Abstract

Polarization-sensitive optical coherence tomography provides high-resolution cross-sectional characterization of birefringence in turbid media. Weakly birefringent biological tissues such as the retinal nerve fiber layer (RNFL) require advanced speckle noise reduction for high-sensitivity measurement of form birefringence. We present a novel method for high-sensitivity birefringence quantification by using enhanced polarization-sensitive optical coherence tomography (EPS-OCT) and introduce the polarimetric signal-to-noise ratio, a mathematical tool for analyzing speckle noise in polarimetry. Multiple incident polarization states and nonlinear fitting of normalized Stokes vectors allow determination of retardation with ±1° uncertainty with invariance to unknown unitary polarization transformations. Results from a weakly birefringent turbid film and in vivo primate RNFL are presented. In addition, we discuss the potential of EPS-OCT for noninvasive quantification of intracellular filamentous nanostructures, such as neurotubules in the RNFL that are lost during the progression of glaucoma.

© 2005 Optical Society of America

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  1. 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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
    [CrossRef] [PubMed]
  2. J. W. Goodman, “Some fundamental properties of speckle,” J. Opt. Soc. Am. 66, 1145–1150 (1976).
    [CrossRef]
  3. J. M. Schmitt, S. H. Xiang, K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4, 95–105 (1999).
    [CrossRef] [PubMed]
  4. B. H. Park, C. Saxer, T. Chen, S. M. Srinivas, J. S. Nelson, J. F. de Boer, “In vivo burn depth determination by high-speed fiber-based polarization sensitive optical coherence tomography,” J. Biomed. Opt. 6, 474–479 (2001).
    [CrossRef] [PubMed]
  5. S. Jiao, L. V. Wang, “Jones-matrix imaging of biological tissues with quadruple-channel optical coherence tomography,” J. Biomed. Opt. 7, 350–358 (2002).
    [CrossRef] [PubMed]
  6. C. K. Hitzenberger, E. Gotzinger, M. Sticker, M. Pircher, A. F. Fercher, “Measurement and imaging of birefringence and optic axis orientation by phase resolved polarization sensitive optical coherence tomography,” Opt. Express 9, 780–790 (2001).
    [CrossRef] [PubMed]
  7. R. E. Ziemer, W. H. Tranter, Principles of Communications: Systems, Modulation, and Noise, 5th ed. (Wiley, New York, 2002).
  8. W. A. Shurcliff, S. S. Ballard, Polarized Light (Van Nostrand, Princeton, N.J., 1964).
  9. C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, New York, 1998).
  10. R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).
  11. A. F. Fercher, P. F. Steeger, “First-order statistics of Stokes parameters in speckle fields,” Opt. Acta 28, 448–448 (1981).
    [CrossRef]
  12. P. F. Steeger, A. F. Fercher, “Experimental investigation of the first-order statistics of Stokes parameters in speckle fields,” Opt. Acta 29, 1395–1400 (1982).
    [CrossRef]
  13. D. Eliyahu, “Vector statistics of correlated Gaussian fields,” Phys. Rev. E 47, 2881–2892 (1993).
    [CrossRef]
  14. D. Eliyahu, “Statistics of Stokes variables for correlated Gaussian fields,” Phys. Rev. E 50, 2381–2384 (1994).
    [CrossRef]
  15. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992), pp. 683–688.
  16. N. A. Nassif, B. Cense, B. H. Park, M. C. Pierce, S. H. Yun, B. E. Bouma, G. J. Tearney, T. C. Chen, J. F. de Boer, “In vivo high-resolution video-rate spectral-domain optical coherence tomography of the human retina and optic nerve,” Opt. Express 12, 367–376 (2004).
    [CrossRef] [PubMed]
  17. B. Cense, N. A. Nassif, T. Chen, M. C. Pierce, S. H. Yun, B. H. Park, B. E. Bouma, G. J. Tearney, J. F. de Boer, “Ultrahigh-resolution high-speed retinal imaging using spectral-domain optical coherence tomography,” Opt. Express 12, 2435–2447 (2004).
    [CrossRef] [PubMed]
  18. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1959).
  19. Q. Zhou, R. W. Knighton, “Light scattering and form birefringence of parallel cylindrical arrays that represent cellular organelles of the retinal nerve fiber layer,” Appl. Opt. 36, 2273–2285 (1997).
    [CrossRef] [PubMed]
  20. D. J. MacDonald, H. M. Finlay, P. B. Canham, “Directional wall strength in saccular brain aneurysms from polarized light microscopy,” Ann. Biomed. Eng. 25, 533–542 (2000).
    [CrossRef]
  21. S. J. Matcher, C. P. Winlove, S. V. Gangnus, “The collagen structure of bovine intervertebral disc studied using polarization-sensitive optical coherence tomography,” Phys. Med. Biol. 49, 1295–1306 (2004).
    [CrossRef] [PubMed]
  22. R. Oldenbourg, E. D. Salmon, P. T. Tran, “Birefringence of single and bundled microtubules,” Biophys. J. 74, 645–654 (1998).
    [CrossRef] [PubMed]
  23. R. Oldenbourg, T. Ruiz, “Birefringence of macromolecules: Wiener’s theory revisited, with applications to DNA and tobacco mosaic virus,” Biophys. J. 56, 195–205 (1989).
    [CrossRef] [PubMed]
  24. O. Wiener, “Die Theorie des Mischkorpers für das Feld der stationaren Stromung,” Abh. Math.-Phys. Kl. Koniglich Saechs. Akad. Wiss. 32, 509–604 (1912).
  25. W. L. Bragg, A. B. Pippard, “The form birefringence of macromolecules,” Acta Crystallogr. 6, 865–867 (1953).
    [CrossRef]
  26. H. Sato, G. W. Ellis, S. Inoue, “Microtubular origin of mitotic spindle form birefringence: demonstration of the applicability of Wiener’s equation,” J. Cell Biol. 67, 501–517 (1975).
    [CrossRef] [PubMed]
  27. L. A. Amos, “Structure of microtubules,” in Microtubules, K. Roberts, J. S. Hyams, eds. (Academic, London, 1979), pp. 1–64.

