Abstract

An all-fiber optic catheter-based polarization-sensitive optical coherence tomography system is demonstrated. A novel multiplexing method was used to illuminate the sample, splitting the light from a 58.5 kHz Fourier-domain mode-locked laser such that two different polarization states, alternated in time, are generated by two semiconductor optical amplifiers. A 2.3 mm forward-view cone-scanning catheter probe was designed, fabricated, and used to acquire sample scattering intensity and phase retardation images. The system was first verified with a quarter-wave plate and then by obtaining intensity and phase retardation images of high-birefringence plastic, human skin in vivo, and untreated and thermally ablated porcine myocardium ex vivo. The system can potentially in vivo image of the cardiac wall to aid radio-frequency ablation therapy for cardiac arrhythmias.

© 2014 Optical Society of America

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References

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  1. W. Rosamond, K. Flegal, G. Friday, K. Furie, A. Go, K. Greenlund, N. Haase, M. Ho, V. Howard, B. Kissela, S. Kittner, D. Lloyd-Jones, M. McDermott, J. Meigs, C. Moy, G. Nichol, C. J. O’Donnell, V. Roger, J. Rumsfeld, P. Sorlie, J. Steinberger, T. Thom, W.-S. Smoller, and Y. Hong, Circulation 115, e69 (2007).
    [CrossRef]
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    [CrossRef]
  4. C. P. Fleming, K. J. Quan, and A. M. Rollins, J. Biomed. Opt. 15, 0415101 (2010).
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    [CrossRef]
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    [CrossRef]
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2013 (3)

2012 (3)

2011 (3)

C. P. Fleming, N. Rosenthal, A. M. Rollins, and M. Arruda, Innovations Card. Rhythm Manage. 2, 199 (2011).

H. Wang, W. Kang, T. Carrigan, A. Bishop, N. Rosenthal, M. Arruda, and A. M. Rollins, J. Biomed. Opt. 16, 110505 (2011).
[CrossRef]

A. D’Silva and M. Wright, Radiol. Res. Pract. 2011, 714864 (2011).

2010 (3)

C. P. Fleming, K. J. Quan, H. Wang, G. Amit, and A. M. Rollins, Opt. Express 18, 3079 (2010).
[CrossRef]

C. P. Fleming, K. J. Quan, and A. M. Rollins, J. Biomed. Opt. 15, 0415101 (2010).

C. P. Fleming, H. Wang, K. J. Quan, and A. M. Rollins, J. Biomed. Opt. 15, 030516 (2010).
[CrossRef]

2008 (1)

2007 (2)

W. Rosamond, K. Flegal, G. Friday, K. Furie, A. Go, K. Greenlund, N. Haase, M. Ho, V. Howard, B. Kissela, S. Kittner, D. Lloyd-Jones, M. McDermott, J. Meigs, C. Moy, G. Nichol, C. J. O’Donnell, V. Roger, J. Rumsfeld, P. Sorlie, J. Steinberger, T. Thom, W.-S. Smoller, and Y. Hong, Circulation 115, e69 (2007).
[CrossRef]

M. Pircher, E. Gotzinger, B. Baumann, and C. K. Hitzenberger, J. Biomed. Opt. 12, 041210 (2007).
[CrossRef]

2006 (1)

2005 (1)

2002 (1)

1999 (1)

Amit, G.

Arruda, M.

C. P. Fleming, N. Rosenthal, A. M. Rollins, and M. Arruda, Innovations Card. Rhythm Manage. 2, 199 (2011).

H. Wang, W. Kang, T. Carrigan, A. Bishop, N. Rosenthal, M. Arruda, and A. M. Rollins, J. Biomed. Opt. 16, 110505 (2011).
[CrossRef]

Baumann, B.

Biedermann, B. R.

Bishop, A.

H. Wang, W. Kang, T. Carrigan, A. Bishop, N. Rosenthal, M. Arruda, and A. M. Rollins, J. Biomed. Opt. 16, 110505 (2011).
[CrossRef]

Bonesi, M.

Bouma, B. E.

Carrigan, T.

H. Wang, W. Kang, T. Carrigan, A. Bishop, N. Rosenthal, M. Arruda, and A. M. Rollins, J. Biomed. Opt. 16, 110505 (2011).
[CrossRef]

Cense, B.

Chen, T. C.

Choi, W.

D’Silva, A.

