Abstract

We propose a transit-time based method to ascertain the azimuth angle of a velocity vector by spectral-domain Doppler optical coherence tomography (DOCT), so that three-dimensional (3-D) velocity vector can be quantified. A custom-designed slit plate with predetermined slit orientation is placed into the sample beam to create three delay-encoded sub-beams of different beam shape for sample probing. Based on the transit-time analysis for Doppler bandwidth, the azimuth angle within 90° range is evaluated by exploitation of the complex signals corresponding to three path length delays. 3-D velocity vector is quantified through further estimating of Doppler angle and flow velocity by combined Doppler shift and Doppler bandwidth measurements. The feasibility of the method is demonstrated by good agreement between the determined azimuth angles and the preset ones, and further confirmed by velocity vector measurement of flowing solution inside a capillary tube.

© 2010 OSA

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2009 (2)

2008 (1)

2007 (4)

Y. C. Ahn, W. Jung, and Z. Chen, “Quantification of a three-dimensional velocity vector using spectral-domain Doppler optical coherence tomography,” Opt. Lett. 32(11), 1587–1589 (2007).
[CrossRef] [PubMed]

R. Michaely, A. H. Bachmann, M. L. Villiger, C. Blatter, T. Lasser, and R. A. Leitgeb, “Vectorial reconstruction of retinal blood flow in three dimensions measured with high resolution resonant Doppler Fourier domain optical coherence tomography,” J. Biomed. Opt. 12(4), 041213 (2007).
[CrossRef] [PubMed]

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]

C. J. Pedersen, D. Huang, M. A. Shure, and A. M. Rollins, “Measurement of absolute flow velocity vector using dual-angle, delay-encoded Doppler optical coherence tomography,” Opt. Lett. 32(5), 506–508 (2007).
[CrossRef] [PubMed]

2006 (1)

A. Royset, T. Storen, F. Stabo-Eeg, and T. Lindmo, “Quantitative measurements of flow velocity and direction using Transversal Doppler Optical Coherence Tomography,” Proc. SPIE 6079, 607925 (2006).
[CrossRef]

2003 (2)

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]

D. Piao, L. L. Otis, and Q. Zhu, “Doppler angle and flow velocity mapping by combined Doppler shift and Doppler bandwidth measurements in optical Doppler tomography,” Opt. Lett. 28(13), 1120–1122 (2003).
[CrossRef] [PubMed]

2002 (1)

2000 (1)

1999 (1)

Z. Chen, Y. Zhao, S. M. Srinivas, J. S. Nelson, N. Prakash, and R. D. Frostig, “Optical Doppler Tomography,” IEEE J. Sel. Top. Quantum Electron. 5(4), 1134–1142 (1999).
[CrossRef]

1980 (1)

V. L. Newhouse, E. S. Furgason, G. F. Johnson, and D. A. Wolf, “The dependence of ultrasound Doppler bandwidth on beam geometry,” IEEE Trans. Sonics Ultrason. SU-27, 50–59 (1980).

Ahn, Y. C.

Bachmann, A. H.

R. Michaely, A. H. Bachmann, M. L. Villiger, C. Blatter, T. Lasser, and R. A. Leitgeb, “Vectorial reconstruction of retinal blood flow in three dimensions measured with high resolution resonant Doppler Fourier domain optical coherence tomography,” J. Biomed. Opt. 12(4), 041213 (2007).
[CrossRef] [PubMed]

Blatter, C.

R. Michaely, A. H. Bachmann, M. L. Villiger, C. Blatter, T. Lasser, and R. A. Leitgeb, “Vectorial reconstruction of retinal blood flow in three dimensions measured with high resolution resonant Doppler Fourier domain optical coherence tomography,” J. Biomed. Opt. 12(4), 041213 (2007).
[CrossRef] [PubMed]

Bouma, B. E.

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]

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]

Brecke, K. M.

Chen, M.

Chen, Z.

Davé, D. P.

Ding, Z.

Fabritius, T.

Frostig, R. D.

Z. Chen, Y. Zhao, S. M. Srinivas, J. S. Nelson, N. Prakash, and R. D. Frostig, “Optical Doppler Tomography,” IEEE J. Sel. Top. Quantum Electron. 5(4), 1134–1142 (1999).
[CrossRef]

Furgason, E. S.

V. L. Newhouse, E. S. Furgason, G. F. Johnson, and D. A. Wolf, “The dependence of ultrasound Doppler bandwidth on beam geometry,” IEEE Trans. Sonics Ultrason. SU-27, 50–59 (1980).

Huang, D.

