Abstract

The full polarization properties of anisotropic biomolecule optical scattering are investigated theoretically. By using a simple ellipsoid model of a single biomolecule, the scattering fields and Mueller matrices are derived from fundamental electromagnetism theory. The energy of scattered photons is not necessarily equal to that of the incident laser beam. This theory can be generally applied to the experiments of fluorescence, Raman scattering, and second-harmonic generation. Fitting of a single tetramethylrhodamine-labeled lipid molecule’s anisotropic imaging experiment is demonstrated. This theory has provided a fundamental simulation analysis tool of understanding and developing the optical polarimetric sensing science and technology of the anisotropic biomolecules and biomedium. The medium dielectric constant of the model ellipsoid provides a theoretic background for correlating the optical polarization properties of a biomolecule to its microscopic electronic structure.

© 2008 Optical Society of America

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  1. Z. Chen, H. Ren, Z. Ding, Y. Zhao, J. Miao, and J. S. Nelson, “Biomedical imaging: simultaneous imaging of in situ tissue structure, blood-flow velocity, standard deviation, birefringence and Stokes vectors in human skin,” Opt. Photon. News, December 2002, p. 14.
  2. C. E. Saxer, J. F. de Boer, B. H. Park, Y. Zhao, Z. Chen, and J. S. Nelson, “High-speed fiber-based polarization-sensitive optical coherence tomography of in vivo human skin,” Opt. Lett. 25, 1355-1357 (2000).
    [CrossRef]
  3. S. Liao and L. V. Wang, “Two-dimensional depth-resolved Mueller matrix of biological tissue measured with double-beam polarization-sensitive optical coherence tomography,” Opt. Lett. 27, 101-103 (2002).
    [CrossRef]
  4. J. F. de Boer and T. E. Milner, “Review of polarization sensitive optical coherence tomography and Stokes vector determination,” J. Biomed. Opt. 7, 359-371 (2002).
    [CrossRef] [PubMed]
  5. C. C. Wu, Y. M. Wang, L. S. Lu, C. W. Sun, C. W. Lu, M. T. Tsai, and C. C. Yang, “Optical birefringence of the hyperlipidemic rat liver with polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 12, 64022 (2007).
    [CrossRef]
  6. M. Hashimoto, R. Kanamaru, K. Yoshiki, T. Araki, and N. Hashimoto, “Second-harmonic microscope with polarization mode converter,” Presented at the Ninth International Conference on Optics Within Life Science (OWLS9), National Yang-Ming University, Taipei, Taiwan, November 26-29, 2006, Paper O4-7.
  7. C. L. Berger, J. S. Craik, D. R. Trentham, J. E. T. Corrie, and Y. E. Goldman, “Fluorescence polarization of skeletal muscle fibers labeled with rhodamine isomers on the myosin heavy chain,” Biophys. J. 71, 3330-3343 (1966).
    [CrossRef]
  8. P. Wu, M. Brasseur, and U. Schindler, “Measurement of specific protease activity utilizing fluorescence polarization,” Anal. Biochem. 247, 83-88 (1997).
    [CrossRef]
  9. G. S. Harms, M. Sonnleitner, G. S. Schutz, H. J. Gruber, and T. Schmidt, “Single-molecule anisotropy imaging,” Biophys. J. 77, 2864-2870 (1999).
    [CrossRef] [PubMed]
  10. G. S. Harms, L. Cognet, P. H. M. Lommerse, G. A. Blab, H. Kahr, R. Gamsjager, H. P. Spanink, N. M. Soldatov, C. Romanin, and T. Schmidt, “Single-molecule imaging of L-type Ca2+ channels in live cells,” Biophys. J. 81, 2639-2646 (2001).
    [CrossRef] [PubMed]
  11. M. Hashimoto, K. Yamada, and T. Araki, “Proposition of single molecular orientation determination using polarization controlled beam by liquid crystal spatial light modulators,” Opt. Rev. 12, 37-41 (2005).
    [CrossRef]
  12. S.-M. F. Nee, “Polarization measurement,” in The Measurement, Instrumentation and Sensors Handbook, J.G.Webster, ed. (CRC Press and IEEE Press, 1999), pp. 60.1-60.24.
  13. T.-W. Nee and S.-M. F. Nee, “Infrared polarization signatures for targets,” Proc. SPIE 2469, 231-241 (1995).
    [CrossRef]
  14. T. W. Nee, S. F. Nee, and E. J. Bevan, “Infrared polarization signatures of a target for enhanced discrimination,” in Proceedings of the IRIS Specialty Group on Targets, Backgrounds and Discrimination (IRIA-IRIS, 1996), Vol. IV, pp. 349-368.
  15. T.-W. Nee and S.-M. F. Nee, “Polarization of holographic grating diffraction. I. General theory,” J. Opt. Soc. Am. A 21, 523-531 (2004).
    [CrossRef]
  16. T.-W. Nee, S.-M. F. Nee, M. Kleinschmit, and S. Shahriar, “Polarization of holographic grating diffraction. II. Experiment,” J. Opt. Soc. Am. A 21, 532-539 (2004).
    [CrossRef]
  17. T.-W. Nee, “Second harmonic diffraction from holographic volume grating,” J. Opt. Soc. Am. A 23, 2510-2518 (2006).
    [CrossRef]
  18. C. Kittel, Solid State Physics (Wiley, 1976), pp. 404-405.
  19. L. Davis, Jr. and J. L. Greenstein, “The polarization of starlight by aligned dust grains,” Astrophys. J. 114, 206-240 (1951).
    [CrossRef]
  20. S.-M. F. Nee, “Ellipsometric analysis for surface roughness and texture,” Appl. Opt. 27, 2819-2831 (1988).
    [CrossRef] [PubMed]
  21. J. D. Jackson, Classical Electrodynamics (Wiley, 1962).
  22. V. Prasad, D. Semwogerere, and E. R. Weeks, “Confocal microscopy of colloids,” J. Phys.: Condens. Matter 19, 113102 (2007).
    [CrossRef]
  23. S. F. Nee, “Polarization of specular reflection and near-specular scattering by a rough surface,” Appl. Opt. 35, 3570-3582 (1996).
    [CrossRef]
  24. S.-M. F. Nee, “Depolarization and retardation of a birefringent slab,” J. Opt. Soc. Am. A 17, 2067-2073 (2000).
    [CrossRef]
  25. S.-M. F. Nee and T.-W. Nee, “Principal Mueller matrix of reflection and scattering measured for a one-dimensional rough surface,” Opt. Eng. (Bellingham) 41, 994-1001 (2002).
    [CrossRef]
  26. V. V. Tuchin, Tissue Optics (SPIE, 2007).
    [CrossRef]

