Abstract

An effective Mie-scattering model is developed to deal with the scattering property of a spherical fractal aggregate consisting of scattering particles. In this model the scattered field of a scattering particle is given by the classical Mie-scattering theory. On the basis of the Monte Carlo simulation method, we determine the physical parameters of a scattering aggregate, the scattering efficiency Q, and the anisotropy value g, as well as their dependence on the size and the effective mean-free-path length of a scattering aggregate. Accordingly, photon migration through a microscope objective focused into a turbid medium including scattering aggregates is simulated to understand the effect of complex tissue on image quality.

© 2004 Optical Society of America

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References

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  1. A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE and Oxford U. Press, New York, 1997).
  2. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  3. S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues. I: Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1989).
    [Crossref] [PubMed]
  4. X. Gan, M. Gu, “Effective point-spread function for fast image modeling and processing in microscopic imaging through turbid media,” Opt. Lett. 24, 741–743 (1999).
    [Crossref]
  5. A. K. Dunn, V. P. Wallace, M. Coleno, M. W. Berns, B. J. Tromberg, “Influence of optical properties on two-photon fluorescence imaging in turbid samples,” Appl. Opt. 39, 1194–1201 (2000).
    [Crossref]
  6. X. Gan, M. Gu, “Fluorescence microscopic imaging through tissue-like turbid media,” J. Appl. Phys. 87, 3214–3221 (2000).
    [Crossref]
  7. M. Gu, X. Gan, A. Kisteman, M. Xu, “Comparison of penetration depth between single-photon excitation and two-photon excitation in imaging through turbid media,” Appl. Phys. Lett. 77, 1551–1553 (2000).
    [Crossref]
  8. X. Deng, X. Gan, M. Gu, “Multi-photon fluorescence microscopic imaging through double-layer turbid tissue media,” J. Appl. Phys. 91, 4659–4665 (2002).
    [Crossref]
  9. A. Wax, C. H. Yang, V. Backman, K. Badizadegan, C. W. Boone, R. R. Dasari, M. S. Feld, “Cellular organization and substructure measured using angle-resolved low-coherence interferometry,” Biophys. J. 82, 2256–2264 (2002).
    [Crossref] [PubMed]
  10. A. Wax, C. Yang, M. Müller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res. 63, 3556–3559 (2003).
    [PubMed]
  11. R. Jullien, R. Botet, Aggregation and Fractal Aggregates (World Scientific, Singapore, 1987).
  12. A. Dogariu, J. Uozumi, T. Asakura, “Enhancement of the backscattered intensity from fractal aggregates,” Waves Random Media 2, 259–263 (1992).
    [Crossref]
  13. Y. L. Xu, “Electromagnetic scattering by an aggregate of spheres,” Appl. Opt. 34, 4573–4588 (1995).
    [Crossref] [PubMed]
  14. K. Ishii, T. Iwai, J. Uozumi, T. Asakura, “Optical freepath-length distribution in a fractal aggregate and its effect on enhanced backscattering,” Appl. Opt. 37, 5014–5018 (1998).
    [Crossref]
  15. B. I. Henry, P. R. Hof, P. Rothnie, S. L. Wearne, “Fractal analysis of aggregates of non-uniformly sized particles: an application to macaque monkey cortical pyramidal neurons,” in Emergent Nature: Patterns, Growth and Scaling in the Sciences, M. M. Novak, ed. (World Scientific, River Edge, N.J., 2002), pp. 65–75.

2003 (1)

A. Wax, C. Yang, M. Müller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res. 63, 3556–3559 (2003).
[PubMed]

2002 (2)

X. Deng, X. Gan, M. Gu, “Multi-photon fluorescence microscopic imaging through double-layer turbid tissue media,” J. Appl. Phys. 91, 4659–4665 (2002).
[Crossref]

A. Wax, C. H. Yang, V. Backman, K. Badizadegan, C. W. Boone, R. R. Dasari, M. S. Feld, “Cellular organization and substructure measured using angle-resolved low-coherence interferometry,” Biophys. J. 82, 2256–2264 (2002).
[Crossref] [PubMed]

2000 (3)

A. K. Dunn, V. P. Wallace, M. Coleno, M. W. Berns, B. J. Tromberg, “Influence of optical properties on two-photon fluorescence imaging in turbid samples,” Appl. Opt. 39, 1194–1201 (2000).
[Crossref]