C. J. Pedersen, D. Huang, M. A. Shure, and A. M. Rollins, “Measurement of absolute flow velocity vector using dual-angle, delay-encoded Doppler optical coherence tomography,” Opt. Lett. 32(5), 506–508 (2007).
[CrossRef] [PubMed]

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]

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. 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]

Johnson, G. F.

V. L. Newhouse, E. S. Furgason, G. F. Johnson, and D. A. Wolf, “The dependence of ultrasound Doppler bandwidth on beam geometry,” IEEE Trans. Sonics Ultrason. SU-27, 50–59 (1980).

Jung, W.

Lasser, T.

R. Michaely, A. H. Bachmann, M. L. Villiger, C. Blatter, T. Lasser, and R. A. Leitgeb, “Vectorial reconstruction of retinal blood flow in three dimensions measured with high resolution resonant Doppler Fourier domain optical coherence tomography,” J. Biomed. Opt. 12(4), 041213 (2007).
[CrossRef] [PubMed]

Leitgeb, R. A.

R. Michaely, A. H. Bachmann, M. L. Villiger, C. Blatter, T. Lasser, and R. A. Leitgeb, “Vectorial reconstruction of retinal blood flow in three dimensions measured with high resolution resonant Doppler Fourier domain optical coherence tomography,” J. Biomed. Opt. 12(4), 041213 (2007).
[CrossRef] [PubMed]

Lindmo, T.

A. Royset, T. Storen, F. Stabo-Eeg, and T. Lindmo, “Quantitative measurements of flow velocity and direction using Transversal Doppler Optical Coherence Tomography,” Proc. SPIE 6079, 607925 (2006).
[CrossRef]

Makita, S.

Meng, J.

Michaely, R.

R. Michaely, A. H. Bachmann, M. L. Villiger, C. Blatter, T. Lasser, and R. A. Leitgeb, “Vectorial reconstruction of retinal blood flow in three dimensions measured with high resolution resonant Doppler Fourier domain optical coherence tomography,” J. Biomed. Opt. 12(4), 041213 (2007).
[CrossRef] [PubMed]

Milner, T. E.

Nelson, J. S.

Newhouse, V. L.

V. L. Newhouse, E. S. Furgason, G. F. Johnson, and D. A. Wolf, “The dependence of ultrasound Doppler bandwidth on beam geometry,” IEEE Trans. Sonics Ultrason. SU-27, 50–59 (1980).

Otis, L. L.

Pedersen, C. J.

Piao, D.

Prakash, N.

Z. Chen, Y. Zhao, S. M. Srinivas, J. S. Nelson, N. Prakash, and R. D. Frostig, “Optical Doppler Tomography,” IEEE J. Sel. Top. Quantum Electron. 5(4), 1134–1142 (1999).
[CrossRef]

Ren, H.

Rollins, A. M.

Royset, A.

A. Royset, T. Storen, F. Stabo-Eeg, and T. Lindmo, “Quantitative measurements of flow velocity and direction using Transversal Doppler Optical Coherence Tomography,” Proc. SPIE 6079, 607925 (2006).
[CrossRef]

Shure, M. A.

Srinivas, S. M.

Z. Chen, Y. Zhao, S. M. Srinivas, J. S. Nelson, N. Prakash, and R. D. Frostig, “Optical Doppler Tomography,” IEEE J. Sel. Top. Quantum Electron. 5(4), 1134–1142 (1999).
[CrossRef]

Stabo-Eeg, F.

A. Royset, T. Storen, F. Stabo-Eeg, and T. Lindmo, “Quantitative measurements of flow velocity and direction using Transversal Doppler Optical Coherence Tomography,” Proc. SPIE 6079, 607925 (2006).
[CrossRef]

Storen, T.

A. Royset, T. Storen, F. Stabo-Eeg, and T. Lindmo, “Quantitative measurements of flow velocity and direction using Transversal Doppler Optical Coherence Tomography,” Proc. SPIE 6079, 607925 (2006).
[CrossRef]

Tan, O.

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]

Tearney, G. J.

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]

Villiger, M. L.

R. Michaely, A. H. Bachmann, M. L. Villiger, C. Blatter, T. Lasser, and R. A. Leitgeb, “Vectorial reconstruction of retinal blood flow in three dimensions measured with high resolution resonant Doppler Fourier domain optical coherence tomography,” J. Biomed. Opt. 12(4), 041213 (2007).
[CrossRef] [PubMed]

Wang, C.

Wang, K.

Wang, Y.

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]

Wolf, D. A.

V. L. Newhouse, E. S. Furgason, G. F. Johnson, and D. A. Wolf, “The dependence of ultrasound Doppler bandwidth on beam geometry,” IEEE Trans. Sonics Ultrason. SU-27, 50–59 (1980).

