Abstract

Polarization mode dispersion (PMD) degrades the performance of Jones-matrix-based polarization-sensitive multifunctional optical coherence tomography (JM-OCT). The problem is specially acute for optically buffered JM-OCT, because the long fiber in the optical buffering module induces a large amount of PMD. This paper aims at presenting a method to correct the effect of PMD in JM-OCT. We first mathematically model the PMD in JM-OCT and then derive a method to correct the PMD. This method is a combination of simple hardware modification and subsequent software correction. The hardware modification is introduction of two polarizers which transform the PMD into global complex modulation of Jones matrix. Subsequently, the software correction demodulates the global modulation. The method is validated with an experimentally obtained point spread function with a mirror sample, as well as by in vivo measurement of a human retina.

© 2014 Optical Society of America

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2014 (4)

Y.-J. Hong, M. Miura, M. J. Ju, S. Makita, T. Iwasaki, and Y. Yasuno, “Simultaneous investigation of vascular and retinal pigment epithelial pathologies of exudative macular diseases by multifunctional optical coherence tomography,” Investigative Ophthalmology & Visual Science 55, 5016–5031 (2014).
[Crossref]

B. Braaf, K. A. Vermeer, M. de Groot, K. V. Vienola, and J. F. de Boer, “Fiber-based polarization-sensitive oct of the human retina with correction of system polarization distortions,” Biomed. Opt. Express 5, 2736–2758 (2014).
[Crossref] [PubMed]

S. Makita, Y.-J. Hong, M. Miura, and Y. Yasuno, “Degree of polarization uniformity with high noise immunity using polarization-sensitive optical coherence tomography,” Opt. Lett. 39, 6783–6786 (2014).
[Crossref]

Z. Wang, H.-C. Lee, O. O. Ahsen, B. Lee, W. Choi, B. Potsaid, J. Liu, V. Jayaraman, A. Cable, M. F. Kraus, K. Liang, J. Hornegger, and J. G. Fujimoto, “Depth-encoded all-fiber swept source polarization sensitive OCT,” Biomedical Optics Express 5, 2931–2949 (2014).
[Crossref] [PubMed]

2013 (7)

T. Torzicky, S. Marschall, M. Pircher, B. Baumann, M. Bonesi, S. Zotter, E. Götzinger, W. Trasischker, T. Klein, W. Wieser, B. Biedermann, R. Huber, P. Andersen, and C. K. Hitzenberger, “Retinal polarization-sensitive optical coherence tomography at 1060 nm with 350 khz a-scan rate using an fourier domain mode locked laser,” Journal of Biomedical Optics 18, 026008 (2013).
[Crossref]

E. Z. Zhang, W.-Y. Oh, M. L. Villiger, L. Chen, B. E. Bouma, and B. J. Vakoc, “Numerical compensation of system polarization mode dispersion in polarization-sensitive optical coherence tomography,” Opt. Express 21, 1163–1180 (2013).
[Crossref] [PubMed]

M. Villiger, E. Z. Zhang, S. K. Nadkarni, W.-Y. Oh, B. J. Vakoc, and B. E. Bouma, “Spectral binning for mitigation of polarization mode dispersion artifacts in catheter-based optical frequency domain imaging,” Opt. Express 21, 16353–16369 (2013).
[Crossref] [PubMed]

C. Blatter, S. Coquoz, B. Grajciar, A. S. G. Singh, M. Bonesi, R. M. Werkmeister, L. Schmetterer, and R. A. Leitgeb, “Dove prism based rotating dual beam bidirectional doppler oct,” Biomed. Opt. Express 4, 1188–1203 (2013).
[Crossref] [PubMed]

Y.-J. Hong, M. Miura, S. Makita, M. J. Ju, B. H. Lee, T. Iwasaki, and Y. Yasuno, “Noninvasive investigation of deep vascular pathologies of exudative macular diseases by high-penetration optical coherence angiography,” Investigative Ophthalmology & Visual Science 54, 3621–3631 (2013).
[Crossref]

M. J. Ju, Y.-J. Hong, S. Makita, Y. Lim, K. Kurokawa, L. Duan, M. Miura, S. Tang, and Y. Yasuno, “Advanced multi-contrast jones matrix optical coherence tomography for doppler and polarization sensitive imaging,” Opt. Express 21, 19412–19436 (2013).
[Crossref] [PubMed]

M. J. Gora, J. S. Sauk, R. W. Carruth, K. A. Gallagher, M. J. Suter, N. S. Nishioka, L. E. Kava, M. Rosenberg, B. E. Bouma, and G. J. Tearney, “Tethered capsule endomicroscopy enables less invasive imaging of gastrointestinal tract microstructure,” Nature Medicine 19, 238–240 (2013).
[Crossref] [PubMed]

2012 (5)

2011 (3)

2010 (4)

2009 (1)

L. M. Sakata, J. DeLeon-Ortega, V. Sakata, and C. A. Girkin, “Optical coherence tomography of the retina and optic nerve a review,” Clinical & Experimental Ophthalmology 37, 90–99 (2009).
[Crossref]

2008 (4)

G. J. Tearney, S. Waxman, M. Shishkov, B. J. Vakoc, M. J. Suter, M. I. Freilich, A. E. Desjardins, W.-Y. Oh, L. A. Bartlett, M. Rosenberg, and B. E. Bouma, “Three-dimensional coronary artery microscopy by intracoronary optical frequency domain imaging,” J Am Coll Cardiol Img 6, 752–761 (2008).
[Crossref]

M. Yamanari, S. Makita, and Y. Yasuno, “Polarization-sensitive swept-source optical coherence tomography with continuous source polarization modulation,” Opt. Express 16, 5892–5906 (2008).
[Crossref] [PubMed]

M. Miura, M. Yamanari, T. Iwasaki, A. E. Elsner, S. Makita, T. Yatagai, and Y. Yasuno, “Imaging polarimetry in age-related macular degeneration,” Investigative Ophthalmology & Visual Science 49, 2661–2667 (2008).
[Crossref]

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

2007 (1)

2006 (3)

2005 (1)

2004 (3)

2003 (3)

2002 (1)

2001 (1)

2000 (1)

L. L. Otis, M. J. Everett, U. S. Sathyam, and B. W. Colston, “Optical coherence tomography: A new imaging technology for dentistry,” The Journal of the American Dental Association 131, 511–514 (2000).
[Crossref] [PubMed]

1997 (2)

1992 (1)

1991 (1)

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

Adler, D. C.

