Abstract

Optical Doppler tomography is demonstrated to be a simple, accurate, and noncontact method for measuring the fluid velocity of laminar flow in small-diameter (∼0.5-mm) ducts. Studies are described that utilize circular (square) plastic (glass) ducts infused with a moving suspension of polymer microspheres in air and buried in an optically turbid medium. The measurement of Doppler-shifted frequencies of backscattered light from moving microspheres is used to construct a high-resolution spatial profile of fluid-flow velocity in the ducts.

© 1997 Optical Society of America

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References

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  1. J. V. Chapman, G. R. Sutherland, “Blood flow measurements by Doppler ultrasound,” in The Noninvasive Evaluation of Hemodynamics in Congenital Heart Disease, (Kluwer, Dordrecht, The Netherlands, 1990), Chap. 3, pp. 55–66.
  2. P. A. J. Bascom, R. S. C. Cobbold, “Effects of transducer beam geometry and flow velocity profile on the Doppler power spectrum—a theoretical study,” Ultrasound Med. Biol. 16, 279–295 (1990).
    [CrossRef]
  3. X. J. Wang, T. E. Milner, M. C. Chang, J. S. Nelson, “Group refractive index measurement of dry and hydrated type I collagen films using optical low-coherence reflectometry,” J. Biomed. Opt. 1, 212–216 (1996).
    [CrossRef] [PubMed]
  4. G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, M. R. Hee, J. G. Fujimoto, “Determination of the refractive index of highly scattering human tissue by optical coherence tomography,” Opt. Lett. 20, 2258–2260 (1995).
    [CrossRef] [PubMed]
  5. J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, J. G. Fujimoto, “Optical coherence microscopy in scattering media,” Opt. Lett. 19, 590–592 (1994).
    [CrossRef] [PubMed]
  6. Y. N. Ning, K. T. V. Grattan, A. W. Palmer, “Fiber-optic interferometric systems using low-coherence light sources,” Sensors Actuators 30, 181–192 (1992).
    [CrossRef]
  7. B. T. Meggit, W. J. O. Boyle, K. T. V. Grattan, A. W. Palmer, Y. N. Ning, “Fiber optic anemometry using an optical delay cavity technique,” in Fiber Optics ’90, P. McGeehin, ed., Proc. SPIE1314, 321–326 (1990).
  8. J. M. Schmitt, A. Knuttel, R. F. Bonner, “Measurement of optical properties of biological tissues by low-coherence reflectometry,” Appl. Opt. 32, 6032–6042 (1993).
    [CrossRef] [PubMed]
  9. X. J. Wang, T. E. Milner, J. S. Nelson, “Characterization of fluid flow velocity by optical Doppler tomography,” Opt. Lett. 20, 1337–1339 (1995).
    [CrossRef] [PubMed]
  10. X. J. Wang, T. E. Milner, S. A. Newton, R. P. Dhond, W. V. Sorin, J. S. Nelson, “Characterization of human scalp hairs by optical low-coherence reflectometry,” Opt. Lett. 20, 524–526 (1995).
    [CrossRef] [PubMed]
  11. J. Goodman, Statistical Optics (Wiley, New York, 1985), p. 157.
  12. W. V. Sorin, D. M. Baney, “A simple intensity noise reduction technique for optical low-coherence reflectometry,” IEEE Photon. Technol. Lett. 4, 1404–1406 (1992).
    [CrossRef]
  13. L. D. Landan, E. M. Lifshitz, Fluid Mechanics, 2nd ed. (Pergamon, Oxford, 1987), Chap. 2.
  14. M. Spiga, G. L. Morini, “A symmetric solution for velocity profile in laminar flow through rectangular ducts,” Int. Comm. Heat Mass Transfer 21, 469–475 (1994).
    [CrossRef]
  15. G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
    [CrossRef]
  16. B. Maheu, G. Gouesbet, G. Gréhan, “A concise presentation of the generalized Lorentz–Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. 19, 59–67 (1988).
    [CrossRef]

1996

X. J. Wang, T. E. Milner, M. C. Chang, J. S. Nelson, “Group refractive index measurement of dry and hydrated type I collagen films using optical low-coherence reflectometry,” J. Biomed. Opt. 1, 212–216 (1996).
[CrossRef] [PubMed]

