Abstract

While phase variation due to ultrasonic modulation of coherent light has been extensively studied in acousto-optical imaging, fewer groups have studied nonphase mechanisms of ultrasonic modulation, which may be important in exploring ultrasonic modulation of incoherent light for imaging. We have developed a versatile Monte Carlo based method that can model not only phase variation due to refractive index changes and scatterer displacement in tissue or tissue-like phantoms, but also amplitude and exit location variations due to the changes in optical properties and refractive index under ultrasonic modulation, in which the exit location variation has not, to the best of our knowledge, been modeled previously. Our results show that the modulation depth due to the exit location variation is three orders of magnitude higher than that due to amplitude variation, but two to three orders of magnitude lower than that due to phase variation for monochromatic light. Furthermore it is found that the modulation depth in reflectance due to the exit location variation is larger than that in transmittance for small source-detector separations.

© 2008 Optical Society of America

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References

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  1. L. V. Wang, “Ultrasound-mediated biophotonic imaging: a review of acousto-optical tomography and photo-acoustic tomography,” Dis. Markers 19, 123-138 (2003).
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    [CrossRef]
  3. S. Sakadzic and L. V. Wang, “Modulation of multiply scattered coherent light by ultrasonic pulses: an analytical model,” Phys. Rev. E 72, 036620 (2005).
    [CrossRef]
  4. S. Sakadzic and L. V. Wang, “Ultrasonic modulation of multiply scattered coherent light: an analytical model for anisotropically scattering media,” Phys. Rev. E 66, 026603 (2002).
    [CrossRef]
  5. L. V. Wang, “Mechanisms of ultrasonic modulation of multiply scattered coherent light: a Monte Carlo model,” Opt. Lett. 26, 1191-1193 (2001).
    [CrossRef]
  6. M. Kempe, M. Larionov, D. Zaslavsky, and A. Z. Genack, “Acousto-optic tomography with multiply scattered light,” J. Opt. Soc. Am. A 14, 1151-1158 (1997).
    [CrossRef]
  7. A. Lev and B. Sfez, “In vivo demonstration of the ultrasound-modulated light technique,” J. Opt. Soc. Am. A 20, 2347-2354(2003).
    [CrossRef]
  8. S. Sakadzic and L. V. Wang, “High-resolution ultrasound-modulated optical tomography in biological tissues,” Opt. Lett. 29, 2770-2772 (2004).
    [CrossRef] [PubMed]
  9. A. Lev and B. G. Sfez, “Direct, noninvasive detection of photon density in turbid media,” Opt. Lett. 27, 473-475 (2002).
    [CrossRef]
  10. S. Leveque-Fort, J. Selb, L. Pottier, and A. C. Boccara, “In situ local tissue characterization and imaging by backscattering acousto-optic imaging,” Opt. Commun. 196, 127-131 (2001).
    [CrossRef]
  11. Y. Gang, J. Shuliang, and L. V. Wang, “Frequency-swept ultrasound-modulated optical tomography in biological tissue by use of parallel detection,” Opt. Lett. 25, 734-736 (2000).
    [CrossRef]
  12. L. Sui, R. A. Roy, C. A. DiMarzio, and T. W. Murray, “Imaging in diffuse media with pulsed-ultrasound-modulated light and the photorefractive effect,” Appl. Opt. 44, 4041-4048 (2005).
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  15. E. Granot, A. Lev, Z. Kotler, B. G. Sfez, and H. Taitelbaum, “Detection of inhomogeneities with ultrasound tagging of light,” J. Opt. Soc. Am. A 18, 1962-1967 (2001).
    [CrossRef]
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  17. M. Kobayashi, T. Mizumoto, Y. Shibuya, M. Enomoto, and M. Takeda, “Fluorescence tomography in turbid media based on acousto-optic modulation imaging,” Appl. Phys. Lett. 89, 181101 (2006).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  24. Y. Gang and L. V. Wang, “Theoretical and experimental studies of ultrasound-modulated optical tomography in biological tissue,” Appl. Opt. 39, 659-664 (2000).
    [CrossRef]
  25. T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879-888 (1992).
    [CrossRef] [PubMed]
  26. T. Khan and J. Huabei, “A new diffusion approximation to the radiative transfer equation for scattering media with spatially varying refractive indices,” J. Opt. A 5, 137-141 (2003).
    [CrossRef]
  27. S. Norton, Q. Liu, and T. Vo-Dinh, “Ultrasonic modulation of diffuse incoherent light--a diffuse theory-based model,” in preparation (2008).
  28. W. Lihong and Z. Xuemei, “Ultrasound-modulated optical tomography of absorbing objects buried in dense tissue-simulating turbid media,” Appl. Opt. 36, 7277-7282 (1997).
    [CrossRef]
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2008 (1)

