Abstract

A Monte Carlo model of the ultrasonic modulation of multiply scattered coherent light in scattering media is provided. The model is based on two mechanisms: the ultrasonic modulation of the index of refraction, which causes a modulation of the optical path lengths between consecutive scattering events, and the ultrasonic modulation of the displacements of scatterers, which causes a modulation of optical path lengths with each scattering event. Multiply scattered light accumulates modulated optical path lengths along its path. Consequently, the intensity of the speckles that are formed by the multiply scattered light is modulated. The contribution from the index of refraction is comparable with the contribution from displacement when the acoustic-wave vector is less than a critical fraction of the transport mean free path and becomes increasingly greater than the contribution from displacement beyond this critical point. This Monte Carlo model agrees well with an independent analytical model for isotropically scattering media. Both mechanisms are coherent phenomena, requiring the use of a coherent light source.

© 2001 Optical Society of America

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  1. F. A. Marks, H. W. Tomlinson, and G. W. Brooksby, Proc. SPIE 1888, 500 (1993).
    [CrossRef]
  2. L.-H. Wang, S. L. Jacques, and X. Zhao, Opt. Lett. 20, 629 (1995).
    [CrossRef] [PubMed]
  3. M. Kempe, M. Larionov, D. Zaslavsky, and A. Z. Genack, J. Opt. Soc. Am. 14, 1151 (1997).
    [CrossRef]
  4. L.-H. V. Wang and G. Ku, Opt. Lett. 23, 975 (1998).
    [CrossRef]
  5. S. Leveque, A. C. Boccara, M. Lebec, and H. Saint-Jalmes, Opt. Lett. 24, 181 (1999).
    [CrossRef]
  6. G. Yao and L.-H. V. Wang, Appl. Opt. 39, 659 (2000).
    [CrossRef]
  7. G. Yao, S.-L. Jiao, and L.-H. V. Wang, Opt. Lett. 25, 734 (2000).
    [CrossRef]
  8. A. Lev, Z. Kotler, and B. G. Sfez, Opt. Lett. 25, 378 (2000).
    [CrossRef]
  9. G. D. Mahan, W. E. Engler, J. J. Tiemann, and E. Uzgiris, Proc. Natl. Acad. Sci. USA 95, 14015 (1998).
    [CrossRef]
  10. W. Leutz and G. Maret, Physica B 204, 14 (1995).
    [CrossRef]
  11. L.-H. Wang, S. L. Jacques, and L.-Q. Zheng, Comput. Methods Programs Biomed. 47, 131 (1995).
    [CrossRef] [PubMed]
  12. Software available at http://oilab.tamu.edu./mc.html .
  13. L.-H. Wang, Proc. SPIE 4256, 208 (2001).
    [CrossRef]
  14. C. A. DiMarzio, R. J. Gaudette, and T. J. Gaudette, Proc. SPIE 3597, 376 (1999).
    [CrossRef]

2001 (1)

L.-H. Wang, Proc. SPIE 4256, 208 (2001).
[CrossRef]

2000 (3)

1999 (2)

C. A. DiMarzio, R. J. Gaudette, and T. J. Gaudette, Proc. SPIE 3597, 376 (1999).
[CrossRef]

S. Leveque, A. C. Boccara, M. Lebec, and H. Saint-Jalmes, Opt. Lett. 24, 181 (1999).
[CrossRef]

1998 (2)

G. D. Mahan, W. E. Engler, J. J. Tiemann, and E. Uzgiris, Proc. Natl. Acad. Sci. USA 95, 14015 (1998).
[CrossRef]

L.-H. V. Wang and G. Ku, Opt. Lett. 23, 975 (1998).
[CrossRef]

1997 (1)

M. Kempe, M. Larionov, D. Zaslavsky, and A. Z. Genack, J. Opt. Soc. Am. 14, 1151 (1997).
[CrossRef]

1995 (3)

L.-H. Wang, S. L. Jacques, and X. Zhao, Opt. Lett. 20, 629 (1995).
[CrossRef] [PubMed]

W. Leutz and G. Maret, Physica B 204, 14 (1995).
[CrossRef]

L.-H. Wang, S. L. Jacques, and L.-Q. Zheng, Comput. Methods Programs Biomed. 47, 131 (1995).
[CrossRef] [PubMed]

1993 (1)

F. A. Marks, H. W. Tomlinson, and G. W. Brooksby, Proc. SPIE 1888, 500 (1993).
[CrossRef]

Boccara, A. C.

Brooksby, G. W.

F. A. Marks, H. W. Tomlinson, and G. W. Brooksby, Proc. SPIE 1888, 500 (1993).
[CrossRef]

DiMarzio, C. A.

C. A. DiMarzio, R. J. Gaudette, and T. J. Gaudette, Proc. SPIE 3597, 376 (1999).
[CrossRef]

Engler, W. E.

G. D. Mahan, W. E. Engler, J. J. Tiemann, and E. Uzgiris, Proc. Natl. Acad. Sci. USA 95, 14015 (1998).
[CrossRef]

Gaudette, R. J.

C. A. DiMarzio, R. J. Gaudette, and T. J. Gaudette, Proc. SPIE 3597, 376 (1999).
[CrossRef]

Gaudette, T. J.

C. A. DiMarzio, R. J. Gaudette, and T. J. Gaudette, Proc. SPIE 3597, 376 (1999).
[CrossRef]

Genack, A. Z.

M. Kempe, M. Larionov, D. Zaslavsky, and A. Z. Genack, J. Opt. Soc. Am. 14, 1151 (1997).
[CrossRef]

Jacques, S. L.