Ahlers, C.

C. Ahlers, E. Gtzinger, M. Pircher, I. Golbaz, F. Prager, C. Schtze, B. Baumann, C. K. Hitzenberger, and U. Schmidt-Erfurth, “Imaging of the retinal pigment epithelium in age-related macular degeneration using polarization-sensitive optical coherence tomography,” Investigative Ophthalmology & Visual Science 51, 2149–2157 (2010).
[Crossref]

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

Ahsen, O. O.

Z. Wang, H.-C. Lee, O. O. Ahsen, B. Lee, W. Choi, B. Potsaid, J. Liu, V. Jayaraman, A. Cable, M. F. Kraus, K. Liang, J. Hornegger, and J. G. Fujimoto, “Depth-encoded all-fiber swept source polarization sensitive OCT,” Biomedical Optics Express 5, 2931–2949 (2014).
[Crossref] [PubMed]

Akiba, M.

Andersen, P.

T. Torzicky, S. Marschall, M. Pircher, B. Baumann, M. Bonesi, S. Zotter, E. Götzinger, W. Trasischker, T. Klein, W. Wieser, B. Biedermann, R. Huber, P. Andersen, and C. K. Hitzenberger, “Retinal polarization-sensitive optical coherence tomography at 1060 nm with 350 khz a-scan rate using an fourier domain mode locked laser,” Journal of Biomedical Optics 18, 026008 (2013).
[Crossref]

Bajraszewski, T.

Barry, S.

Bartlett, L. A.

G. J. Tearney, S. Waxman, M. Shishkov, B. J. Vakoc, M. J. Suter, M. I. Freilich, A. E. Desjardins, W.-Y. Oh, L. A. Bartlett, M. Rosenberg, and B. E. Bouma, “Three-dimensional coronary artery microscopy by intracoronary optical frequency domain imaging,” J Am Coll Cardiol Img 6, 752–761 (2008).
[Crossref]

Baumann, B.

T. Torzicky, S. Marschall, M. Pircher, B. Baumann, M. Bonesi, S. Zotter, E. Götzinger, W. Trasischker, T. Klein, W. Wieser, B. Biedermann, R. Huber, P. Andersen, and C. K. Hitzenberger, “Retinal polarization-sensitive optical coherence tomography at 1060 nm with 350 khz a-scan rate using an fourier domain mode locked laser,” Journal of Biomedical Optics 18, 026008 (2013).
[Crossref]

B. Baumann, W. Choi, B. Potsaid, D. Huang, J. S. Duker, and J. G. Fujimoto, “Swept source / fourier domain polarization sensitive optical coherence tomography with a passive polarization delay unit,” Opt. Express 20, 10229–10241 (2012).
[Crossref] [PubMed]

M. Bonesi, H. Sattmann, T. Torzicky, S. Zotter, B. Baumann, M. Pircher, E. Götzinger, C. Eigenwillig, W. Wieser, R. Huber, and C. K. Hitzenberger, “High-speed polarization sensitive optical coherence tomography scan engine based onfourier domain mode locked laser,” Biomed. Opt. Express 3, 2987–3000 (2012).
[Crossref] [PubMed]

B. Baumann, B. Potsaid, M. F. Kraus, J. J. Liu, D. Huang, J. Hornegger, A. E. Cable, J. S. Duker, and J. G. Fujimoto, “Total retinal blood flow measurement with ultrahigh speed swept source/fourier domain oct,” Biomed. Opt. Express 2, 1539–1552 (2011).
[Crossref] [PubMed]

B. Potsaid, B. Baumann, D. Huang, S. Barry, A. E. Cable, J. S. Schuman, J. S. Duker, and J. G. Fujimoto, “Ultrahigh speed 1050nm swept source / fourier domain oct retinal and anterior segment imaging at 100,000 to 400,000 axial scans per second,” Opt. Express 18, 20029–20048 (2010).
[Crossref] [PubMed]

C. Ahlers, E. Gtzinger, M. Pircher, I. Golbaz, F. Prager, C. Schtze, B. Baumann, C. K. Hitzenberger, and U. Schmidt-Erfurth, “Imaging of the retinal pigment epithelium in age-related macular degeneration using polarization-sensitive optical coherence tomography,” Investigative Ophthalmology & Visual Science 51, 2149–2157 (2010).
[Crossref]

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

Biedermann, B.

T. Torzicky, S. Marschall, M. Pircher, B. Baumann, M. Bonesi, S. Zotter, E. Götzinger, W. Trasischker, T. Klein, W. Wieser, B. Biedermann, R. Huber, P. Andersen, and C. K. Hitzenberger, “Retinal polarization-sensitive optical coherence tomography at 1060 nm with 350 khz a-scan rate using an fourier domain mode locked laser,” Journal of Biomedical Optics 18, 026008 (2013).
[Crossref]

Bisland, S.

Blatter, C.

Bonesi, M.

Bouma, B.

Bouma, B. E.

E. Z. Zhang, W.-Y. Oh, M. L. Villiger, L. Chen, B. E. Bouma, and B. J. Vakoc, “Numerical compensation of system polarization mode dispersion in polarization-sensitive optical coherence tomography,” Opt. Express 21, 1163–1180 (2013).
[Crossref] [PubMed]

M. Villiger, E. Z. Zhang, S. K. Nadkarni, W.-Y. Oh, B. J. Vakoc, and B. E. Bouma, “Spectral binning for mitigation of polarization mode dispersion artifacts in catheter-based optical frequency domain imaging,” Opt. Express 21, 16353–16369 (2013).
[Crossref] [PubMed]

M. J. Gora, J. S. Sauk, R. W. Carruth, K. A. Gallagher, M. J. Suter, N. S. Nishioka, L. E. Kava, M. Rosenberg, B. E. Bouma, and G. J. Tearney, “Tethered capsule endomicroscopy enables less invasive imaging of gastrointestinal tract microstructure,” Nature Medicine 19, 238–240 (2013).
[Crossref] [PubMed]

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Lee, B.