2007

C. C. Wu, Y. M. Wang, L. S. Lu, C. W. Sun, C. W. Lu, M. T. Tsai, and C. C. Yang, “Optical birefringence of the hyperlipidemic rat liver with polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 12, 64022 (2007).
[CrossRef]

V. Prasad, D. Semwogerere, and E. R. Weeks, “Confocal microscopy of colloids,” J. Phys.: Condens. Matter 19, 113102 (2007).
[CrossRef]

2006

2005

M. Hashimoto, K. Yamada, and T. Araki, “Proposition of single molecular orientation determination using polarization controlled beam by liquid crystal spatial light modulators,” Opt. Rev. 12, 37-41 (2005).
[CrossRef]

2004

2002

S. Liao and L. V. Wang, “Two-dimensional depth-resolved Mueller matrix of biological tissue measured with double-beam polarization-sensitive optical coherence tomography,” Opt. Lett. 27, 101-103 (2002).
[CrossRef]

J. F. de Boer and T. E. Milner, “Review of polarization sensitive optical coherence tomography and Stokes vector determination,” J. Biomed. Opt. 7, 359-371 (2002).
[CrossRef] [PubMed]

S.-M. F. Nee and T.-W. Nee, “Principal Mueller matrix of reflection and scattering measured for a one-dimensional rough surface,” Opt. Eng. (Bellingham) 41, 994-1001 (2002).
[CrossRef]

2001

G. S. Harms, L. Cognet, P. H. M. Lommerse, G. A. Blab, H. Kahr, R. Gamsjager, H. P. Spanink, N. M. Soldatov, C. Romanin, and T. Schmidt, “Single-molecule imaging of L-type Ca2+ channels in live cells,” Biophys. J. 81, 2639-2646 (2001).
[CrossRef] [PubMed]

2000

1999

G. S. Harms, M. Sonnleitner, G. S. Schutz, H. J. Gruber, and T. Schmidt, “Single-molecule anisotropy imaging,” Biophys. J. 77, 2864-2870 (1999).
[CrossRef] [PubMed]

1997

P. Wu, M. Brasseur, and U. Schindler, “Measurement of specific protease activity utilizing fluorescence polarization,” Anal. Biochem. 247, 83-88 (1997).
[CrossRef]

1996

1995

T.-W. Nee and S.-M. F. Nee, “Infrared polarization signatures for targets,” Proc. SPIE 2469, 231-241 (1995).
[CrossRef]

1988

1966

C. L. Berger, J. S. Craik, D. R. Trentham, J. E. T. Corrie, and Y. E. Goldman, “Fluorescence polarization of skeletal muscle fibers labeled with rhodamine isomers on the myosin heavy chain,” Biophys. J. 71, 3330-3343 (1966).
[CrossRef]

1951

L. Davis, Jr. and J. L. Greenstein, “The polarization of starlight by aligned dust grains,” Astrophys. J. 114, 206-240 (1951).
[CrossRef]

Araki, T.

