Abstract

We present an improved method of polarization sensitive optical coherence tomography that enables measurement and imaging of backscattered intensity, birefringence, and fast optic axis orientation simultaneously with only one single A-scan per transverse measurement location. While intensity and birefringence data are obtained in a conventional way, the optic axis orientation is determined from the phase difference recorded in two orthogonal polarization channels. We report on accuracy and precision of the method by measuring birefringence and optic axis orientation of well defined polarization states in a technical object and present maps of birefringence and, what we believe for the first time, of optic axis orientation in biological tissue.

© Optical Society of America

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References

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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. A.F. Fercher, "Optical coherence tomography," J. Biomed. Opt. 1, 157-173 (1996).
    [CrossRef] [PubMed]
  3. A. F. Fercher and C. K. Hitzenberger, "Optical coherence tomography in medicine" in International trends in optics and photonics ICO IV, T. Asakura, ed. (Springer, Berlin, 1999).
  4. J. F. de Boer, T. E. Milner, M. J. C. van Gemert, J. S. Nelson, "Two-dimensional birefringence imaging in biological tissue by polarization sensitive optical coherence tomography," Opt. Lett. 22, 934-936 (1997).
    [CrossRef] [PubMed]
  5. M. J. Everett, K. Schoenenberger, B. W. Colston Jr., L. B. Da Silva, "Birefringence characterization of biological tissue by use of optical coherence tomography," Opt. Lett. 23, 228-230 (1998).
    [CrossRef]
  6. K. Schoenenberger, B. W. Colston Jr., D. J. Maitland, L. B. Da Silva, M. J. Everett, "Mapping of birefringence and thermal damage in tissue by use of polarization-sensitive optical coherence tomography," Appl. Opt. 37, 6026-6036 (1998).
    [CrossRef]
  7. J. F. de Boer, S. M. Srinivas, B. H. Park, T. H. Pham, Z. Chen, T. E. Milner, J. S. Nelson, "Polarization effects in optical coherence tomography of various biological tissues," IEEE J. Sel. Top. Quant. Electron. 5, 1200-1203 (1999).
    [CrossRef]
  8. A. Baumgartner, S. Dichtl, C. K. Hitzenberger, H. Sattmann, B. Robl, A. Moritz, A. F. Fercher: "Polarization-sensitive optical coherence tomography of dental structures," Caries Res. 34, 59-69 (2000).
    [CrossRef]
  9. M. R. Hee, D. Huang, E. A. Swanson, J. G. Fujimoto, "Polarization-sensitive low-coherence reflectometer for birefringence characterization and ranging," J. Opt. Soc. Am. B 9, 903-908 (1992).
    [CrossRef]
  10. J. F. de Boer, T. E. Milner, J. S. Nelson, "Determination of the depth-resolved Stokes parameters of light backscattered from turbid media by use of polarization-sensitive optical coherence tomography," Opt. Lett. 24, 300-302 (1999).
    [CrossRef]
  11. S. Jiao, G. Yao, L.V. Wang, "Depth-resolved two-dimensional Stokes vectors of backscattered light and Mueller matrices of biological tissue measured with optical coherence tomography," Appl. Opt. 39, 6318-6324 (2000).
    [CrossRef]
  12. C. E. Saxer, J. F. de Boer, B. H. Park, Y. Zhao, Z. Chen, J. S. Nelson, "High-speed fiber based polarizationsensitive optical coherence tomography of in vivo human skin," Opt. Lett. 25, 1355-1357 (2000).
    [CrossRef]
  13. J. E. Roth, J. A. Kozak, S. Yazdanfar, A. M. Rollins, J. A. Izatt, "Simplified method for polarizationsensitive optical coherence tomography," Opt. Lett. 26, 1069-1071 (2001).
    [CrossRef]
  14. Y. Zhao., Z. Chen, C. Saxer, S. Xiang, J. F. de Boer, J. S. Nelson, "Phase-resolved optical coherence tomography and optical Doppler tomography for imaging blood flow in human skin with fast scanning speed and high velocity sensitivity," Opt. Lett. 25, 114-116 (2000).
    [CrossRef]
  15. M. Sticker, C. K. Hitzenberger, R. Leitgeb, A. F. Fercher, "Quantitative differential phase measurement and imaging in transparent and turbid media using optical coherence tomography," Opt. Lett. 26, 518-520 (2001).
    [CrossRef]
  16. E. A. Swanson, D. Huang, M. R. Hee, J. G. Fujimoto, C. P. Lin, C. A. Puliafito, "High-speed optical coherence domain reflectometry," Opt Lett 17, 151-153 (1992).
    [CrossRef] [PubMed]
  17. C. R. Jones, "A new calculus for the treatment of optical systems. I. Description and discussion of the calculus," J. Opt. Soc. Am. 31, 488-493 (1941).
    [CrossRef]
  18. H. Hurwitz and C. R. Jones, "A new calculus for the treatment of optical systems. II. Proof of the three general equivalence theorems," J. Opt. Soc. Am 31, 493-499 (1941).
  19. A. Gerrard and J. M. Burch, Introduction to matrix methods in optics (John Wiley & Sons, London, 1975).
  20. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1987), Chap. 10.
  21. F. V. Salomon, Lehrbuch der Geflügelanatomie (Gustav Fischer, Jena, 1993).
  22. M. A. Villain, D. S. Greenfield, R. W. Knighton, J. Schiffman, W. Feuer, "Normative retardation data corrected for corneal polarization axis using scanning laser polarimetry," Invest. Ophthalmol. Vis. Sci. 42, S135, abstract no. 716 (2001).
    [PubMed]