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Y.-J. Hong, M. Miura, S. Makita, M. J. Ju, B. H. Lee, T. Iwasaki, and Y. Yasuno, “Noninvasive investigation of deep vascular pathologies of exudative macular diseases by high-penetration optical coherence angiography,” Investigative Ophthalmology & Visual Science 54, 3621–3631 (2013).
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Z. Wang, H.-C. Lee, O. O. Ahsen, B. Lee, W. Choi, B. Potsaid, J. Liu, V. Jayaraman, A. Cable, M. F. Kraus, K. Liang, J. Hornegger, and J. G. Fujimoto, “Depth-encoded all-fiber swept source polarization sensitive OCT,” Biomedical Optics Express 5, 2931–2949 (2014).
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Pierce, M.

Pierce, M. C.

M. C. Pierce, J. Strasswimmer, B. H. Park, B. Cense, and J. F. de Boer, “Advances in optical coherence tomography imaging for dermatology,” Journal of Investigative Dermatology 123, 458–463 (2004).
[Crossref] [PubMed]

B. H. Park, M. C. Pierce, B. Cense, and J. F. de Boer, “Jones matrix analysis for a polarization-sensitive optical coherencetomography system using fiber-optic components,” Opt. Lett. 29, 2512–2514 (2004).
[Crossref] [PubMed]

Pircher, M.

T. Torzicky, S. Marschall, M. Pircher, B. Baumann, M. Bonesi, S. Zotter, E. Götzinger, W. Trasischker, T. Klein, W. Wieser, B. Biedermann, R. Huber, P. Andersen, and C. K. Hitzenberger, “Retinal polarization-sensitive optical coherence tomography at 1060 nm with 350 khz a-scan rate using an fourier domain mode locked laser,” Journal of Biomedical Optics 18, 026008 (2013).
[Crossref]

M. Bonesi, H. Sattmann, T. Torzicky, S. Zotter, B. Baumann, M. Pircher, E. Götzinger, C. Eigenwillig, W. Wieser, R. Huber, and C. K. Hitzenberger, “High-speed polarization sensitive optical coherence tomography scan engine based onfourier domain mode locked laser,” Biomed. Opt. Express 3, 2987–3000 (2012).
[Crossref] [PubMed]

C. Ahlers, E. Gtzinger, M. Pircher, I. Golbaz, F. Prager, C. Schtze, B. Baumann, C. K. Hitzenberger, and U. Schmidt-Erfurth, “Imaging of the retinal pigment epithelium in age-related macular degeneration using polarization-sensitive optical coherence tomography,” Investigative Ophthalmology & Visual Science 51, 2149–2157 (2010).
[Crossref]

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

M. Pircher, E. Götzinger, R. Leitgeb, H. Sattmann, O. Findl, and C. Hitzenberger, “Imaging of polarization properties of human retina in vivo with phase resolved transversal ps-oct,” Opt. Express 12, 5940–5951 (2004).
[Crossref] [PubMed]

C. Hitzenberger, E. Goetzinger, M. Sticker, M. Pircher, and A. 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]

Potsaid, B.

Prager, F.

C. Ahlers, E. Gtzinger, M. Pircher, I. Golbaz, F. Prager, C. Schtze, B. Baumann, C. K. Hitzenberger, and U. Schmidt-Erfurth, “Imaging of the retinal pigment epithelium in age-related macular degeneration using polarization-sensitive optical coherence tomography,” Investigative Ophthalmology & Visual Science 51, 2149–2157 (2010).
[Crossref]

Puliafito, C.

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

Qi, B.

Rosenberg, M.

M. J. Gora, J. S. Sauk, R. W. Carruth, K. A. Gallagher, M. J. Suter, N. S. Nishioka, L. E. Kava, M. Rosenberg, B. E. Bouma, and G. J. Tearney, “Tethered capsule endomicroscopy enables less invasive imaging of gastrointestinal tract microstructure,” Nature Medicine 19, 238–240 (2013).
[Crossref] [PubMed]

G. J. Tearney, S. Waxman, M. Shishkov, B. J. Vakoc, M. J. Suter, M. I. Freilich, A. E. Desjardins, W.-Y. Oh, L. A. Bartlett, M. Rosenberg, and B. E. Bouma, “Three-dimensional coronary artery microscopy by intracoronary optical frequency domain imaging,” J Am Coll Cardiol Img 6, 752–761 (2008).
[Crossref]

Sakai, T.

Sakata, L. M.

L. M. Sakata, J. DeLeon-Ortega, V. Sakata, and C. A. Girkin, “Optical coherence tomography of the retina and optic nerve a review,” Clinical & Experimental Ophthalmology 37, 90–99 (2009).
[Crossref]

Sakata, V.

L. M. Sakata, J. DeLeon-Ortega, V. Sakata, and C. A. Girkin, “Optical coherence tomography of the retina and optic nerve a review,” Clinical & Experimental Ophthalmology 37, 90–99 (2009).
[Crossref]

Sathyam, U. S.

L. L. Otis, M. J. Everett, U. S. Sathyam, and B. W. Colston, “Optical coherence tomography: A new imaging technology for dentistry,” The Journal of the American Dental Association 131, 511–514 (2000).
[Crossref] [PubMed]

Sattmann, H.

Sauk, J. S.

M. J. Gora, J. S. Sauk, R. W. Carruth, K. A. Gallagher, M. J. Suter, N. S. Nishioka, L. E. Kava, M. Rosenberg, B. E. Bouma, and G. J. Tearney, “Tethered capsule endomicroscopy enables less invasive imaging of gastrointestinal tract microstructure,” Nature Medicine 19, 238–240 (2013).
[Crossref] [PubMed]

Schmetterer, L.

Schmidt-Erfurth, U.

