Abstract

For phase-related imaging modalities using interferometric techniques, it is important to develop effective method to recover phase information that is mathematically wrapped. In this paper, we propose and demonstrate a two-dimensional (2D) method to achieve effective phase unwrapping in Doppler Fourier-domain (FD) optical coherence tomography (OCT), and recover the discontinuous phase distribution in retinal blood flow successfully for the first time in Doppler OCT studies. The proposed method is based on phase gradient approach in the axial dimension, with phase denoising performed through 2D window moving average in the sampled phase image using complex Doppler OCT data. The 2D unwrapping is carried out to correct phase discontinuities in the wrapped Doppler phase map, and the abrupt phase changes can be identified and corrected accurately. The proposed algorithm is computationally efficient and easy to be implemented.

© 2016 Optical Society of America

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2016 (2)

2014 (1)

2013 (1)

2012 (3)

2010 (1)

2009 (2)

2008 (5)

2007 (3)

2005 (2)

M. A. Choma, A. K. Ellerbee, C. Yang, T. L. Creazzo, and J. A. Izatt, “Spectral-domain phase microscopy,” Opt. Lett. 30(10), 1162–1164 (2005).
[Crossref] [PubMed]

Q. Kemao, S. H. Soon, and A. Asundi, “A simple phase unwrapping approach based on filtering by windowed Fourier transform,” Opt. Laser Technol. 37(6), 458–462 (2005).
[Crossref]

2004 (1)

2003 (4)

2002 (1)

C. Lopez-Martinez and X. Fàbregas, “Modeling and reduction of SAR interferometric phase noise in the wavelet domains,” IEEE Trans. Geosci. Remote Sens. 40(12), 2553–2566 (2002).
[Crossref]

2001 (1)

2000 (1)

1999 (1)

1998 (2)

M. R. Goldstein and C. L. Werner, “Radar interferogram filtering for geophysical applications,” Geophys. Res. Lett. 25(21), 4035–4038 (1998).
[Crossref]

J. S. Lee, K. P. Papathanassiou, T. L. Ainsworth, M. H. Grunes, and A. Reigber, “A new technique for noise filtering of SAR interferometric phase images,” IEEE Trans. Geosci. Remote Sens. 36(5), 1456–1465 (1998).
[Crossref]

1997 (5)

1995 (2)

1994 (1)

1991 (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

1989 (1)

1988 (1)

1987 (1)

1985 (1)

1982 (1)

1977 (1)

1944 (1)

O. W. Richards, “Phase Difference Microscopy,” Nature 154(3917), 672 (1944).
[Crossref]

Ainsworth, T. L.

J. S. Lee, K. P. Papathanassiou, T. L. Ainsworth, M. H. Grunes, and A. Reigber, “A new technique for noise filtering of SAR interferometric phase images,” IEEE Trans. Geosci. Remote Sens. 36(5), 1456–1465 (1998).
[Crossref]

Asundi, A.

Q. Kemao, S. H. Soon, and A. Asundi, “A simple phase unwrapping approach based on filtering by windowed Fourier transform,” Opt. Laser Technol. 37(6), 458–462 (2005).
[Crossref]

Badizadegan, K.

Bajraszewski, T.

Barbastathis, G.

Barton, J. K.

Baumann, B.

Bernabeu, E.

Bevilacqua, F.

Boppart, S. A.

Bouma, B.

Bouma, B. E.

Bower, B. A.

Y. Wang, B. A. Bower, J. A. Izatt, O. Tan, and D. Huang, “In vivo total retinal blood flow measurement by Fourier domain Doppler optical coherence tomography,” J. Biomed. Opt. 12(4), 041215 (2007).
[Crossref] [PubMed]

Brezinski, M. E.

Brown, W. J.

Carruth, R. W.

Cense, B.

Chalut, K. J.

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Chen, T.

Chen, Z.

Cheng, K. H. Y.

Choma, M. A.

Courtney, B.

Creath, K.

