Abstract

A rigorous error analysis is presented for the scattering coefficient of biological random continuous media in the Born (or single-scattering) approximation. The analysis is done in two dimensions (2-D) for simplicity of numerical computation. Scattering coefficients of various tissue-like random media are numerically calculated via statistical finite-difference-time-domain analysis. The results are then checked against analytical formulas for the scattering coefficient in the Born approximation. The validity ranges for the correlation length and the refractive index fluctuation strength of the medium are clearly identified. These 2-D results show promise for future 3-D investigations.

© 2009 Optical Society of America

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References

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  1. A. Ishimaru, Wave Propagation and Scattering in Random Media (Wiley-IEEE, 1999).
  2. M. Mishchenko, L. Travis, and A. Lacis, Multiple Scattering of Light by Particles (Cambridge U. Press, 2006).
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    [CrossRef]
  5. B. van Tiggelen and H. Stark, Rev. Mod. Phys. 72, 1017 (2000).
    [CrossRef]
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    [CrossRef] [PubMed]
  7. A. Taflove and S. C. Hagness, Computational Electrodynamics, 3rd ed. (Artech House, 2005).
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    [CrossRef] [PubMed]
  9. F. Charriere, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, Opt. Lett. 31, 178 (2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  12. H. C. Van De Hulst, Light Scattering by Small Particles (Dover, 1981).

2009

2006

2000

B. van Tiggelen and H. Stark, Rev. Mod. Phys. 72, 1017 (2000).
[CrossRef]

1996

L. Ryzhik, G. Papanicolaou, and J. Keller, Wave Motion 24, 327 (1996).
[CrossRef]

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Muller, Phys. Med. Biol. 41, 369 (1996).
[CrossRef] [PubMed]

Backman, V.

J. D. Rogers, I. R. Capoglu, and V. Backman, Opt. Lett. 34, 1891 (2009).
[CrossRef] [PubMed]

I. R. Capoglu and V. Backman, presented at the IEEE AP-S International Symposium, Charleston, S.C., June 1-5, 2009.

Badizadegan, K.

Beuthan, J.

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Muller, Phys. Med. Biol. 41, 369 (1996).
[CrossRef] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Capoglu, I. R.

J. D. Rogers, I. R. Capoglu, and V. Backman, Opt. Lett. 34, 1891 (2009).
[CrossRef] [PubMed]

I. R. Capoglu and V. Backman, presented at the IEEE AP-S International Symposium, Charleston, S.C., June 1-5, 2009.

Charriere, F.

Colomb, T.

Cuche, E.

Dasari, R. R.

Depeursinge, C.

Feld, M. S.

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics, 3rd ed. (Artech House, 2005).

Helfmann, J.

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Muller, Phys. Med. Biol. 41, 369 (1996).
[CrossRef] [PubMed]

Herrig, M.

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Muller, Phys. Med. Biol. 41, 369 (1996).
[CrossRef] [PubMed]

Ikeda, T.

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Wiley-IEEE, 1999).

Keller, J.

L. Ryzhik, G. Papanicolaou, and J. Keller, Wave Motion 24, 327 (1996).
[CrossRef]

Kuehn, J.

Lacis, A.

M. Mishchenko, L. Travis, and A. Lacis, Multiple Scattering of Light by Particles (Cambridge U. Press, 2006).

Lue, N.

Marian, A.

Marquet, P.

Minet, O.

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Muller, Phys. Med. Biol. 41, 369 (1996).
[CrossRef] [PubMed]

Mishchenko, M.

M. Mishchenko, L. Travis, and A. Lacis, Multiple Scattering of Light by Particles (Cambridge U. Press, 2006).

Montfort, F.

Muller, G.

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Muller, Phys. Med. Biol. 41, 369 (1996).
[CrossRef] [PubMed]

Papanicolaou, G.

L. Ryzhik, G. Papanicolaou, and J. Keller, Wave Motion 24, 327 (1996).
[CrossRef]

Popescu, G.

Rogers, J. D.

Ryzhik, L.

L. Ryzhik, G. Papanicolaou, and J. Keller, Wave Motion 24, 327 (1996).
[CrossRef]

Stark, H.

B. van Tiggelen and H. Stark, Rev. Mod. Phys. 72, 1017 (2000).
[CrossRef]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics, 3rd ed. (Artech House, 2005).

Travis, L.

M. Mishchenko, L. Travis, and A. Lacis, Multiple Scattering of Light by Particles (Cambridge U. Press, 2006).

Van De Hulst, H. C.

H. C. Van De Hulst, Light Scattering by Small Particles (Dover, 1981).

van Tiggelen, B.

B. van Tiggelen and H. Stark, Rev. Mod. Phys. 72, 1017 (2000).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Opt. Lett.

Phys. Med. Biol.

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Muller, Phys. Med. Biol. 41, 369 (1996).
[CrossRef] [PubMed]

Rev. Mod. Phys.

B. van Tiggelen and H. Stark, Rev. Mod. Phys. 72, 1017 (2000).
[CrossRef]

Wave Motion

L. Ryzhik, G. Papanicolaou, and J. Keller, Wave Motion 24, 327 (1996).
[CrossRef]

Other

A. Ishimaru, Wave Propagation and Scattering in Random Media (Wiley-IEEE, 1999).

M. Mishchenko, L. Travis, and A. Lacis, Multiple Scattering of Light by Particles (Cambridge U. Press, 2006).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

I. R. Capoglu and V. Backman, presented at the IEEE AP-S International Symposium, Charleston, S.C., June 1-5, 2009.

H. C. Van De Hulst, Light Scattering by Small Particles (Dover, 1981).

A. Taflove and S. C. Hagness, Computational Electrodynamics, 3rd ed. (Artech House, 2005).

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Figures (2)

Fig. 1
Fig. 1

Normalized TE scattering coefficient μ s TE k as a function of the normalized sample dimension k L : (a) small-error case, (b) large-error case.

Fig. 2
Fig. 2

Percentage error caused by the Born approximation in calculating the TE scattering coefficient μ s TE .

Equations (7)

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B n ( Δ ρ ) = σ n 2 Δ ρ l c K 1 ( Δ ρ l c ) ,
σ ( k ̂ o , k ̂ i ) = | f ( k ̂ o , k ̂ i ) | 2 S ,
σ TM ( k ̂ o , k ̂ i ) = 2 σ n 2 k 3 l c 2 ( 1 + 4 k 2 l c 2 sin 2 ( θ 2 ) ) 2 ,
μ s TM = 4 σ n 2 k 3 l c 2 ( 1 + 2 k 2 l c 2 ) π ( 1 + 4 k 2 l c 2 ) 3 2 ,
μ s TE = σ n 2 [ 1 4 k 4 l c 4 + 8 k 6 l c 6 + 1 + 4 k 2 l c 2 + 2 k 2 l c 2 ( 3 + 2 1 + 4 k 2 l c 2 ) ] π k l c 2 ( 1 + 4 k 2 l c 2 ) 3 2 .
σ n 2 ( k l c ) 3 1 for k l c 1 σ n 2 ( k l c ) 2 1 for k l c 1 .
σ n 2 ( k l c ) 2 1 .

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