2004 (3)

2002 (1)

S. Jiao, L. V. Wang, “Jones-matrix imaging of biological tissues with quadruple-channel optical coherence tomography,” J. Biomed. Opt. 7, 350–358 (2002).
[CrossRef] [PubMed]

2001 (2)

B. H. Park, C. Saxer, T. Chen, S. M. Srinivas, J. S. Nelson, J. F. de Boer, “In vivo burn depth determination by high-speed fiber-based polarization sensitive optical coherence tomography,” J. Biomed. Opt. 6, 474–479 (2001).
[CrossRef] [PubMed]

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

2000 (1)

D. J. MacDonald, H. M. Finlay, P. B. Canham, “Directional wall strength in saccular brain aneurysms from polarized light microscopy,” Ann. Biomed. Eng. 25, 533–542 (2000).
[CrossRef]

1999 (1)

J. M. Schmitt, S. H. Xiang, K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4, 95–105 (1999).
[CrossRef] [PubMed]

1998 (1)

R. Oldenbourg, E. D. Salmon, P. T. Tran, “Birefringence of single and bundled microtubules,” Biophys. J. 74, 645–654 (1998).
[CrossRef] [PubMed]

1997 (1)

1994 (1)

D. Eliyahu, “Statistics of Stokes variables for correlated Gaussian fields,” Phys. Rev. E 50, 2381–2384 (1994).
[CrossRef]

1993 (1)

D. Eliyahu, “Vector statistics of correlated Gaussian fields,” Phys. Rev. E 47, 2881–2892 (1993).
[CrossRef]

1991 (1)

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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

1989 (2)

R. Oldenbourg, T. Ruiz, “Birefringence of macromolecules: Wiener’s theory revisited, with applications to DNA and tobacco mosaic virus,” Biophys. J. 56, 195–205 (1989).
[CrossRef] [PubMed]

R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).

1982 (1)

P. F. Steeger, A. F. Fercher, “Experimental investigation of the first-order statistics of Stokes parameters in speckle fields,” Opt. Acta 29, 1395–1400 (1982).
[CrossRef]

1981 (1)

A. F. Fercher, P. F. Steeger, “First-order statistics of Stokes parameters in speckle fields,” Opt. Acta 28, 448–448 (1981).
[CrossRef]

1976 (1)

1975 (1)

H. Sato, G. W. Ellis, S. Inoue, “Microtubular origin of mitotic spindle form birefringence: demonstration of the applicability of Wiener’s equation,” J. Cell Biol. 67, 501–517 (1975).
[CrossRef] [PubMed]

1953 (1)

W. L. Bragg, A. B. Pippard, “The form birefringence of macromolecules,” Acta Crystallogr. 6, 865–867 (1953).
[CrossRef]

1912 (1)

O. Wiener, “Die Theorie des Mischkorpers für das Feld der stationaren Stromung,” Abh. Math.-Phys. Kl. Koniglich Saechs. Akad. Wiss. 32, 509–604 (1912).