Wu, T.

Xu, L.

Yasuno, Y.

Zeng, Y.

Zhao, Y.

Zhu, Q.

IEEE J. Sel. Top. Quantum Electron. (1)

Z. Chen, Y. Zhao, S. M. Srinivas, J. S. Nelson, N. Prakash, and R. D. Frostig, “Optical Doppler Tomography,” IEEE J. Sel. Top. Quantum Electron. 5(4), 1134–1142 (1999).
[CrossRef]

IEEE Trans. Sonics Ultrason. (1)

V. L. Newhouse, E. S. Furgason, G. F. Johnson, and D. A. Wolf, “The dependence of ultrasound Doppler bandwidth on beam geometry,” IEEE Trans. Sonics Ultrason. SU-27, 50–59 (1980).

J. Biomed. Opt. (3)

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]

R. Michaely, A. H. Bachmann, M. L. Villiger, C. Blatter, T. Lasser, and R. A. Leitgeb, “Vectorial reconstruction of retinal blood flow in three dimensions measured with high resolution resonant Doppler Fourier domain optical coherence tomography,” J. Biomed. Opt. 12(4), 041213 (2007).
[CrossRef] [PubMed]

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]

Opt. Express (2)

Opt. Lett. (6)

Proc. SPIE (1)

A. Royset, T. Storen, F. Stabo-Eeg, and T. Lindmo, “Quantitative measurements of flow velocity and direction using Transversal Doppler Optical Coherence Tomography,” Proc. SPIE 6079, 607925 (2006).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Custom-designed slit plate for the quantification of 3-D velocity vector. Inset figures demonstrating the top view of the slit plate with specified parameters (a), and the layout of the sample arm in the spectral-domain DOCT system (b).

Fig. 2
Fig. 2

Simulation results of normalized intensity patterns in the focal plane corresponding to collimated illumination via air slit (a) and glass (b), respectively. Contours of the central maximum corresponding to case (b) with different width of air slit (c).

Fig. 3
Fig. 3

Flow chart of signal processig procedure to quantify the velocity vector.

Fig. 4
Fig. 4

Doppler shift image (left) and Doppler bandwidth image (right) of the capillary tube with the slit plate inserted in the sample arm corresponding to parameter setting of α=76°, φ=45°, V=4.72 mm/s, d=1 mm.

Fig. 5
Fig. 5

Estimated azimuth angle using B AA/B sum (a) and B GG/B sum (b) with different preset azimuth angles for two values of d corresponding to parameter setting of α=76°, V=4.72 mm/s.

Fig. 6
Fig. 6

Estimated flow velocity (a), Doppler angle (b) with different preset flow velocities for two values of d corresponding to parameter setting of α=76°, φ=45°.

Fig. 7
Fig. 7

Reconstructed flow velocity vector profile inside the capillary tube corresponding to parameter setting of α=76°, φ=45°, V=4.72 mm/s.

Tables (1)

Tables Icon

Table 1 RMS Errors for Estimation of Azimuth Angle

Equations (11)

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T t = w V sin α .
B = 1 T t = V sin α w + B 0 .
w A A = { 2 λ f D cos φ , φ tan 1 ( D / d ) 2 λ f d sin φ , φ > tan 1 ( D / d ) } .
Γ ˜ s u m ( z ) = Γ ˜ A A ( z ) + Γ ˜ A G + G A ( z + δ ) + Γ ˜ G G ( z + 2 δ ) .
B A A B s u m = { 8 λ f / π D 2 λ f / D cos φ = 4 cos φ π , φ tan 1 ( D / d ) 8 λ f / π D 2 λ f / d sin φ = 4 d sin φ π D , φ > tan 1 ( D / d ) } .
B G G B s u m = 8 λ f / π D 2 x 0 2 cos 2 φ + y 0 2 sin 2 φ = 4 λ f / π D ( x 0 2 y 0 2 ) cos 2 φ + y 0 2 .
σ 2 = 1 T 2 { 1 | j = 1 N Γ ~ j ( z ) Γ ~ j + 1 * ( z ) | j = 1 N Γ ~ j ( z ) Γ ~ j * ( z ) } .
f d = 2 V cos α λ ,
f d = 1 2 π T arc tan { Im ( j = 1 N Γ ~ j ( z ) Γ ~ j + 1 * ( z ) ) Re ( j = 1 N Γ ~ j ( z ) Γ ~ j + 1 * ( z ) ) } .
α = tan 1 ( 2 w ( B B 0 ) f d λ ) ,
V = f d λ 2 cos α .

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