X. Gan, M. Gu, “Fluorescence microscopic imaging through tissue-like turbid media,” J. Appl. Phys. 87, 3214–3221 (2000).
[Crossref]

M. Gu, X. Gan, A. Kisteman, M. Xu, “Comparison of penetration depth between single-photon excitation and two-photon excitation in imaging through turbid media,” Appl. Phys. Lett. 77, 1551–1553 (2000).
[Crossref]

1999 (1)

1998 (1)

1995 (1)

1992 (1)

A. Dogariu, J. Uozumi, T. Asakura, “Enhancement of the backscattered intensity from fractal aggregates,” Waves Random Media 2, 259–263 (1992).
[Crossref]

1989 (1)

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues. I: Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1989).
[Crossref] [PubMed]

Asakura, T.

K. Ishii, T. Iwai, J. Uozumi, T. Asakura, “Optical freepath-length distribution in a fractal aggregate and its effect on enhanced backscattering,” Appl. Opt. 37, 5014–5018 (1998).
[Crossref]

A. Dogariu, J. Uozumi, T. Asakura, “Enhancement of the backscattered intensity from fractal aggregates,” Waves Random Media 2, 259–263 (1992).
[Crossref]

Backman, V.

A. Wax, C. H. Yang, V. Backman, K. Badizadegan, C. W. Boone, R. R. Dasari, M. S. Feld, “Cellular organization and substructure measured using angle-resolved low-coherence interferometry,” Biophys. J. 82, 2256–2264 (2002).
[Crossref] [PubMed]

Badizadegan, K.

A. Wax, C. H. Yang, V. Backman, K. Badizadegan, C. W. Boone, R. R. Dasari, M. S. Feld, “Cellular organization and substructure measured using angle-resolved low-coherence interferometry,” Biophys. J. 82, 2256–2264 (2002).
[Crossref] [PubMed]

Berns, M. W.

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Boone, C. W.

A. Wax, C. Yang, M. Müller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res. 63, 3556–3559 (2003).
[PubMed]

A. Wax, C. H. Yang, V. Backman, K. Badizadegan, C. W. Boone, R. R. Dasari, M. S. Feld, “Cellular organization and substructure measured using angle-resolved low-coherence interferometry,” Biophys. J. 82, 2256–2264 (2002).
[Crossref] [PubMed]

Botet, R.

R. Jullien, R. Botet, Aggregation and Fractal Aggregates (World Scientific, Singapore, 1987).

Coleno, M.

Dasari, R. R.

A. Wax, C. Yang, M. Müller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res. 63, 3556–3559 (2003).
[PubMed]

A. Wax, C. H. Yang, V. Backman, K. Badizadegan, C. W. Boone, R. R. Dasari, M. S. Feld, “Cellular organization and substructure measured using angle-resolved low-coherence interferometry,” Biophys. J. 82, 2256–2264 (2002).
[Crossref] [PubMed]

Deng, X.

X. Deng, X. Gan, M. Gu, “Multi-photon fluorescence microscopic imaging through double-layer turbid tissue media,” J. Appl. Phys. 91, 4659–4665 (2002).
[Crossref]

Dogariu, A.

A. Dogariu, J. Uozumi, T. Asakura, “Enhancement of the backscattered intensity from fractal aggregates,” Waves Random Media 2, 259–263 (1992).
[Crossref]

Dunn, A. K.

Feld, M. S.

A. Wax, C. Yang, M. Müller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res. 63, 3556–3559 (2003).
[PubMed]

A. Wax, C. H. Yang, V. Backman, K. Badizadegan, C. W. Boone, R. R. Dasari, M. S. Feld, “Cellular organization and substructure measured using angle-resolved low-coherence interferometry,” Biophys. J. 82, 2256–2264 (2002).
[Crossref] [PubMed]

Flock, S. T.

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues. I: Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1989).
[Crossref] [PubMed]

Gan, X.

X. Deng, X. Gan, M. Gu, “Multi-photon fluorescence microscopic imaging through double-layer turbid tissue media,” J. Appl. Phys. 91, 4659–4665 (2002).
[Crossref]

X. Gan, M. Gu, “Fluorescence microscopic imaging through tissue-like turbid media,” J. Appl. Phys. 87, 3214–3221 (2000).
[Crossref]

M. Gu, X. Gan, A. Kisteman, M. Xu, “Comparison of penetration depth between single-photon excitation and two-photon excitation in imaging through turbid media,” Appl. Phys. Lett. 77, 1551–1553 (2000).
[Crossref]

X. Gan, M. Gu, “Effective point-spread function for fast image modeling and processing in microscopic imaging through turbid media,” Opt. Lett. 24, 741–743 (1999).
[Crossref]

Gu, M.

