Estimation of light penetration depth in turbid media using laser speckles

Igor S. Sidorov; Serguei V. Miridonov; Ervin Nippolainen; Alexei A. Kamshilin

doi:10.1364/OE.20.013692

Abstract

We present novel experimental method for estimation of the light penetration depth (LPD) in turbid media based on the analysis of the speckle pattern structure. Under the certain illumination conditions this structure is strongly dependent on the penetration depth. Presented theoretical model based on the Bragg diffraction from the thick holograms allows LPD estimation if only one parameter of the material, namely refractive index, of the material is known. Feasibility of the method was checked experimentally. Experimental results obtained for variety of the materials are in good agreement with the theoretical assumptions. It was shown that qualitative LPD comparison does not require knowledge of the material properties.

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References

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K. Thyagarajan and A. Ghatak, Lasers: Fundamentals and Applications (Springer, 2010).
L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[Crossref] [PubMed]
S. L. Jacques and L. Wang, “Monte Carlo modeling of light transport in tissues,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch and M. J. C. van Gemert, eds. (Plenum, 1995), Chap. 4.
A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43(5), 1285–1302 (1998).
[Crossref] [PubMed]
R. A. J. Groenhuis, H. A. Ferwerda, and J. J. T. Bosch, “Scattering and absorption of turbid materials determined from reflection measurements. 1: theory,” Appl. Opt. 22(16), 2456–2462 (1983).
[Crossref] [PubMed]
S. A. Carp, S. A. Prahl, and V. Venugopalan, “Radiative transport in the delta-P1 approximation: accuracy of fluence rate and optical penetration depth predictions in turbid semi-infinite media,” J. Biomed. Opt. 9(3), 632–647 (2004).
[Crossref] [PubMed]
S. Xie, H. Li, and B. Li, “Measurement of optical penetration depth and refractive index of human tissue,” Chin. Opt. Lett. 1, 44–46 (2003).
V. V. Tuchin, Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis (SPIE Press, 2007), Chap. 6.
M. P. Petrov, S. I. Stepanov, and A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer-Verlag, 1991).
F. P. Bolin, L. E. Preuss, R. C. Taylor, and R. J. Ference, “Refractive index of some mammalian tissues using a fiber optic cladding method,” Appl. Opt. 28(12), 2297–2303 (1989).
[Crossref] [PubMed]

2004 (1)

S. A. Carp, S. A. Prahl, and V. Venugopalan, “Radiative transport in the delta-P1 approximation: accuracy of fluence rate and optical penetration depth predictions in turbid semi-infinite media,” J. Biomed. Opt. 9(3), 632–647 (2004).
[Crossref] [PubMed]

2003 (1)

S. Xie, H. Li, and B. Li, “Measurement of optical penetration depth and refractive index of human tissue,” Chin. Opt. Lett. 1, 44–46 (2003).

1998 (1)

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43(5), 1285–1302 (1998).
[Crossref] [PubMed]

1995 (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(2), 131–146 (1995).
[Crossref] [PubMed]

1989 (1)

F. P. Bolin, L. E. Preuss, R. C. Taylor, and R. J. Ference, “Refractive index of some mammalian tissues using a fiber optic cladding method,” Appl. Opt. 28(12), 2297–2303 (1989).
[Crossref] [PubMed]

1983 (1)

R. A. J. Groenhuis, H. A. Ferwerda, and J. J. T. Bosch, “Scattering and absorption of turbid materials determined from reflection measurements. 1: theory,” Appl. Opt. 22(16), 2456–2462 (1983).
[Crossref] [PubMed]

Alcouffe, R. E.

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43(5), 1285–1302 (1998).
[Crossref] [PubMed]

Barbour, R. L.

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43(5), 1285–1302 (1998).
[Crossref] [PubMed]

Bolin, F. P.

F. P. Bolin, L. E. Preuss, R. C. Taylor, and R. J. Ference, “Refractive index of some mammalian tissues using a fiber optic cladding method,” Appl. Opt. 28(12), 2297–2303 (1989).
[Crossref] [PubMed]

Bosch, J. J. T.

