Abstract

We have investigated the modulation of the optical field transmitted through a colloid of polystyrene spheres by a narrow quasi-cw ultrasound beam. Measurements of the scale dependence of the heterodyne modulation signal at the acoustic frequency are obtained for samples that are up to 140 scattering lengths thick. A calculation of the modulation signal predicts the possibility of tomographic imaging, which is confirmed experimentally.

© 1997 Optical Society of America

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References

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  1. 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).
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    [CrossRef]
  6. J. C. Hebden, D. T. Delpy, “Enhanced time-resolved imaging with a diffusion model of photon transport,” Opt. Lett. 19, 311–313 (1994).
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    [CrossRef]
  8. L. Wang, S. L. Jacques, X. Zhao, “Continuous-wave ultrasonic modulation of scattered laser light to image objects in turbid media,” Opt. Lett. 20, 629–631 (1995).
    [CrossRef] [PubMed]
  9. W. Leutz, G. Maret, “Ultrasonic modulation of multiply scattered light,” Physica B 204, 14–19 (1995).
    [CrossRef]
  10. G. Maret, P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motion of scatterers,” Z. Phys. B. 65, 409–413 (1987).
    [CrossRef]
  11. M. J. Stephen, “Temporal fluctuations in wave propagation in random media,” Phys. Rev. B 37, 1–5 (1988).
    [CrossRef]
  12. D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
    [CrossRef] [PubMed]
  13. A. G. Yodh, P. D. Kaplan, D. J. Pine, “Pulsed diffusing-wave spectroscopy: High resolution through nonlinear optical grating,” Phys. Rev. B 42, 4744–4747 (1990).
    [CrossRef]
  14. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  15. L. Wang, X. Zhao, S. L. Jacques, “Ultrasound modulated optical tomography,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto, eds., Vol. 2 of 1996 TOPS (Optical Society of America, Washington, D.C., 1996).
  16. B. Chance, K. Kang, E. Sevick, “Photon diffusion in breast and brain: Spectroscopy and imaging,” Opt. Photon. News 4, 9–13 (1993).
    [CrossRef]
  17. J. C. Hebden, D. J. Hall, M. Firbank, D. T. Delpy, “Time-resolved optical imaging of a solid tissue-equivalent phantom,” Appl. Opt. 34, 8038–8047 (1995).
    [CrossRef] [PubMed]
  18. N. Garcia, A. Z. Genack, A. A. Lisyansky, “Measurement of the transport mean free path of diffusing photons,” Phys. Rev. B 46, 14475–14479 (1992).
    [CrossRef]

1995

1994

1993

B. Chance, K. Kang, E. Sevick, “Photon diffusion in breast and brain: Spectroscopy and imaging,” Opt. Photon. News 4, 9–13 (1993).
[CrossRef]

1992

N. Garcia, A. Z. Genack, A. A. Lisyansky, “Measurement of the transport mean free path of diffusing photons,” Phys. Rev. B 46, 14475–14479 (1992).
[CrossRef]

1990

A. G. Yodh, P. D. Kaplan, D. J. Pine, “Pulsed diffusing-wave spectroscopy: High resolution through nonlinear optical grating,” Phys. Rev. B 42, 4744–4747 (1990).
[CrossRef]

1988

M. J. Stephen, “Temporal fluctuations in wave propagation in random media,” Phys. Rev. B 37, 1–5 (1988).
[CrossRef]

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[CrossRef] [PubMed]

1987

G. Maret, P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motion of scatterers,” Z. Phys. B. 65, 409–413 (1987).
[CrossRef]

A. Z. Genack, “Transmission in disordered media,” Phys. Rev. Lett. 58, 2043–2046 (1987).
[CrossRef] [PubMed]

Boas, D. A.

Brooksby, G. W.