1995

1994

M. Spiga, G. L. Morini, “A symmetric solution for velocity profile in laminar flow through rectangular ducts,” Int. Comm. Heat Mass Transfer 21, 469–475 (1994).
[CrossRef]

J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, J. G. Fujimoto, “Optical coherence microscopy in scattering media,” Opt. Lett. 19, 590–592 (1994).
[CrossRef] [PubMed]

1993

1992

Y. N. Ning, K. T. V. Grattan, A. W. Palmer, “Fiber-optic interferometric systems using low-coherence light sources,” Sensors Actuators 30, 181–192 (1992).
[CrossRef]

W. V. Sorin, D. M. Baney, “A simple intensity noise reduction technique for optical low-coherence reflectometry,” IEEE Photon. Technol. Lett. 4, 1404–1406 (1992).
[CrossRef]

1990

P. A. J. Bascom, R. S. C. Cobbold, “Effects of transducer beam geometry and flow velocity profile on the Doppler power spectrum—a theoretical study,” Ultrasound Med. Biol. 16, 279–295 (1990).
[CrossRef]

1988

B. Maheu, G. Gouesbet, G. Gréhan, “A concise presentation of the generalized Lorentz–Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. 19, 59–67 (1988).
[CrossRef]

G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
[CrossRef]

Baney, D. M.

W. V. Sorin, D. M. Baney, “A simple intensity noise reduction technique for optical low-coherence reflectometry,” IEEE Photon. Technol. Lett. 4, 1404–1406 (1992).
[CrossRef]

Bascom, P. A. J.

P. A. J. Bascom, R. S. C. Cobbold, “Effects of transducer beam geometry and flow velocity profile on the Doppler power spectrum—a theoretical study,” Ultrasound Med. Biol. 16, 279–295 (1990).
[CrossRef]

Bonner, R. F.

Bouma, B. E.

Boyle, W. J. O.

B. T. Meggit, W. J. O. Boyle, K. T. V. Grattan, A. W. Palmer, Y. N. Ning, “Fiber optic anemometry using an optical delay cavity technique,” in Fiber Optics ’90, P. McGeehin, ed., Proc. SPIE1314, 321–326 (1990).

Brezinski, M. E.

Chang, M. C.

X. J. Wang, T. E. Milner, M. C. Chang, J. S. Nelson, “Group refractive index measurement of dry and hydrated type I collagen films using optical low-coherence reflectometry,” J. Biomed. Opt. 1, 212–216 (1996).
[CrossRef] [PubMed]

Chapman, J. V.

J. V. Chapman, G. R. Sutherland, “Blood flow measurements by Doppler ultrasound,” in The Noninvasive Evaluation of Hemodynamics in Congenital Heart Disease, (Kluwer, Dordrecht, The Netherlands, 1990), Chap. 3, pp. 55–66.

Cobbold, R. S. C.

P. A. J. Bascom, R. S. C. Cobbold, “Effects of transducer beam geometry and flow velocity profile on the Doppler power spectrum—a theoretical study,” Ultrasound Med. Biol. 16, 279–295 (1990).
[CrossRef]

Dhond, R. P.

Fujimoto, J. G.

Goodman, J.

J. Goodman, Statistical Optics (Wiley, New York, 1985), p. 157.

Gouesbet, G.

B. Maheu, G. Gouesbet, G. Gréhan, “A concise presentation of the generalized Lorentz–Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. 19, 59–67 (1988).
[CrossRef]

G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
[CrossRef]

Grattan, K. T. V.

Y. N. Ning, K. T. V. Grattan, A. W. Palmer, “Fiber-optic interferometric systems using low-coherence light sources,” Sensors Actuators 30, 181–192 (1992).
[CrossRef]

B. T. Meggit, W. J. O. Boyle, K. T. V. Grattan, A. W. Palmer, Y. N. Ning, “Fiber optic anemometry using an optical delay cavity technique,” in Fiber Optics ’90, P. McGeehin, ed., Proc. SPIE1314, 321–326 (1990).

Gréhan, G.

B. Maheu, G. Gouesbet, G. Gréhan, “A concise presentation of the generalized Lorentz–Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. 19, 59–67 (1988).
[CrossRef]

G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
[CrossRef]

Hee, M. R.

Izatt, J. A.

Knuttel, A.

Landan, L. D.