A. D’Silva and M. Wright, Radiol. Res. Pract. 2011, 714864 (2011).

de Boer, J. F.

Desjardins, A. E.

Duan, L.

Duker, J.

Eigenwillig, C.

Eigenwillig, C. M.

Fan, C.

Flegal, K.

W. Rosamond, K. Flegal, G. Friday, K. Furie, A. Go, K. Greenlund, N. Haase, M. Ho, V. Howard, B. Kissela, S. Kittner, D. Lloyd-Jones, M. McDermott, J. Meigs, C. Moy, G. Nichol, C. J. O’Donnell, V. Roger, J. Rumsfeld, P. Sorlie, J. Steinberger, T. Thom, W.-S. Smoller, and Y. Hong, Circulation 115, e69 (2007).
[CrossRef]

Fleming, C. P.

C. P. Fleming, N. Rosenthal, A. M. Rollins, and M. Arruda, Innovations Card. Rhythm Manage. 2, 199 (2011).

C. P. Fleming, K. J. Quan, and A. M. Rollins, J. Biomed. Opt. 15, 0415101 (2010).

C. P. Fleming, H. Wang, K. J. Quan, and A. M. Rollins, J. Biomed. Opt. 15, 030516 (2010).
[CrossRef]

C. P. Fleming, K. J. Quan, H. Wang, G. Amit, and A. M. Rollins, Opt. Express 18, 3079 (2010).
[CrossRef]

Friday, G.

W. Rosamond, K. Flegal, G. Friday, K. Furie, A. Go, K. Greenlund, N. Haase, M. Ho, V. Howard, B. Kissela, S. Kittner, D. Lloyd-Jones, M. McDermott, J. Meigs, C. Moy, G. Nichol, C. J. O’Donnell, V. Roger, J. Rumsfeld, P. Sorlie, J. Steinberger, T. Thom, W.-S. Smoller, and Y. Hong, Circulation 115, e69 (2007).
[CrossRef]

Fujimoto, J. G.

Furie, K.

W. Rosamond, K. Flegal, G. Friday, K. Furie, A. Go, K. Greenlund, N. Haase, M. Ho, V. Howard, B. Kissela, S. Kittner, D. Lloyd-Jones, M. McDermott, J. Meigs, C. Moy, G. Nichol, C. J. O’Donnell, V. Roger, J. Rumsfeld, P. Sorlie, J. Steinberger, T. Thom, W.-S. Smoller, and Y. Hong, Circulation 115, e69 (2007).
[CrossRef]

Go, A.

W. Rosamond, K. Flegal, G. Friday, K. Furie, A. Go, K. Greenlund, N. Haase, M. Ho, V. Howard, B. Kissela, S. Kittner, D. Lloyd-Jones, M. McDermott, J. Meigs, C. Moy, G. Nichol, C. J. O’Donnell, V. Roger, J. Rumsfeld, P. Sorlie, J. Steinberger, T. Thom, W.-S. Smoller, and Y. Hong, Circulation 115, e69 (2007).
[CrossRef]

Gotzinger, E.

Greenlund, K.

W. Rosamond, K. Flegal, G. Friday, K. Furie, A. Go, K. Greenlund, N. Haase, M. Ho, V. Howard, B. Kissela, S. Kittner, D. Lloyd-Jones, M. McDermott, J. Meigs, C. Moy, G. Nichol, C. J. O’Donnell, V. Roger, J. Rumsfeld, P. Sorlie, J. Steinberger, T. Thom, W.-S. Smoller, and Y. Hong, Circulation 115, e69 (2007).
[CrossRef]

Haase, N.

W. Rosamond, K. Flegal, G. Friday, K. Furie, A. Go, K. Greenlund, N. Haase, M. Ho, V. Howard, B. Kissela, S. Kittner, D. Lloyd-Jones, M. McDermott, J. Meigs, C. Moy, G. Nichol, C. J. O’Donnell, V. Roger, J. Rumsfeld, P. Sorlie, J. Steinberger, T. Thom, W.-S. Smoller, and Y. Hong, Circulation 115, e69 (2007).
[CrossRef]

Hitzenberger, C. K.

M. Pircher, E. Gotzinger, B. Baumann, and C. K. Hitzenberger, J. Biomed. Opt. 12, 041210 (2007).
[CrossRef]

Hitzenberger, K.

Ho, M.