Other

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]

A.F. Fercher, "Optical coherence tomography," J. Biomed. Opt. 1, 157-173 (1996).
[CrossRef] [PubMed]

A. F. Fercher and C. K. Hitzenberger, "Optical coherence tomography in medicine" in International trends in optics and photonics ICO IV, T. Asakura, ed. (Springer, Berlin, 1999).

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

M. J. Everett, K. Schoenenberger, B. W. Colston Jr., L. B. Da Silva, "Birefringence characterization of biological tissue by use of optical coherence tomography," Opt. Lett. 23, 228-230 (1998).
[CrossRef]

K. Schoenenberger, B. W. Colston Jr., D. J. Maitland, L. B. Da Silva, M. J. Everett, "Mapping of birefringence and thermal damage in tissue by use of polarization-sensitive optical coherence tomography," Appl. Opt. 37, 6026-6036 (1998).
[CrossRef]

J. F. de Boer, S. M. Srinivas, B. H. Park, T. H. Pham, Z. Chen, T. E. Milner, J. S. Nelson, "Polarization effects in optical coherence tomography of various biological tissues," IEEE J. Sel. Top. Quant. Electron. 5, 1200-1203 (1999).
[CrossRef]

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

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

J. F. de Boer, T. E. Milner, J. S. Nelson, "Determination of the depth-resolved Stokes parameters of light backscattered from turbid media by use of polarization-sensitive optical coherence tomography," Opt. Lett. 24, 300-302 (1999).
[CrossRef]

S. Jiao, G. Yao, L.V. Wang, "Depth-resolved two-dimensional Stokes vectors of backscattered light and Mueller matrices of biological tissue measured with optical coherence tomography," Appl. Opt. 39, 6318-6324 (2000).
[CrossRef]

C. E. Saxer, J. F. de Boer, B. H. Park, Y. Zhao, Z. Chen, J. S. Nelson, "High-speed fiber based polarizationsensitive optical coherence tomography of in vivo human skin," Opt. Lett. 25, 1355-1357 (2000).
[CrossRef]

J. E. Roth, J. A. Kozak, S. Yazdanfar, A. M. Rollins, J. A. Izatt, "Simplified method for polarizationsensitive optical coherence tomography," Opt. Lett. 26, 1069-1071 (2001).
[CrossRef]

Y. Zhao., Z. Chen, C. Saxer, S. Xiang, J. F. de Boer, J. S. Nelson, "Phase-resolved optical coherence tomography and optical Doppler tomography for imaging blood flow in human skin with fast scanning speed and high velocity sensitivity," Opt. Lett. 25, 114-116 (2000).
[CrossRef]

M. Sticker, C. K. Hitzenberger, R. Leitgeb, A. F. Fercher, "Quantitative differential phase measurement and imaging in transparent and turbid media using optical coherence tomography," Opt. Lett. 26, 518-520 (2001).
[CrossRef]