S. Norton, Q. Liu, and T. Vo-Dinh, “Ultrasonic modulation of diffuse incoherent light--a diffuse theory-based model,” in preparation (2008).

2006 (1)

M. Kobayashi, T. Mizumoto, Y. Shibuya, M. Enomoto, and M. Takeda, “Fluorescence tomography in turbid media based on acousto-optic modulation imaging,” Appl. Phys. Lett. 89, 181101 (2006).
[CrossRef]

2005 (3)

2004 (2)

S. Sakadzic and L. V. Wang, “High-resolution ultrasound-modulated optical tomography in biological tissues,” Opt. Lett. 29, 2770-2772 (2004).
[CrossRef] [PubMed]

A. Sassaroli and S. Fantini, “Comment on the modified Beer-Lambert law for scattering media,” Phys. Med. Biol. 49, N255-N257 (2004).
[CrossRef] [PubMed]

2003 (3)

T. Khan and J. Huabei, “A new diffusion approximation to the radiative transfer equation for scattering media with spatially varying refractive indices,” J. Opt. A 5, 137-141 (2003).
[CrossRef]

L. V. Wang, “Ultrasound-mediated biophotonic imaging: a review of acousto-optical tomography and photo-acoustic tomography,” Dis. Markers 19, 123-138 (2003).

A. Lev and B. Sfez, “In vivo demonstration of the ultrasound-modulated light technique,” J. Opt. Soc. Am. A 20, 2347-2354(2003).
[CrossRef]

2002 (2)

A. Lev and B. G. Sfez, “Direct, noninvasive detection of photon density in turbid media,” Opt. Lett. 27, 473-475 (2002).
[CrossRef]

S. Sakadzic and L. V. Wang, “Ultrasonic modulation of multiply scattered coherent light: an analytical model for anisotropically scattering media,” Phys. Rev. E 66, 026603 (2002).
[CrossRef]

2001 (4)

L. V. Wang, “Mechanisms of ultrasonic modulation of multiply scattered coherent light: a Monte Carlo model,” Opt. Lett. 26, 1191-1193 (2001).
[CrossRef]

S. Leveque-Fort, J. Selb, L. Pottier, and A. C. Boccara, “In situ local tissue characterization and imaging by backscattering acousto-optic imaging,” Opt. Commun. 196, 127-131 (2001).
[CrossRef]

E. Granot, A. Lev, Z. Kotler, B. G. Sfez, and H. Taitelbaum, “Detection of inhomogeneities with ultrasound tagging of light,” J. Opt. Soc. Am. A 18, 1962-1967 (2001).
[CrossRef]

L. V. Wang, “Mechanisms of ultrasonic modulation of multiply scattered coherent light: an analytic model,” Phys. Rev. Lett. 87, 043903 (2001).
[CrossRef] [PubMed]

2000 (2)

1998 (1)

G. D. Mahan, W. E. Engler, J. J. Tiemann, and E. Uzgiris, “Ultrasonic tagging of light: theory,” Proc. Natl. Acad. Sci. USA 95, 14015-14019 (1998).
[CrossRef] [PubMed]

1997 (2)

1995 (2)

L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

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

1992 (2)

T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879-888 (1992).
[CrossRef] [PubMed]

R. Graaff, J. G. Aarnoudse, J. R. Zijp, P. M. A. Sloot, F. F. M. de Mul, J. Greve, and M. H. Koelink, “Reduced light-scattering properties for mixtures of spherical particles: a simple approximation derived from Mie calculations,” Appl. Opt. 31, 1370-1376 (1992).
[CrossRef] [PubMed]

1982 (1)

S. J. Norton and M. Linzer, “Correcting for ray refraction in velocity and attenuation tomography: a perturbation approach,” Ultrason. Imag. 4, 201-233 (1982).
[CrossRef]

Aarnoudse, J. G.