P. A. Marks, H. W. Tomlinson, G. W. Brooksby, “A comprehensive approach to breast cancer detection using light: photon localization by ultrasound modulation and tissue characterization by spectral discrimination,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. SPIE1888, 500–510 (1993).
[CrossRef]

Chaikin, P. M.

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[CrossRef] [PubMed]

Chance, B.

Delpy, D. T.

Firbank, M.

Fujimoto, J. G.

Garcia, N.

N. Garcia, A. Z. Genack, A. A. Lisyansky, “Measurement of the transport mean free path of diffusing photons,” Phys. Rev. B 46, 14475–14479 (1992).
[CrossRef]

Genack, A. Z.

N. Garcia, A. Z. Genack, A. A. Lisyansky, “Measurement of the transport mean free path of diffusing photons,” Phys. Rev. B 46, 14475–14479 (1992).
[CrossRef]

A. Z. Genack, “Transmission in disordered media,” Phys. Rev. Lett. 58, 2043–2046 (1987).
[CrossRef] [PubMed]

Goodman, J. W.

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

Hall, D. J.

Hebden, J. C.

Hee, M. R.

Herbolzheimer, E.

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[CrossRef] [PubMed]

Izatt, J. A.

Jacques, S. L.

L. Wang, S. L. Jacques, X. Zhao, “Continuous-wave ultrasonic modulation of scattered laser light to image objects in turbid media,” Opt. Lett. 20, 629–631 (1995).
[CrossRef] [PubMed]

L. Wang, X. Zhao, S. L. Jacques, “Ultrasound modulated optical tomography,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto, eds., Vol. 2 of 1996 TOPS (Optical Society of America, Washington, D.C., 1996).

Kang, K.

B. Chance, K. Kang, E. Sevick, “Photon diffusion in breast and brain: Spectroscopy and imaging,” Opt. Photon. News 4, 9–13 (1993).
[CrossRef]

Kaplan, P. D.

A. G. Yodh, P. D. Kaplan, D. J. Pine, “Pulsed diffusing-wave spectroscopy: High resolution through nonlinear optical grating,” Phys. Rev. B 42, 4744–4747 (1990).
[CrossRef]

Kempe, M.

Leutz, W.

W. Leutz, G. Maret, “Ultrasonic modulation of multiply scattered light,” Physica B 204, 14–19 (1995).
[CrossRef]

Lisyansky, A. A.

N. Garcia, A. Z. Genack, A. A. Lisyansky, “Measurement of the transport mean free path of diffusing photons,” Phys. Rev. B 46, 14475–14479 (1992).
[CrossRef]

Maret, G.

W. Leutz, G. Maret, “Ultrasonic modulation of multiply scattered light,” Physica B 204, 14–19 (1995).
[CrossRef]

G. Maret, P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motion of scatterers,” Z. Phys. B. 65, 409–413 (1987).
[CrossRef]

Marks, P. A.

P. A. Marks, H. W. Tomlinson, G. W. Brooksby, “A comprehensive approach to breast cancer detection using light: photon localization by ultrasound modulation and tissue characterization by spectral discrimination,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. SPIE1888, 500–510 (1993).
[CrossRef]

O’Leary, M. A.

Owen, G. M.

Pine, D. J.

A. G. Yodh, P. D. Kaplan, D. J. Pine, “Pulsed diffusing-wave spectroscopy: High resolution through nonlinear optical grating,” Phys. Rev. B 42, 4744–4747 (1990).
[CrossRef]

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[CrossRef] [PubMed]

Rudolph, W.

Sevick, E.

B. Chance, K. Kang, E. Sevick, “Photon diffusion in breast and brain: Spectroscopy and imaging,” Opt. Photon. News 4, 9–13 (1993).
[CrossRef]

Stephen, M. J.

M. J. Stephen, “Temporal fluctuations in wave propagation in random media,” Phys. Rev. B 37, 1–5 (1988).
[CrossRef]

Swanson, E. A.

Tomlinson, H. W.

