Abstract

In this manuscript, a two-dimensional (2D) micro-electro-mechanical system (MEMS)-based, high-speed beam-shifting spectral domain optical coherence tomography (MHB-SDOCT) is proposed for speckle noise reduction and absolute flow rate measurement. By combining a zigzag scanning protocol, the frame rates of 45.2 Hz for speckle reduction and 25.6 Hz for flow rate measurement are achieved for in-vivo tissue imaging. Phantom experimental results have shown that by setting the incident beam angle to ϕ = 4.76° (between optical axis of objective lens and beam axis) and rotating the beam about the optical axis in 17 discrete angular positions, 91% of speckle noise in the structural images can be reduced. Furthermore, a precision of 0.0032 µl/s is achieved for flow rate measurement with the same beam angle, using three discrete angular positions around the optical axis. In-vivo experiments on human skin and chicken embryo were also implemented to further verify the performance of speckle noise reduction and flow rate measurement of MHB-SDOCT.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (1)

2018 (4)

2017 (3)

S. Xia, Y. Huang, S. Peng, Y. Wu, and X. Tan, “Robust phase unwrapping for phase images in Fourier domain Doppler optical coherence tomography,” J. Biomed. Opt. 22(3), 36014 (2017).
[Crossref] [PubMed]

O. Liba, M. D. Lew, E. D. SoRelle, R. Dutta, D. Sen, D. M. Moshfeghi, S. Chu, and A. de la Zerda, “Speckle-modulating optical coherence tomography in living mice and humans,” Nat. Commun. 8, 15845 (2017).
[Crossref] [PubMed]

D. Cui, E. Bo, Y. Luo, X. Liu, X. Wang, S. Chen, X. Yu, S. Chen, P. Shum, and L. Liu, “Multifiber angular compounding optical coherence tomography for speckle reduction,” Opt. Lett. 42(1), 125–128 (2017).
[Crossref] [PubMed]

2016 (2)

2013 (1)

M. R. N. Avanaki, R. Cernat, P. J. Tadrous, T. Tatla, A. G. Podoleanu, and S. A. Hojjatoleslami, “Spatial Compounding Algorithm for Speckle Reduction of Dynamic Focus OCT Images,” IEEE Photonics Technol. Lett. 25(15), 1439–1442 (2013).
[Crossref]

2012 (1)

2011 (1)

2010 (3)

2008 (1)

2007 (4)

2006 (1)

2004 (1)

2003 (3)

V. Yang, M. Gordon, B. Qi, J. Pekar, S. Lo, E. Seng-Yue, A. Mok, B. Wilson, and I. Vitkin, “High speed, wide velocity dynamic range Doppler optical coherence tomography (Part I): System design, signal processing, and performance,” Opt. Express 11(7), 794–809 (2003).
[Crossref] [PubMed]

N. Iftimia, B. E. Bouma, and G. J. Tearney, “Speckle reduction in optical coherence tomography by “path length encoded” angular compounding,” J. Biomed. Opt. 8(2), 260–263 (2003).
[Crossref] [PubMed]

M. Pircher, E. Gotzinger, R. Leitgeb, A. F. Fercher, and C. K. Hitzenberger, “Speckle reduction in optical coherence tomography by frequency compounding,” J. Biomed. Opt. 8(3), 565–569 (2003).
[Crossref] [PubMed]

2000 (3)

1999 (1)

J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4(1), 95–105 (1999).
[Crossref] [PubMed]

1997 (3)

1991 (1)

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

Adler, D. C.

Avanaki, M. R. N.

M. R. N. Avanaki, R. Cernat, P. J. Tadrous, T. Tatla, A. G. Podoleanu, and S. A. Hojjatoleslami, “Spatial Compounding Algorithm for Speckle Reduction of Dynamic Focus OCT Images,” IEEE Photonics Technol. Lett. 25(15), 1439–1442 (2013).
[Crossref]

Barton, J. K.

Bashkansky, M.

Baumann, B.

Beer, F.

A. Wartak, F. Beer, B. Baumann, M. Pircher, and C. K. Hitzenberger, “Adaptable switching schemes for time-encoded multichannel optical coherence tomography,” J. Biomed. Opt. 23(5), 1–12 (2018).
[Crossref] [PubMed]

Bilenca, A.

Bizheva, K.

Bo, E.

Bouma, B. E.

Brezinski, M. E.

J. Rogowska and M. E. Brezinski, “Evaluation of the adaptive speckle suppression filter for coronary optical coherence tomography imaging,” IEEE Trans. Med. Imaging 19(12), 1261–1266 (2000).
[Crossref] [PubMed]

Cable, A. E.