Atlan, M.

Boccara, A. C.

M. Atlan, B. C. Forget, F. Ramaz, A. C. Boccara, and M. Gross, “Pulsed acousto-optic imaging in dynamic scattering media with heterodyne parallel speckle detection,” Opt. Lett. 30, 1360-1362 (2005).
[CrossRef] [PubMed]

S. Leveque-Fort, J. Selb, L. Pottier, and A. C. Boccara, “In situ local tissue characterization and imaging by backscattering acousto-optic imaging,” Opt. Commun. 196, 127-131 (2001).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
[PubMed]

de Mul, F. F. M.

DiMarzio, C. A.

Engler, W. E.

G. D. Mahan, W. E. Engler, J. J. Tiemann, and E. Uzgiris, “Ultrasonic tagging of light: theory,” Proc. Natl. Acad. Sci. USA 95, 14015-14019 (1998).
[CrossRef] [PubMed]

Enomoto, M.

M. Kobayashi, T. Mizumoto, Y. Shibuya, M. Enomoto, and M. Takeda, “Fluorescence tomography in turbid media based on acousto-optic modulation imaging,” Appl. Phys. Lett. 89, 181101 (2006).
[CrossRef]

Fantini, S.

A. Sassaroli and S. Fantini, “Comment on the modified Beer-Lambert law for scattering media,” Phys. Med. Biol. 49, N255-N257 (2004).
[CrossRef] [PubMed]

Farrell, T. J.

T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879-888 (1992).
[CrossRef] [PubMed]

Fomitchov, P.

K. B. Krishnan, P. Fomitchov, S. J. Lomnes, M. Kollegal, and F. P. Jansen, “A theory for the ultrasonic modulation of incoherent light in turbid medium,” in Optical Methods in Drug Discovery and Development, M.Analoui and D.A.Dunn, eds. (International Society for Optical Engineering, 2005), p. 60090.

Forget, B. C.

Gang, Y.

Genack, A. Z.

Graaff, R.

Granot, E.

Greve, J.

Gross, M.

Huabei, J.

T. Khan and J. Huabei, “A new diffusion approximation to the radiative transfer equation for scattering media with spatially varying refractive indices,” J. Opt. A 5, 137-141 (2003).
[CrossRef]

Jacques, S. L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

Jansen, F. P.

K. B. Krishnan, P. Fomitchov, S. J. Lomnes, M. Kollegal, and F. P. Jansen, “A theory for the ultrasonic modulation of incoherent light in turbid medium,” in Optical Methods in Drug Discovery and Development, M.Analoui and D.A.Dunn, eds. (International Society for Optical Engineering, 2005), p. 60090.

Kempe, M.

Khan, T.

T. Khan and J. Huabei, “A new diffusion approximation to the radiative transfer equation for scattering media with spatially varying refractive indices,” J. Opt. A 5, 137-141 (2003).
[CrossRef]

Kobayashi, M.

M. Kobayashi, T. Mizumoto, Y. Shibuya, M. Enomoto, and M. Takeda, “Fluorescence tomography in turbid media based on acousto-optic modulation imaging,” Appl. Phys. Lett. 89, 181101 (2006).
[CrossRef]

Koelink, M. H.

Kollegal, M.

K. B. Krishnan, P. Fomitchov, S. J. Lomnes, M. Kollegal, and F. P. Jansen, “A theory for the ultrasonic modulation of incoherent light in turbid medium,” in Optical Methods in Drug Discovery and Development, M.Analoui and D.A.Dunn, eds. (International Society for Optical Engineering, 2005), p. 60090.

Kotler, Z.

Krishnan, K. B.