M. Hashimoto, K. Yamada, and T. Araki, “Proposition of single molecular orientation determination using polarization controlled beam by liquid crystal spatial light modulators,” Opt. Rev. 12, 37-41 (2005).
[CrossRef]

M. Hashimoto, R. Kanamaru, K. Yoshiki, T. Araki, and N. Hashimoto, “Second-harmonic microscope with polarization mode converter,” Presented at the Ninth International Conference on Optics Within Life Science (OWLS9), National Yang-Ming University, Taipei, Taiwan, November 26-29, 2006, Paper O4-7.

Berger, C. L.

C. L. Berger, J. S. Craik, D. R. Trentham, J. E. T. Corrie, and Y. E. Goldman, “Fluorescence polarization of skeletal muscle fibers labeled with rhodamine isomers on the myosin heavy chain,” Biophys. J. 71, 3330-3343 (1966).
[CrossRef]

Bevan, E. J.

T. W. Nee, S. F. Nee, and E. J. Bevan, “Infrared polarization signatures of a target for enhanced discrimination,” in Proceedings of the IRIS Specialty Group on Targets, Backgrounds and Discrimination (IRIA-IRIS, 1996), Vol. IV, pp. 349-368.

Blab, G. A.

G. S. Harms, L. Cognet, P. H. M. Lommerse, G. A. Blab, H. Kahr, R. Gamsjager, H. P. Spanink, N. M. Soldatov, C. Romanin, and T. Schmidt, “Single-molecule imaging of L-type Ca2+ channels in live cells,” Biophys. J. 81, 2639-2646 (2001).
[CrossRef] [PubMed]

Brasseur, M.

P. Wu, M. Brasseur, and U. Schindler, “Measurement of specific protease activity utilizing fluorescence polarization,” Anal. Biochem. 247, 83-88 (1997).
[CrossRef]

Chen, Z.

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

Z. Chen, H. Ren, Z. Ding, Y. Zhao, J. Miao, and J. S. Nelson, “Biomedical imaging: simultaneous imaging of in situ tissue structure, blood-flow velocity, standard deviation, birefringence and Stokes vectors in human skin,” Opt. Photon. News, December 2002, p. 14.

Cognet, L.

G. S. Harms, L. Cognet, P. H. M. Lommerse, G. A. Blab, H. Kahr, R. Gamsjager, H. P. Spanink, N. M. Soldatov, C. Romanin, and T. Schmidt, “Single-molecule imaging of L-type Ca2+ channels in live cells,” Biophys. J. 81, 2639-2646 (2001).
[CrossRef] [PubMed]

Corrie, J. E. T.

C. L. Berger, J. S. Craik, D. R. Trentham, J. E. T. Corrie, and Y. E. Goldman, “Fluorescence polarization of skeletal muscle fibers labeled with rhodamine isomers on the myosin heavy chain,” Biophys. J. 71, 3330-3343 (1966).
[CrossRef]

Craik, J. S.

C. L. Berger, J. S. Craik, D. R. Trentham, J. E. T. Corrie, and Y. E. Goldman, “Fluorescence polarization of skeletal muscle fibers labeled with rhodamine isomers on the myosin heavy chain,” Biophys. J. 71, 3330-3343 (1966).
[CrossRef]

Davis, L.

L. Davis, Jr. and J. L. Greenstein, “The polarization of starlight by aligned dust grains,” Astrophys. J. 114, 206-240 (1951).
[CrossRef]

de Boer, J. F.

J. F. de Boer and T. E. Milner, “Review of polarization sensitive optical coherence tomography and Stokes vector determination,” J. Biomed. Opt. 7, 359-371 (2002).
[CrossRef] [PubMed]

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

Ding, Z.

Z. Chen, H. Ren, Z. Ding, Y. Zhao, J. Miao, and J. S. Nelson, “Biomedical imaging: simultaneous imaging of in situ tissue structure, blood-flow velocity, standard deviation, birefringence and Stokes vectors in human skin,” Opt. Photon. News, December 2002, p. 14.

Gamsjager, R.