Creazzo, T. L.

Cuche, E.

Darga, D.

Dasari, R. R.

Dave, D.

Davis, A. M.

de Boer, J.

de Boer, J. F.

Deflores, L. P.

Depeursinge, C.

Drexler, W.

Ellerbee, A. K.

Fàbregas, X.

C. Lopez-Martinez and X. Fàbregas, “Modeling and reduction of SAR interferometric phase noise in the wavelet domains,” IEEE Trans. Geosci. Remote Sens. 40(12), 2553–2566 (2002).
[Crossref]

Fabritius, T.

Fard, A. M.

Feld, M. S.

Fercher, A.

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Fried, D. L.

Fujimoto, J. G.

Gao, W.

Gardecki, J. A.

Ghiglia, D. C.

Goldstein, M. R.

M. R. Goldstein and C. L. Werner, “Radar interferogram filtering for geophysical applications,” Geophys. Res. Lett. 25(21), 4035–4038 (1998).
[Crossref]

Gordon, M.

Gregori, G.

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Grulkowski, I.

Grunes, M. H.

J. S. Lee, K. P. Papathanassiou, T. L. Ainsworth, M. H. Grunes, and A. Reigber, “A new technique for noise filtering of SAR interferometric phase images,” IEEE Trans. Geosci. Remote Sens. 36(5), 1456–1465 (1998).
[Crossref]

Hahn, M. S.

Haindl, R.

Hamidi, E.

Hee, M. R.

B. Bouma, M. E. Brezinski, J. G. Fujimoto, G. J. Tearney, S. A. Boppart, and M. R. Hee, “High-resolution optical coherence tomographic imaging using a mode-locked Ti:Al2O3 laser source,” Opt. Lett. 20(13), 1486–1488 (1995).
[Crossref] [PubMed]

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, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Hendargo, H. C.

Heshmat, S.

Hitzenberger, C. K.

Huang, D.

Y. Wang, B. A. Bower, J. A. Izatt, O. Tan, and D. Huang, “In vivo total retinal blood flow measurement by Fourier domain Doppler optical coherence tomography,” J. Biomed. Opt. 12(4), 041215 (2007).
[Crossref] [PubMed]

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, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Huang, H. Y. H.

Itoh, K.

Iwai, H.

Izatt, J. A.

Jiao, S.

Kemao, Q.

Q. Kemao, W. Gao, and H. Wang, “Windowed Fourier-filtered and quality-guided phase-unwrapping algorithm,” Appl. Opt. 47(29), 5420–5428 (2008).
[Crossref] [PubMed]

Q. Kemao, S. H. Soon, and A. Asundi, “A simple phase unwrapping approach based on filtering by windowed Fourier transform,” Opt. Laser Technol. 37(6), 458–462 (2005).
[Crossref]

Kowalczyk, A.

Kulkarni, M. D.

Lam, S.

Lane, P.

Lee, A. M. D.

Lee, J. S.

J. S. Lee, K. P. Papathanassiou, T. L. Ainsworth, M. H. Grunes, and A. Reigber, “A new technique for noise filtering of SAR interferometric phase images,” IEEE Trans. Geosci. Remote Sens. 36(5), 1456–1465 (1998).
[Crossref]

Lee, K. K. C.

Leitgeb, R.

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Liu, Y.

Lo, S.

Lopez-Martinez, C.

C. Lopez-Martinez and X. Fàbregas, “Modeling and reduction of SAR interferometric phase noise in the wavelet domains,” IEEE Trans. Geosci. Remote Sens. 40(12), 2553–2566 (2002).
[Crossref]

Luk, T. W. H.

Makita, S.

Mariampillai, A.

Marotta, T. R.

Mastin, G. A.

Milner, T. E.

Miyamoto, N.

Mok, A.

Nassif, N.

Nelson, J. S.

Nishiyama, S.

Nolte, F.

Papathanassiou, K. P.