K. B. Krishnan, P. Fomitchov, S. J. Lomnes, M. Kollegal, and F. P. Jansen, “A theory for the ultrasonic modulation of incoherent light in turbid medium,” in Optical Methods in Drug Discovery and Development, M.Analoui and D.A.Dunn, eds. (International Society for Optical Engineering, 2005), p. 60090.

Larionov, M.

Leutz, W.

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

Lev, A.

Leveque-Fort, S.

S. Leveque-Fort, J. Selb, L. Pottier, and A. C. Boccara, “In situ local tissue characterization and imaging by backscattering acousto-optic imaging,” Opt. Commun. 196, 127-131 (2001).
[CrossRef]

Lihong, W.

Linzer, M.

S. J. Norton and M. Linzer, “Correcting for ray refraction in velocity and attenuation tomography: a perturbation approach,” Ultrason. Imag. 4, 201-233 (1982).
[CrossRef]

Liu, Q.

S. Norton, Q. Liu, and T. Vo-Dinh, “Ultrasonic modulation of diffuse incoherent light--a diffuse theory-based model,” in preparation (2008).

Lomnes, S. J.

K. B. Krishnan, P. Fomitchov, S. J. Lomnes, M. Kollegal, and F. P. Jansen, “A theory for the ultrasonic modulation of incoherent light in turbid medium,” in Optical Methods in Drug Discovery and Development, M.Analoui and D.A.Dunn, eds. (International Society for Optical Engineering, 2005), p. 60090.

Mahan, G. D.

G. D. Mahan, W. E. Engler, J. J. Tiemann, and E. Uzgiris, “Ultrasonic tagging of light: theory,” Proc. Natl. Acad. Sci. USA 95, 14015-14019 (1998).
[CrossRef] [PubMed]

Maret, G.

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

Mizumoto, T.

M. Kobayashi, T. Mizumoto, Y. Shibuya, M. Enomoto, and M. Takeda, “Fluorescence tomography in turbid media based on acousto-optic modulation imaging,” Appl. Phys. Lett. 89, 181101 (2006).
[CrossRef]

Murray, T. W.

Norton, S.

S. Norton, Q. Liu, and T. Vo-Dinh, “Ultrasonic modulation of diffuse incoherent light--a diffuse theory-based model,” in preparation (2008).

Norton, S. J.

S. J. Norton and M. Linzer, “Correcting for ray refraction in velocity and attenuation tomography: a perturbation approach,” Ultrason. Imag. 4, 201-233 (1982).
[CrossRef]

Patterson, M. S.

T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879-888 (1992).
[CrossRef] [PubMed]

Pottier, L.

S. Leveque-Fort, J. Selb, L. Pottier, and A. C. Boccara, “In situ local tissue characterization and imaging by backscattering acousto-optic imaging,” Opt. Commun. 196, 127-131 (2001).
[CrossRef]

Ramaz, F.

Roy, R. A.

Sakadzic, S.

S. Sakadzic and L. V. Wang, “Modulation of multiply scattered coherent light by ultrasonic pulses: an analytical model,” Phys. Rev. E 72, 036620 (2005).
[CrossRef]

S. Sakadzic and L. V. Wang, “High-resolution ultrasound-modulated optical tomography in biological tissues,” Opt. Lett. 29, 2770-2772 (2004).
[CrossRef] [PubMed]

S. Sakadzic and L. V. Wang, “Ultrasonic modulation of multiply scattered coherent light: an analytical model for anisotropically scattering media,” Phys. Rev. E 66, 026603 (2002).
[CrossRef]

Sassaroli, A.

A. Sassaroli and S. Fantini, “Comment on the modified Beer-Lambert law for scattering media,” Phys. Med. Biol. 49, N255-N257 (2004).
[CrossRef] [PubMed]

Selb, J.

S. Leveque-Fort, J. Selb, L. Pottier, and A. C. Boccara, “In situ local tissue characterization and imaging by backscattering acousto-optic imaging,” Opt. Commun. 196, 127-131 (2001).
[CrossRef]

Sfez, B.

Sfez, B. G.

Shibuya, Y.