Cernat, R.

M. R. N. Avanaki, R. Cernat, P. J. Tadrous, T. Tatla, A. G. Podoleanu, and S. A. Hojjatoleslami, “Spatial Compounding Algorithm for Speckle Reduction of Dynamic Focus OCT Images,” IEEE Photonics Technol. Lett. 25(15), 1439–1442 (2013).
[Crossref]

Chang, W.

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

Chen, C.

Chen, S.

Chen, Z.

Chu, S.

O. Liba, M. D. Lew, E. D. SoRelle, R. Dutta, D. Sen, D. M. Moshfeghi, S. Chu, and A. de la Zerda, “Speckle-modulating optical coherence tomography in living mice and humans,” Nat. Commun. 8, 15845 (2017).
[Crossref] [PubMed]

Clausi, D. A.

Cui, D.

Curatolo, A.

de Boer, J. F.

de la Zerda, A.

O. Liba, M. D. Lew, E. D. SoRelle, R. Dutta, D. Sen, D. M. Moshfeghi, S. Chu, and A. de la Zerda, “Speckle-modulating optical coherence tomography in living mice and humans,” Nat. Commun. 8, 15845 (2017).
[Crossref] [PubMed]

Deorajh, R.

Desjardins, A. E.

Dragostinoff, N.

Duker, J. S.

Dutta, R.

O. Liba, M. D. Lew, E. D. SoRelle, R. Dutta, D. Sen, D. M. Moshfeghi, S. Chu, and A. de la Zerda, “Speckle-modulating optical coherence tomography in living mice and humans,” Nat. Commun. 8, 15845 (2017).
[Crossref] [PubMed]

Fercher, A. F.

M. Pircher, E. Gotzinger, R. Leitgeb, A. F. Fercher, and C. K. Hitzenberger, “Speckle reduction in optical coherence tomography by frequency compounding,” J. Biomed. Opt. 8(3), 565–569 (2003).
[Crossref] [PubMed]

Flotte, T.

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

Fujimoto, J. G.

Ge, X.

Gorczynska, I.

Gordon, M.

Gotzinger, E.

M. Pircher, E. Gotzinger, R. Leitgeb, A. F. Fercher, and C. K. Hitzenberger, “Speckle reduction in optical coherence tomography by frequency compounding,” J. Biomed. Opt. 8(3), 565–569 (2003).
[Crossref] [PubMed]

Götzinger, E.

Gregory, K.

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

Haindl, R.

Hee, M.

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

Hillman, T. R.

Hitzenberger, C. K.

Hojjatoleslami, S. A.

M. R. N. Avanaki, R. Cernat, P. J. Tadrous, T. Tatla, A. G. Podoleanu, and S. A. Hojjatoleslami, “Spatial Compounding Algorithm for Speckle Reduction of Dynamic Focus OCT Images,” IEEE Photonics Technol. Lett. 25(15), 1439–1442 (2013).
[Crossref]

Hornegger, J.

Huang, D.

Huang, Y.

S. Xia, Y. Huang, S. Peng, Y. Wu, and X. Tan, “Robust phase unwrapping for phase images in Fourier domain Doppler optical coherence tomography,” J. Biomed. Opt. 22(3), 36014 (2017).
[Crossref] [PubMed]

Iftimia, N.

N. Iftimia, B. E. Bouma, and G. J. Tearney, “Speckle reduction in optical coherence tomography by “path length encoded” angular compounding,” J. Biomed. Opt. 8(2), 260–263 (2003).
[Crossref] [PubMed]

Izatt, J.

Izatt, J. A.

Jian, Y.

Kennedy, B. F.

Ko, T. H.

Kowalczyk, A.

Kraus, M. F.

Kulkarni, M.

Kulkarni, M. D.

Leitgeb, R.

M. Pircher, E. Gotzinger, R. Leitgeb, A. F. Fercher, and C. K. Hitzenberger, “Speckle reduction in optical coherence tomography by frequency compounding,” J. Biomed. Opt. 8(3), 565–569 (2003).
[Crossref] [PubMed]

Leitgeb, R. A.

Lew, M. D.

O. Liba, M. D. Lew, E. D. SoRelle, R. Dutta, D. Sen, D. M. Moshfeghi, S. Chu, and A. de la Zerda, “Speckle-modulating optical coherence tomography in living mice and humans,” Nat. Commun. 8, 15845 (2017).
[Crossref] [PubMed]

Liba, O.