X. Deng, X. Gan, M. Gu, “Multi-photon fluorescence microscopic imaging through double-layer turbid tissue media,” J. Appl. Phys. 91, 4659–4665 (2002).
[Crossref]

X. Gan, M. Gu, “Fluorescence microscopic imaging through tissue-like turbid media,” J. Appl. Phys. 87, 3214–3221 (2000).
[Crossref]

M. Gu, X. Gan, A. Kisteman, M. Xu, “Comparison of penetration depth between single-photon excitation and two-photon excitation in imaging through turbid media,” Appl. Phys. Lett. 77, 1551–1553 (2000).
[Crossref]

X. Gan, M. Gu, “Effective point-spread function for fast image modeling and processing in microscopic imaging through turbid media,” Opt. Lett. 24, 741–743 (1999).
[Crossref]

Henry, B. I.

B. I. Henry, P. R. Hof, P. Rothnie, S. L. Wearne, “Fractal analysis of aggregates of non-uniformly sized particles: an application to macaque monkey cortical pyramidal neurons,” in Emergent Nature: Patterns, Growth and Scaling in the Sciences, M. M. Novak, ed. (World Scientific, River Edge, N.J., 2002), pp. 65–75.

Hof, P. R.

B. I. Henry, P. R. Hof, P. Rothnie, S. L. Wearne, “Fractal analysis of aggregates of non-uniformly sized particles: an application to macaque monkey cortical pyramidal neurons,” in Emergent Nature: Patterns, Growth and Scaling in the Sciences, M. M. Novak, ed. (World Scientific, River Edge, N.J., 2002), pp. 65–75.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Ishii, K.

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE and Oxford U. Press, New York, 1997).

Iwai, T.

Jullien, R.

R. Jullien, R. Botet, Aggregation and Fractal Aggregates (World Scientific, Singapore, 1987).

Kisteman, A.

M. Gu, X. Gan, A. Kisteman, M. Xu, “Comparison of penetration depth between single-photon excitation and two-photon excitation in imaging through turbid media,” Appl. Phys. Lett. 77, 1551–1553 (2000).
[Crossref]

Müller, M.

A. Wax, C. Yang, M. Müller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res. 63, 3556–3559 (2003).
[PubMed]

Nines, R.

A. Wax, C. Yang, M. Müller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res. 63, 3556–3559 (2003).
[PubMed]

Patterson, M. S.

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues. I: Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1989).
[Crossref] [PubMed]

Rothnie, P.

B. I. Henry, P. R. Hof, P. Rothnie, S. L. Wearne, “Fractal analysis of aggregates of non-uniformly sized particles: an application to macaque monkey cortical pyramidal neurons,” in Emergent Nature: Patterns, Growth and Scaling in the Sciences, M. M. Novak, ed. (World Scientific, River Edge, N.J., 2002), pp. 65–75.

Steele, V. E.

A. Wax, C. Yang, M. Müller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res. 63, 3556–3559 (2003).
[PubMed]

Stoner, G. D.

A. Wax, C. Yang, M. Müller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res. 63, 3556–3559 (2003).
[PubMed]

Tromberg, B. J.

Uozumi, J.

K. Ishii, T. Iwai, J. Uozumi, T. Asakura, “Optical freepath-length distribution in a fractal aggregate and its effect on enhanced backscattering,” Appl. Opt. 37, 5014–5018 (1998).
[Crossref]

A. Dogariu, J. Uozumi, T. Asakura, “Enhancement of the backscattered intensity from fractal aggregates,” Waves Random Media 2, 259–263 (1992).
[Crossref]

Wallace, V. P.

Wax, A.

A. Wax, C. Yang, M. Müller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res. 63, 3556–3559 (2003).
[PubMed]

A. Wax, C. H. Yang, V. Backman, K. Badizadegan, C. W. Boone, R. R. Dasari, M. S. Feld, “Cellular organization and substructure measured using angle-resolved low-coherence interferometry,” Biophys. J. 82, 2256–2264 (2002).
[Crossref] [PubMed]

Wearne, S. L.