Amos, L. A.

L. A. Amos, “Structure of microtubules,” in Microtubules, K. Roberts, J. S. Hyams, eds. (Academic, London, 1979), pp. 1–64.

Ballard, S. S.

W. A. Shurcliff, S. S. Ballard, Polarized Light (Van Nostrand, Princeton, N.J., 1964).

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1959).

Bouma, B. E.

Bragg, W. L.

W. L. Bragg, A. B. Pippard, “The form birefringence of macromolecules,” Acta Crystallogr. 6, 865–867 (1953).
[CrossRef]

Brosseau, C.

C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, New York, 1998).

Canham, P. B.

D. J. MacDonald, H. M. Finlay, P. B. Canham, “Directional wall strength in saccular brain aneurysms from polarized light microscopy,” Ann. Biomed. Eng. 25, 533–542 (2000).
[CrossRef]

Cense, B.

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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Chen, T.

B. Cense, N. A. Nassif, T. Chen, M. C. Pierce, S. H. Yun, B. H. Park, B. E. Bouma, G. J. Tearney, J. F. de Boer, “Ultrahigh-resolution high-speed retinal imaging using spectral-domain optical coherence tomography,” Opt. Express 12, 2435–2447 (2004).
[CrossRef] [PubMed]

B. H. Park, C. Saxer, T. Chen, S. M. Srinivas, J. S. Nelson, J. F. de Boer, “In vivo burn depth determination by high-speed fiber-based polarization sensitive optical coherence tomography,” J. Biomed. Opt. 6, 474–479 (2001).
[CrossRef] [PubMed]

Chen, T. C.

Chipman, R. A.

R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).

de Boer, J. F.

Eliyahu, D.

D. Eliyahu, “Statistics of Stokes variables for correlated Gaussian fields,” Phys. Rev. E 50, 2381–2384 (1994).
[CrossRef]

D. Eliyahu, “Vector statistics of correlated Gaussian fields,” Phys. Rev. E 47, 2881–2892 (1993).
[CrossRef]

Ellis, G. W.

H. Sato, G. W. Ellis, S. Inoue, “Microtubular origin of mitotic spindle form birefringence: demonstration of the applicability of Wiener’s equation,” J. Cell Biol. 67, 501–517 (1975).
[CrossRef] [PubMed]

Fercher, A. F.

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

P. F. Steeger, A. F. Fercher, “Experimental investigation of the first-order statistics of Stokes parameters in speckle fields,” Opt. Acta 29, 1395–1400 (1982).
[CrossRef]

A. F. Fercher, P. F. Steeger, “First-order statistics of Stokes parameters in speckle fields,” Opt. Acta 28, 448–448 (1981).
[CrossRef]

Finlay, H. M.

D. J. MacDonald, H. M. Finlay, P. B. Canham, “Directional wall strength in saccular brain aneurysms from polarized light microscopy,” Ann. Biomed. Eng. 25, 533–542 (2000).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992), pp. 683–688.

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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Gangnus, S. V.

S. J. Matcher, C. P. Winlove, S. V. Gangnus, “The collagen structure of bovine intervertebral disc studied using polarization-sensitive optical coherence tomography,” Phys. Med. Biol. 49, 1295–1306 (2004).
[CrossRef] [PubMed]

Goodman, J. W.

Gotzinger, E.

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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Hitzenberger, C. K.

Huang, D.

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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Inoue, S.

H. Sato, G. W. Ellis, S. Inoue, “Microtubular origin of mitotic spindle form birefringence: demonstration of the applicability of Wiener’s equation,” J. Cell Biol. 67, 501–517 (1975).
[CrossRef] [PubMed]

Jiao, S.

S. Jiao, L. V. Wang, “Jones-matrix imaging of biological tissues with quadruple-channel optical coherence tomography,” J. Biomed. Opt. 7, 350–358 (2002).
[CrossRef] [PubMed]

Knighton, R. W.

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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

MacDonald, D. J.

D. J. MacDonald, H. M. Finlay, P. B. Canham, “Directional wall strength in saccular brain aneurysms from polarized light microscopy,” Ann. Biomed. Eng. 25, 533–542 (2000).
[CrossRef]

Matcher, S. J.

S. J. Matcher, C. P. Winlove, S. V. Gangnus, “The collagen structure of bovine intervertebral disc studied using polarization-sensitive optical coherence tomography,” Phys. Med. Biol. 49, 1295–1306 (2004).
[CrossRef] [PubMed]

Nassif, N. A.