W. Rosamond, K. Flegal, G. Friday, K. Furie, A. Go, K. Greenlund, N. Haase, M. Ho, V. Howard, B. Kissela, S. Kittner, D. Lloyd-Jones, M. McDermott, J. Meigs, C. Moy, G. Nichol, C. J. O’Donnell, V. Roger, J. Rumsfeld, P. Sorlie, J. Steinberger, T. Thom, W.-S. Smoller, and Y. Hong, Circulation 115, e69 (2007).
[CrossRef]

Hong, Y.

M. J. Ju, Y. Hong, S. Makita, Y. Lim, K. Kurokawa, L. Duan, M. Miura, S. Tang, and Y. Yasuno, Opt. Express 21, 19412 (2013).
[CrossRef]

W. Rosamond, K. Flegal, G. Friday, K. Furie, A. Go, K. Greenlund, N. Haase, M. Ho, V. Howard, B. Kissela, S. Kittner, D. Lloyd-Jones, M. McDermott, J. Meigs, C. Moy, G. Nichol, C. J. O’Donnell, V. Roger, J. Rumsfeld, P. Sorlie, J. Steinberger, T. Thom, W.-S. Smoller, and Y. Hong, Circulation 115, e69 (2007).
[CrossRef]

Howard, V.

W. Rosamond, K. Flegal, G. Friday, K. Furie, A. Go, K. Greenlund, N. Haase, M. Ho, V. Howard, B. Kissela, S. Kittner, D. Lloyd-Jones, M. McDermott, J. Meigs, C. Moy, G. Nichol, C. J. O’Donnell, V. Roger, J. Rumsfeld, P. Sorlie, J. Steinberger, T. Thom, W.-S. Smoller, and Y. Hong, Circulation 115, e69 (2007).
[CrossRef]

Huang, D.

Huber, R.

Izatt, J. A.

Ju, M. J.

Kang, W.

H. Wang, W. Kang, T. Carrigan, A. Bishop, N. Rosenthal, M. Arruda, and A. M. Rollins, J. Biomed. Opt. 16, 110505 (2011).
[CrossRef]

Kissela, B.

W. Rosamond, K. Flegal, G. Friday, K. Furie, A. Go, K. Greenlund, N. Haase, M. Ho, V. Howard, B. Kissela, S. Kittner, D. Lloyd-Jones, M. McDermott, J. Meigs, C. Moy, G. Nichol, C. J. O’Donnell, V. Roger, J. Rumsfeld, P. Sorlie, J. Steinberger, T. Thom, W.-S. Smoller, and Y. Hong, Circulation 115, e69 (2007).
[CrossRef]

Kittner, S.

W. Rosamond, K. Flegal, G. Friday, K. Furie, A. Go, K. Greenlund, N. Haase, M. Ho, V. Howard, B. Kissela, S. Kittner, D. Lloyd-Jones, M. McDermott, J. Meigs, C. Moy, G. Nichol, C. J. O’Donnell, V. Roger, J. Rumsfeld, P. Sorlie, J. Steinberger, T. Thom, W.-S. Smoller, and Y. Hong, Circulation 115, e69 (2007).
[CrossRef]

Kurokawa, K.

Lim, Y.

Lloyd-Jones, D.

W. Rosamond, K. Flegal, G. Friday, K. Furie, A. Go, K. Greenlund, N. Haase, M. Ho, V. Howard, B. Kissela, S. Kittner, D. Lloyd-Jones, M. McDermott, J. Meigs, C. Moy, G. Nichol, C. J. O’Donnell, V. Roger, J. Rumsfeld, P. Sorlie, J. Steinberger, T. Thom, W.-S. Smoller, and Y. Hong, Circulation 115, e69 (2007).
[CrossRef]

Makita, S.

McDermott, M.

W. Rosamond, K. Flegal, G. Friday, K. Furie, A. Go, K. Greenlund, N. Haase, M. Ho, V. Howard, B. Kissela, S. Kittner, D. Lloyd-Jones, M. McDermott, J. Meigs, C. Moy, G. Nichol, C. J. O’Donnell, V. Roger, J. Rumsfeld, P. Sorlie, J. Steinberger, T. Thom, W.-S. Smoller, and Y. Hong, Circulation 115, e69 (2007).
[CrossRef]

Meigs, J.

