Abstract

Analyzing the experimental data of the velocity distribution in a fluid flow using Doppler Optical Coherence Tomography (OCT), we compared the Wigner distribution method to the short-time Fourier transform method, the Hilbert-based phase-resolved method and the autocorrelation method. We conclude that the pseudo Wigner-distribution signal processing method is overall more precise than other often-used methods in Doppler OCT for the analysis of cross-sectional velocity distributions.

© 2007 Optical Society of America

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References

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  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, 1178-1181 (1991).
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  2. W. Drexler, U. Morgner, F. X. Kartner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, and J. G. Fujimoto, "In vivo ultrahigh-resolution optical coherence tomography," Opt. Lett. 24, 1221-1223 (1999).
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    [CrossRef]
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  16. Auger,F. , Flandrin, P. , Gonçalvès, P. , and Lemoine, O. , "Time-Frequency Toolbox tutorial", CNRS (France), Rice U. (U.S.A.), http://tftb.nongnu.org/ (2005) and http://gdr-isis.org/tftb/tutorial/tutorial.html.
  17. Claasen, T. C. M.  and Mecklenbräuker, W. F. G. "The Wigner distribution - a tool for time-frequency signal analysis" Part II: Discrete time signals.Philips J. Res. 35,276-300 (1980).
  18. L. Wu, "Simultaneous measurement of flow velocity and Doppler angle by the use of Doppler optical coherence tomography," Opt. Lasers Eng. 42, 303-313 (2004).
    [CrossRef]
  19. Bergmann, N.  "New formulation of discrete Wigner-Ville distribution", Electron. Lett. 27, 111-112 (1991).
    [CrossRef]
  20. Zielinski, T. P. , "Wigner transform instantaneous phase estimator", Eusipco-96, Trieste, PDE.10 (1996)
  21. Yang, Victor X. D., Gordon, M. L, Mok, A. Zhao, Y., Chen, Z., Cobbold, R. S. C., Wilson, Brian C., and Vitkin, I. Alex. "Improved phase-resolved optical Doppler tomography using the Kasai velocity estimator and histogram segmentation", Opt. Comm. 208, 209-214 (2002).
    [CrossRef]
  22. Piao, Daqing, Otis, Linda L., Dutta, Niloy K., and Zhu, Quing, "Quantitative assessment of flow velocity-estimation algorithms for optical Doppler tomography imaging", App. Opt. 41, 6118-6127 (2002).
    [CrossRef]
  23. Zielinski, T. P. , "On a software implementation of the Wigner-Ville transform", Comp. Phys. Comm. 50, 269-272 (1988).
    [CrossRef]
  24. Chen, Y. , Willett, P. , and Zhu, Q. , "Frequency tracking in optical Doppler tomography using an adaptive notch filter", J. Biomed. Opt. 12, 014018-1 to 014018-9 (2007).
    [CrossRef]

2007 (1)

2005 (2)

2004 (2)

L. Wu, "Simultaneous measurement of flow velocity and Doppler angle by the use of Doppler optical coherence tomography," Opt. Lasers Eng. 42, 303-313 (2004).
[CrossRef]

L. Wang, W. Xu, M. Bachman, G. P. Li, and Z. P. Chen, "Phase-resolved optical Doppler tomography for imaging flow dynamics in microfluidic channels," Appl. Phys. Lett. 85, 1855-1857 (2004).
[CrossRef]

2003 (1)

2002 (3)

Rollins, Andrew M., Yazdanfar, Siavash, Barton, Jennifer K., and Izatt, Joseph A., "Real-time in vivo color Doppler optical coherence tomography", J. Biomed. Opt. 7,123-129 (2002).
[CrossRef] [PubMed]

Yang, Victor X. D., Gordon, M. L, Mok, A. Zhao, Y., Chen, Z., Cobbold, R. S. C., Wilson, Brian C., and Vitkin, I. Alex. "Improved phase-resolved optical Doppler tomography using the Kasai velocity estimator and histogram segmentation", Opt. Comm. 208, 209-214 (2002).
[CrossRef]

Piao, Daqing, Otis, Linda L., Dutta, Niloy K., and Zhu, Quing, "Quantitative assessment of flow velocity-estimation algorithms for optical Doppler tomography imaging", App. Opt. 41, 6118-6127 (2002).
[CrossRef]

2001 (1)

Yazdanfar, S. , Rollins, A. M. , and Izatt, J. A.  "Ultrahigh velocity resolution imaging of the microcirculation in vivo using color Doppler optical coherence tomography". Proc. SPIE,  4251, 156-164 (2001).
[CrossRef]

2000 (1)

1999 (3)

W. Drexler, U. Morgner, F. X. Kartner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, and J. G. Fujimoto, "In vivo ultrahigh-resolution optical coherence tomography," Opt. Lett. 24, 1221-1223 (1999).
[CrossRef]

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

Rollins, Andrew M., Yazdanfar, Siavash, Ung-arunyawee, Rujchai, and Izatt, Joseph A. "Real time color Doppler optical coherence tomography using an autocorrelation technique", Proc. SPIE. 3598, 168-176 (1999).
[CrossRef]

1997 (2)

1991 (2)

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, 1178-1181 (1991).
[CrossRef] [PubMed]

Bergmann, N.  "New formulation of discrete Wigner-Ville distribution", Electron. Lett. 27, 111-112 (1991).
[CrossRef]

1988 (1)

Zielinski, T. P. , "On a software implementation of the Wigner-Ville transform", Comp. Phys. Comm. 50, 269-272 (1988).
[CrossRef]

1980 (1)

Claasen, T. C. M.  and Mecklenbräuker, W. F. G. "The Wigner distribution - a tool for time-frequency signal analysis" Part II: Discrete time signals.Philips J. Res. 35,276-300 (1980).