Nelson, J. S.

B. H. Park, C. Saxer, T. Chen, S. M. Srinivas, J. S. Nelson, J. F. de Boer, “In vivo burn depth determination by high-speed fiber-based polarization sensitive optical coherence tomography,” J. Biomed. Opt. 6, 474–479 (2001).
[CrossRef] [PubMed]

Oldenbourg, R.

R. Oldenbourg, E. D. Salmon, P. T. Tran, “Birefringence of single and bundled microtubules,” Biophys. J. 74, 645–654 (1998).
[CrossRef] [PubMed]

R. Oldenbourg, T. Ruiz, “Birefringence of macromolecules: Wiener’s theory revisited, with applications to DNA and tobacco mosaic virus,” Biophys. J. 56, 195–205 (1989).
[CrossRef] [PubMed]

Park, B. H.

Pierce, M. C.

Pippard, A. B.

W. L. Bragg, A. B. Pippard, “The form birefringence of macromolecules,” Acta Crystallogr. 6, 865–867 (1953).
[CrossRef]

Pircher, M.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992), pp. 683–688.

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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Ruiz, T.

R. Oldenbourg, T. Ruiz, “Birefringence of macromolecules: Wiener’s theory revisited, with applications to DNA and tobacco mosaic virus,” Biophys. J. 56, 195–205 (1989).
[CrossRef] [PubMed]

Salmon, E. D.

R. Oldenbourg, E. D. Salmon, P. T. Tran, “Birefringence of single and bundled microtubules,” Biophys. J. 74, 645–654 (1998).
[CrossRef] [PubMed]

Sato, H.

H. Sato, G. W. Ellis, S. Inoue, “Microtubular origin of mitotic spindle form birefringence: demonstration of the applicability of Wiener’s equation,” J. Cell Biol. 67, 501–517 (1975).
[CrossRef] [PubMed]

Saxer, C.

B. H. Park, C. Saxer, T. Chen, S. M. Srinivas, J. S. Nelson, J. F. de Boer, “In vivo burn depth determination by high-speed fiber-based polarization sensitive optical coherence tomography,” J. Biomed. Opt. 6, 474–479 (2001).
[CrossRef] [PubMed]

Schmitt, J. M.

J. M. Schmitt, S. H. Xiang, K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4, 95–105 (1999).
[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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Shurcliff, W. A.

W. A. Shurcliff, S. S. Ballard, Polarized Light (Van Nostrand, Princeton, N.J., 1964).

Srinivas, S. M.

B. H. Park, C. Saxer, T. Chen, S. M. Srinivas, J. S. Nelson, J. F. de Boer, “In vivo burn depth determination by high-speed fiber-based polarization sensitive optical coherence tomography,” J. Biomed. Opt. 6, 474–479 (2001).
[CrossRef] [PubMed]

Steeger, P. F.

P. F. Steeger, A. F. Fercher, “Experimental investigation of the first-order statistics of Stokes parameters in speckle fields,” Opt. Acta 29, 1395–1400 (1982).
[CrossRef]

A. F. Fercher, P. F. Steeger, “First-order statistics of Stokes parameters in speckle fields,” Opt. Acta 28, 448–448 (1981).
[CrossRef]

Sticker, M.

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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Swanson, E. 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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Tearney, G. J.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992), pp. 683–688.

Tran, P. T.

R. Oldenbourg, E. D. Salmon, P. T. Tran, “Birefringence of single and bundled microtubules,” Biophys. J. 74, 645–654 (1998).
[CrossRef] [PubMed]

Tranter, W. H.

R. E. Ziemer, W. H. Tranter, Principles of Communications: Systems, Modulation, and Noise, 5th ed. (Wiley, New York, 2002).

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992), pp. 683–688.

Wang, L. V.

S. Jiao, L. V. Wang, “Jones-matrix imaging of biological tissues with quadruple-channel optical coherence tomography,” J. Biomed. Opt. 7, 350–358 (2002).
[CrossRef] [PubMed]

Wiener, O.

O. Wiener, “Die Theorie des Mischkorpers für das Feld der stationaren Stromung,” Abh. Math.-Phys. Kl. Koniglich Saechs. Akad. Wiss. 32, 509–604 (1912).

Winlove, C. P.

S. J. Matcher, C. P. Winlove, S. V. Gangnus, “The collagen structure of bovine intervertebral disc studied using polarization-sensitive optical coherence tomography,” Phys. Med. Biol. 49, 1295–1306 (2004).
[CrossRef] [PubMed]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1959).