C. Ahlers, E. Gtzinger, M. Pircher, I. Golbaz, F. Prager, C. Schtze, B. Baumann, C. K. Hitzenberger, and U. Schmidt-Erfurth, “Imaging of the retinal pigment epithelium in age-related macular degeneration using polarization-sensitive optical coherence tomography,” Investigative Ophthalmology & Visual Science 51, 2149–2157 (2010).
[Crossref]

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

Schtze, C.

C. Ahlers, E. Gtzinger, M. Pircher, I. Golbaz, F. Prager, C. Schtze, B. Baumann, C. K. Hitzenberger, and U. Schmidt-Erfurth, “Imaging of the retinal pigment epithelium in age-related macular degeneration using polarization-sensitive optical coherence tomography,” Investigative Ophthalmology & Visual Science 51, 2149–2157 (2010).
[Crossref]

Schuman, J.

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

Schuman, J. S.

Seng-Yue, E.

Shepherd, N.

Shia, K.

Shishkov, M.

G. J. Tearney, S. Waxman, M. Shishkov, B. J. Vakoc, M. J. Suter, M. I. Freilich, A. E. Desjardins, W.-Y. Oh, L. A. Bartlett, M. Rosenberg, and B. E. Bouma, “Three-dimensional coronary artery microscopy by intracoronary optical frequency domain imaging,” J Am Coll Cardiol Img 6, 752–761 (2008).
[Crossref]

Singh, A. S. G.

Sticker, M.

Stinson, W.

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

Strasswimmer, J.

M. C. Pierce, J. Strasswimmer, B. H. Park, B. Cense, and J. F. de Boer, “Advances in optical coherence tomography imaging for dermatology,” Journal of Investigative Dermatology 123, 458–463 (2004).
[Crossref] [PubMed]

Suter, M. J.

M. J. Gora, J. S. Sauk, R. W. Carruth, K. A. Gallagher, M. J. Suter, N. S. Nishioka, L. E. Kava, M. Rosenberg, B. E. Bouma, and G. J. Tearney, “Tethered capsule endomicroscopy enables less invasive imaging of gastrointestinal tract microstructure,” Nature Medicine 19, 238–240 (2013).
[Crossref] [PubMed]

G. J. Tearney, S. Waxman, M. Shishkov, B. J. Vakoc, M. J. Suter, M. I. Freilich, A. E. Desjardins, W.-Y. Oh, L. A. Bartlett, M. Rosenberg, and B. E. Bouma, “Three-dimensional coronary artery microscopy by intracoronary optical frequency domain imaging,” J Am Coll Cardiol Img 6, 752–761 (2008).
[Crossref]

Sutoh, Y.

Swanson, E.

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

Swanson, E. A.

Tang, S.

Tearney, G.

Tearney, G. J.

M. J. Gora, J. S. Sauk, R. W. Carruth, K. A. Gallagher, M. J. Suter, N. S. Nishioka, L. E. Kava, M. Rosenberg, B. E. Bouma, and G. J. Tearney, “Tethered capsule endomicroscopy enables less invasive imaging of gastrointestinal tract microstructure,” Nature Medicine 19, 238–240 (2013).
[Crossref] [PubMed]

G. J. Tearney, S. Waxman, M. Shishkov, B. J. Vakoc, M. J. Suter, M. I. Freilich, A. E. Desjardins, W.-Y. Oh, L. A. Bartlett, M. Rosenberg, and B. E. Bouma, “Three-dimensional coronary artery microscopy by intracoronary optical frequency domain imaging,” J Am Coll Cardiol Img 6, 752–761 (2008).
[Crossref]

Torzicky, T.

T. Torzicky, S. Marschall, M. Pircher, B. Baumann, M. Bonesi, S. Zotter, E. Götzinger, W. Trasischker, T. Klein, W. Wieser, B. Biedermann, R. Huber, P. Andersen, and C. K. Hitzenberger, “Retinal polarization-sensitive optical coherence tomography at 1060 nm with 350 khz a-scan rate using an fourier domain mode locked laser,” Journal of Biomedical Optics 18, 026008 (2013).
[Crossref]

M. Bonesi, H. Sattmann, T. Torzicky, S. Zotter, B. Baumann, M. Pircher, E. Götzinger, C. Eigenwillig, W. Wieser, R. Huber, and C. K. Hitzenberger, “High-speed polarization sensitive optical coherence tomography scan engine based onfourier domain mode locked laser,” Biomed. Opt. Express 3, 2987–3000 (2012).
[Crossref] [PubMed]

Trasischker, W.

T. Torzicky, S. Marschall, M. Pircher, B. Baumann, M. Bonesi, S. Zotter, E. Götzinger, W. Trasischker, T. Klein, W. Wieser, B. Biedermann, R. Huber, P. Andersen, and C. K. Hitzenberger, “Retinal polarization-sensitive optical coherence tomography at 1060 nm with 350 khz a-scan rate using an fourier domain mode locked laser,” Journal of Biomedical Optics 18, 026008 (2013).
[Crossref]

Vakoc, B. J.

van Gemert, M. J. C.

Vermeer, K. A.

Vienola, K. V.

Villiger, M.

Villiger, M. L.

Vitkin, I.

Wang, Z.

Z. Wang, H.-C. Lee, O. O. Ahsen, B. Lee, W. Choi, B. Potsaid, J. Liu, V. Jayaraman, A. Cable, M. F. Kraus, K. Liang, J. Hornegger, and J. G. Fujimoto, “Depth-encoded all-fiber swept source polarization sensitive OCT,” Biomedical Optics Express 5, 2931–2949 (2014).
[Crossref] [PubMed]

Waxman, S.

G. J. Tearney, S. Waxman, M. Shishkov, B. J. Vakoc, M. J. Suter, M. I. Freilich, A. E. Desjardins, W.-Y. Oh, L. A. Bartlett, M. Rosenberg, and B. E. Bouma, “Three-dimensional coronary artery microscopy by intracoronary optical frequency domain imaging,” J Am Coll Cardiol Img 6, 752–761 (2008).
[Crossref]

Werkmeister, R. M.

White, B.

Wieser, W.