O. Liba, M. D. Lew, E. D. SoRelle, R. Dutta, D. Sen, D. M. Moshfeghi, S. Chu, and A. de la Zerda, “Speckle-modulating optical coherence tomography in living mice and humans,” Nat. Commun. 8, 15845 (2017).
[Crossref] [PubMed]

Lin, C.

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

Liu, A.

Liu, J. J.

Liu, L.

Liu, X.

Lo, S.

Luo, Y.

Ma, Z.

Malekafzali, A.

Manna, S. K.

Marques, A.

Meleppat, R. K.

Miller, E. B.

Milner, T. E.

Mishra, A.

Mo, J.

Mok, A.

Moshfeghi, D. M.

O. Liba, M. D. Lew, E. D. SoRelle, R. Dutta, D. Sen, D. M. Moshfeghi, S. Chu, and A. de la Zerda, “Speckle-modulating optical coherence tomography in living mice and humans,” Nat. Commun. 8, 15845 (2017).
[Crossref] [PubMed]

Motaghiannezam, S. M. R.

Nelson, J. S.

Nguyen, N.

Oh, W. Y.

Ozcan, A.

Pedersen, C. J.

Pekar, J.

Peng, S.

S. Xia, Y. Huang, S. Peng, Y. Wu, and X. Tan, “Robust phase unwrapping for phase images in Fourier domain Doppler optical coherence tomography,” J. Biomed. Opt. 22(3), 36014 (2017).
[Crossref] [PubMed]

Pircher, M.

Podoleanu, A. G.

M. R. N. Avanaki, R. Cernat, P. J. Tadrous, T. Tatla, A. G. Podoleanu, and S. A. Hojjatoleslami, “Spatial Compounding Algorithm for Speckle Reduction of Dynamic Focus OCT Images,” IEEE Photonics Technol. Lett. 25(15), 1439–1442 (2013).
[Crossref]

Potsaid, B.

Pugh, E. N.

Puliafito, C.

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

Puvanathasan, P.

Qi, B.

Ramjist, J.

Reintjes, J.

Reyes, R.

Rogowska, J.

J. Rogowska and M. E. Brezinski, “Evaluation of the adaptive speckle suppression filter for coronary optical coherence tomography imaging,” IEEE Trans. Med. Imaging 19(12), 1261–1266 (2000).
[Crossref] [PubMed]

Rollins, A. M.

Rugonyi, S.

Sampson, D. D.

Sarunic, M. V.

Saxer, C.

Schmetterer, L.

Schmitt, J. M.

J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4(1), 95–105 (1999).
[Crossref] [PubMed]

Schuman, J.

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

Sen, D.

O. Liba, M. D. Lew, E. D. SoRelle, R. Dutta, D. Sen, D. M. Moshfeghi, S. Chu, and A. de la Zerda, “Speckle-modulating optical coherence tomography in living mice and humans,” Nat. Commun. 8, 15845 (2017).
[Crossref] [PubMed]

Seng-Yue, E.

Shi, W.

Shum, P.

Shure, M. A.

SoRelle, E. D.

O. Liba, M. D. Lew, E. D. SoRelle, R. Dutta, D. Sen, D. M. Moshfeghi, S. Chu, and A. de la Zerda, “Speckle-modulating optical coherence tomography in living mice and humans,” Nat. Commun. 8, 15845 (2017).
[Crossref] [PubMed]

Srinivas, S.

Stinson, W.

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

Swanson, E.

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

Sylwestrzak, M.

Szkulmowski, M.

Szlag, D.

Tadrous, P. J.

M. R. N. Avanaki, R. Cernat, P. J. Tadrous, T. Tatla, A. G. Podoleanu, and S. A. Hojjatoleslami, “Spatial Compounding Algorithm for Speckle Reduction of Dynamic Focus OCT Images,” IEEE Photonics Technol. Lett. 25(15), 1439–1442 (2013).
[Crossref]

Tan, X.

S. Xia, Y. Huang, S. Peng, Y. Wu, and X. Tan, “Robust phase unwrapping for phase images in Fourier domain Doppler optical coherence tomography,” J. Biomed. Opt. 22(3), 36014 (2017).
[Crossref] [PubMed]

Tatla, T.

M. R. N. Avanaki, R. Cernat, P. J. Tadrous, T. Tatla, A. G. Podoleanu, and S. A. Hojjatoleslami, “Spatial Compounding Algorithm for Speckle Reduction of Dynamic Focus OCT Images,” IEEE Photonics Technol. Lett. 25(15), 1439–1442 (2013).
[Crossref]

Tearney, G. J.

Thornburg, K.

Trasischker, W.

Troyer, A.

Vakoc, B. J.

van Gemert, M. J. C.

Vitkin, I.