P. A. Marks, H. W. Tomlinson, G. W. Brooksby, “A comprehensive approach to breast cancer detection using light: photon localization by ultrasound modulation and tissue characterization by spectral discrimination,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. SPIE1888, 500–510 (1993).
[CrossRef]

Wang, L.

L. Wang, S. L. Jacques, X. Zhao, “Continuous-wave ultrasonic modulation of scattered laser light to image objects in turbid media,” Opt. Lett. 20, 629–631 (1995).
[CrossRef] [PubMed]

L. Wang, X. Zhao, S. L. Jacques, “Ultrasound modulated optical tomography,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto, eds., Vol. 2 of 1996 TOPS (Optical Society of America, Washington, D.C., 1996).

Weitz, D. A.

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[CrossRef] [PubMed]

Wolf, P. E.

G. Maret, P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motion of scatterers,” Z. Phys. B. 65, 409–413 (1987).
[CrossRef]

Yodh, A. G.

M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Experimental images of heterogeneous turbid media by frequency domain diffusing-photon tomography,” Opt. Lett. 20, 426–428 (1995).
[CrossRef]

A. G. Yodh, P. D. Kaplan, D. J. Pine, “Pulsed diffusing-wave spectroscopy: High resolution through nonlinear optical grating,” Phys. Rev. B 42, 4744–4747 (1990).
[CrossRef]

Zhao, X.

L. Wang, S. L. Jacques, X. Zhao, “Continuous-wave ultrasonic modulation of scattered laser light to image objects in turbid media,” Opt. Lett. 20, 629–631 (1995).
[CrossRef] [PubMed]

L. Wang, X. Zhao, S. L. Jacques, “Ultrasound modulated optical tomography,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto, eds., Vol. 2 of 1996 TOPS (Optical Society of America, Washington, D.C., 1996).

Appl. Opt.

Opt. Lett.

Opt. Photon. News

B. Chance, K. Kang, E. Sevick, “Photon diffusion in breast and brain: Spectroscopy and imaging,” Opt. Photon. News 4, 9–13 (1993).
[CrossRef]

Phys. Rev. B

N. Garcia, A. Z. Genack, A. A. Lisyansky, “Measurement of the transport mean free path of diffusing photons,” Phys. Rev. B 46, 14475–14479 (1992).
[CrossRef]

M. J. Stephen, “Temporal fluctuations in wave propagation in random media,” Phys. Rev. B 37, 1–5 (1988).
[CrossRef]

A. G. Yodh, P. D. Kaplan, D. J. Pine, “Pulsed diffusing-wave spectroscopy: High resolution through nonlinear optical grating,” Phys. Rev. B 42, 4744–4747 (1990).
[CrossRef]

Phys. Rev. Lett.

D. J. Pine, D. A. Weitz, P. M. Chaikin, E. Herbolzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[CrossRef] [PubMed]

A. Z. Genack, “Transmission in disordered media,” Phys. Rev. Lett. 58, 2043–2046 (1987).
[CrossRef] [PubMed]

Physica B

W. Leutz, G. Maret, “Ultrasonic modulation of multiply scattered light,” Physica B 204, 14–19 (1995).
[CrossRef]

Z. Phys. B.

G. Maret, P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motion of scatterers,” Z. Phys. B. 65, 409–413 (1987).
[CrossRef]

Other

P. A. Marks, H. W. Tomlinson, G. W. Brooksby, “A comprehensive approach to breast cancer detection using light: photon localization by ultrasound modulation and tissue characterization by spectral discrimination,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. SPIE1888, 500–510 (1993).
[CrossRef]

R. R. Alfano, ed., Advances in Optical Imaging and Photon Migration, Vol. 21 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1994).

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

L. Wang, X. Zhao, S. L. Jacques, “Ultrasound modulated optical tomography,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto, eds., Vol. 2 of 1996 TOPS (Optical Society of America, Washington, D.C., 1996).

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Figures (8)

Fig. 1
Fig. 1

Experimental setup. The inset shows the sample used.