T. Torzicky, S. Marschall, M. Pircher, B. Baumann, M. Bonesi, S. Zotter, E. Götzinger, W. Trasischker, T. Klein, W. Wieser, B. Biedermann, R. Huber, P. Andersen, and C. K. Hitzenberger, “Retinal polarization-sensitive optical coherence tomography at 1060 nm with 350 khz a-scan rate using an fourier domain mode locked laser,” Journal of Biomedical Optics 18, 026008 (2013).
[Crossref]

M. Bonesi, H. Sattmann, T. Torzicky, S. Zotter, B. Baumann, M. Pircher, E. Götzinger, C. Eigenwillig, W. Wieser, R. Huber, and C. K. Hitzenberger, “High-speed polarization sensitive optical coherence tomography scan engine based onfourier domain mode locked laser,” Biomed. Opt. Express 3, 2987–3000 (2012).
[Crossref] [PubMed]

Wilson, B.

Yamanari, M.

Y. Lim, Y.-J. Hong, L. Duan, M. Yamanari, and Y. Yasuno, “Passive component based multifunctional jones matrix swept source optical coherence tomography for doppler and polarization imaging,” Opt. Lett. 37, 1958–1960 (2012).
[Crossref] [PubMed]

S. Makita, M. Yamanari, and Y. Yasuno, “Generalized jones matrix optical coherence tomography: performance and local birefringence imaging,” Opt. Express 18, 854–876 (2010).
[Crossref] [PubMed]

M. Yamanari, S. Makita, and Y. Yasuno, “Polarization-sensitive swept-source optical coherence tomography with continuous source polarization modulation,” Opt. Express 16, 5892–5906 (2008).
[Crossref] [PubMed]

M. Miura, M. Yamanari, T. Iwasaki, A. E. Elsner, S. Makita, T. Yatagai, and Y. Yasuno, “Imaging polarimetry in age-related macular degeneration,” Investigative Ophthalmology & Visual Science 49, 2661–2667 (2008).
[Crossref]

Y. Yasuno, Y. Hong, S. Makita, M. Yamanari, M. Akiba, M. Miura, and T. Yatagai, “In vivo high-contrast imaging of deep posterior eye by 1-um swept source optical coherence tomography andscattering optical coherence angiography,” Opt. Express 15, 6121–6139 (2007).
[Crossref] [PubMed]

S. Makita, Y. Hong, M. Yamanari, T. Yatagai, and Y. Yasuno, “Optical coherence angiography,” Opt. Express 14, 7821–7840 (2006).
[Crossref] [PubMed]

M. Yamanari, S. Makita, V. D. Madjarova, T. Yatagai, and Y. Yasuno, “Fiber-based polarization-sensitive fourier domain optical coherence tomography using b-scan-oriented polarization modulation method,” Opt. Express 14, 6502–6515 (2006).
[Crossref] [PubMed]

Yang, V. X. D.

Yasuno, Y.

Y.-J. Hong, M. Miura, M. J. Ju, S. Makita, T. Iwasaki, and Y. Yasuno, “Simultaneous investigation of vascular and retinal pigment epithelial pathologies of exudative macular diseases by multifunctional optical coherence tomography,” Investigative Ophthalmology & Visual Science 55, 5016–5031 (2014).
[Crossref]

S. Makita, Y.-J. Hong, M. Miura, and Y. Yasuno, “Degree of polarization uniformity with high noise immunity using polarization-sensitive optical coherence tomography,” Opt. Lett. 39, 6783–6786 (2014).
[Crossref]

Y.-J. Hong, M. Miura, S. Makita, M. J. Ju, B. H. Lee, T. Iwasaki, and Y. Yasuno, “Noninvasive investigation of deep vascular pathologies of exudative macular diseases by high-penetration optical coherence angiography,” Investigative Ophthalmology & Visual Science 54, 3621–3631 (2013).
[Crossref]

M. J. Ju, Y.-J. Hong, S. Makita, Y. Lim, K. Kurokawa, L. Duan, M. Miura, S. Tang, and Y. Yasuno, “Advanced multi-contrast jones matrix optical coherence tomography for doppler and polarization sensitive imaging,” Opt. Express 21, 19412–19436 (2013).
[Crossref] [PubMed]

Y. Lim, Y.-J. Hong, L. Duan, M. Yamanari, and Y. Yasuno, “Passive component based multifunctional jones matrix swept source optical coherence tomography for doppler and polarization imaging,” Opt. Lett. 37, 1958–1960 (2012).
[Crossref] [PubMed]

S. Makita, M. Yamanari, and Y. Yasuno, “Generalized jones matrix optical coherence tomography: performance and local birefringence imaging,” Opt. Express 18, 854–876 (2010).
[Crossref] [PubMed]

M. Yamanari, S. Makita, and Y. Yasuno, “Polarization-sensitive swept-source optical coherence tomography with continuous source polarization modulation,” Opt. Express 16, 5892–5906 (2008).
[Crossref] [PubMed]

M. Miura, M. Yamanari, T. Iwasaki, A. E. Elsner, S. Makita, T. Yatagai, and Y. Yasuno, “Imaging polarimetry in age-related macular degeneration,” Investigative Ophthalmology & Visual Science 49, 2661–2667 (2008).
[Crossref]

Y. Yasuno, Y. Hong, S. Makita, M. Yamanari, M. Akiba, M. Miura, and T. Yatagai, “In vivo high-contrast imaging of deep posterior eye by 1-um swept source optical coherence tomography andscattering optical coherence angiography,” Opt. Express 15, 6121–6139 (2007).
[Crossref] [PubMed]

S. Makita, Y. Hong, M. Yamanari, T. Yatagai, and Y. Yasuno, “Optical coherence angiography,” Opt. Express 14, 7821–7840 (2006).
[Crossref] [PubMed]

M. Yamanari, S. Makita, V. D. Madjarova, T. Yatagai, and Y. Yasuno, “Fiber-based polarization-sensitive fourier domain optical coherence tomography using b-scan-oriented polarization modulation method,” Opt. Express 14, 6502–6515 (2006).
[Crossref] [PubMed]

Y. Yasuno, V. D. Madjarova, S. Makita, M. Akiba, A. Morosawa, C. Chong, T. Sakai, K.-P. Chan, M. Itoh, and T. Yatagai, “Three-dimensional and high-speed swept-source optical coherence tomography for in vivo investigation of human anterior eye segments,” Opt. Express 13, 10652–10664 (2005).
[Crossref] [PubMed]

Y. Yasuno, S. Makita, Y. Sutoh, M. Itoh, and T. Yatagai, “Birefringence imaging of human skin by polarization-sensitive spectral interferometric optical coherence tomography,” Opt. Lett. 27, 1803–1805 (2002).
[Crossref]

Yatagai, T.