M. Kobayashi, T. Mizumoto, Y. Shibuya, M. Enomoto, and M. Takeda, “Fluorescence tomography in turbid media based on acousto-optic modulation imaging,” Appl. Phys. Lett. 89, 181101 (2006).
[CrossRef]

Shuliang, J.

Sloot, P. M. A.

Sui, L.

Taitelbaum, H.

Takeda, M.

M. Kobayashi, T. Mizumoto, Y. Shibuya, M. Enomoto, and M. Takeda, “Fluorescence tomography in turbid media based on acousto-optic modulation imaging,” Appl. Phys. Lett. 89, 181101 (2006).
[CrossRef]

Tiemann, J. J.

G. D. Mahan, W. E. Engler, J. J. Tiemann, and E. Uzgiris, “Ultrasonic tagging of light: theory,” Proc. Natl. Acad. Sci. USA 95, 14015-14019 (1998).
[CrossRef] [PubMed]

Uzgiris, E.

G. D. Mahan, W. E. Engler, J. J. Tiemann, and E. Uzgiris, “Ultrasonic tagging of light: theory,” Proc. Natl. Acad. Sci. USA 95, 14015-14019 (1998).
[CrossRef] [PubMed]

Vo-Dinh, T.

S. Norton, Q. Liu, and T. Vo-Dinh, “Ultrasonic modulation of diffuse incoherent light--a diffuse theory-based model,” in preparation (2008).

Wang, L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

Wang, L. V.

S. Sakadzic and L. V. Wang, “Modulation of multiply scattered coherent light by ultrasonic pulses: an analytical model,” Phys. Rev. E 72, 036620 (2005).
[CrossRef]

S. Sakadzic and L. V. Wang, “High-resolution ultrasound-modulated optical tomography in biological tissues,” Opt. Lett. 29, 2770-2772 (2004).
[CrossRef] [PubMed]

L. V. Wang, “Ultrasound-mediated biophotonic imaging: a review of acousto-optical tomography and photo-acoustic tomography,” Dis. Markers 19, 123-138 (2003).

S. Sakadzic and L. V. Wang, “Ultrasonic modulation of multiply scattered coherent light: an analytical model for anisotropically scattering media,” Phys. Rev. E 66, 026603 (2002).
[CrossRef]

L. V. Wang, “Mechanisms of ultrasonic modulation of multiply scattered coherent light: a Monte Carlo model,” Opt. Lett. 26, 1191-1193 (2001).
[CrossRef]

L. V. Wang, “Mechanisms of ultrasonic modulation of multiply scattered coherent light: an analytic model,” Phys. Rev. Lett. 87, 043903 (2001).
[CrossRef] [PubMed]

Y. Gang and L. V. Wang, “Theoretical and experimental studies of ultrasound-modulated optical tomography in biological tissue,” Appl. Opt. 39, 659-664 (2000).
[CrossRef]

Y. Gang, J. Shuliang, and L. V. Wang, “Frequency-swept ultrasound-modulated optical tomography in biological tissue by use of parallel detection,” Opt. Lett. 25, 734-736 (2000).
[CrossRef]

Weisstein, E. W.

E. W. Weisstein, “Rotation formula,” http://mathworld.wolfram.com/RotationFormula.html.

Wilson, B.

T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879-888 (1992).
[CrossRef] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
[PubMed]

Xuemei, Z.

Zaslavsky, D.

Zheng, L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

Zijp, J. R.

Appl. Opt. (4)

Appl. Phys. Lett. (1)

M. Kobayashi, T. Mizumoto, Y. Shibuya, M. Enomoto, and M. Takeda, “Fluorescence tomography in turbid media based on acousto-optic modulation imaging,” Appl. Phys. Lett. 89, 181101 (2006).
[CrossRef]

Comput. Methods Programs Biomed. (1)

L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

Dis. Markers (1)

L. V. Wang, “Ultrasound-mediated biophotonic imaging: a review of acousto-optical tomography and photo-acoustic tomography,” Dis. Markers 19, 123-138 (2003).