R. A. J. Groenhuis, H. A. Ferwerda, and J. J. T. Bosch, “Scattering and absorption of turbid materials determined from reflection measurements. 1: theory,” Appl. Opt. 22(16), 2456–2462 (1983).
[Crossref] [PubMed]

Carp, S. A.

S. A. Carp, S. A. Prahl, and V. Venugopalan, “Radiative transport in the delta-P1 approximation: accuracy of fluence rate and optical penetration depth predictions in turbid semi-infinite media,” J. Biomed. Opt. 9(3), 632–647 (2004).
[Crossref] [PubMed]

Hielscher, A. H.

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43(5), 1285–1302 (1998).
[Crossref] [PubMed]

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(2), 131–146 (1995).
[Crossref] [PubMed]

Li, B.

S. Xie, H. Li, and B. Li, “Measurement of optical penetration depth and refractive index of human tissue,” Chin. Opt. Lett. 1, 44–46 (2003).

Li, H.

S. Xie, H. Li, and B. Li, “Measurement of optical penetration depth and refractive index of human tissue,” Chin. Opt. Lett. 1, 44–46 (2003).

Prahl, S. A.

S. A. Carp, S. A. Prahl, and V. Venugopalan, “Radiative transport in the delta-P1 approximation: accuracy of fluence rate and optical penetration depth predictions in turbid semi-infinite media,” J. Biomed. Opt. 9(3), 632–647 (2004).
[Crossref] [PubMed]

Preuss, L. E.

F. P. Bolin, L. E. Preuss, R. C. Taylor, and R. J. Ference, “Refractive index of some mammalian tissues using a fiber optic cladding method,” Appl. Opt. 28(12), 2297–2303 (1989).
[Crossref] [PubMed]

Taylor, R. C.

F. P. Bolin, L. E. Preuss, R. C. Taylor, and R. J. Ference, “Refractive index of some mammalian tissues using a fiber optic cladding method,” Appl. Opt. 28(12), 2297–2303 (1989).
[Crossref] [PubMed]

Venugopalan, V.

S. A. Carp, S. A. Prahl, and V. Venugopalan, “Radiative transport in the delta-P1 approximation: accuracy of fluence rate and optical penetration depth predictions in turbid semi-infinite media,” J. Biomed. Opt. 9(3), 632–647 (2004).
[Crossref] [PubMed]

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(2), 131–146 (1995).
[Crossref] [PubMed]

Xie, S.

S. Xie, H. Li, and B. Li, “Measurement of optical penetration depth and refractive index of human tissue,” Chin. Opt. Lett. 1, 44–46 (2003).

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(2), 131–146 (1995).
[Crossref] [PubMed]

Appl. Opt. (2)

F. P. Bolin, L. E. Preuss, R. C. Taylor, and R. J. Ference, “Refractive index of some mammalian tissues using a fiber optic cladding method,” Appl. Opt. 28(12), 2297–2303 (1989).
[Crossref] [PubMed]

R. A. J. Groenhuis, H. A. Ferwerda, and J. J. T. Bosch, “Scattering and absorption of turbid materials determined from reflection measurements. 1: theory,” Appl. Opt. 22(16), 2456–2462 (1983).
[Crossref] [PubMed]

Chin. Opt. Lett. (1)

S. Xie, H. Li, and B. Li, “Measurement of optical penetration depth and refractive index of human tissue,” Chin. Opt. Lett. 1, 44–46 (2003).

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(2), 131–146 (1995).
[Crossref] [PubMed]

J. Biomed. Opt. (1)

S. A. Carp, S. A. Prahl, and V. Venugopalan, “Radiative transport in the delta-P1 approximation: accuracy of fluence rate and optical penetration depth predictions in turbid semi-infinite media,” J. Biomed. Opt. 9(3), 632–647 (2004).
[Crossref] [PubMed]

Phys. Med. Biol. (1)

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43(5), 1285–1302 (1998).
[Crossref] [PubMed]

Other (4)

K. Thyagarajan and A. Ghatak, Lasers: Fundamentals and Applications (Springer, 2010).

S. L. Jacques and L. Wang, “Monte Carlo modeling of light transport in tissues,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch and M. J. C. van Gemert, eds. (Plenum, 1995), Chap. 4.

