rubber toughening,” Polymer (Guildf.) 26, 1855–1863 (1985).
[CrossRef]

Proc. SPIE

J. S. Chen and Y. K. Huang, “Full-field mapping of stress-induced birefringence using a polarized low coherence interference microscope,” Proc. SPIE 7133, 7133I–1 (2009).

Science

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[CrossRef] [PubMed]

Strain

B. Heise, K. Wiesauer, E. Götzinger, M. Pircher, C. K. Hitzenberger, R. Engelke, G. Ahrens, G. Grützner, and D. Stifter, “Spatially resolved stress measurements in materials with polarization-sensitive optical coherence tomography: image acquisition and processing aspects,” Strain 46, 61–68 (2010).
[CrossRef]

P. Jacquot, “Speckle interferometry: a review of the principal methods in use for experimental mechanics applications,” Strain 44, 57–59 (2008).
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T. Bülow, D. Pallek, and G. Sommer, “Riesz Transforms for the Isotropic Estimation of the Local Phase of Moiré Interferograms”, Mustererkennung2000, ed., G. Sommer et al. (Springer Verlag, Berlin, DAGM 2000), 333–340.

e.g.: R. J. Young, and P. A. Lovell, Introduction to Polymers (Chapman & Hall, 1991).

J. W. Goodman, “Random phasor sums,” in Speckle phenomena in optics (Roberts and Comp., Englewood, 2007), 7–25.

K. Ramesh, Digital Photoelasticity: Advanced Techniques and Applications. (Springer, 2000).

K. Wiesauer, M. Pircher, E. Götzinger, C. K. Hitzenberger, R. Engelke, G. Ahrens, G. Grützner, R. Oster, and D. Stifter, “Ultrahigh-resolution transversal polarization-sensitive optical coherence tomography: structural analysis and strain-mapping,” in: Fracture of Nano and Engineering Materials and Structures, E.E. Gdoutos, ed., (Springer, 2006).

B. Jähne, Digital Image Processing, (Springer, Heidelberg-Berlin, 2002).

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B. G. Zagar, B. Arminger, and B. Heise, “Comparison of Various Algorithms for Phase Unwrapping in Optical Phase Microscopy,” IEEE Proc. IMTC Warsaw, Poland (2007).

B. Hofmann, Mathematik inverser Probleme (Teubner, Stuttgart-Leipzig, 1999).

Supplementary Material (5)

» Media 1: MOV (1356 KB)     
» Media 2: MOV (3168 KB)     
» Media 3: MOV (927 KB)     
» Media 4: MOV (1067 KB)     
» Media 5: MOV (1043 KB)     

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Figures (7)

Fig. 1
Fig. 1

Schematic sketch of combined tensile testing apparatus and SD-PS-OCT setup, with: reference mirror (RM), polarizer (P), beamsplitter (BS), polarizing BS (PBS), quarter wave plates (QWP), galvano-scanner mirror (GM), diffraction gratings (DG), line cameras (CCD), tensile force F and indicated coordinate system (x,y,z).

Fig. 2
Fig. 2

(a)-(d) Single-frame excerpts from a SD-PS-OCT recording (Media 1) showing a rubber particle filled PP polymer test bar (thickness: 1mm) under increasing tensile load (velocity: 1mm/s). (e) Simultaneously measured strain-stress curve indicating different regions which correspond to the sample stages (a)-(d): (a) linear elastic region, (b) non-linear elastic region and beginning of plastic deformation leading to increased scattering, (c) permanent plastic deformation after crossing the yield point and onset of necking, (d) pronounced necking (necking front indicated with arrow) finally leading to fracture. (f) Statistical evaluation of cross-sections taken in between regimes (c) and (d) to visualize front of material flow during necking, as indicated by dotted line (scale bar: value of standard deviation with respect to maximum signal intensity).

Fig. 3
Fig. 3

Single-frame excerpts from SD-PS-OCT recordings of PA polymer test bars (thickness: 1mm) under increasing tensile load with conventional intensity cross-sections (upper images) and corresponding gray-scale encoded retardation images (bottom images). (a) Sample exhibiting a surface defect (Media 2). (b) Sample with internal defect (visible as slightly darker, bow-shaped feature within marked region) (Media 3).

Fig. 4
Fig. 4

Illustration of the signal analysis scheme on simulated retardation fringe data. (a) Normalized, originally assumed stress/birefringence distribution exhibiting a 2D Gaussian profile. (b) Retardation fringe image deduced from (a) superimposed with speckle noise. (c) CED-denoised and normalized retardation fringe image (in-phase component). (d) Computed quadrature image by means of a 2D demodulation approach. (e) Wrapped phase image obtained from (c) and (d). (f) Orientation image. (g) Unwrapped phase image (corresponding to cumulative retardation over depth). (h) Reconstructed stress image obtained by differentiation of (g) in z-direction.

Fig. 5
Fig. 5

Comparison of birefringence values of an A-scan running through the maximum of the original (simulated) data according to Fig. 4(a) and the reconstructed one from Fig. 4(h), with the deviation given below (in percent with respect to the maximum birefringence value).

Fig. 6
Fig. 6

Single-frame excerpt from SD-PS-OCT recordings (Media 4) of an elastomer test sample with irregularly shaped cross-section (average thickness: 1 mm) under cyclic loading, showing the original reflectivity and retardation images (top images, retardation image: color encoded), the calculated wrapped and unwrapped phase images (middle row), the obtained stress image with indicated average stress obtained from the cross-sectional image (bottom left) and the simultaneously measured global strain-stress curve (bottom right).

Fig. 7
Fig. 7

Single-frame excerpts from SD-PS-OCT recordings (Media 5) of a glass-fiber composite during fracture. (a) Intensity images. (b) Color-encoded retardation images. (c) Color-encoded optical axis images, (d) Images with color-encoded degree of polarization uniformity - DOPU (with two regions marked by squares in the second row). Fiber-matrix delaminations are indicated with arrows (in enlarged view in inset of the third intensity image and in bottom intensity image). The single spots in the bottom images correspond to debris flying off the sample during fracture.

Equations (8)

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I P ( x , z ) = A ( x , z ) cos ( φ C ( x , z ) ) ,
I Q ( x , z ) = A ( x , z )     sin ( φ C ( x , z ) ) ,
A ( x , z ) = | I M ( x , z ) | = | ( I P ( x , z ) + i I Q ( x , z ) ) | , φ W ( x , z ) = ( I M ( x , z ) ) = ( I P ( x , z ) + i I Q ( x , z ) ) .
1 { { I P ( x , z ) } exp ( i Θ ( u , v ) ) } = i exp ( i β ( x , z ) ) I Q ( x , z ) .
E Θ { φ R ( x , z ) } = ( 1 { exp ( i Θ ( u , v ) ) { φ R ( x , z ) } } ) 2 φ R ( x , z ) 1 { exp ( i 2 Θ ( u , v ) ) { φ R ( x , z ) } } .
β ( x , z ) = 1 2 arctan 2 J x z J x x J z z
J = [ J x x J x z J x z J z z ] = [ φ R ( x , z ) φ R ( x , z ) ρ ] [ I P ( x , z ) I P ( x , z ) ρ ] .
I Q ( x , z ) = i exp ( i β ( x , z ) ) 1 { { I P ( x , z ) } exp ( i Θ ) } ,

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