A study on forward scattering Mueller matrix decomposition in anisotropic medium

Yihong Guo; Nan Zeng; Honghui He; Tianliang Yun; E Du; Ran Liao; Yonghong He; Hui Ma

doi:10.1364/OE.21.018361

Optics Express
Vol. 21,
Issue 15,
pp. 18361-18370
(2013)
•https://doi.org/10.1364/OE.21.018361

A study on forward scattering Mueller matrix decomposition in anisotropic medium

Yihong Guo, Nan Zeng, Honghui He, Tianliang Yun, E Du, Ran Liao, Yonghong He, and Hui Ma

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Yihong Guo, Nan Zeng, Honghui He, Tianliang Yun, E Du, Ran Liao, Yonghong He, and Hui Ma, "A study on forward scattering Mueller matrix decomposition in anisotropic medium," Opt. Express 21, 18361-18370 (2013)

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- Scattering
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About this Article
History
- Original Manuscript: May 9, 2013
- Revised Manuscript: June 28, 2013
- Manuscript Accepted: July 16, 2013
- Published: July 24, 2013
Virtual Issues
Virtual Journal for Biomedical Optics Vol. 8, Iss. 8

Abstract

In this work, we apply Mueller matrix polar decomposition (MMPD) method in a forward scattering configuration on anisotropic scattering samples and look for the physics origin of depolarization and retardance. Using Monte Carlo simulations on the sphere-cylinder birefringence model (SCBM), and forward scattering experiments on samples containing polystyrene microspheres, well-aligned glass fibers and polyacrylamide, we examine in detail the relationship between the MMPD parameters and the microscopic structure of the samples. The results show that the spherical scatterers and birefringent medium contribute to depolarization and retardance respectively, but the cylindrical scatterers contribute to both. Retardance due to the cylindrical scatterers changes with their density, size and order of alignment. Total retardance is a simple sum of both contributions when cylinders are in parallel to the extraordinary axis of birefringence.

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Fig. 1 (a) Schematic of forward Mueller matrix experiment set up. Light source is LED; P1, P2: polarizers; QW1, QW2: quarter wave plates; L1, L2: lenses. (b) Schematic of clamps used to strain the samples to induce birefringence, the direction of strain is vertical in the laboratory reference frame. The direction of glass fibers is 30° angle to the y-axis.

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Fig. 2 Mueller matrix polar decomposition: (a) Monte Carlo simulations and (b) experiments, in the forward direction, through a 1 × 2 × 4cm sample containing microspheres of 0.5μm radius embedded in polyacrylamide medium, the refractive index is 1.393. The results are shown for both clear (μ_s = 0cm⁻¹) and turbid (μ_s = 22cm⁻¹) samples.

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Fig. 3 Mueller matrix polar decomposition results using (a) Monte Carlo simulations on a layer of 5μm radius well aligned cylinders with fixed thickness and varying scattering coefficient, and (b) experiments on varying number of layers of glass fibers. In both cases, the refractive index of the surrounding media is 1.

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Fig. 4 Mueller matrix polar decomposition on the simulated results: (a) linear retardance (δ) and (b) depolarization (Δ) for different cylinder radius; (c) δ and Δ corresponding to different orientation distributions, the cylinder scattering coefficient is 45cm⁻¹, the radius of the cylinder is 5μm. In all the simulations, the refractive index of the surrounding medium is 1.

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Fig. 5 Mueller matrix polar decomposition results using (a) simulation, the radius of cylinder is 5μm, cylinder scattering coefficient is 50cm⁻¹, the refractive index of the surrounding media is 1. (b) experiment, 4 layers of glass fiber immersed in birefringent medium.

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Fig. 6 Mueller matrix polar decomposition (a) Monte Carlo simulation result, the radius of cylinder is 5μm, sphere and cylinder scattering coefficient are 20cm⁻¹ and 50cm⁻¹ respectively, the refractive index of the surrounding media is 1.393. (b) experiment result of 4 layers of glass fiber immersed in birefringent sample.

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Equations (10)

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M = M_{Δ} M_{R} M_{D}

\vec{D} = \frac{1}{m_{11}} (\begin{matrix} m_{12} \\ m_{13} \\ m_{14} \end{matrix})

D = \frac{1}{m_{11}} \sqrt{m_{12}^{2} + m_{13}^{2} + m_{14}^{2}} .

Δ = 1 - \frac{| t r a c e (m_{Δ}) |}{3}, 0 < Δ < 1

R = \cos^{- 1} [\frac{t r a c e (M_{R})}{2} - 1]

Ψ = \tan^{- 1} [\frac{M_{R} (3, 2) - M_{R} (2, 3)}{M_{R} (2, 2) + M_{R} (3, 3)}]

δ = \cos^{- 1} {\sqrt{{[M_{R} (2, 2) + M_{R} (3, 3)]}^{2} + {[M_{R} (3, 2) - M_{R} (2, 3)]}^{2}} - 1}

δ_{b} = \frac{2 π s \bar{n}}{λ} \cdot Δ n^{'}

Δ n^{'} = n_{e}^{'} (θ) - n_{o} = \frac{n_{o} n_{e}}{{(n_{o}^{2} \sin^{2} θ + n_{e}^{2} \cos^{2} θ)}^{1 / 2}} - n_{o}

\begin{matrix} M = (\begin{matrix} m 11 & m 12 & m 13 & m 14 \\ m 21 & m 22 & m 23 & m 24 \\ m 31 & m 32 & m 33 & m 34 \\ m 41 & m 42 & m 43 & m 44 \end{matrix}) \\ = \frac{1}{2} (\begin{matrix} H H + H V + V H + V V & H H + H V - V H - V V & P H + P V - M P - M M & R H + R V - L H - L V \\ H H - H V + V H - V V & H H - H V - V H + V V & P H - P V - M H - M V & R H - R V - L H + L V \\ H P - H M + V P - V M & H P - H M - V P + V M & P P - P M - M P + M M & R P - R M - L P + L M \\ V R + H R - L L - R L & V L + H R - H L - V R & M L + P R - P L - M R & R R + L L - L R - R L \end{matrix}) \end{matrix}

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Equations (10)

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