L.-H. Wang, S. L. Jacques, and X. Zhao, Opt. Lett. 20, 629 (1995).
[CrossRef] [PubMed]

L.-H. Wang, S. L. Jacques, and L.-Q. Zheng, Comput. Methods Programs Biomed. 47, 131 (1995).
[CrossRef] [PubMed]

Jiao, S.-L.

Kempe, M.

M. Kempe, M. Larionov, D. Zaslavsky, and A. Z. Genack, J. Opt. Soc. Am. 14, 1151 (1997).
[CrossRef]

Kotler, Z.

Ku, G.

Larionov, M.

M. Kempe, M. Larionov, D. Zaslavsky, and A. Z. Genack, J. Opt. Soc. Am. 14, 1151 (1997).
[CrossRef]

Lebec, M.

Leutz, W.

W. Leutz and G. Maret, Physica B 204, 14 (1995).
[CrossRef]

Lev, A.

Leveque, S.

Mahan, G. D.

G. D. Mahan, W. E. Engler, J. J. Tiemann, and E. Uzgiris, Proc. Natl. Acad. Sci. USA 95, 14015 (1998).
[CrossRef]

Maret, G.

W. Leutz and G. Maret, Physica B 204, 14 (1995).
[CrossRef]

Marks, F. A.

F. A. Marks, H. W. Tomlinson, and G. W. Brooksby, Proc. SPIE 1888, 500 (1993).
[CrossRef]

Saint-Jalmes, H.

Sfez, B. G.

Tiemann, J. J.

G. D. Mahan, W. E. Engler, J. J. Tiemann, and E. Uzgiris, Proc. Natl. Acad. Sci. USA 95, 14015 (1998).
[CrossRef]

Tomlinson, H. W.

F. A. Marks, H. W. Tomlinson, and G. W. Brooksby, Proc. SPIE 1888, 500 (1993).
[CrossRef]

Uzgiris, E.

G. D. Mahan, W. E. Engler, J. J. Tiemann, and E. Uzgiris, Proc. Natl. Acad. Sci. USA 95, 14015 (1998).
[CrossRef]

Wang, L.-H.

L.-H. Wang, Proc. SPIE 4256, 208 (2001).
[CrossRef]

L.-H. Wang, S. L. Jacques, and L.-Q. Zheng, Comput. Methods Programs Biomed. 47, 131 (1995).
[CrossRef] [PubMed]

L.-H. Wang, S. L. Jacques, and X. Zhao, Opt. Lett. 20, 629 (1995).
[CrossRef] [PubMed]

Wang, L.-H. V.

Yao, G.

Zaslavsky, D.

M. Kempe, M. Larionov, D. Zaslavsky, and A. Z. Genack, J. Opt. Soc. Am. 14, 1151 (1997).
[CrossRef]

Zhao, X.

Zheng, L.-Q.

L.-H. Wang, S. L. Jacques, and L.-Q. Zheng, Comput. Methods Programs Biomed. 47, 131 (1995).
[CrossRef] [PubMed]

Appl. Opt. (1)

Comput. Methods Programs Biomed. (1)

L.-H. Wang, S. L. Jacques, and L.-Q. Zheng, Comput. Methods Programs Biomed. 47, 131 (1995).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

M. Kempe, M. Larionov, D. Zaslavsky, and A. Z. Genack, J. Opt. Soc. Am. 14, 1151 (1997).
[CrossRef]

Opt. Lett. (5)

Physica B (1)

W. Leutz and G. Maret, Physica B 204, 14 (1995).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

G. D. Mahan, W. E. Engler, J. J. Tiemann, and E. Uzgiris, Proc. Natl. Acad. Sci. USA 95, 14015 (1998).
[CrossRef]

Proc. SPIE (3)

F. A. Marks, H. W. Tomlinson, and G. W. Brooksby, Proc. SPIE 1888, 500 (1993).
[CrossRef]

L.-H. Wang, Proc. SPIE 4256, 208 (2001).
[CrossRef]

C. A. DiMarzio, R. J. Gaudette, and T. J. Gaudette, Proc. SPIE 3597, 376 (1999).
[CrossRef]

Other (1)

Software available at http://oilab.tamu.edu./mc.html .

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Figures (2)

Fig. 1
Fig. 1

(a) Mn, Md, and Msum and (b) Mn/Md versus ka. The parameters are n/p=1.466×10-10m2/N, ρ=1000 kg/m3, νa=1480 m/s, A=0.1 nm, n0=1.33, λ0=500 nm, μs=10 cm-1, g=0, and L=5 cm.

Fig. 2
Fig. 2

Mn and Md versus g while μs1-g is kept constant. The subscript mc indicates the results from the Monte Carlo model; and the subscript eq represents the results from the analytical model, where the modulation depths for g>0 are assumed to be equal to those for g=0. The parameters in Fig.  1 are used, except that Ta=10 μs and μs1-g=10 cm-1.

Equations (6)

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

G1τ=0psEstEs*t+τds,
EstEs*t+τ=exp-iΔϕt,τ,
ϕnjt=0ljk0Δnrj-1,sj,θj,tdsj,
Δnrj-1,sj,θ,t=n0ηkaAsinka·rj-1+kasjcosθj-ωat,
ϕnjt=2n0k0ηAsinka·rj-1+kaljcosθj/2-ωat×sinkaljcosθj/2/cosθj.
ϕdjt=-n0k0k^j+1-k^j·Asinka·rj-ωat,

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