Xiang, S. H.

J. M. Schmitt, S. H. Xiang, K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4, 95–105 (1999).
[CrossRef] [PubMed]

Yun, S. H.

Yung, K. M.

J. M. Schmitt, S. H. Xiang, K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4, 95–105 (1999).
[CrossRef] [PubMed]

Zhou, Q.

Ziemer, R. E.

R. E. Ziemer, W. H. Tranter, Principles of Communications: Systems, Modulation, and Noise, 5th ed. (Wiley, New York, 2002).

Abh. Math.-Phys. Kl. Koniglich Saechs. Akad. Wiss. (1)

O. Wiener, “Die Theorie des Mischkorpers für das Feld der stationaren Stromung,” Abh. Math.-Phys. Kl. Koniglich Saechs. Akad. Wiss. 32, 509–604 (1912).

Acta Crystallogr. (1)

W. L. Bragg, A. B. Pippard, “The form birefringence of macromolecules,” Acta Crystallogr. 6, 865–867 (1953).
[CrossRef]

Ann. Biomed. Eng. (1)

D. J. MacDonald, H. M. Finlay, P. B. Canham, “Directional wall strength in saccular brain aneurysms from polarized light microscopy,” Ann. Biomed. Eng. 25, 533–542 (2000).
[CrossRef]

Appl. Opt. (1)

Biophys. J. (2)

R. Oldenbourg, E. D. Salmon, P. T. Tran, “Birefringence of single and bundled microtubules,” Biophys. J. 74, 645–654 (1998).
[CrossRef] [PubMed]

R. Oldenbourg, T. Ruiz, “Birefringence of macromolecules: Wiener’s theory revisited, with applications to DNA and tobacco mosaic virus,” Biophys. J. 56, 195–205 (1989).
[CrossRef] [PubMed]

J. Biomed. Opt. (3)

J. M. Schmitt, S. H. Xiang, K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4, 95–105 (1999).
[CrossRef] [PubMed]

B. H. Park, C. Saxer, T. Chen, S. M. Srinivas, J. S. Nelson, J. F. de Boer, “In vivo burn depth determination by high-speed fiber-based polarization sensitive optical coherence tomography,” J. Biomed. Opt. 6, 474–479 (2001).
[CrossRef] [PubMed]

S. Jiao, L. V. Wang, “Jones-matrix imaging of biological tissues with quadruple-channel optical coherence tomography,” J. Biomed. Opt. 7, 350–358 (2002).
[CrossRef] [PubMed]

J. Cell Biol. (1)

H. Sato, G. W. Ellis, S. Inoue, “Microtubular origin of mitotic spindle form birefringence: demonstration of the applicability of Wiener’s equation,” J. Cell Biol. 67, 501–517 (1975).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

Opt. Acta (2)

A. F. Fercher, P. F. Steeger, “First-order statistics of Stokes parameters in speckle fields,” Opt. Acta 28, 448–448 (1981).
[CrossRef]

P. F. Steeger, A. F. Fercher, “Experimental investigation of the first-order statistics of Stokes parameters in speckle fields,” Opt. Acta 29, 1395–1400 (1982).
[CrossRef]

Opt. Eng. (1)

R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).

Opt. Express (3)

Phys. Med. Biol. (1)

S. J. Matcher, C. P. Winlove, S. V. Gangnus, “The collagen structure of bovine intervertebral disc studied using polarization-sensitive optical coherence tomography,” Phys. Med. Biol. 49, 1295–1306 (2004).
[CrossRef] [PubMed]

Phys. Rev. E (2)

D. Eliyahu, “Vector statistics of correlated Gaussian fields,” Phys. Rev. E 47, 2881–2892 (1993).
[CrossRef]

D. Eliyahu, “Statistics of Stokes variables for correlated Gaussian fields,” Phys. Rev. E 50, 2381–2384 (1994).
[CrossRef]

Science (1)

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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Other (6)

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1959).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992), pp. 683–688.

R. E. Ziemer, W. H. Tranter, Principles of Communications: Systems, Modulation, and Noise, 5th ed. (Wiley, New York, 2002).

W. A. Shurcliff, S. S. Ballard, Polarized Light (Van Nostrand, Princeton, N.J., 1964).

C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley, New York, 1998).

L. A. Amos, “Structure of microtubules,” in Microtubules, K. Roberts, J. S. Hyams, eds. (Academic, London, 1979), pp. 1–64.