J. Opt. A (1)

T. Khan and J. Huabei, “A new diffusion approximation to the radiative transfer equation for scattering media with spatially varying refractive indices,” J. Opt. A 5, 137-141 (2003).
[CrossRef]

J. Opt. Soc. Am. A (3)

Med. Phys. (1)

T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879-888 (1992).
[CrossRef] [PubMed]

Opt. Commun. (1)

S. Leveque-Fort, J. Selb, L. Pottier, and A. C. Boccara, “In situ local tissue characterization and imaging by backscattering acousto-optic imaging,” Opt. Commun. 196, 127-131 (2001).
[CrossRef]

Opt. Lett. (5)

Phys. Med. Biol. (1)

A. Sassaroli and S. Fantini, “Comment on the modified Beer-Lambert law for scattering media,” Phys. Med. Biol. 49, N255-N257 (2004).
[CrossRef] [PubMed]

Phys. Rev. E (2)

S. Sakadzic and L. V. Wang, “Modulation of multiply scattered coherent light by ultrasonic pulses: an analytical model,” Phys. Rev. E 72, 036620 (2005).
[CrossRef]

S. Sakadzic and L. V. Wang, “Ultrasonic modulation of multiply scattered coherent light: an analytical model for anisotropically scattering media,” Phys. Rev. E 66, 026603 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

L. V. Wang, “Mechanisms of ultrasonic modulation of multiply scattered coherent light: an analytic model,” Phys. Rev. Lett. 87, 043903 (2001).
[CrossRef] [PubMed]

Physica B (1)

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

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

G. D. Mahan, W. E. Engler, J. J. Tiemann, and E. Uzgiris, “Ultrasonic tagging of light: theory,” Proc. Natl. Acad. Sci. USA 95, 14015-14019 (1998).
[CrossRef] [PubMed]

Ultrason. Imag. (1)

S. J. Norton and M. Linzer, “Correcting for ray refraction in velocity and attenuation tomography: a perturbation approach,” Ultrason. Imag. 4, 201-233 (1982).
[CrossRef]

Other (4)

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
[PubMed]

S. Norton, Q. Liu, and T. Vo-Dinh, “Ultrasonic modulation of diffuse incoherent light--a diffuse theory-based model,” in preparation (2008).

E. W. Weisstein, “Rotation formula,” http://mathworld.wolfram.com/RotationFormula.html.

K. B. Krishnan, P. Fomitchov, S. J. Lomnes, M. Kollegal, and F. P. Jansen, “A theory for the ultrasonic modulation of incoherent light in turbid medium,” in Optical Methods in Drug Discovery and Development, M.Analoui and D.A.Dunn, eds. (International Society for Optical Engineering, 2005), p. 60090.

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Figures (6)

Fig. 1
Fig. 1

A photon is assumed to start from A ( 0 , 0 , 0 ) and travel along the z axis, which would end at ( 0 , 0 , z ) for a uniform distribution of the refractive index. In the presence of a refractive index gradient, the photon path deviates from the straight line and ends at B ( x , y , z ) .

Fig. 2
Fig. 2

Schematic of a photon step and the corresponding temporary coordinate system ( x , y , z ) for the calculation of x and y displacements due to ultrasonic modulation. r j 1 is the start position and r j is the end position in the absence of ultrasonic modulation. s j = r j r j 1 , which makes an angle of θ j with the ultrasonic wave vector k a . The + z axis of the temporary coordinate system is aligned with s j and the x and y axes are arbitrarily chosen so that they are orthogonal to the z axis and to each other.

Fig. 3
Fig. 3

(a) Setup in simulations. The bold horizontal lines represent the top and bottom surfaces of the tissue model. The two cylinders on the top surface are the circular detectors for detecting reflectance, while the two cylinders on the bottom surface are for detecting transmittance. The straight line with an arrow pointing at the top surface is a pencil incident beam. The four curved lines with arrows represent the trajectories of those photons detected on the top or bottom surfaces. The gray block arrow represents a planar ultrasound that travels downward. It can be seen that the setup is radially symmetrical about the incident beam. (b) The relation between a ring detector and the corresponding circular detector. The central dark spot is the source location, the light gray annular ring is the ring detector, and the dark gray circle with the bold line is the corresponding circular detector. The thickness of the ring detector is equal to the diameter of the corresponding circular detector.

