Scattering through fluids: speckle size measurement and Monte Carlo simulations close to and into the multiple scattering

Y. Piederrière; J. Cariou; Y. Guern; B. Le Jeune; G. Le Brun; J. Lotrian

doi:10.1364/OPEX.12.000176

Optics Express
Vol. 12,
Issue 1,
pp. 176-188
(2004)
•https://doi.org/10.1364/OPEX.12.000176

Scattering through fluids: speckle size measurement and Monte Carlo simulations close to and into the multiple scattering

Y. Piederrière, J. Cariou, Y. Guern, B. Le Jeune, G. Le Brun, and J. Lotrian

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Y. Piederrière, J. Cariou, Y. Guern, B. Le Jeune, G. Le Brun, and J. Lotrian, "Scattering through fluids: speckle size measurement and Monte Carlo simulations close to and into the multiple scattering," Opt. Express 12, 176-188 (2004)

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Abstract

We report on measurements in transmission of the speckle produced by scattering liquid media: diluted milk and water solutions of polystyrene-microspheres of different diameters. The speckle size is affected not only by scattering parameters such as the optical thickness, but also by the dimensions of the scatters. From the speckle measurement, we propose a method to differentiate media. Moreover, a calculation of the transmitted light profile by Monte Carlo simulation allowed us to get a better insight on the speckle size evolution versus scattering.

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Fig. 1. Speckle produced by a weak diffusing medium.

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Fig. 2.

c_{I}^{m}

(x, 0) calculated from speckle of fig. 1.

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Fig. 3. Experimental set-up (top view).

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Fig. 4. dx^m versus θ.

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Fig. 5. dy^m versus θ.

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Fig. 6. dy^m versus ls, the opticalthickness for semi-skimmed milk.

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Fig. 7. dy^m versus ls, the optical thickness for skimmed milk.

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Fig. 8. d^c versus ls for skimmed milk.

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Fig.9. . dy^m versus ls and linear fit for different polystyrene-microspheres.

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Fig. 10. Contrast evolution versus ls for different polystyrene-microspheres.

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Fig. 11. d^c versus ls for the polystyrene-microspheres.

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Tables (3)

Table 1. Scattering coefficients of polystyrene microspheres measured.

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Table 2. Anisotropy factor of polystyrene microspheres calculated.

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Table 3. Parameters obtained with the proposed method for polystyrene microspheres.

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Equations (18)

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\frac{\partial P (r, q)}{\partial s} = - μ_{t} P (r, q) + \frac{μ_{s}}{4 π} \int_{4 π} P (r, q') β (q, q') d Ω'

R_{I} (Δ x, Δ y) = 〈 I (x_{1}, y_{1}) I (x_{2}, y_{2}) 〉

R_{I} (Δ x, Δ y) = R_{I} (x, y)

c_{I} (x, y) = \frac{R_{I} (x, y) - {〈 I (x, y) 〉}^{2}}{〈 I {(x, y)}^{2} 〉 - {〈 I (x, y) 〉}^{2}}

R_{I} (x, y) = {FT}^{- 1} [{PSD}_{I} (υ_{x}, υ_{y})]

{PSD}_{I} (υ_{x}, υ_{y}) = {∣ FT [I (x, y)] ∣}^{2}

c_{I}^{m} (x, y) = \frac{{FT}^{- 1} [{∣ FT [I (x, y)] ∣}^{2}] - {〈 I (x, y) 〉}^{2}}{〈 I {(x, y)}^{2} 〉 - {〈 I (x, y) 〉}^{2}}

R_{I} (x, y) = {〈 I 〉}^{2} [1 + {∣ μ_{A} (x, y) ∣}^{2}]

{∣ μ_{A} (x, y) ∣}^{2} = {∣ \frac{\int_{- \infty}^{\infty} \int_{- \infty}^{\infty} P (u, v) \exp [i \frac{2 π}{λ z} (ux + vy)] dudv}{\int_{- \infty}^{\infty} \int_{- \infty}^{\infty} P (u, v) dudv} ∣}^{2} = c_{I} (x, y)

{\begin{matrix} X = \frac{x}{λ z} \\ Y = \frac{y}{λ z} \end{matrix}

c_{I} (x, y) = \frac{{∣ F p (X, Y) ∣}^{2}}{{∣ \int_{- \infty}^{\infty} \int_{- \infty}^{\infty} P (u, v) dudv ∣}^{2}}

F p (X, Y) = \int_{- \infty}^{\infty} \int_{- \infty}^{\infty} P (u, v) \exp [i 2 π (uX + vY)] dudv

c_{I}^{c} (x) = \frac{{∣ F p (X) ∣}^{2}}{{∣ \int_{- \infty}^{\infty} P (u) du ∣}^{2}}

d y^{m} (θ = 5 °) \sim d y^{m} (θ = 0 °)

d y^{m} = - 30 l s + 219

d y^{m} = - 48 l s + 218

d^{c} = - 66 l s + 216

C = \frac{\sqrt{〈 I^{2} (x, y) 〉 - {〈 I (x, y) 〉}^{2}}}{〈 I (x, y) 〉}

Ø (µm)	N (m^-3) (c=100%)	µ_s (cm^-1)
0.20	5.759 *10¹⁶	1.8c
0.53	3.147 *10¹⁵	6.23c
1.44	1.705 *10¹⁴	9.3c
3.17	1.484 *10¹³	2.15c
6.36	1.873 *10¹²	1.43c

Ø (µm)	g
0.20	0.323
0.53	0.838
1.44	0.928
3.17	0.826
6.36	0.823

	Measured	Calculat ed
	Fig.9	Fig.11
Ø (µm)	dy^m (µm)	d^c (µm)	d^c ² (µm)
0.20	-45ls+225	×	-15ls+210
0.53	-70ls+224	×	-41ls+214
1.44	-43ls+226	-71ls+218	-55ls+207
3.17	-16ls+217	-49ls+216	-43ls+208
6.36	-11ls+216	-41ls+214	-32ls+205

Ø (µm)	N (m^-3) (c=100%)	µ_s (cm^-1)
0.20	5.759 *10¹⁶	1.8c
0.53	3.147 *10¹⁵	6.23c
1.44	1.705 *10¹⁴	9.3c
3.17	1.484 *10¹³	2.15c
6.36	1.873 *10¹²	1.43c

Ø (µm)	g
0.20	0.323
0.53	0.838
1.44	0.928
3.17	0.826
6.36	0.823

Abstract

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Figures (11)

Tables (3)

Equations (18)

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