W. Rosamond, K. Flegal, G. Friday, K. Furie, A. Go, K. Greenlund, N. Haase, M. Ho, V. Howard, B. Kissela, S. Kittner, D. Lloyd-Jones, M. McDermott, J. Meigs, C. Moy, G. Nichol, C. J. O’Donnell, V. Roger, J. Rumsfeld, P. Sorlie, J. Steinberger, T. Thom, W.-S. Smoller, and Y. Hong, Circulation 115, e69 (2007).
[CrossRef]

Miura, M.

Moy, C.

W. Rosamond, K. Flegal, G. Friday, K. Furie, A. Go, K. Greenlund, N. Haase, M. Ho, V. Howard, B. Kissela, S. Kittner, D. Lloyd-Jones, M. McDermott, J. Meigs, C. Moy, G. Nichol, C. J. O’Donnell, V. Roger, J. Rumsfeld, P. Sorlie, J. Steinberger, T. Thom, W.-S. Smoller, and Y. Hong, Circulation 115, e69 (2007).
[CrossRef]

Nadkarni, S.

Nassif, N. A.

Nichol, G.

W. Rosamond, K. Flegal, G. Friday, K. Furie, A. Go, K. Greenlund, N. Haase, M. Ho, V. Howard, B. Kissela, S. Kittner, D. Lloyd-Jones, M. McDermott, J. Meigs, C. Moy, G. Nichol, C. J. O’Donnell, V. Roger, J. Rumsfeld, P. Sorlie, J. Steinberger, T. Thom, W.-S. Smoller, and Y. Hong, Circulation 115, e69 (2007).
[CrossRef]

O’Donnell, C. J.

W. Rosamond, K. Flegal, G. Friday, K. Furie, A. Go, K. Greenlund, N. Haase, M. Ho, V. Howard, B. Kissela, S. Kittner, D. Lloyd-Jones, M. McDermott, J. Meigs, C. Moy, G. Nichol, C. J. O’Donnell, V. Roger, J. Rumsfeld, P. Sorlie, J. Steinberger, T. Thom, W.-S. Smoller, and Y. Hong, Circulation 115, e69 (2007).
[CrossRef]

Oh, W.

Oh, W. Y.

Palte, G.

Park, B. H.

Pfeiffer, T.

Pierce, M. C.

Piercher, M.

Pircher, M.

M. Pircher, E. Gotzinger, B. Baumann, and C. K. Hitzenberger, J. Biomed. Opt. 12, 041210 (2007).
[CrossRef]

Potsaid, B.

Quan, K. J.

C. P. Fleming, K. J. Quan, H. Wang, G. Amit, and A. M. Rollins, Opt. Express 18, 3079 (2010).
[CrossRef]

C. P. Fleming, K. J. Quan, and A. M. Rollins, J. Biomed. Opt. 15, 0415101 (2010).

C. P. Fleming, H. Wang, K. J. Quan, and A. M. Rollins, J. Biomed. Opt. 15, 030516 (2010).
[CrossRef]

Roger, V.

W. Rosamond, K. Flegal, G. Friday, K. Furie, A. Go, K. Greenlund, N. Haase, M. Ho, V. Howard, B. Kissela, S. Kittner, D. Lloyd-Jones, M. McDermott, J. Meigs, C. Moy, G. Nichol, C. J. O’Donnell, V. Roger, J. Rumsfeld, P. Sorlie, J. Steinberger, T. Thom, W.-S. Smoller, and Y. Hong, Circulation 115, e69 (2007).
[CrossRef]

Rollins, A. M.

H. Wang, W. Kang, T. Carrigan, A. Bishop, N. Rosenthal, M. Arruda, and A. M. Rollins, J. Biomed. Opt. 16, 110505 (2011).
[CrossRef]

C. P. Fleming, N. Rosenthal, A. M. Rollins, and M. Arruda, Innovations Card. Rhythm Manage. 2, 199 (2011).

C. P. Fleming, H. Wang, K. J. Quan, and A. M. Rollins, J. Biomed. Opt. 15, 030516 (2010).
[CrossRef]

C. P. Fleming, K. J. Quan, and A. M. Rollins, J. Biomed. Opt. 15, 0415101 (2010).

C. P. Fleming, K. J. Quan, H. Wang, G. Amit, and A. M. Rollins, Opt. Express 18, 3079 (2010).
[CrossRef]

A. M. Rollins and J. A. Izatt, Opt. Lett. 24, 1484 (1999).
[CrossRef]

Rosamond, W.