Fig. 4
Fig. 4

(a)  cos ( ω a t ) coefficient and (b)  sin ( ω a t ) coefficient in Δ w (change in the exit weight) for albedo modulation; (c)  cos ( ω a t ) coefficient and (d)  sin ( ω a t ) coefficient in Δ r (change in the exit radial distance) for total attenuation coefficient modulation; and (e)  cos ( ω a t ) coefficient and (f)  sin ( ω a t ) coefficient in Δ r for refractive index modulation as a function of the radial distance, which was calculated for diffuse reflectance simulated for a detector with a diameter of 64 μm and an ultrasound frequency of 1 MHz . The circles are the simulated results, and the continuous curves represent the fitted polynomials. The units in (c)–(e) are in cm .

Fig. 5
Fig. 5

Modulation depth in intensity as a function of ultrasonic frequency for (a) amplitude variation due to albedo modulation, (b) exit location variation due to the total attenuation coefficient modulation, and (c) exit location variation due to refractive index modulation. The optical properties of the tissue model were kept unchanged in all simulations. Both the optical properties and ultrasonic properties are shown in Table 2. The diameter of the circular detector [in (a)] or the radial thickness of the ring detector [in (b) and (c)] was fixed at 10 μm .

Fig. 6
Fig. 6

Absolute values of the second-order derivatives of the reflectance and the transmittance as a function of the radial distance. The optical properties of the simulation that generated the result are shown in Table 2.

Tables (4)

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Table 1 Mechanisms of Ultrasonic Modulation

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Table 2 Optical Parameters and Ultrasonic Parameters Used in Simulations a

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Table 3 Modulation Depths in Reflectance and Transmittance for the Mechanisms of the Exit Location Variation and Two Separations (One Small and One Large) a

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Table 4 Comparison in γ, Δ w , and Δ L Between the Different Ratios of Δ n p and Δ n med

Equations (41)