E. A. Swanson, D. Huang, M. R. Hee, J. G. Fujimoto, C. P. Lin, C. A. Puliafito, "High-speed optical coherence domain reflectometry," Opt Lett 17, 151-153 (1992).
[CrossRef] [PubMed]

C. R. Jones, "A new calculus for the treatment of optical systems. I. Description and discussion of the calculus," J. Opt. Soc. Am. 31, 488-493 (1941).
[CrossRef]

H. Hurwitz and C. R. Jones, "A new calculus for the treatment of optical systems. II. Proof of the three general equivalence theorems," J. Opt. Soc. Am 31, 493-499 (1941).

A. Gerrard and J. M. Burch, Introduction to matrix methods in optics (John Wiley & Sons, London, 1975).

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1987), Chap. 10.

F. V. Salomon, Lehrbuch der Geflügelanatomie (Gustav Fischer, Jena, 1993).

M. A. Villain, D. S. Greenfield, R. W. Knighton, J. Schiffman, W. Feuer, "Normative retardation data corrected for corneal polarization axis using scanning laser polarimetry," Invest. Ophthalmol. Vis. Sci. 42, S135, abstract no. 716 (2001).
[PubMed]

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Figures (4)

Fig. 1.
Fig. 1.

Sketch of instrument. BS, beam splitter; QWP, quarter wave plate.

Fig. 2.
Fig. 2.

Measured versus set retardation. (a) Plot of measured retardation (data points) and standard deviation (error bars) as a function of set retardation for a fast axis orientation of 40°. For better comparison, the expected (set) retardation value is indicated as solid line. (b) Polar plot of measured retardation versus set retardation for several fixed values of fast axis orientation (indicated along circumference of the plot). The color of a data point indicates the set value of retardation, the radial distance from the half-circle center indicates the corresponding measured value. Ideally, the data points should lie on the corresponding half-circle.

Fig. 3.
Fig. 3.

Measured versus set fast axis orientation. (a) Plot of measured axis orientation (data points) and standard deviation (error bars) as a function of set fast axis for a retardation of 30°. For better comparison, the expected (set) axis orientation is indicated as solid line. (b) Polar plot of measured axis orientation versus set fast axis for several fixed values of retardation (indicated along circumference of the plot). The color of a data point indicates the set value of axis orientation, the radial distance from the quarter-circle center indicates the corresponding measured value. Ideally, the data points should lie on the corresponding quarter-circle.

Fig. 4.
Fig. 4.

OCT images recorded in a chicken myocardium in vitro. Dimensions are indicated in mm (the ordinate shows optical distance). (a) Intensity image (color bar: logarithmic intensity scale); (b) phase retardation image (color bar: retardation [deg]); (c) image of fast axis distribution; interpretation: see text (color bar: axis orientation [deg]).

Equations (10)

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

E = E 0 ( 0 1 )
M ( δ , θ ) = [ cos 2 ( θ ) + sin 2 ( θ ) · exp ( i δ ) cos ( θ ) · sin ( θ ) · ( 1 exp ( i δ ) ) cos ( θ ) · sin ( θ ) · ( 1 exp ( i δ ) ) cos 2 ( θ ) · exp ( i δ ) + sin 2 ( θ ) ]
E r = 1 2 M QWP 2 · M QWP 2 · ( 0 1 ) = 1 2 2 ( 1 1 ) .
E s = 1 2 M QWP 1 · M sample ( δ , θ ) · R · M sample ( δ , θ ) · M QWP 1 · ( 0 1 )
= R 2 ( cos ( δ ) exp ( i δ ) sin ( δ ) exp ( i ( π δ 2 θ ) ) )
I k ( z ) = I r , k + I s , k + 2 I r , k I s , k · γ ( z z 0 ) · cos ( Φ k ) .
A ˜ k ( z ) = I k ( z ) + i · H { I k ( z ) } = A k ( z ) · exp [ i · Φ k ( z ) ]
R ( z ) A 1 ( z ) 2 + A 2 ( z ) 2
δ ( z ) = arctan ( A 2 ( z ) A 1 ( z ) ) .
θ = ( 180 o Φ ) / 2 .

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