J. S. Lee, K. P. Papathanassiou, T. L. Ainsworth, M. H. Grunes, and A. Reigber, “A new technique for noise filtering of SAR interferometric phase images,” IEEE Trans. Geosci. Remote Sens. 36(5), 1456–1465 (1998).
[Crossref]

Park, B.

Pekar, J.

Pierce, M.

Pircher, M.

Pitris, C.

Popescu, G.

Puliafito, C. A.

H. Wehbe, M. Ruggeri, S. Jiao, G. Gregori, C. A. Puliafito, and W. Zhao, “Automatic retinal blood flow calculation using spectral domain optical coherence tomography,” Opt. Express 15(23), 15193–15206 (2007).
[Crossref] [PubMed]

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, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Qi, B.

Quiroga, J. A.

Reigber, A.

J. S. Lee, K. P. Papathanassiou, T. L. Ainsworth, M. H. Grunes, and A. Reigber, “A new technique for noise filtering of SAR interferometric phase images,” IEEE Trans. Geosci. Remote Sens. 36(5), 1456–1465 (1998).
[Crossref]

Richards, O. W.

O. W. Richards, “Phase Difference Microscopy,” Nature 154(3917), 672 (1944).
[Crossref]

Romero, L. A.

Rosowsky, J. J.

Ruggeri, M.

Saxer, C.

Schmetterer, L.

Schofield, M. A.

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Scott Carney, P.

Seng-Yue, E.

Shen, Q.

Shepherd, N.

Smid, J.

Soon, S. H.

Q. Kemao, S. H. Soon, and A. Asundi, “A simple phase unwrapping approach based on filtering by windowed Fourier transform,” Opt. Laser Technol. 37(6), 458–462 (2005).
[Crossref]

Standish, B. A.

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Sun, C.

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Szkulmowska, A.

Szkulmowski, M.

Szlag, D.

Takahashi, T.

Takajo, H.

Tan, O.

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Appl. Opt. (6)

Biomed. Opt. Express (2)

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IEEE Trans. Geosci. Remote Sens. (2)

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Y. Wang, B. A. Bower, J. A. Izatt, O. Tan, and D. Huang, “In vivo total retinal blood flow measurement by Fourier domain Doppler optical coherence tomography,” J. Biomed. Opt. 12(4), 041215 (2007).
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M. Szkulmowski, I. Grulkowski, D. Szlag, A. Szkulmowska, A. Kowalczyk, and M. Wojtkowski, “Flow velocity estimation by complex ambiguity free joint Spectral and Time domain Optical Coherence Tomography,” Opt. Express 17(16), 14281–14297 (2009).
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B. Vuong, A. M. D. Lee, T. W. H. Luk, C. Sun, S. Lam, P. Lane, and V. X. D. Yang, “High speed, wide velocity dynamic range Doppler optical coherence tomography (Part IV): split spectrum processing in rotary catheter probes,” Opt. Express 22(7), 7399–7415 (2014).
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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(25), 3490–3497 (2003).
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A. M. Fard, P. Vacas-Jacques, E. Hamidi, H. Wang, R. W. Carruth, J. A. Gardecki, and G. J. Tearney, “Optical coherence tomography - near infrared spectroscopy system and catheter for intravascular imaging,” Opt. Express 21(25), 30849–30858 (2013).
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H. Y. H. Huang, L. Tian, Z. Zhang, Y. Liu, Z. Chen, and G. Barbastathis, “Path-independent phase unwrapping using phase gradient and total-variation (TV) denoising,” Opt. Express 20(13), 14075–14089 (2012).
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H. C. Hendargo, M. Zhao, N. Shepherd, and J. A. Izatt, “Synthetic wavelength based phase unwrapping in spectral domain optical coherence tomography,” Opt. Express 17(7), 5039–5051 (2009).
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V. X. D. Yang, M. Gordon, E. Seng-Yue, S. Lo, B. Qi, J. Pekar, A. Mok, B. Wilson, and I. Vitkin, “High speed, wide velocity dynamic range Doppler optical coherence tomography (Part II): Imaging in vivo cardiac dynamics of Xenopus laevis,” Opt. Express 11(14), 1650–1658 (2003).
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Y. K. Tao, A. M. Davis, and J. A. Izatt, “Single-pass volumetric bidirectional blood flow imaging spectral domain optical coherence tomography using a modified Hilbert transform,” Opt. Express 16(16), 12350–12361 (2008).
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Opt. Laser Technol. (1)