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Figures (7)

Fig. 1
Fig. 1

(a) Accumulated phase delays from individual fibrillar structures trace a circular P ( z j ) arc around rotation axis A on the Poincaré sphere. (b) Alternate aspect of geometry in (a) viewed along rotation axis A. Dashed curves indicate circular trajectory of P ( z j ) ; only when 2 δ = 360 ° is an entire circle traced by P ( z j ) .

Fig. 2
Fig. 2

(a) Arc length ( l arc ) of P ( z j ) depends on separation angle (γ) and is relevant because longer l arc allows a more accurate estimate of retardation (δ). (b) Alternate aspect of geometry in (a) viewed along rotation axis A.

Fig. 3
Fig. 3

EPS-OCT instrumentation for recording depth-resolved interference fringe intensities for horizontal [ Γ h ( z ) ] and vertical [ Γ v ( z ) ] polarization components in intact retinal specimens. NPBS, nonpolarizing beam splitter; LCVR, liquid-crystal variable retarder; RNFL, retinal nerve fiber layer; sm fiber, single-mode fiber; galvo, galvanometer.

Fig. 4
Fig. 4

(a) Ensemble averaging N A uncorrelated speckle fields increases the PSNR by a factor of N A 1 / 2 . (b) Birefringent film S m ( z j ) for m = 1 plotted on the Poincaré sphere before (gray) and after (black) averaging N A = 36 speckle fields. Averaged S ( z j ) begins to resemble the noise-free model polarization arc P ( z j ) .

Fig. 5
Fig. 5

Depth-resolved polarization data [ S m ( z j ) , gray] for M = 6 incident polarization states in a (a) thick RNFL 1 mm inferior to the ONH and (b) thin RNFL 1 mm nasal to the ONH. Model polarization arc [ P m ( z j ) , black] and rotation axis (A) are extracted by the multistate nonlinear algorithm. (Note: m = 3 , 4, and 5 are on the far side of the Poincaré sphere.)

Fig. 6
Fig. 6

RNFL birefringence ( Δ n ) in locations 1 mm inferior and 1 mm nasal to the center of the ONH on two separate days. Error bars indicate approximate EPS-OCT birefringence sensitivity.

Fig. 7
Fig. 7

Sampled specimen volume ( V ) is defined by the cylinder of light with beam waist radius ( w o ) and thickness ( Δ z ) . Volume occupied by one fibril ( v o ) within the sampled specimen volume is shaded gray.

Tables (1)

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Table 1 Thickness and Birefringence of in Vivo Primate RNFL

Equations (15)

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S ( z j ) = I ( z j ) Q ( z j ) U ( z j ) V ( z j ) = E h ( z j ) 2 + E v ( z j ) 2 E h ( z j ) 2 - E v ( z j ) 2 2 E h ( z j ) E v ( z j ) cos [ ϕ diff ( z j ) ] 2 E h ( z j ) E v ( z j ) sin [ ϕ diff ( z j ) ] .
S ( z j ) = S 1 ( z j ) S 2 ( z j ) S 3 ( z j ) = Q ( z j ) / I ( z j ) U ( z j ) / I ( z j ) V ( z j ) / I ( z j ) = E h ( z j ) 2 - E v ( z j ) 2 2 E h ( z j ) E v ( z j ) cos [ ϕ diff ( z j ) ] 2 E h ( z j ) E v ( z j ) sin [ ϕ diff ( z j ) ] / [ E h ( z j ) 2 + E v ( z j ) 2 ] .
Δ n = λ o δ 360 Δ z ,
l arc = 2 δ sin ( γ ) ,
γ = cos - 1 [ A P ( 0 ) ] .
PSNR = l arc σ speckle = 2 δ sin ( γ ) σ speckle ,
σ speckle = 1 J   j { cos - 1 [ S ( z j ) P ( z j ) ] } 2 1 / 2 ,
R o = j | S ( z j ) - P [ z j ;   2 δ ,   A ,   P ( 0 ) ] | 2 .
R M = m = 1 M R o [ S m ( z j ) ;   δ ,   A ,   P m ( 0 ) ] .
δ = 360 Δ n Δ z λ o = 360 f Δ n t Δ z λ o ,
f = N t v o V ,
V = π w o 2 Δ z .
v o = 4 w o A o π ,
N t = π 2 λ o w o 1440 Δ n t A o   δ ,
ρ t = π λ o 1440 Δ n t A o w o   δ Δ z = π 4 Δ n t A o w o   Δ n .

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