Wang, R. K.

Wang, X.

Wartak, A.

Welch, A. J.

Werkmeister, R. M.

Wilson, B.

Wojtkowski, M.

Wong, A.

Wu, Y.

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Xia, S.

S. Xia, Y. Huang, S. Peng, Y. Wu, and X. Tan, “Robust phase unwrapping for phase images in Fourier domain Doppler optical coherence tomography,” J. Biomed. Opt. 22(3), 36014 (2017).
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Xiang, S.

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J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4(1), 95–105 (1999).
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Yang, V.

Yang, V. X. D.

Yazdanfar, S.

Yin, X.

Yu, X.

Yung, K. M.

J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4(1), 95–105 (1999).
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Zawadzki, R. J.

Zhang, P.

Zhao, Y.

Appl. Opt. (1)

Biomed. Opt. Express (6)

R. Haindl, W. Trasischker, A. Wartak, B. Baumann, M. Pircher, and C. K. Hitzenberger, “Total retinal blood flow measurement by three beam Doppler optical coherence tomography,” Biomed. Opt. Express 7(2), 287–301 (2016).
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A. Wartak, R. Haindl, W. Trasischker, B. Baumann, M. Pircher, and C. K. Hitzenberger, “Active-passive path-length encoded (APPLE) Doppler OCT,” Biomed. Opt. Express 7(12), 5233–5251 (2016).
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Z. Ma, A. Liu, X. Yin, A. Troyer, K. Thornburg, R. K. Wang, and S. Rugonyi, “Measurement of absolute blood flow velocity in outflow tract of HH18 chicken embryo based on 4D reconstruction using spectral domain optical coherence tomography,” Biomed. Opt. Express 1(3), 798–811 (2010).
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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(6), 1539–1552 (2011).
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C. Chen, W. Shi, R. Reyes, and V. X. D. Yang, “Buffer-averaging super-continuum source based spectral domain optical coherence tomography for high speed imaging,” Biomed. Opt. Express 9(12), 6529–6544 (2018).
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P. Zhang, S. K. Manna, E. B. Miller, Y. Jian, R. K. Meleppat, M. V. Sarunic, E. N. Pugh, and R. J. Zawadzki, “Aperture phase modulation with adaptive optics: a novel approach for speckle reduction and structure extraction in optical coherence tomography,” Biomed. Opt. Express 10(2), 552–570 (2019).
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IEEE Photonics Technol. Lett. (1)

M. R. N. Avanaki, R. Cernat, P. J. Tadrous, T. Tatla, A. G. Podoleanu, and S. A. Hojjatoleslami, “Spatial Compounding Algorithm for Speckle Reduction of Dynamic Focus OCT Images,” IEEE Photonics Technol. Lett. 25(15), 1439–1442 (2013).
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IEEE Trans. Med. Imaging (1)

J. Rogowska and M. E. Brezinski, “Evaluation of the adaptive speckle suppression filter for coronary optical coherence tomography imaging,” IEEE Trans. Med. Imaging 19(12), 1261–1266 (2000).
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J. Biomed. Opt. (5)

J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4(1), 95–105 (1999).
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M. Pircher, E. Gotzinger, R. Leitgeb, A. F. Fercher, and C. K. Hitzenberger, “Speckle reduction in optical coherence tomography by frequency compounding,” J. Biomed. Opt. 8(3), 565–569 (2003).
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N. Iftimia, B. E. Bouma, and G. J. Tearney, “Speckle reduction in optical coherence tomography by “path length encoded” angular compounding,” J. Biomed. Opt. 8(2), 260–263 (2003).
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S. Xia, Y. Huang, S. Peng, Y. Wu, and X. Tan, “Robust phase unwrapping for phase images in Fourier domain Doppler optical coherence tomography,” J. Biomed. Opt. 22(3), 36014 (2017).
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A. Wartak, F. Beer, B. Baumann, M. Pircher, and C. K. Hitzenberger, “Adaptable switching schemes for time-encoded multichannel optical coherence tomography,” J. Biomed. Opt. 23(5), 1–12 (2018).
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J. Opt. Soc. Am. A (1)

Nat. Commun. (1)

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Opt. Express (7)

A. E. Desjardins, B. J. Vakoc, G. J. Tearney, and B. E. Bouma, “Speckle reduction in OCT using massively-parallel detection and frequency-domain ranging,” Opt. Express 14(11), 4736–4745 (2006).
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Opt. Lett. (10)