G. S. Harms, L. Cognet, P. H. M. Lommerse, G. A. Blab, H. Kahr, R. Gamsjager, H. P. Spanink, N. M. Soldatov, C. Romanin, and T. Schmidt, “Single-molecule imaging of L-type Ca2+ channels in live cells,” Biophys. J. 81, 2639-2646 (2001).
[CrossRef] [PubMed]

Goldman, Y. E.

C. L. Berger, J. S. Craik, D. R. Trentham, J. E. T. Corrie, and Y. E. Goldman, “Fluorescence polarization of skeletal muscle fibers labeled with rhodamine isomers on the myosin heavy chain,” Biophys. J. 71, 3330-3343 (1966).
[CrossRef]

Greenstein, J. L.

L. Davis, Jr. and J. L. Greenstein, “The polarization of starlight by aligned dust grains,” Astrophys. J. 114, 206-240 (1951).
[CrossRef]

Gruber, H. J.

G. S. Harms, M. Sonnleitner, G. S. Schutz, H. J. Gruber, and T. Schmidt, “Single-molecule anisotropy imaging,” Biophys. J. 77, 2864-2870 (1999).
[CrossRef] [PubMed]

Harms, G. S.

G. S. Harms, L. Cognet, P. H. M. Lommerse, G. A. Blab, H. Kahr, R. Gamsjager, H. P. Spanink, N. M. Soldatov, C. Romanin, and T. Schmidt, “Single-molecule imaging of L-type Ca2+ channels in live cells,” Biophys. J. 81, 2639-2646 (2001).
[CrossRef] [PubMed]

G. S. Harms, M. Sonnleitner, G. S. Schutz, H. J. Gruber, and T. Schmidt, “Single-molecule anisotropy imaging,” Biophys. J. 77, 2864-2870 (1999).
[CrossRef] [PubMed]

Hashimoto, M.

M. Hashimoto, K. Yamada, and T. Araki, “Proposition of single molecular orientation determination using polarization controlled beam by liquid crystal spatial light modulators,” Opt. Rev. 12, 37-41 (2005).
[CrossRef]

M. Hashimoto, R. Kanamaru, K. Yoshiki, T. Araki, and N. Hashimoto, “Second-harmonic microscope with polarization mode converter,” Presented at the Ninth International Conference on Optics Within Life Science (OWLS9), National Yang-Ming University, Taipei, Taiwan, November 26-29, 2006, Paper O4-7.

Hashimoto, N.

M. Hashimoto, R. Kanamaru, K. Yoshiki, T. Araki, and N. Hashimoto, “Second-harmonic microscope with polarization mode converter,” Presented at the Ninth International Conference on Optics Within Life Science (OWLS9), National Yang-Ming University, Taipei, Taiwan, November 26-29, 2006, Paper O4-7.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, 1962).

Kahr, H.

G. S. Harms, L. Cognet, P. H. M. Lommerse, G. A. Blab, H. Kahr, R. Gamsjager, H. P. Spanink, N. M. Soldatov, C. Romanin, and T. Schmidt, “Single-molecule imaging of L-type Ca2+ channels in live cells,” Biophys. J. 81, 2639-2646 (2001).
[CrossRef] [PubMed]

Kanamaru, R.

M. Hashimoto, R. Kanamaru, K. Yoshiki, T. Araki, and N. Hashimoto, “Second-harmonic microscope with polarization mode converter,” Presented at the Ninth International Conference on Optics Within Life Science (OWLS9), National Yang-Ming University, Taipei, Taiwan, November 26-29, 2006, Paper O4-7.

Kittel, C.

C. Kittel, Solid State Physics (Wiley, 1976), pp. 404-405.

Kleinschmit, M.

Liao, S.

Lommerse, P. H. M.

G. S. Harms, L. Cognet, P. H. M. Lommerse, G. A. Blab, H. Kahr, R. Gamsjager, H. P. Spanink, N. M. Soldatov, C. Romanin, and T. Schmidt, “Single-molecule imaging of L-type Ca2+ channels in live cells,” Biophys. J. 81, 2639-2646 (2001).
[CrossRef] [PubMed]

Lu, C. W.

C. C. Wu, Y. M. Wang, L. S. Lu, C. W. Sun, C. W. Lu, M. T. Tsai, and C. C. Yang, “Optical birefringence of the hyperlipidemic rat liver with polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 12, 64022 (2007).
[CrossRef]

Lu, L. S.

C. C. Wu, Y. M. Wang, L. S. Lu, C. W. Sun, C. W. Lu, M. T. Tsai, and C. C. Yang, “Optical birefringence of the hyperlipidemic rat liver with polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 12, 64022 (2007).
[CrossRef]

Miao, J.