B. I. Henry, P. R. Hof, P. Rothnie, S. L. Wearne, “Fractal analysis of aggregates of non-uniformly sized particles: an application to macaque monkey cortical pyramidal neurons,” in Emergent Nature: Patterns, Growth and Scaling in the Sciences, M. M. Novak, ed. (World Scientific, River Edge, N.J., 2002), pp. 65–75.

Wilson, B. C.

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues. I: Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1989).
[Crossref] [PubMed]

Wyman, D. R.

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues. I: Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1989).
[Crossref] [PubMed]

Xu, M.

M. Gu, X. Gan, A. Kisteman, M. Xu, “Comparison of penetration depth between single-photon excitation and two-photon excitation in imaging through turbid media,” Appl. Phys. Lett. 77, 1551–1553 (2000).
[Crossref]

Xu, Y. L.

Yang, C.

A. Wax, C. Yang, M. Müller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res. 63, 3556–3559 (2003).
[PubMed]

Yang, C. H.

A. Wax, C. H. Yang, V. Backman, K. Badizadegan, C. W. Boone, R. R. Dasari, M. S. Feld, “Cellular organization and substructure measured using angle-resolved low-coherence interferometry,” Biophys. J. 82, 2256–2264 (2002).
[Crossref] [PubMed]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

M. Gu, X. Gan, A. Kisteman, M. Xu, “Comparison of penetration depth between single-photon excitation and two-photon excitation in imaging through turbid media,” Appl. Phys. Lett. 77, 1551–1553 (2000).
[Crossref]

Biophys. J. (1)

A. Wax, C. H. Yang, V. Backman, K. Badizadegan, C. W. Boone, R. R. Dasari, M. S. Feld, “Cellular organization and substructure measured using angle-resolved low-coherence interferometry,” Biophys. J. 82, 2256–2264 (2002).
[Crossref] [PubMed]

Cancer Res. (1)

A. Wax, C. Yang, M. Müller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res. 63, 3556–3559 (2003).
[PubMed]

IEEE Trans. Biomed. Eng. (1)

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues. I: Model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1989).
[Crossref] [PubMed]

J. Appl. Phys. (2)

X. Deng, X. Gan, M. Gu, “Multi-photon fluorescence microscopic imaging through double-layer turbid tissue media,” J. Appl. Phys. 91, 4659–4665 (2002).
[Crossref]

X. Gan, M. Gu, “Fluorescence microscopic imaging through tissue-like turbid media,” J. Appl. Phys. 87, 3214–3221 (2000).
[Crossref]

Opt. Lett. (1)

Waves Random Media (1)

A. Dogariu, J. Uozumi, T. Asakura, “Enhancement of the backscattered intensity from fractal aggregates,” Waves Random Media 2, 259–263 (1992).
[Crossref]

Other (4)

R. Jullien, R. Botet, Aggregation and Fractal Aggregates (World Scientific, Singapore, 1987).

B. I. Henry, P. R. Hof, P. Rothnie, S. L. Wearne, “Fractal analysis of aggregates of non-uniformly sized particles: an application to macaque monkey cortical pyramidal neurons,” in Emergent Nature: Patterns, Growth and Scaling in the Sciences, M. M. Novak, ed. (World Scientific, River Edge, N.J., 2002), pp. 65–75.

A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE and Oxford U. Press, New York, 1997).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of the EMS model for an aggregate consisting of spherical particles.

Fig. 2
Fig. 2

Phase functions ρ(θ) of an aggregate based on the effective Mie-scattering model (l m = 1.0 and l m = 5.0 μm) and the phase function ρ(θ) based on Mie scattering: (a) logarithmic scale, (b) polar coordinate system.

Fig. 3
Fig. 3

Scattering efficiency Q a (left axes) and anisotropy g a value (right axes) of an aggregate as a function of its size (a) D/λ and (b) mean-free-path length l m /D.

Fig. 4
Fig. 4

Logarithmic representation of the excitation profiles (i.e., the focal spots) of an objective (numerical aperture of 0.25) in a homogeneously random medium consisting of fractal aggregates with a concentration of 0.002/μm3. The incident photon number is 107.

Equations (2)

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

lm=a4m-2KmmQp1/m-2,
ρθ=Nsθ/sin θ02πdϕ 0πNsθ/sin θdθ.

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