Abstract

Which range of structures contributes to light scattering in a continuous random media, such as biological tissue? In this Letter, we present a model to study the structural length-scale sensitivity of scattering in continuous random media under the Born approximation. The scattering coefficient μs, backscattering coefficient μb, anisotropy factor g, and reduced scattering coefficient μs* as well as the shape of the spatial reflectance profile are calculated under this model. For media with a biologically relevant Henyey–Greenstein phase function with g0.93 at wavelength λ=633nm, we report that μs* is sensitive to structural length-scales from 46.9 nm to 2.07 μm (i.e., λ/13 to 3λ), μb is sensitive from 26.7 to 320 nm (i.e., λ/24 to λ/2), and the spatial reflectance profile is sensitive from 30.8 nm to 2.71 μm (i.e., λ/21 to 4λ).

© 2012 Optical Society of America

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References

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  1. P. Guttorp and T. Gneiting, “On the Whittle–Matérn correlation family,” National Research Center for Statistics and the Environment, Technical Report Series (2005).
  2. J. D. Rogers, İ. R. Çapoğlu, and V. Backman, Opt. Lett. 34, 1891 (2009).
    [CrossRef]
  3. A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE, 1997).
  4. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  5. A. J. Radosevich, J. D. Rogers, İ. R. Çapoğlu, N. N. Mutyal, P. Pradhan, and V. Backman, J. Biomed. Opt. 17, 115001 (2012).
    [CrossRef]

2012

A. J. Radosevich, J. D. Rogers, İ. R. Çapoğlu, N. N. Mutyal, P. Pradhan, and V. Backman, J. Biomed. Opt. 17, 115001 (2012).
[CrossRef]

2009

Backman, V.

A. J. Radosevich, J. D. Rogers, İ. R. Çapoğlu, N. N. Mutyal, P. Pradhan, and V. Backman, J. Biomed. Opt. 17, 115001 (2012).
[CrossRef]

J. D. Rogers, İ. R. Çapoğlu, and V. Backman, Opt. Lett. 34, 1891 (2009).
[CrossRef]

Bohren, C. F.

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

Çapoglu, I. R.

A. J. Radosevich, J. D. Rogers, İ. R. Çapoğlu, N. N. Mutyal, P. Pradhan, and V. Backman, J. Biomed. Opt. 17, 115001 (2012).
[CrossRef]

J. D. Rogers, İ. R. Çapoğlu, and V. Backman, Opt. Lett. 34, 1891 (2009).
[CrossRef]

Gneiting, T.

P. Guttorp and T. Gneiting, “On the Whittle–Matérn correlation family,” National Research Center for Statistics and the Environment, Technical Report Series (2005).

Guttorp, P.

P. Guttorp and T. Gneiting, “On the Whittle–Matérn correlation family,” National Research Center for Statistics and the Environment, Technical Report Series (2005).

Huffman, D. R.

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

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE, 1997).

Mutyal, N. N.

A. J. Radosevich, J. D. Rogers, İ. R. Çapoğlu, N. N. Mutyal, P. Pradhan, and V. Backman, J. Biomed. Opt. 17, 115001 (2012).
[CrossRef]

Pradhan, P.

A. J. Radosevich, J. D. Rogers, İ. R. Çapoğlu, N. N. Mutyal, P. Pradhan, and V. Backman, J. Biomed. Opt. 17, 115001 (2012).
[CrossRef]

Radosevich, A. J.

A. J. Radosevich, J. D. Rogers, İ. R. Çapoğlu, N. N. Mutyal, P. Pradhan, and V. Backman, J. Biomed. Opt. 17, 115001 (2012).
[CrossRef]

Rogers, J. D.

A. J. Radosevich, J. D. Rogers, İ. R. Çapoğlu, N. N. Mutyal, P. Pradhan, and V. Backman, J. Biomed. Opt. 17, 115001 (2012).
[CrossRef]

J. D. Rogers, İ. R. Çapoğlu, and V. Backman, Opt. Lett. 34, 1891 (2009).
[CrossRef]

J. Biomed. Opt.

A. J. Radosevich, J. D. Rogers, İ. R. Çapoğlu, N. N. Mutyal, P. Pradhan, and V. Backman, J. Biomed. Opt. 17, 115001 (2012).
[CrossRef]

Opt. Lett.

Other

A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE, 1997).

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

P. Guttorp and T. Gneiting, “On the Whittle–Matérn correlation family,” National Research Center for Statistics and the Environment, Technical Report Series (2005).

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Figures (6)

Fig. 1.
Fig. 1.

Lower length-scale analysis for Wl=0, 10, 50, and 100 nm with D=3, lc=1μm, and λ=633nm. The normalized (a) Bnl(rd) and (b) Φsl(ks). In each panel the arrow indicates increasing Wl.

Fig. 2.
Fig. 2.

Upper length-scale analysis for Wh=, 10, 5, and 1 μm with D=3, lc=1μm, and λ=633nm. (a) Bnh(rd) where the dashed curves indicate locations in which the curve is negative. (b) Φsh(ks). In each panel the arrow indicates decreasing Wh.

Fig. 3.
Fig. 3.

Example media with D=3 and lc=1μm. (a) nΔ(r⃗), (b) nΔl(r⃗), and (c) nΔh(r⃗) for Wl=Wh=100nm.

Fig. 4.
Fig. 4.

Percent change in scattering parameters with varying values of Wl and Wh for D=3, lc=1μm, and λ=633nm. (a) Lower and (b) upper length-scale percent changes. The dotted line indicates the ±5% threshold.

Fig. 5.
Fig. 5.

Monte Carlo simulations of Poo with D=3, lc=1μm, and λ=633nm. (a) Lower length-scale analysis for Wl=0, 30, 60, and 90 nm. Arrow indicates increasing Wl. (b) Upper length-scale analysis for Wh=, 10, 2, 0.5 μm. Arrows indicate decreasing Wh.

Fig. 6.
Fig. 6.

(a) rmin and (b) rmax for μs* with different shapes of Bn(rd) and λ=633nm.

Equations (11)

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Bn(rd)=An·(rdlc)D32·KD32(rdlc),
Φs(ks)=Anlc3Γ(D2)π3/22(5D)/2·(1+ks2lc2)D/2,
G(r⃗)=(16πln(2)W2)3/2·exp(4ln(2)W2r⃗2),
Bnl(rd)=F1[|F[nΔ(r⃗)]|2·|F[G(r⃗)]|2]=4π0Φsl(ks)kssin(ksr)rdks,
Φsl(ks)=Anlc3Γ(D2)π3/22(5D)/2·exp(ks2Wl28ln(2))(1+ks2lc2)D/2.
Bnh(rd)=F1[|F[nΔ(r⃗)]|2·|1F[G(r⃗)]|2]=4π0Φsh(ks)kssin(ksr)rdks,
Φsh(ks)=Anlc3Γ(D2)π3/22(5D)/2·(1exp(ks2Wh216ln(2)))2(1+ks2lc2)D/2.
σ(θ)=2πk4(1+cos2θ)Φs(ks).
μs=2π11σ(cosθ)dcosθ,
μb=4π·σ(θ=π),
g=2πμs11cosθ·σ(cosθ)dcosθ.

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