App. Opt. (1)

Piao, Daqing, Otis, Linda L., Dutta, Niloy K., and Zhu, Quing, "Quantitative assessment of flow velocity-estimation algorithms for optical Doppler tomography imaging", App. Opt. 41, 6118-6127 (2002).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

L. Wang, W. Xu, M. Bachman, G. P. Li, and Z. P. Chen, "Phase-resolved optical Doppler tomography for imaging flow dynamics in microfluidic channels," Appl. Phys. Lett. 85, 1855-1857 (2004).
[CrossRef]

Comp. Phys. Comm. (1)

Zielinski, T. P. , "On a software implementation of the Wigner-Ville transform", Comp. Phys. Comm. 50, 269-272 (1988).
[CrossRef]

Electron. Lett. (1)

Bergmann, N.  "New formulation of discrete Wigner-Ville distribution", Electron. Lett. 27, 111-112 (1991).
[CrossRef]

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

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

J. Biomed. Opt. (1)

Rollins, Andrew M., Yazdanfar, Siavash, Barton, Jennifer K., and Izatt, Joseph A., "Real-time in vivo color Doppler optical coherence tomography", J. Biomed. Opt. 7,123-129 (2002).
[CrossRef] [PubMed]

Opt. Comm. (1)

Yang, Victor X. D., Gordon, M. L, Mok, A. Zhao, Y., Chen, Z., Cobbold, R. S. C., Wilson, Brian C., and Vitkin, I. Alex. "Improved phase-resolved optical Doppler tomography using the Kasai velocity estimator and histogram segmentation", Opt. Comm. 208, 209-214 (2002).
[CrossRef]

Opt. Express (2)

Opt. Lasers Eng. (1)

L. Wu, "Simultaneous measurement of flow velocity and Doppler angle by the use of Doppler optical coherence tomography," Opt. Lasers Eng. 42, 303-313 (2004).
[CrossRef]

Opt. Lett. (5)

Philips J. Res. (1)

Claasen, T. C. M.  and Mecklenbräuker, W. F. G. "The Wigner distribution - a tool for time-frequency signal analysis" Part II: Discrete time signals.Philips J. Res. 35,276-300 (1980).

Proc. SPIE (1)

Yazdanfar, S. , Rollins, A. M. , and Izatt, J. A.  "Ultrahigh velocity resolution imaging of the microcirculation in vivo using color Doppler optical coherence tomography". Proc. SPIE,  4251, 156-164 (2001).
[CrossRef]

Proc. SPIE. (1)

Rollins, Andrew M., Yazdanfar, Siavash, Ung-arunyawee, Rujchai, and Izatt, Joseph A. "Real time color Doppler optical coherence tomography using an autocorrelation technique", Proc. SPIE. 3598, 168-176 (1999).
[CrossRef]

Science (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, 1178-1181 (1991).
[CrossRef] [PubMed]

Other (4)

Leon Cohen, Time-frequency analysis,Prentice Hall, Englewood Cliffs, N.J. (1995).

Auger,F. , Flandrin, P. , Gonçalvès, P. , and Lemoine, O. , "Time-Frequency Toolbox tutorial", CNRS (France), Rice U. (U.S.A.), http://tftb.nongnu.org/ (2005) and http://gdr-isis.org/tftb/tutorial/tutorial.html.

Zielinski, T. P. , "Wigner transform instantaneous phase estimator", Eusipco-96, Trieste, PDE.10 (1996)

Chen, Y. , Willett, P. , and Zhu, Q. , "Frequency tracking in optical Doppler tomography using an adaptive notch filter", J. Biomed. Opt. 12, 014018-1 to 014018-9 (2007).
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

Experimental setup for the Doppler frequency-shift measurements. FC: fiber coupler, PC: polarization controller, MO: microscope objective

Fig. 2.
Fig. 2.

OCT image of the tube profile. The superimposed contour map indicates the frequency calculated using experimental values and the pseudo Wigner method. The white line indicates the A-scan that is studied afterwards in this work.

Fig. 3.
Fig. 3.

Small segment of the detected signal at a 100 kHz sampling rate. The boxed region represents the STFT window size.

Fig. 4.
Fig. 4.

STFT time-frequency distribution of the sample signal.

Fig. 5.
Fig. 5.

Time-frequency distribution of the sample signal obtained with the Wigner distribution.

Fig. 6.
Fig. 6.

Comparison of the frequency spectra calculated with two time-frequency methods.

Fig. 7
Fig. 7

Spectra calculated at each sampling point of the signal using the Wigner distribution.

Fig. 8
Fig. 8

Computed flow profiles using a quadratic fit.

Tables (1)

Tables Icon

Table 1. Main parameters of the plots in Fig. 8

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

Δ f D = 1 2 π ( k s k i ) × v .
v ODT = λ 0 Δ f D 2 n ¯ cos ( θ ) .
STFT ( f , τ ) = y ( t ) w ( t + τ ) e j 2 πft dt .
f c = m f m STFT ( f m , τ i ) m STFT ( f m , τ i ) .
W ( t , ω ) = 1 2 π y * ( t 1 2 τ ) y ( t + 1 2 τ ) e j ωτ .
W ( t , ω ) dt = Y ( ω ) 2 .
W ( t , ω ) = y ( t ) 2 .
PW ( t , ω ) = 1 2 π h ( τ ) y * ( t 1 2 τ ) y ( t + 1 2 τ ) e jωτ .
V ( r ) = V c [ 1 ( r d 2 ) 2 ] .

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