Zawadzki, R.

Zhang, E. Z.

Zotter, S.

T. Torzicky, S. Marschall, M. Pircher, B. Baumann, M. Bonesi, S. Zotter, E. Götzinger, W. Trasischker, T. Klein, W. Wieser, B. Biedermann, R. Huber, P. Andersen, and C. K. Hitzenberger, “Retinal polarization-sensitive optical coherence tomography at 1060 nm with 350 khz a-scan rate using an fourier domain mode locked laser,” Journal of Biomedical Optics 18, 026008 (2013).
[Crossref]

M. Bonesi, H. Sattmann, T. Torzicky, S. Zotter, B. Baumann, M. Pircher, E. Götzinger, C. Eigenwillig, W. Wieser, R. Huber, and C. K. Hitzenberger, “High-speed polarization sensitive optical coherence tomography scan engine based onfourier domain mode locked laser,” Biomed. Opt. Express 3, 2987–3000 (2012).
[Crossref] [PubMed]

Biomed. Opt. Express (6)

B. Baumann, B. Potsaid, M. F. Kraus, J. J. Liu, D. Huang, J. Hornegger, A. E. Cable, J. S. Duker, and J. G. Fujimoto, “Total retinal blood flow measurement with ultrahigh speed swept source/fourier domain oct,” Biomed. Opt. Express 2, 1539–1552 (2011).
[Crossref] [PubMed]

H. C. Hendargo, R. P. McNabb, A.-H. Dhalla, N. Shepherd, and J. A. Izatt, “Doppler velocity detection limitations in spectrometer-based versus swept-source optical coherence tomography,” Biomed. Opt. Express 2, 2175–2188 (2011).
[Crossref] [PubMed]

C. Blatter, S. Coquoz, B. Grajciar, A. S. G. Singh, M. Bonesi, R. M. Werkmeister, L. Schmetterer, and R. A. Leitgeb, “Dove prism based rotating dual beam bidirectional doppler oct,” Biomed. Opt. Express 4, 1188–1203 (2013).
[Crossref] [PubMed]

A.-H. Dhalla, K. Shia, and J. A. Izatt, “Efficient sweep buffering in swept source optical coherence tomography using a fast optical switch,” Biomed. Opt. Express 3, 3054–3066 (2012).
[Crossref] [PubMed]

B. Braaf, K. A. Vermeer, M. de Groot, K. V. Vienola, and J. F. de Boer, “Fiber-based polarization-sensitive oct of the human retina with correction of system polarization distortions,” Biomed. Opt. Express 5, 2736–2758 (2014).
[Crossref] [PubMed]

M. Bonesi, H. Sattmann, T. Torzicky, S. Zotter, B. Baumann, M. Pircher, E. Götzinger, C. Eigenwillig, W. Wieser, R. Huber, and C. K. Hitzenberger, “High-speed polarization sensitive optical coherence tomography scan engine based onfourier domain mode locked laser,” Biomed. Opt. Express 3, 2987–3000 (2012).
[Crossref] [PubMed]

Biomedical Optics Express (1)

Z. Wang, H.-C. Lee, O. O. Ahsen, B. Lee, W. Choi, B. Potsaid, J. Liu, V. Jayaraman, A. Cable, M. F. Kraus, K. Liang, J. Hornegger, and J. G. Fujimoto, “Depth-encoded all-fiber swept source polarization sensitive OCT,” Biomedical Optics Express 5, 2931–2949 (2014).
[Crossref] [PubMed]

Clinical & Experimental Ophthalmology (1)

L. M. Sakata, J. DeLeon-Ortega, V. Sakata, and C. A. Girkin, “Optical coherence tomography of the retina and optic nerve a review,” Clinical & Experimental Ophthalmology 37, 90–99 (2009).
[Crossref]

Investigative Ophthalmology & Visual Science (4)

Y.-J. Hong, M. Miura, M. J. Ju, S. Makita, T. Iwasaki, and Y. Yasuno, “Simultaneous investigation of vascular and retinal pigment epithelial pathologies of exudative macular diseases by multifunctional optical coherence tomography,” Investigative Ophthalmology & Visual Science 55, 5016–5031 (2014).
[Crossref]

Y.-J. Hong, M. Miura, S. Makita, M. J. Ju, B. H. Lee, T. Iwasaki, and Y. Yasuno, “Noninvasive investigation of deep vascular pathologies of exudative macular diseases by high-penetration optical coherence angiography,” Investigative Ophthalmology & Visual Science 54, 3621–3631 (2013).
[Crossref]

M. Miura, M. Yamanari, T. Iwasaki, A. E. Elsner, S. Makita, T. Yatagai, and Y. Yasuno, “Imaging polarimetry in age-related macular degeneration,” Investigative Ophthalmology & Visual Science 49, 2661–2667 (2008).
[Crossref]

C. Ahlers, E. Gtzinger, M. Pircher, I. Golbaz, F. Prager, C. Schtze, B. Baumann, C. K. Hitzenberger, and U. Schmidt-Erfurth, “Imaging of the retinal pigment epithelium in age-related macular degeneration using polarization-sensitive optical coherence tomography,” Investigative Ophthalmology & Visual Science 51, 2149–2157 (2010).
[Crossref]

J Am Coll Cardiol Img (1)