Z. Chen, H. Ren, Z. Ding, Y. Zhao, J. Miao, and J. S. Nelson, “Biomedical imaging: simultaneous imaging of in situ tissue structure, blood-flow velocity, standard deviation, birefringence and Stokes vectors in human skin,” Opt. Photon. News, December 2002, p. 14.

Milner, T. E.

J. F. de Boer and T. E. Milner, “Review of polarization sensitive optical coherence tomography and Stokes vector determination,” J. Biomed. Opt. 7, 359-371 (2002).
[CrossRef] [PubMed]

Nee, S. F.

S. F. Nee, “Polarization of specular reflection and near-specular scattering by a rough surface,” Appl. Opt. 35, 3570-3582 (1996).
[CrossRef]

T. W. Nee, S. F. Nee, and E. J. Bevan, “Infrared polarization signatures of a target for enhanced discrimination,” in Proceedings of the IRIS Specialty Group on Targets, Backgrounds and Discrimination (IRIA-IRIS, 1996), Vol. IV, pp. 349-368.

Nee, S.-M. F.

T.-W. Nee, S.-M. F. Nee, M. Kleinschmit, and S. Shahriar, “Polarization of holographic grating diffraction. II. Experiment,” J. Opt. Soc. Am. A 21, 532-539 (2004).
[CrossRef]

T.-W. Nee and S.-M. F. Nee, “Polarization of holographic grating diffraction. I. General theory,” J. Opt. Soc. Am. A 21, 523-531 (2004).
[CrossRef]

S.-M. F. Nee and T.-W. Nee, “Principal Mueller matrix of reflection and scattering measured for a one-dimensional rough surface,” Opt. Eng. (Bellingham) 41, 994-1001 (2002).
[CrossRef]

S.-M. F. Nee, “Depolarization and retardation of a birefringent slab,” J. Opt. Soc. Am. A 17, 2067-2073 (2000).
[CrossRef]

T.-W. Nee and S.-M. F. Nee, “Infrared polarization signatures for targets,” Proc. SPIE 2469, 231-241 (1995).
[CrossRef]

S.-M. F. Nee, “Ellipsometric analysis for surface roughness and texture,” Appl. Opt. 27, 2819-2831 (1988).
[CrossRef] [PubMed]

S.-M. F. Nee, “Polarization measurement,” in The Measurement, Instrumentation and Sensors Handbook, J.G.Webster, ed. (CRC Press and IEEE Press, 1999), pp. 60.1-60.24.

Nee, T. W.

T. W. Nee, S. F. Nee, and E. J. Bevan, “Infrared polarization signatures of a target for enhanced discrimination,” in Proceedings of the IRIS Specialty Group on Targets, Backgrounds and Discrimination (IRIA-IRIS, 1996), Vol. IV, pp. 349-368.

Nee, T.-W.

Nelson, J. S.

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

Z. Chen, H. Ren, Z. Ding, Y. Zhao, J. Miao, and J. S. Nelson, “Biomedical imaging: simultaneous imaging of in situ tissue structure, blood-flow velocity, standard deviation, birefringence and Stokes vectors in human skin,” Opt. Photon. News, December 2002, p. 14.

Park, B. H.

Prasad, V.

V. Prasad, D. Semwogerere, and E. R. Weeks, “Confocal microscopy of colloids,” J. Phys.: Condens. Matter 19, 113102 (2007).
[CrossRef]

Ren, H.

Z. Chen, H. Ren, Z. Ding, Y. Zhao, J. Miao, and J. S. Nelson, “Biomedical imaging: simultaneous imaging of in situ tissue structure, blood-flow velocity, standard deviation, birefringence and Stokes vectors in human skin,” Opt. Photon. News, December 2002, p. 14.

Romanin, C.

G. S. Harms, L. Cognet, P. H. M. Lommerse, G. A. Blab, H. Kahr, R. Gamsjager, H. P. Spanink, N. M. Soldatov, C. Romanin, and T. Schmidt, “Single-molecule imaging of L-type Ca2+ channels in live cells,” Biophys. J. 81, 2639-2646 (2001).
[CrossRef] [PubMed]

Saxer, C. E.

Schindler, U.

P. Wu, M. Brasseur, and U. Schindler, “Measurement of specific protease activity utilizing fluorescence polarization,” Anal. Biochem. 247, 83-88 (1997).
[CrossRef]

Schmidt, T.