Q. Kemao, S. H. Soon, and A. Asundi, “A simple phase unwrapping approach based on filtering by windowed Fourier transform,” Opt. Laser Technol. 37(6), 458–462 (2005).
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Science (1)

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Figures (14)

Fig. 1
Fig. 1 (a) Retina structure image; (b) Doppler OCT phase image; (c) Phase difference Δφ of the adjacent two pixels for the data between points P1 and Pn in image (b); (d) Plot of Doppler FD-OCT complex data in a complex plane.
Fig. 2
Fig. 2 Effect of noise B on phase unwrapping; (a) B in the region COA; (b) B in the region AOC’; (C) B in the region A’OC; (d) B in the region C’OA’.
Fig. 3
Fig. 3 Doppler OCT phase profile before and after unwrapping.
Fig. 4
Fig. 4 Column a: Original Doppler phase φ of three vessels; Column b: Phase unwrapping result without noise filtering; Column c: Wrapped phase map after window smoothing; column d: Unwrapped phase result after noise filtering.
Fig. 5
Fig. 5 (a) Wrapped (circular symbols) and recovered (triangle symbols) phase for the A-line Lrn1; (b) Doppler phase difference before and after window smoothing; (c) Noise point Pr in a complex plane; (d) Recovered Doppler phase with (triangle symbols) and without (circular symbols) noise filtering.
Fig. 6
Fig. 6 (a) Unwrapped Doppler OCT phase map using PTM algorithm; (b) Recovered Doppler phase profile with PTM method(triangle symbols) and complex averaging algorithm (square symbols).
Fig. 7
Fig. 7 (a) Sampled Doppler OCT phase image; (b) Restored phase image by means of 3x3 window smoothing.
Fig. 8
Fig. 8 (a) Four A-lines distribute laterally; (b) Phase unwrapping result for the A-line Lright. Black dot: Phase result unwrapped axially; White circle: Phase result unwrapped laterally.
Fig. 9
Fig. 9 Lateral phase unwrapping result for A-line L3.
Fig. 10
Fig. 10 Determination of true phase values for A-line L3.
Fig. 11
Fig. 11 (a) Corrected phase result for the A-line L2; (b) Corrected phase result for the A-line L1; (c) Searching failed points for the A-line L4; (d) Corrected phase result for the A-line L4.
Fig. 12
Fig. 12 (a) Doppler OCT phase map after 2D unwrapping; (b) 3D phase distribution at the area marked as a dashed window in (a); Unit for the grey scale bar: radian.
Fig. 13
Fig. 13 Flow chart of the proposed algorithm.
Fig. 14
Fig. 14 (a) Retina structure image; (b) Doppler OCT image; (c) Unwrapped phase with discontinuous points; (d) Recovered phase image after the correction of discontinuous points.

Equations (3)

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φ(z)= tan 1 [ Im( j=1 N F j ( z )· F j+1 ( z ) ) Re( j=1 N F j ( z )· F j+1 ( z ) ) ].
ψ 1 = φ 1 ψ m = ψ m1 +Δ φ m,m1 Δ φ m,m1 = tan 1 [ Im( f m f m1 )/Re( f m f m1 ) ]. m=2U
Re( f( x,m ) ) ¯ = 1 9 q=1 1 p=1 1 Re( f( x+p,m+q ) ) Im( f( x,m ) ) ¯ = 1 9 q=1 1 p=1 1 Im( f( x+p,m+q ) ) .

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