G. J. Tearney, S. Waxman, M. Shishkov, B. J. Vakoc, M. J. Suter, M. I. Freilich, A. E. Desjardins, W.-Y. Oh, L. A. Bartlett, M. Rosenberg, and B. E. Bouma, “Three-dimensional coronary artery microscopy by intracoronary optical frequency domain imaging,” J Am Coll Cardiol Img 6, 752–761 (2008).
[Crossref]

J. Opt. Soc. Am. B (1)

Journal of Biomedical Optics (1)

T. Torzicky, S. Marschall, M. Pircher, B. Baumann, M. Bonesi, S. Zotter, E. Götzinger, W. Trasischker, T. Klein, W. Wieser, B. Biedermann, R. Huber, P. Andersen, and C. K. Hitzenberger, “Retinal polarization-sensitive optical coherence tomography at 1060 nm with 350 khz a-scan rate using an fourier domain mode locked laser,” Journal of Biomedical Optics 18, 026008 (2013).
[Crossref]

Journal of Investigative Dermatology (1)

M. C. Pierce, J. Strasswimmer, B. H. Park, B. Cense, and J. F. de Boer, “Advances in optical coherence tomography imaging for dermatology,” Journal of Investigative Dermatology 123, 458–463 (2004).
[Crossref] [PubMed]

Nature Medicine (1)

M. J. Gora, J. S. Sauk, R. W. Carruth, K. A. Gallagher, M. J. Suter, N. S. Nishioka, L. E. Kava, M. Rosenberg, B. E. Bouma, and G. J. Tearney, “Tethered capsule endomicroscopy enables less invasive imaging of gastrointestinal tract microstructure,” Nature Medicine 19, 238–240 (2013).
[Crossref] [PubMed]

Opt. Express (20)

B. White, M. Pierce, N. Nassif, B. Cense, B. Park, G. Tearney, B. Bouma, T. Chen, and J. de Boer, “In vivo dynamic human retinal blood flow imaging using ultra-high-speed spectral domain optical coherence tomography,” Opt. Express 11, 3490–3497 (2003).
[Crossref] [PubMed]

R. Leitgeb, L. Schmetterer, W. Drexler, A. Fercher, R. Zawadzki, and T. Bajraszewski, “Real-time assessment of retinal blood flow with ultrafast acquisition by color doppler fourier domain optical coherence tomography,” Opt. Express 11, 3116–3121 (2003).
[Crossref] [PubMed]

C. Hitzenberger, E. Goetzinger, M. Sticker, M. Pircher, and A. 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]

M. Yamanari, S. Makita, V. D. Madjarova, T. Yatagai, and Y. Yasuno, “Fiber-based polarization-sensitive fourier domain optical coherence tomography using b-scan-oriented polarization modulation method,” Opt. Express 14, 6502–6515 (2006).
[Crossref] [PubMed]

M. Yamanari, S. Makita, and Y. Yasuno, “Polarization-sensitive swept-source optical coherence tomography with continuous source polarization modulation,” Opt. Express 16, 5892–5906 (2008).
[Crossref] [PubMed]

V. X. D. Yang, M. Gordon, S. jiang Tang, N. Marcon, G. Gardiner, B. Qi, S. Bisland, E. Seng-Yue, S. Lo, J. Pekar, B. Wilson, and I. Vitkin, “High speed, wide velocity dynamic range doppler optical coherence tomography (part iii): in vivo endoscopic imaging of blood flow in the rat and human gastrointestinal tracts,” Opt. Express 11, 2416–2424 (2003).
[Crossref] [PubMed]

S. Makita, Y. Hong, M. Yamanari, T. Yatagai, and Y. Yasuno, “Optical coherence angiography,” Opt. Express 14, 7821–7840 (2006).
[Crossref] [PubMed]

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

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Figures (6)

Fig. 1
Fig. 1 Schematic diagram of the optically buffered JM-OCT system. An (a) optical buffering module makes a 200 kHz laser sweep. The JM-OCT system is composed of a (b) reference arm, (c) passive polarization delay unit (PP-delay unit), (d) polarization diversity detection unit (PD-detection unit), (e) retinal scanner, and (f) calibration mirror. PC: polarization controller, FG: function generator, FBG: fiber Bragg grating, PD: photo-detector, FC: fiber collimator, PBS: polarizing beam-splitter, DP: dove prism, BS: non-polarizing beam splitter, BPD: balanced photo-detector. Point-B and -C indicate particular points which are discussed in Section 6.3 and PC-1 and -2 correspond to those in Fig. 6.
Fig. 2
Fig. 2 Schematic model of the polarization properties of the JM-OCT interferometer. JOB(k), JR(k), and JPD(k) are the Jones matrices of the buffering module, the reference arm, and the PP-delay unit, respectively. Jin(k) and Jout(k) are the Jones matrices of the illumination and the collection paths of the probe arm, and Js(k) is the Jones matrix of the sample. P45° represents a polarizer oriented at 45°. ESRC(k) is the Jones vector of the source light.
Fig. 3
Fig. 3 Averaged A-line signals of a mirror sample with different processing options for PMD correction. The black dotted and the red solid lines indicate unbuffered and buffered Alines, respectively. The panels on the right were processed with envelope correction, while the left panels were not. The dispersion and modulation phase were corrected separately for buffered and unbuffered modes in the bottom panels, while the same correction phase was applied for the both modes in the top panels. Black arrowheads indicate FPN, and red arrowheads indicate a side peak created by the envelope correction.
Fig. 4
Fig. 4 Comparison of in vivo retinal OCT images (a), (c) without and (b), (d) with PMD correction. Panels (c) and (d) are magnified images of the red rectangular regions in (a) and (b), respectively. The scale bar in (a) represents 0.5 mm × 0.5 mm
Fig. 5
Fig. 5 An example of our high-speed multifunctional OCT images of in vivo human optic nerve head. (a), (c) En face projection and a representative cross section of scattering (intensity) OCT, respectively; (d)–(f) power Doppler, phase retardation, and M-DOPU′ cross-sections, respectively; (b) an en face pseudo-color composite of power Doppler and M-DOPU′ signals. Yellow dashed lines in (a) and (b) represent the location of the cross-sectional images. The scale bars in (a) and (c) represent 0.5 mm × 0.5 mm.
Fig. 6
Fig. 6 Schematic model of the polarization properties of the JM-OCT interferometer with a specific FOS model and polarizers with arbitrary orientations. U(k), U′(k), and U″(k) are SU(2) matrices representing the Jones matrices of the optical fibers. R(θ) is a rotation matrix with rotation angle θ and P represents a polarizer oriented at 0°.