G. S. Harms, L. Cognet, P. H. M. Lommerse, G. A. Blab, H. Kahr, R. Gamsjager, H. P. Spanink, N. M. Soldatov, C. Romanin, and T. Schmidt, “Single-molecule imaging of L-type Ca2+ channels in live cells,” Biophys. J. 81, 2639-2646 (2001).
[CrossRef] [PubMed]

G. S. Harms, M. Sonnleitner, G. S. Schutz, H. J. Gruber, and T. Schmidt, “Single-molecule anisotropy imaging,” Biophys. J. 77, 2864-2870 (1999).
[CrossRef] [PubMed]

Schutz, G. S.

G. S. Harms, M. Sonnleitner, G. S. Schutz, H. J. Gruber, and T. Schmidt, “Single-molecule anisotropy imaging,” Biophys. J. 77, 2864-2870 (1999).
[CrossRef] [PubMed]

Semwogerere, D.

V. Prasad, D. Semwogerere, and E. R. Weeks, “Confocal microscopy of colloids,” J. Phys.: Condens. Matter 19, 113102 (2007).
[CrossRef]

Shahriar, S.

Soldatov, N. M.

G. S. Harms, L. Cognet, P. H. M. Lommerse, G. A. Blab, H. Kahr, R. Gamsjager, H. P. Spanink, N. M. Soldatov, C. Romanin, and T. Schmidt, “Single-molecule imaging of L-type Ca2+ channels in live cells,” Biophys. J. 81, 2639-2646 (2001).
[CrossRef] [PubMed]

Sonnleitner, M.

G. S. Harms, M. Sonnleitner, G. S. Schutz, H. J. Gruber, and T. Schmidt, “Single-molecule anisotropy imaging,” Biophys. J. 77, 2864-2870 (1999).
[CrossRef] [PubMed]

Spanink, H. P.

G. S. Harms, L. Cognet, P. H. M. Lommerse, G. A. Blab, H. Kahr, R. Gamsjager, H. P. Spanink, N. M. Soldatov, C. Romanin, and T. Schmidt, “Single-molecule imaging of L-type Ca2+ channels in live cells,” Biophys. J. 81, 2639-2646 (2001).
[CrossRef] [PubMed]

Sun, C. W.

C. C. Wu, Y. M. Wang, L. S. Lu, C. W. Sun, C. W. Lu, M. T. Tsai, and C. C. Yang, “Optical birefringence of the hyperlipidemic rat liver with polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 12, 64022 (2007).
[CrossRef]

Trentham, D. R.

C. L. Berger, J. S. Craik, D. R. Trentham, J. E. T. Corrie, and Y. E. Goldman, “Fluorescence polarization of skeletal muscle fibers labeled with rhodamine isomers on the myosin heavy chain,” Biophys. J. 71, 3330-3343 (1966).
[CrossRef]

Tsai, M. T.

C. C. Wu, Y. M. Wang, L. S. Lu, C. W. Sun, C. W. Lu, M. T. Tsai, and C. C. Yang, “Optical birefringence of the hyperlipidemic rat liver with polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 12, 64022 (2007).
[CrossRef]

Tuchin, V. V.

V. V. Tuchin, Tissue Optics (SPIE, 2007).
[CrossRef]

Wang, L. V.

Wang, Y. M.

C. C. Wu, Y. M. Wang, L. S. Lu, C. W. Sun, C. W. Lu, M. T. Tsai, and C. C. Yang, “Optical birefringence of the hyperlipidemic rat liver with polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 12, 64022 (2007).
[CrossRef]

Weeks, E. R.

V. Prasad, D. Semwogerere, and E. R. Weeks, “Confocal microscopy of colloids,” J. Phys.: Condens. Matter 19, 113102 (2007).
[CrossRef]

Wu, C. C.

C. C. Wu, Y. M. Wang, L. S. Lu, C. W. Sun, C. W. Lu, M. T. Tsai, and C. C. Yang, “Optical birefringence of the hyperlipidemic rat liver with polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 12, 64022 (2007).
[CrossRef]

Wu, P.

P. Wu, M. Brasseur, and U. Schindler, “Measurement of specific protease activity utilizing fluorescence polarization,” Anal. Biochem. 247, 83-88 (1997).
[CrossRef]

Yamada, K.

M. Hashimoto, K. Yamada, and T. Araki, “Proposition of single molecular orientation determination using polarization controlled beam by liquid crystal spatial light modulators,” Opt. Rev. 12, 37-41 (2005).
[CrossRef]

Yang, C. C.

C. C. Wu, Y. M. Wang, L. S. Lu, C. W. Sun, C. W. Lu, M. T. Tsai, and C. C. Yang, “Optical birefringence of the hyperlipidemic rat liver with polarization-sensitive optical coherence tomography,” J. Biomed. Opt. 12, 64022 (2007).
[CrossRef]

Yoshiki, K.