W. Rosamond, K. Flegal, G. Friday, K. Furie, A. Go, K. Greenlund, N. Haase, M. Ho, V. Howard, B. Kissela, S. Kittner, D. Lloyd-Jones, M. McDermott, J. Meigs, C. Moy, G. Nichol, C. J. O’Donnell, V. Roger, J. Rumsfeld, P. Sorlie, J. Steinberger, T. Thom, W.-S. Smoller, and Y. Hong, Circulation 115, e69 (2007).
[CrossRef]

Rosenthal, N.

C. P. Fleming, N. Rosenthal, A. M. Rollins, and M. Arruda, Innovations Card. Rhythm Manage. 2, 199 (2011).

H. Wang, W. Kang, T. Carrigan, A. Bishop, N. Rosenthal, M. Arruda, and A. M. Rollins, J. Biomed. Opt. 16, 110505 (2011).
[CrossRef]

Rumsfeld, J.

W. Rosamond, K. Flegal, G. Friday, K. Furie, A. Go, K. Greenlund, N. Haase, M. Ho, V. Howard, B. Kissela, S. Kittner, D. Lloyd-Jones, M. McDermott, J. Meigs, C. Moy, G. Nichol, C. J. O’Donnell, V. Roger, J. Rumsfeld, P. Sorlie, J. Steinberger, T. Thom, W.-S. Smoller, and Y. Hong, Circulation 115, e69 (2007).
[CrossRef]

Sattmann, H.

Shishkov, M.

Smoller, W.-S.

W. Rosamond, K. Flegal, G. Friday, K. Furie, A. Go, K. Greenlund, N. Haase, M. Ho, V. Howard, B. Kissela, S. Kittner, D. Lloyd-Jones, M. McDermott, J. Meigs, C. Moy, G. Nichol, C. J. O’Donnell, V. Roger, J. Rumsfeld, P. Sorlie, J. Steinberger, T. Thom, W.-S. Smoller, and Y. Hong, Circulation 115, e69 (2007).
[CrossRef]

Sorlie, P.

W. Rosamond, K. Flegal, G. Friday, K. Furie, A. Go, K. Greenlund, N. Haase, M. Ho, V. Howard, B. Kissela, S. Kittner, D. Lloyd-Jones, M. McDermott, J. Meigs, C. Moy, G. Nichol, C. J. O’Donnell, V. Roger, J. Rumsfeld, P. Sorlie, J. Steinberger, T. Thom, W.-S. Smoller, and Y. Hong, Circulation 115, e69 (2007).
[CrossRef]

Steinberger, J.

W. Rosamond, K. Flegal, G. Friday, K. Furie, A. Go, K. Greenlund, N. Haase, M. Ho, V. Howard, B. Kissela, S. Kittner, D. Lloyd-Jones, M. McDermott, J. Meigs, C. Moy, G. Nichol, C. J. O’Donnell, V. Roger, J. Rumsfeld, P. Sorlie, J. Steinberger, T. Thom, W.-S. Smoller, and Y. Hong, Circulation 115, e69 (2007).
[CrossRef]

Tang, S.

Tearney, G. J.

Thom, T.

W. Rosamond, K. Flegal, G. Friday, K. Furie, A. Go, K. Greenlund, N. Haase, M. Ho, V. Howard, B. Kissela, S. Kittner, D. Lloyd-Jones, M. McDermott, J. Meigs, C. Moy, G. Nichol, C. J. O’Donnell, V. Roger, J. Rumsfeld, P. Sorlie, J. Steinberger, T. Thom, W.-S. Smoller, and Y. Hong, Circulation 115, e69 (2007).
[CrossRef]

Torzicky, T.

Vakoc, B. J.

Villiger, M.

Wang, H.

H. Wang, W. Kang, T. Carrigan, A. Bishop, N. Rosenthal, M. Arruda, and A. M. Rollins, J. Biomed. Opt. 16, 110505 (2011).
[CrossRef]

C. P. Fleming, K. J. Quan, H. Wang, G. Amit, and A. M. Rollins, Opt. Express 18, 3079 (2010).
[CrossRef]

C. P. Fleming, H. Wang, K. J. Quan, and A. M. Rollins, J. Biomed. Opt. 15, 030516 (2010).
[CrossRef]

Wieser, W.