Equations (24)

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J OB ( k ) = [ a ( k ) b ( k ) b ( k ) a ( k ) ] = { [ a B ( k ) b B ( k ) b B ( k ) a B ( k ) ] , for buffered mode , [ a U ( k ) b U ( k ) b U ( k ) a U ( k ) ] , for unbuffered mode ,
J R ( k ) = [ α ( k ) β * ( k ) β ( k ) α * ( k ) , ] ,
E R ( k ) = P 45 ° J R ( k ) J OB ( k ) E SRC ( k ) e i k z r ,
E P ( k ) = J all ( k ) J PD ( k ) P 45 ° J OB ( k ) E SRC ( k ) e i k z p ,
E P ( k ) = 1 2 ( a ( k ) + b ( k ) ) S ( k ) [ J 11 ( k ) + d ( k ) J 12 ( k ) J 21 ( k ) + d ( k ) J 22 ( k ) ] e i k z p ,
E R ( k ) = 1 2 { ( α ( k ) + β ( k ) ) a ( k ) + ( α * ( k ) β * ( k ) ) b ( k ) S ( k ) } [ 1 1 ] e i k z r .
| E P ( k ) + E R ( k ) | 2 = | E P ( k ) | 2 + | E R ( k ) | 2 + E P ( k ) E R * ( k ) + E P * ( k ) E R ( k ) ,
E P ( k ) E R * ( k ) = | S ( k ) | 2 ε ( k ) [ J 11 ( k ) + d ( k ) J 12 ( k ) J 21 ( k ) + d ( k ) J 22 ( k ) ] e i k Δ z ,
ε ( k ) = 1 4 [ { α * ( k ) + β * ( k ) } { | a ( k ) | 2 + a * ( k ) b ( k ) } + { α ( k ) β ( k ) } { | b ( k ) | 2 + a ( k ) b * ( k ) } ] .
J m ( k ) = | S ( k ) | 2 ε ( k ) [ J 11 ( k ) J 12 ( k ) J 21 ( k ) J 22 ( k ) ] = | S ( k ) | 2 ε ( k ) J out ( k ) J s ( k ) J in ( k ) .
f n = | S ( k ) | 2 ε ( k ) J n ( k , x ) ,
I e ( k ) | f 11 ( k , x ) | 2 x + | f 21 ( k , x ) | 2 x = | S ( k ) | 2 ε ( k ) | J 11 ( k , x ) | 2 x + | J 21 ( k , x ) | 2 x = C | S ( k ) | 2 | ε ( k ) | ,
h ( k ) G ( k ) I e ( k ) ,
( E P ( k ) E R * ( k ) ) h ( k ) = G ( k ) C e i ε ( k ) [ J 11 ( k ) + d ( k ) J 12 ( k ) J 21 ( k ) + d ( k ) J 22 ( k ) ] e i k Δ z = G ( k ) C e i ε ( k ) e i ϕ ( k ) [ J 11 ( k ) + d ( k ) J 12 ( k ) J 21 ( k ) + d ( k ) J 22 ( k ) ] e i k Δ z ,
E P ( k ) E R ( k ) * = | S ( k ) | 2 [ ε 11 ( k ) J 11 ( k ) + d ( k ) ε 12 ( k ) J 12 ( k ) ε 21 ( k ) J 21 ( k ) + d ( k ) ε 22 ( k ) J 22 ( k ) ] e i k Δ z ,
ε 11 ( k ) = α * ( k ) | a ( k ) | 2 β ( k ) a ( k ) b * ( k ) , ε 12 ( k ) = β ( k ) | b ( k ) | 2 + α * ( k ) a * ( k ) b ( k ) , ε 21 ( k ) = β * ( k ) | a ( k ) | 2 + α ( k ) a ( k ) b * ( k ) , ε 22 ( k ) = α ( k ) | b ( k ) | 2 + β * ( k ) a * ( k ) b ( k ) .
E P ( k ) E R * ( k ) = | S ( k ) | 2 ε ( k ) [ J 11 ( k ) cos θ R cos θ P + d ( k ) J 12 ( k ) cos θ R sin θ P J 21 ( k ) sin θ R cos θ P + d ( k ) J 22 ( k ) sin θ R sin θ P ] e i k Δ z ,
ε ( k ) = ( α * ( k ) cos θ R + β * ( k ) sin θ R ) ( | a ( k ) | 2 cos θ P + a * ( k ) b ( k ) sin θ P ) + ( α ( k ) sin θ R β ( k ) cos θ R ) ( | b ( k ) | 2 sin θ P + a ( k ) b * ( k ) cos θ P ) .
J m ( k ) = | S ( k ) | 2 ε ( k ) [ cos θ R 0 0 sin θ R ] [ J 11 ( k ) J 12 ( k ) J 21 ( k ) J 22 ( k ) ] [ cos θ P 0 0 sin θ P ] .
U ( k ) U ( k ) = R ( θ P ) [ p ( k ) 0 0 p * ( k ) ] R ( φ ) ,
J R ( k ) U ( k ) U ( k ) = R ( θ R ) [ q ( k ) 0 0 q * ( k ) ] R ( φ ) ,
J R ( k ) = R ( θ R ) [ γ ( k ) 0 0 γ * ( k ) ] R ( θ P ) ,
ε ( k ) = | a ( k ) | 2 γ * ( k ) cos 2 θ P + a ( k ) b * ( k ) γ * ( k ) sin θ P cos θ P + | b ( k ) | 2 γ * ( k ) sin 2 θ P + a * ( k ) b ( k ) γ * ( k ) sin θ P cos θ P .
ε ( k ) = arctan Im [ ε ( k ) ] Re [ ε ( k ) ] = arctan Re [ γ ( k ) ] Im [ γ ( k ) ] .

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