L. D. Landan, E. M. Lifshitz, Fluid Mechanics, 2nd ed. (Pergamon, Oxford, 1987), Chap. 2.

Lifshitz, E. M.

L. D. Landan, E. M. Lifshitz, Fluid Mechanics, 2nd ed. (Pergamon, Oxford, 1987), Chap. 2.

Maheu, B.

G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
[CrossRef]

B. Maheu, G. Gouesbet, G. Gréhan, “A concise presentation of the generalized Lorentz–Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. 19, 59–67 (1988).
[CrossRef]

Meggit, B. T.

B. T. Meggit, W. J. O. Boyle, K. T. V. Grattan, A. W. Palmer, Y. N. Ning, “Fiber optic anemometry using an optical delay cavity technique,” in Fiber Optics ’90, P. McGeehin, ed., Proc. SPIE1314, 321–326 (1990).

Milner, T. E.

Morini, G. L.

M. Spiga, G. L. Morini, “A symmetric solution for velocity profile in laminar flow through rectangular ducts,” Int. Comm. Heat Mass Transfer 21, 469–475 (1994).
[CrossRef]

Nelson, J. S.

Newton, S. A.

Ning, Y. N.

Y. N. Ning, K. T. V. Grattan, A. W. Palmer, “Fiber-optic interferometric systems using low-coherence light sources,” Sensors Actuators 30, 181–192 (1992).
[CrossRef]

B. T. Meggit, W. J. O. Boyle, K. T. V. Grattan, A. W. Palmer, Y. N. Ning, “Fiber optic anemometry using an optical delay cavity technique,” in Fiber Optics ’90, P. McGeehin, ed., Proc. SPIE1314, 321–326 (1990).

Owen, G. M.

Palmer, A. W.

Y. N. Ning, K. T. V. Grattan, A. W. Palmer, “Fiber-optic interferometric systems using low-coherence light sources,” Sensors Actuators 30, 181–192 (1992).
[CrossRef]

B. T. Meggit, W. J. O. Boyle, K. T. V. Grattan, A. W. Palmer, Y. N. Ning, “Fiber optic anemometry using an optical delay cavity technique,” in Fiber Optics ’90, P. McGeehin, ed., Proc. SPIE1314, 321–326 (1990).

Schmitt, J. M.

Sorin, W. V.

X. J. Wang, T. E. Milner, S. A. Newton, R. P. Dhond, W. V. Sorin, J. S. Nelson, “Characterization of human scalp hairs by optical low-coherence reflectometry,” Opt. Lett. 20, 524–526 (1995).
[CrossRef] [PubMed]

W. V. Sorin, D. M. Baney, “A simple intensity noise reduction technique for optical low-coherence reflectometry,” IEEE Photon. Technol. Lett. 4, 1404–1406 (1992).
[CrossRef]

Southern, J. F.

Spiga, M.

M. Spiga, G. L. Morini, “A symmetric solution for velocity profile in laminar flow through rectangular ducts,” Int. Comm. Heat Mass Transfer 21, 469–475 (1994).
[CrossRef]

Sutherland, G. R.

J. V. Chapman, G. R. Sutherland, “Blood flow measurements by Doppler ultrasound,” in The Noninvasive Evaluation of Hemodynamics in Congenital Heart Disease, (Kluwer, Dordrecht, The Netherlands, 1990), Chap. 3, pp. 55–66.

Swanson, E. A.

Tearney, G. J.

Wang, X. J.

Appl. Opt.

IEEE Photon. Technol. Lett.

W. V. Sorin, D. M. Baney, “A simple intensity noise reduction technique for optical low-coherence reflectometry,” IEEE Photon. Technol. Lett. 4, 1404–1406 (1992).
[CrossRef]

Int. Comm. Heat Mass Transfer

M. Spiga, G. L. Morini, “A symmetric solution for velocity profile in laminar flow through rectangular ducts,” Int. Comm. Heat Mass Transfer 21, 469–475 (1994).
[CrossRef]

J. Biomed. Opt.

X. J. Wang, T. E. Milner, M. C. Chang, J. S. Nelson, “Group refractive index measurement of dry and hydrated type I collagen films using optical low-coherence reflectometry,” J. Biomed. Opt. 1, 212–216 (1996).
[CrossRef] [PubMed]

J. Opt.

B. Maheu, G. Gouesbet, G. Gréhan, “A concise presentation of the generalized Lorentz–Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. 19, 59–67 (1988).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Lett.