Fig. 2
Fig. 2

(a), (b) Averaged data trace and (c), (d) averaged power spectra. The averages were performed over 50 traces for (a), (b) L/ls = 10 and (c), (d) more than 2000 traces for L/ls=85.

Fig. 3
Fig. 3

Heterodyne signal normalized to the signal in clear water for various concentrations of latex spheres in water. For each concentration the sample thickness was varied from 12 to 30 mm. The signal falloff for ballistic light according to Mie theory is shown as solid line. The LO beam was wave front matched to the ballistic light, and the Bragg condition was satisfied.

Fig. 4
Fig. 4

Same signal as in Fig. 3 normalized by L0/L with L0=16 mm as a function of L/l. The solid curve is a fit to the data according to a power law Lp.

Fig. 5
Fig. 5

Normalized spectra from Fig. 2 in the neighborhood of f = 3.5 MHz.

Fig. 6
Fig. 6

Signal for L/ls=20 (upper curve) and L/ls = 45 (lower curve) normalized to the signal in clear water as a function of driving voltage of the transducer. The water signal is linear in U (slope: 1.01 ± 0.01) in the voltage range considered. In the diffusive regime, however, the dependence changes from linear to quadratic.

Fig. 7
Fig. 7

Signal as a function of scan position in the sample. The light is incident on the left sample boundary.

Fig. 8
Fig. 8

On the left, scans of the sound across a black teflon sphere at various positions y within the sample (L/ls=37). On the right, predicted signal as explained in the text.

Equations (19)

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Δϕ(r, r; t+τ, t; α)=-j=1n(α)qj·Δrj(t+τ, t),
Δrj(t+τ, t)=A(rj){sin[ks·rj-ωs(t+τ)]-sin(ks·rj-ωst)}+Δrj(t+τ, t).
G1(r, r, τ; α)=E(r, r, t+τ; α)E*(r, r, t; α)=I0P(r, r; α)exp[-iΔϕ(r, r, τ; α)],
exp[-iΔϕ(r, r, τ; α)]
=expj=1n(α)iqj·(A(rj)×{sin[ks·rj-ωs(t+τ)]-sin(ks·rj-ωst)}+Δrj).
exp[-iΔϕ(r, r, τ; α)]
=m=01m!j=1n(α)jqj·A(rj){sin[ks·rj-ωs(t+τ)]-sin(ks·rj-ωst)}m×j=1n(α)exp(iqj·Δrj).
G1(r, r, τ)=αG1(r, r, τ; α)
G1(r, r, τ)=I0αP(r, r; α)m=01m!j=1n(α)iqj·A(rj) {sin[ks·rj-ωs(t-τ)]-sin(ks·rj-ωst)}m×j=1n(α)exp(iqj·Δrj).
qj·A(rj)qj·A(rj)=[qj·A(rj)]2δjj.
G1(r, r, τ)=-k23I0αj=1n(α)P(r, r; α)A2(rj)×(1-cos ωsτ)exp[iΔϕ(τ)].
P(r, r; α)=P(rj, r; α)P(r, rj; α).
G1(r, r, τ)=-k23I0 j=1n(α)ααP(rj, r; α)×P(r, rj; α)A2(rj)(1-cos ωsτ)×exp[iΔϕ(τ)].
G1(r, τ)-k23l3drI(r)P(r, r)A2(r)×(1-cos ωsτ)exp[iΔϕ(τ)].
I=|ELO+ET|2=|ELO|2+|ET|2+2|ELO|m|ET|cos(ωst+φ)
+2|ELO|(1-m)|ET|cos(ψ),
AdI=Ad[|ELO|2+|ET|2+2|ELO|m|ET|cos(ωst+φ)+2|ELO|(1-m)|ET|cos(ψ)].
2Ad|ELO|m|ET|cos(ωst+φ).
S(2PLOPT)1/2meff,

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