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Δ n ( t ) = n η k a A sin ( k a · r j ω a t ) ,
μ a = 2.303 i ε i C i ,
Δ μ a ( t ) = μ a δ 1 j ( t ) ,
δ 1 j ( t ) = k a A sin ( k a · r j ω a t ) .
μ s = ρ s Q s A s ,
Δ ρ s ( t ) = ρ s δ 1 j ( t ) ,
ρ s ( t ) = ρ s + Δ ρ s ( t ) = ρ s [ 1 + δ 1 j ( t ) ] ,
Q s = 3.28 x 0.37 ( n r 1 ) 2.09 ,
n med ( t ) = n med + Δ n med ( t ) = n med [ 1 + η δ 1 j ( t ) ] ,
Q s ( t ) = Q s [ 1 + 0.37 η δ 1 j ( t ) ] ,
μ s ( t ) = ρ s ( t ) Q s ( t ) A s μ s [ 1 + δ 1 j ( t ) + 0.37 η δ 1 j ( t ) ] ,
Δ μ s ( t ) = μ s [ 1 + 0.37 η ] k a A sin ( k a · k j ω a t ) .
γ = 1 + 0.37 η ,
Δ μ s ( t ) = μ s γ k a A sin ( k a · r j ω a t ) .
a ( t ) = μ s + Δ μ s ( t ) μ t + Δ μ t ( t ) = μ s [ 1 + γ δ 1 j ( t ) ] μ t + [ ( μ a + μ s γ ) δ 1 j ( t ) ] a · [ 1 + ( γ 1 ) · ( 1 a ) · δ 1 j ( t ) ] ,
j = 1 N [ a ( t ) ] = a N · j = 1 N [ 1 + ( γ 1 ) · ( 1 a ) · δ 1 j ( t ) ] a N · [ 1 + i = 1 N ( γ 1 ) · ( 1 a ) · δ 1 j ( t ) ] .
Δ w ( t ) = ( γ 1 ) · ( 1 a ) · δ 1 j ( t ) .
Δ μ t ( t ) = Δ ( μ a + μ s ) ( t ) = ( μ a + μ s γ ) k a A sin ( k a · r j ω a t ) .
ln ( ξ ) = 0 L μ t ( s ) d s = 0 L [ μ t + Δ μ t ( s ) ] d s .
Δ L ( t ) = L L = 2 μ a + μ s γ μ t δ 2 j ( t ) = 2 [ 1 + ( γ 1 ) · a ] δ 2 j ( t ) ,
δ 2 j ( t ) = A sin ( k a · r j 1 + k a L cos θ j 2 ω a t ) sin ( k a L cos θ j 2 ) / cos θ j .
n ( x , y , z ) = n 0 + ε h ( x , y , z ) ,
x ( z ) = ε f ( z ) , y ( z ) = ε g ( z ) ,
n ( x , y , z ) = n ( ε f , ε g , z ) = n 0 + ε h ( ε f , ε g , z ) = n 0 + ε h 0 ( z ) + ε 2 f h x ( z ) + ε 2 g h y ( z ) + o ( ε 3 ) ,
n x x 2 + y 2 + 1 = d d z ( n x x 2 + y 2 + 1 ) , n y x 2 + y 2 + 1 = d d z ( n y x 2 + y 2 + 1 ) ,
n 0 d 2 f d z 2 = h x ( z ) , n 0 d 2 g d z 2 = h y ( z ) .
f ( z ) = 1 n 0 0 z ( z z ) h x ( z ) d z , g ( z ) = 1 n 0 0 z ( z z ) h y ( z ) d z .
n ( r j ) = n + n η k a A sin ( k a · r j ω a t ) = n + n η k a A sin [ k a · ( r j 1 + s j ) ω a t ] = n + n η k a A sin [ k a · r j 1 + k a s j ω a t ] .
n ( s ) = n + n η k a A sin [ k a · r j 1 + k a · s ω a t ] = n + n η k a A sin [ k a · r j 1 + k a x x + k a y y + k a z z ω a t ] .
ε = n η k a A and h ( x , y , z ) = sin [ k a · r j 1 + k a x x + k a y y + k a z z ω a t ] .
x ( z ) = ε k a x D ( z ) , y ( z ) = ε k a y D ( z ) ,
Δ w = ( γ 1 ) · ( 1 a ) · δ 1 j = ( γ 1 ) · ( 1 a ) · k a A sin ( k a · r j ω a t ) = ( γ 1 ) · ( 1 a ) · k a A sin ( k a · r j ) cos ( ω a t ) ( γ 1 ) · ( 1 a ) · k a A · cos ( k a · r j ) sin ( ω a t ) = F j · cos ( ω a t ) + G j · sin ( ω a t ) ,
M ( n ^ , θ ) = [ cos θ + ( 1 cos θ ) x 2 ( 1 cos θ ) x y ( sin θ ) z ( 1 cos θ ) x z + ( sin θ ) y ( 1 cos θ ) x y + ( sin θ ) z cos θ + ( 1 cos θ ) y 2 ( 1 cos θ ) y z ( sin θ ) x ( 1 cos θ ) x z ( sin θ ) y ( 1 cos θ ) y z + ( sin θ ) x cos θ + ( 1 cos θ ) z 2 ] .
M ( n ^ , π ) = [ 1 + 2 x 2 2 x y 2 x z 2 x y 1 + 2 y 2 2 y z 2 x z 2 y z 1 + 2 z 2 ] .
v = M ( n ^ , π ) · ( x , y , z ) T + r r ,
d D / 2 < r + Δ r c ( r ) · cos ( ω a t ) + Δ r s ( r ) · sin ( ω a t ) < d + D / 2 ,
Δ r c ( r ) · cos ( ω a t ) + Δ r s ( r ) · sin ( ω a t ) + r ( d D / 2 ) = 0 ,
Δ r c ( r ) · cos ( ω a t ) + Δ r s ( r ) · sin ( ω a t ) + r ( d + D / 2 ) = 0.
r 1 r 2 F ( r ) · W ( r ) d r .
r 1 r 2 F ( r ) · W ( r ) · S ( r ) d r .
S ( r ) = cos 1 ( d 2 + r 2 D 2 / 4 2 d r ) π , when     r 1 < r < r 2 ; otherwise     S ( r ) = 0.

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