Wojtkowskin, M.

Wright, M.

A. D’Silva and M. Wright, Radiol. Res. Pract. 2011, 714864 (2011).

Yao, G.

Yasuno, Y.

Yun, S. H.

Zhang, E. Z.

Zotter, S.

Biomed. Opt. Express (2)

Circulation (1)

W. Rosamond, K. Flegal, G. Friday, K. Furie, A. Go, K. Greenlund, N. Haase, M. Ho, V. Howard, B. Kissela, S. Kittner, D. Lloyd-Jones, M. McDermott, J. Meigs, C. Moy, G. Nichol, C. J. O’Donnell, V. Roger, J. Rumsfeld, P. Sorlie, J. Steinberger, T. Thom, W.-S. Smoller, and Y. Hong, Circulation 115, e69 (2007).
[CrossRef]

Innovations Card. Rhythm Manage. (1)

C. P. Fleming, N. Rosenthal, A. M. Rollins, and M. Arruda, Innovations Card. Rhythm Manage. 2, 199 (2011).

J. Biomed. Opt. (4)

H. Wang, W. Kang, T. Carrigan, A. Bishop, N. Rosenthal, M. Arruda, and A. M. Rollins, J. Biomed. Opt. 16, 110505 (2011).
[CrossRef]

C. P. Fleming, K. J. Quan, and A. M. Rollins, J. Biomed. Opt. 15, 0415101 (2010).

C. P. Fleming, H. Wang, K. J. Quan, and A. M. Rollins, J. Biomed. Opt. 15, 030516 (2010).
[CrossRef]

M. Pircher, E. Gotzinger, B. Baumann, and C. K. Hitzenberger, J. Biomed. Opt. 12, 041210 (2007).
[CrossRef]

Opt. Express (7)

Opt. Lett. (3)

Radiol. Res. Pract. (1)

A. D’Silva and M. Wright, Radiol. Res. Pract. 2011, 714864 (2011).

Other (1)

B. H. Park and J. F. de Boer, in Optical Coherence Tomography, W. Drexler and J. G. Fujimoto, eds. (Springer, 2008), p. 653.

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of the catheter PSOCT system. The system consists of a 58.5 kHz FDML laser, 2 SOAs to generate alternating laser sweeps with different polarization states, an unbalanced Mach–Zehnder OCT interferometer, a polarization-diversity detector unit, and a forward-view cone-scanning catheter (FDML, Fourier-domain mode-locked; SOA, semiconductor optical amplifier; PC, polarization controller; FC, fiber coupler; CIR, optical circulator; PS, fiber based polarizing beam splitter; RJ, rotary joint).

Fig. 2.
Fig. 2.

PSOCT images of the skin at the proximal interphalangeal joint of the human little finger using bench-top linear scanner. (a) combined intensity image. (b) Phase retardation image, with blue and red representing phase retardations of 0 and 90°, respectively. The images are the averages of five frames.

Fig. 3.
Fig. 3.

PSOCT forward-viewing probe. (a) Schematic diagram of the probe. (b) Beam profile of the probe at the focus point. (c) Image of the probe without the plastic sheath, glass window, and sapphire tube compared to a penny.

Fig. 4.
Fig. 4.

Single frame catheter PSOCT images. (a) and (b) are combined intensity and phase retardation images of a high birefringence plastic. (c) and (d) are single channel intensity and phase retardation images of a human finger.

Fig. 5.
Fig. 5.

Single frame catheter PSOCT images of left atrium wedges from swine heart. (a), (c), and (e) are intensity (two-channel), single channel, and phase retardance images before RFA. (b), (d), and (f) are intensity, single channel, and phase retardance images after RFA, taken at the edge of the RFA lesion such that the two sides are untreated and the middle is the treated area.

Equations (7)

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M(θ,φ)=[10000cos22θ+cosφsin22θ(1cosφ)sin2θcos2θsinφsin2θ0(1cosφ)sin2θcos2θsin22θ+cosφcos22θsinφcos2θ0sinφsin2θsinφcos2θcosφ].
S0=[1100]T,
S45=[1010]T.
Sout0=M((θ,φ))S0,Sout45=M((θ,φ))S45.
S1out0=(cos22θ+cosφsin22θ),
S2out0=S1out45=(1cosφ)sin2θcos2θ,
φ=acos(S3out021+S1out01),

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