M. Hashimoto, R. Kanamaru, K. Yoshiki, T. Araki, and N. Hashimoto, “Second-harmonic microscope with polarization mode converter,” Presented at the Ninth International Conference on Optics Within Life Science (OWLS9), National Yang-Ming University, Taipei, Taiwan, November 26-29, 2006, Paper O4-7.

Zhao, Y.

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

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Figures (9)

Fig. 1
Fig. 1

Incident and scattering beams and the model ellipsoid orientations in the 3-D coordinate system ( x , y , z axes).

Fig. 2
Fig. 2

Depolarization factors of a uniaxial ellipsoid: ε = 1.1896 , q z , q x versus u ( = b a ) .

Fig. 3
Fig. 3

Polarization ratio β versus u ( = b a ) . Curves for ε = 1.1 , 1.1896, and 1.3 are shown for comparison. The data of ε = 1.1896 and u = 3 and 1 used in the experimental fitting (see Table 1) are marked.

Fig. 4
Fig. 4

For ε = 1.1 , 1.1896, and 1.3, the ellipsometric parameter ψ versus u ( = b a ) curves are shown.

Fig. 5
Fig. 5

For u = 3 and ε = 1.1896 , 1.1, and 1.3, the ellipsometric parameter ψ versus θ d curves are shown.

Fig. 6
Fig. 6

Two-ellipsoid model to imitate the TMR-DPPE molecule shown in Fig. 1 of [9].

Fig. 7
Fig. 7

Phase difference effect: ψ for the two-ellipsoid molecule with u = 3 and 1; ε r = 1.1896 and ε i = 0 , 0.5, and 1.

Fig. 8
Fig. 8

Phase difference effect: Δ for the two-ellipsoid molecule with u = 3 and 1; ε r = 1.1896 and ε i = 0 , 0.5, and 1.

Fig. 9
Fig. 9

Phase difference effect: I 90 I 0 (incident circular polarization case) for the two-ellipsoid molecule with u = 3 and 1.

Tables (3)

Tables Icon

Table 1 Depolarization Factors and Polarizability Ratios of Ellipsoid Molecules with ε = 1.1896

Tables Icon

Table 2 Polarization Properties of a Scattering System Consisting of Three Uncorrelated Ellipsoid Molecules of Different Shapes with ε = 1.1896 a

Tables Icon

Table 3 Polarization Properties of a Scattering System Consisting of Three Correlated Ellipsoid Molecules of Different Shapes with ε = 1.1896 a

Equations (51)