Sensors Actuators

Y. N. Ning, K. T. V. Grattan, A. W. Palmer, “Fiber-optic interferometric systems using low-coherence light sources,” Sensors Actuators 30, 181–192 (1992).
[CrossRef]

Ultrasound Med. Biol.

P. A. J. Bascom, R. S. C. Cobbold, “Effects of transducer beam geometry and flow velocity profile on the Doppler power spectrum—a theoretical study,” Ultrasound Med. Biol. 16, 279–295 (1990).
[CrossRef]

Other

J. V. Chapman, G. R. Sutherland, “Blood flow measurements by Doppler ultrasound,” in The Noninvasive Evaluation of Hemodynamics in Congenital Heart Disease, (Kluwer, Dordrecht, The Netherlands, 1990), Chap. 3, pp. 55–66.

L. D. Landan, E. M. Lifshitz, Fluid Mechanics, 2nd ed. (Pergamon, Oxford, 1987), Chap. 2.

B. T. Meggit, W. J. O. Boyle, K. T. V. Grattan, A. W. Palmer, Y. N. Ning, “Fiber optic anemometry using an optical delay cavity technique,” in Fiber Optics ’90, P. McGeehin, ed., Proc. SPIE1314, 321–326 (1990).

J. Goodman, Statistical Optics (Wiley, New York, 1985), p. 157.

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Figures (10)

Fig. 1
Fig. 1

Schematic of ODT instrumentation.

Fig. 2
Fig. 2

Diagram of the probe light beam focused into duct and laminar fluid. ϕ and ϕ′ represent angles between the flow velocity and the optical axis of incoming light in air and fluid, respectively; D is the inner dimension of the duct, x is the probe depth, and V is the fluid-flow velocity at position x.

Fig. 3
Fig. 3

Power spectra of four flow velocities [a, 188; b, 287; c, 423; d, 620 (µm/s)] at a single position in a square glass duct (curves offset by 20 dB). The bandwidth resolution of the spectrum analyzer is 10 Hz.

Fig. 4
Fig. 4

Power spectra of 12 flow velocities [a, 14; b, 26; c, 134; d, 228; e, 268; f, 323; g, 341; h, 328; i, 300; j, 254; k, 191; l, 122 (µm/s)] at sequential positions along a linear grid [a, 5; b, 6; c, 37; d, 73; e, 110; f, 147; g, 183; h, 220; i, 257; j, 294; k, 330; l, 367 (µm)] coincident with the diameter of a circular glass duct. The bandwidth resolution of the spectrum analyzer is 3 Hz.

Fig. 5
Fig. 5

Linear relationship between maximum fluid flow velocity V and measured Doppler shift Δ f in a circular glass duct.

Fig. 6
Fig. 6

Experimental (circles) and theoretical (solid curve) fluid-flow-velocity profiles in a circular glass duct.

Fig. 7
Fig. 7

Experimental (circles) and theoretical (solid curve) fluid-flow-velocity profiles in a square glass duct.

Fig. 8
Fig. 8

Experimental (circles) and theoretical (solid curve) fluid-flow-velocity profiles along the vertical diameter in a diffusive plastic duct (circular) buried in a highly scattering intralipid solution. The inset is a schematic setup of the sample and the probe beam.

Fig. 9
Fig. 9

Solid curve shows the measured interference fringe intensity of single microsphere passing through the coherent detection volume. The dashed–dotted curve shows the best fit to a double-sided exponential function.

Fig. 10
Fig. 10

Exponential decay of interference fringe intensity versus depth in a turbid intralipid solution.

Equations (10)

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

NR=VDρη
2Vx2+2Vy2=-ΔpηΔL,
x=R cosϕn,
Vx=Δfxλ02 cosϕ.
1rddrrdVdr=-ΔpηΔL.
Vr=d2Δp16ηΔL1-2rd2.
Vmax=CRApumpAductVpump,
Vx=0, y=Vx=D, y=Vx, y=0=Vx, y=D=0.
Vx, y=D2=16D2Δpπ4πηΔLn=2i+1m=2j+1×sinnπ/2sinmπx/Dnmn2+m2, i, j=0, 1, 2 .
wt=w0 expt-t0/Δtt<t0w0 exp-t-t0/Δtt>t0.

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