C. Chen, W. Shi, R. Deorajh, N. Nguyen, J. Ramjist, A. Marques, and V. X. D. Yang, “Beam-shifting technique for speckle reduction and flow rate measurement in optical coherence tomography,” Opt. Lett. 43(24), 5921–5924 (2018).
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Science (1)

D. Huang, E. Swanson, C. Lin, J. Schuman, W. Stinson, W. Chang, M. Hee, T. Flotte, K. Gregory, and C. Puliafito, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
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Figures (9)

Fig. 1
Fig. 1 Schematics of beam-shifting technique: (a) Optical path before (red) and after (green) beam shift. (b) Overhead view of beam-shifting path (left) on objective lens aperture and corresponding change of incident angle on sample (right). (c) The relationship between the measured Doppler velocity and three orthogonal velocity components after beam-shifting, where θ = 0° in left panel and θ = −2/3π in right panel.
Fig. 2
Fig. 2 Schematic of MHB-SDOCT. DP: dispersion compensation; PC: polarization controller; L1-L7: lens.
Fig. 3
Fig. 3 Schematic of scanning protocols for speckle reduction (a) and for flow rate measurement (b), where 5 sub-steps are used for each full B-scan in both cases.
Fig. 4
Fig. 4 Statistical data of speckle noise reduction. (a)-(e) The representative cross sectional structure images with different incident angles. (f) Averaged structural image of 17 different incident angle images. (g) Plots of normalized pixel counts versus normalized intensity with different averaging number (N) at incident angle of ϕ = 0°. (h) Plots of normalized pixel counts versus normalized intensity with different averaging number (N) at incident angle of ϕ = 4.76°. (i) Plots of normalized intensity STD versus averaging number and theoretical model. In (h) and (i), the Δθ between two consecutive positions is always evenly divided according to total frame number N.
Fig. 5
Fig. 5 Phantom results for speckle noise reduction. Structural images obtained by standard OCT (a) and MHB-SDOCT (b) of a two-layer phantom, in which first layer is agar with intralipid and the second layer is ager with polymer beads with 10 µm diameter. (c) Intensity plots at the position marked by a dashed red line in (a) and (b), where black curve and red curve are from (a) and (b), respectively. (d)-(e) The histograms of pixel intensities within the local regions marked by dashed green rectangles in (a) and (b) respectively. Structural images obtained by standard OCT (f) and MHB-SDOCT (g) of a phantom made by mixing two kinds of phantom mentioned above.
Fig. 6
Fig. 6 Human skin images for speckle reduction. (a) Photograph of the volunteer's left hand, and the marked region by the black rectangle was scanned. (b)-(c) The cross sectional structural image of standard OCT and MHB-SDOCT respectively. (d)-(e) The histograms of pixel intensities within the regions of dashed green rectangles in (a) and (b). (f)-(g) En face structural images of standard OCT and MHB-SDOCT at depth of 200 µm below surface.
Fig. 7
Fig. 7 Flow phantom results. (a) Measured Doppler velocity images with different flow direction (ϕD) and different incident positions (θ), where ϕD is the angle between optical axis of objective lens and flow direction. (b) Plot of the calculated flow rate versus ϕD. (c) Measured Doppler velocity images with different starting angle (θ0). (d) Plot of measured flow rates versus different starting angle (θ0).
Fig. 8
Fig. 8 In-vivo chicken embryo blood flow results. (a) Photograph of a 5-day old chicken embryo, the vessel position marked by a black arrow was scanned. (b) Cross-sectional structural image. (c) Binary mask for Doppler velocity calculation with surface removed. (d) The measured mean velocity plots versus time with different incident angle θ. (e) Calculated flow rate plot versus time. (f) Representative Doppler velocity images at the five time points marked by red arrows in (e).
Fig. 9
Fig. 9 The plot of lateral resolution degradation versus depth, where ZR is Rayleigh length.

Equations (3)

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{ v ¯ θ=2/3π =cosϕ v ¯ z ( cos(π/6) v ¯ y +cos(π/3) v ¯ x )sinϕ v ¯ θ=0 =cosϕ v ¯ z + v ¯ x sinϕ v ¯ θ=2/3π =cosϕ v ¯ z +( cos(π/6) v ¯ y cos(π/3) v ¯ x )sinϕ ,
{ v ¯ x = ( 2 v ¯ θ=0 v ¯ θ=2/3π v ¯ θ=2/3π )/ ( 3sinϕ ) v ¯ y = ( v ¯ θ=2/3π v ¯ θ=2/3π )/ ( 3 sinϕ ) v ¯ z = ( v ¯ θ=0 + v ¯ θ=2/3π + v ¯ θ=2/3π )/ ( 3cosϕ ) .
Q= v ¯ a s v ,

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