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E = E o + E 1 .
E 1 z = 4 π q z P z = 4 π χ z E z ,
χ z = q z ( ε 1 ) 4 π .
q z = 1 1 u 2 ( 1 u cos 1 u 1 u 2 ) for u < 1 ,
= 1 u 2 1 ( u cosh 1 u u 2 1 1 ) for u > 1 ,
q x = q y = ( 1 q z ) 2 .
p z = V P z = 1 3 a 2 b ( ε 1 ) 1 + q z ( ε 1 ) E o z .
α j = 1 3 a 2 b ( ε 1 ) 1 + q j ( ε 1 ) , j = x , y , z .
β = α z α x = 1 + q x ( ε 1 ) 1 + q z ( ε 1 ) ,
E i ( x , t ) = E i o exp ( i k i x i ω t ) ,
E i o = s ̂ i E i s + p ̂ i E i p ,
s ̂ i = k ̂ i × z ̂ k ̂ i × z ̂ , p ̂ i = s ̂ i × k ̂ i .
E ( x , t ) = exp ( i k s r i ω s t ) k s × ( k s × p ) exp ( i k s x ) r .
E ( x , t ) = E s c exp ( i k s x i ω s t ) ,
E s c = ρ ̂ s E s p + s ̂ s E s s ,
s ̂ s = k ̂ s × z ̂ k ̂ s × z ̂ , p ̂ s = s ̂ s × k ̂ s .
E s p = k s 2 p ̂ s p exp ( i k s x ) r ,
E s s = k s 2 s ̂ s p exp ( i k s x ) r .
p = α E i o exp ( i k i x ) ,
α = x ̂ d α x x ̂ d + y ̂ d α y y ̂ d + z ̂ d α z z ̂ d .
E s c = ( E s p E s s ) = ( J p p J p s J s p J s s ) ( E i p E i s ) = J E i .
J = j k s 2 exp [ i ( k i k s ) x ] r ,
j = ( p ̂ s α p ̂ i p ̂ s α s ̂ i s ̂ s α p ̂ i s ̂ s α s ̂ i ) .
k ̂ i = x ̂ sin θ i z ̂ cos θ i ,
p ̂ i = x ̂ cos θ i + z ̂ sin θ i ,
s ̂ i = y ̂ .
k ̂ s = x ̂ sin θ s cos φ s + y ̂ sin θ s sin φ s + z ̂ cos θ s ,
p ̂ s = x ̂ cos θ s cos φ s y ̂ cos θ s sin φ s + z ̂ sin θ s ,
s ̂ s = x ̂ sin φ s y ̂ cos φ s .
z ̂ d = x ̂ sin θ d cos φ d + y ̂ sin θ d sin φ d + z ̂ cos θ d ,
x ̂ d = x ̂ sin φ d y ̂ cos φ d ,
y ̂ d = x ̂ cos θ d cos φ d + y ̂ cos θ d sin φ d z ̂ sin θ d .
J ( r , θ s , φ s , θ d , φ d ) = J o u ( ε 1 ) 1 + q x ( ε 1 ) ( cos θ s cos φ s cos θ s sin φ s sin θ s sin φ s cos φ s 0 ) ( 1 + ( β 1 ) sin 2 θ d cos 2 φ d ( 1 β ) sin 2 θ d sin φ d cos φ d ( β 1 ) sin 2 θ d sin φ d cos φ d 1 + ( 1 β ) sin 2 θ d sin 2 φ d ( β 1 ) sin θ d cos θ d cos φ d ( 1 β ) sin θ d cos θ d sin φ d ) ,
J o = 4 π 2 a 3 3 r λ s 2 ,
tan ψ exp ( i Δ ) = j p p j s s .
( I s Q s U s V s ) ( r , θ s , φ s , θ d , φ d ) = M ( r , θ s , φ s , θ d , φ d ) ( I i Q i U i V i ) ,
M = R ( 1 cos 2 ψ 0 0 cos 2 ψ 1 0 0 0 0 sin 2 ψ cos Δ sin 2 ψ sin Δ 0 0 sin 2 ψ sin Δ sin 2 ψ cos Δ ) .
J ( θ d ) = J o u ( ε 1 ) 1 + q x ( ε 1 ) ( 1 + ( β 1 ) sin 2 θ d 0 0 1 ) ,
Δ = 180 ° , ψ = tan 1 [ 1 + ( β 1 ) sin 2 θ d ] .
J ( r , θ s , φ s , θ d 1 , φ d 1 , θ d 2 , φ d 2 ) = J 1 ( r , θ s , φ s , θ d 1 , φ d 1 ) + J 2 ( r , θ s , φ s , θ d 2 , φ d 2 ) .
J 1 ( r , θ s , φ s , θ d 1 , φ d 1 ) = 4.58 J o ( 1 0 0 0.9411 ) ,
J 2 ( r , θ s , φ s , θ d 2 , φ d 2 ) = 1.47 J o ( 1 0 0 1 ) .
J ( r , θ s , φ s , θ d 1 , φ d 1 , θ d 2 , φ d 2 ) = 6.05 J o ( 1 0 0 0.9554 ) .
M ( r , θ s , φ s , θ d 1 , φ d 1 , θ d 2 , φ d 2 ) = R ( 1 0.0456 0 0 0.0456 1 0 0 0 0 0.9990 0 0 0 0 0.9990 ) ,
( I 0 Q 0 U 0 V 0 ) = R I i 2 ( 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 ) ( 1 0.046 0 0.999 ) = R I i 2 ( 1.046 1.046 0 0 ) ,
( I 90 Q 90 U 90 V 90 ) = R I i 2 ( 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 ) ( 1 0.046 0 0.999 ) = R I i 2 ( 0.954 0.954 0 0 ) .
M = R ( 1 P cos 2 ψ 0 0 P cos 2 ψ 1 2 D v 0 0 0 0 P sin 2 ψ cos Δ P sin 2 ψ sin Δ 0 0 P sin 2 ψ sin Δ P sin 2 ψ cos Δ ) .
M ( r , θ s , φ s ) = M 1 ( r , θ s , φ s , θ d 1 , φ d 1 ) + M 2 ( r , θ s , φ s , θ d 2 , φ d 2 ) + M 3 ( r , θ s , φ s , θ d 3 , φ d 3 ) .
J ( r , θ s , φ s ) = j J j ( r , θ s , φ s , θ d j , φ d j ) exp ( i δ j ) ,
δ j = ( k i k s ) x j ,
ε ( ω ) = ε r ( ω ) + i ε i ( ω ) .

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