V. V. Tuchin, Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis (SPIE Press, 2007), Chap. 6.

M. P. Petrov, S. I. Stepanov, and A. V. Khomenko, Photorefractive Crystals in Coherent Optical Systems (Springer-Verlag, 1991).

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Fig. 1 Schematic representation of the diffraction from the thick hologram in spatial-frequency domain. Spheres with the radiuses of 2π/λ and 2πn/λ are representing Ewald spheres for all possible light waves in the air and medium, respectively. Angles θ and δθ are incidence angle and its change due to rotation in the air, while θ_n and δθ_n – in the medium. Two vectors pointing up-left are representing incident and refracted waves. The horizontal vector pointing right is a diffracted wave. Vector denoted as K is a hologram vector.

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Fig. 2 Schematic layout of the experimental setup.

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Fig. 3 Correlation peak amplitude versus illumination angle measured for different materials.

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Fig. 4 Correlation peak amplitude versus illumination angle only for the light scattered inside the material. Dots are representing the experimental data, while solid lines – least squares fitting.

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Tables (1)

Table 1 Reciprocal Value of the Parameter α for Different Materials

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Equations (12)

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I = I_{0} e^{- \frac{z}{Z}},

E = E_{0} e^{- \frac{z}{2 Z}} .

δ E_{R} \propto E e^{- \frac{z}{2 Z}} = E_{0} e^{- \frac{z}{Z}} .

E (ζ) = \int_{0}^{\infty} e^{- \frac{z}{Z}} e^{- i ζ z} d z .

E (ζ) = \frac{Z}{1 + i ζ Z} .

I_{R} \propto \frac{Z^{2}}{1 + ζ^{2} Z^{2}} .

- \frac{2 π n}{λ} \cos θ_{n} = - \frac{2 π n}{λ} \sqrt{1 - \sin^{2} θ_{n}} = - \frac{2 π n}{λ} \sqrt{1 - \frac{\sin^{2} θ}{n^{2}}} .

ζ = \frac{2 π δ θ s i n 2 θ}{λ \sqrt{4 n^{2} - 2 + 2 \cos 2 θ}} .

C = \frac{C_{0}}{1 + ζ^{2} Z^{2}} + A \cdot δ θ + B,

ζ = ζ_{1} δ θ; β^{2} = \frac{C_{0}}{ζ_{1}^{2} Z^{2}}; α^{2} = \frac{1}{ζ_{1}^{2} Z^{2}} .

C = \frac{β^{2}}{α^{2} + δ θ^{2}} + A \cdot δ θ + B,

Z = \frac{1}{ζ_{1} α} = \frac{1}{α} \frac{λ \sqrt{4 n^{2} - 2 + 2 \cos 2 θ}}{2 π \sin 2 θ} .

Material	1/α
Cardboard	834.44
Pine wood	3596.58
White plastic	4056.03
Teflon	4768.94

Abstract

References

2004 (1)

2003 (1)

1998 (1)

1995 (1)

1989 (1)

1983 (1)

Alcouffe, R. E.

Barbour, R. L.

Bolin, F. P.

Bosch, J. J. T.

Carp, S. A.

Ference, R. J.

Ferwerda, H. A.

Groenhuis, R. A. J.

Hielscher, A. H.

Jacques, S. L.

Li, B.

Li, H.

Prahl, S. A.

Preuss, L. E.

Taylor, R. C.

Venugopalan, V.

Wang, L.

Xie, S.

Zheng, L.

Appl. Opt. (2)

Chin. Opt. Lett. (1)

Comput. Methods Programs Biomed. (1)

J. Biomed. Opt. (1)

Phys. Med. Biol. (1)

Other (4)

Cited By

Figures (4)

Tables (1)

Equations (12)

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