Abstract

Color Doppler optical coherence tomography (CDOCT) is a recent innovation that allows spatially localized flow-velocity mapping simultaneously with microstructural imaging. We present a theoretical model for velocity-image formation in CDOCT. The proportionality between the heterodyne detector current Doppler power spectrum in CDOCT and the optical source power spectrum is established. We show that stochastic modifications of the Doppler spectrum by fluctuating scatterer distributions in the flow field give rise to unavoidable velocity-estimation inaccuracies as well as to a fundamental trade-off between image-acquisition rate and velocity precision. Novel algorithms that permit high-fidelity depth-resolved measurements of velocities in turbid media are also reported.

© 1998 Optical Society of America

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References

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  1. J. A. Izatt and M. Kulkarni, in Conference on Lasers and Electro-Optics, Vol. 9 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), postdeadline paper CPD3-1.
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. V. Gusmeroli and M. Martinelli, Opt. Lett. 16, 1358 (1991).
    [CrossRef] [PubMed]
  5. X.-J. Wang, T. E. Milner, and J. S. Nelson, Opt. Lett. 20, 1337 (1995).
    [CrossRef] [PubMed]
  6. A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).
  7. J. A. Izatt, M. D. Kulkarni, S. Yazdanfar, J. K. Barton, and A. J. Welch, Opt. Lett. 22, 1439 (1997).
    [CrossRef]
  8. S. Yazdanfar, M. D. Kulkarni, and J. A. Izatt, Opt. Express 1, 424 (1997); www.osa.org .
    [CrossRef] [PubMed]
  9. M. D. Kulkarni, C. W. Thomas, and J. A. Izatt, Electron. Lett. 16, 1365 (1997).
    [CrossRef]

1997 (4)

1995 (1)

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, Science 254, 1178 (1991).
[CrossRef] [PubMed]

V. Gusmeroli and M. Martinelli, Opt. Lett. 16, 1358 (1991).
[CrossRef] [PubMed]

Barton, J. K.

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, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Chen, Z.

Dave, D.

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, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Fujimoto, J. 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, Science 254, 1178 (1991).
[CrossRef] [PubMed]

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, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Gusmeroli, V.

Hee, M. R.

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, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Huang, D.

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, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Izatt, J. A.

J. A. Izatt, M. D. Kulkarni, S. Yazdanfar, J. K. Barton, and A. J. Welch, Opt. Lett. 22, 1439 (1997).
[CrossRef]

S. Yazdanfar, M. D. Kulkarni, and J. A. Izatt, Opt. Express 1, 424 (1997); www.osa.org .
[CrossRef] [PubMed]

M. D. Kulkarni, C. W. Thomas, and J. A. Izatt, Electron. Lett. 16, 1365 (1997).
[CrossRef]

J. A. Izatt and M. Kulkarni, in Conference on Lasers and Electro-Optics, Vol. 9 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), postdeadline paper CPD3-1.

Kulkarni, M.

J. A. Izatt and M. Kulkarni, in Conference on Lasers and Electro-Optics, Vol. 9 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), postdeadline paper CPD3-1.

Kulkarni, M. D.

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, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Martinelli, M.

Milner, T. E.

Nelson, J. S.

Papoulis, A.

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).

Puliafito, C. 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, Science 254, 1178 (1991).
[CrossRef] [PubMed]

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, Science 254, 1178 (1991).
[CrossRef] [PubMed]

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, Science 254, 1178 (1991).
[CrossRef] [PubMed]

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, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Thomas, C. W.

M. D. Kulkarni, C. W. Thomas, and J. A. Izatt, Electron. Lett. 16, 1365 (1997).
[CrossRef]

Wang, X.-J.

Welch, A. J.

Yazdanfar, S.

Electron. Lett. (1)

M. D. Kulkarni, C. W. Thomas, and J. A. Izatt, Electron. Lett. 16, 1365 (1997).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

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, Science 254, 1178 (1991).
[CrossRef] [PubMed]

Other (2)

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).

J. A. Izatt and M. Kulkarni, in Conference on Lasers and Electro-Optics, Vol. 9 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), postdeadline paper CPD3-1.

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Figures (3)

Fig. 1
Fig. 1

a, Cross-power spectra (dashed and dotted curves) obtained by Fourier transformation of complex CDOCT A scans measured from a turbid sample. Ensemble averaging with 500 A scans allows us to recover the source power spectrum (solid curve). b, Doppler-shifted spectra measured from a flowing intralipid solution. The individual spectra (dotted curves) are jagged, resulting in corrupted velocity estimates. The vertical lines indicate the centroids of the spectra. The solid curve is an average of six spectra. Its centroid (3.81 mm/s) provides an estimate close to that obtained from flow measurements (3.87 mm/s). The horizontal (frequency) axis is converted to the velocity axis by use of Doppler’s law.

Fig. 2
Fig. 2

Velocity images 1984 axial×100 lateral pixels of laminar flow in a turbid medium. Gray scales indicate velocities in millimeters per second. All distances are in millimeters. a, Velocity image calculated with the traditional centroid algorithm.1,2,5 The image is noisy, the estimates are inaccurate by a factor of >2 from actual velocities, and the lower surface of the tube is not resolved. b, Velocity image obtained from the centroids of averages of 15 Doppler spectra at each depth. Noise is significantly reduced, contributing to the clarity of the lower tube wall. The velocity estimates are still inaccurate by a factor of >2. c, CDOCT image obtained with an adaptive velocity-estimation algorithm, which achieves a striking enhancement in clarity. The capability of locating duct walls accurately may prove useful in identifying blood vessel boundaries. d, Velocity profiles along the white lines in b and c. The profile obtained with the adaptive algorithm closely matches the actual profile calculated from a measurement of flow rate 3.84 µL/s.

Fig. 3
Fig. 3

Velocity-precision limits versus frame-acquisition rate calculated with the parameters shown in the figure. The solid line plots the ultimate velocity precision obtained with the Fourier transform relationship [Eq. (2)]. Because of the specular modulation of the Doppler spectra, the dashed line provides the practical velocity precision, which is also limited by source bandwidth [Eq. (3)].

Equations (3)

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Δf=2Vr-VsΔν/c,
Vsup=c2ν0nt cos θKLRfNρ.
Vspp=MVsup.

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